0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n004.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 : 960 0.12/0.33 % DateTime : Thu Jul 2 15:32:58 EDT 2020 0.12/0.34 % CPUTime : 1.42/1.73 ============================== Prover9 =============================== 1.42/1.73 Prover9 (32) version 2009-11A, November 2009. 1.42/1.73 Process 26730 was started by sandbox2 on n004.cluster.edu, 1.42/1.73 Thu Jul 2 15:33:00 2020 1.42/1.73 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_26577_n004.cluster.edu". 1.42/1.73 ============================== end of head =========================== 1.42/1.73 1.42/1.73 ============================== INPUT ================================= 1.42/1.73 1.42/1.73 % Reading from file /tmp/Prover9_26577_n004.cluster.edu 1.42/1.73 1.42/1.73 set(prolog_style_variables). 1.42/1.73 set(auto2). 1.42/1.73 % set(auto2) -> set(auto). 1.42/1.73 % set(auto) -> set(auto_inference). 1.42/1.73 % set(auto) -> set(auto_setup). 1.42/1.73 % set(auto_setup) -> set(predicate_elim). 1.42/1.73 % set(auto_setup) -> assign(eq_defs, unfold). 1.42/1.73 % set(auto) -> set(auto_limits). 1.42/1.73 % set(auto_limits) -> assign(max_weight, "100.000"). 1.42/1.73 % set(auto_limits) -> assign(sos_limit, 20000). 1.42/1.73 % set(auto) -> set(auto_denials). 1.42/1.73 % set(auto) -> set(auto_process). 1.42/1.73 % set(auto2) -> assign(new_constants, 1). 1.42/1.74 % set(auto2) -> assign(fold_denial_max, 3). 1.42/1.74 % set(auto2) -> assign(max_weight, "200.000"). 1.42/1.74 % set(auto2) -> assign(max_hours, 1). 1.42/1.74 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.42/1.74 % set(auto2) -> assign(max_seconds, 0). 1.42/1.74 % set(auto2) -> assign(max_minutes, 5). 1.42/1.74 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.42/1.74 % set(auto2) -> set(sort_initial_sos). 1.42/1.74 % set(auto2) -> assign(sos_limit, -1). 1.42/1.74 % set(auto2) -> assign(lrs_ticks, 3000). 1.42/1.74 % set(auto2) -> assign(max_megs, 400). 1.42/1.74 % set(auto2) -> assign(stats, some). 1.42/1.74 % set(auto2) -> clear(echo_input). 1.42/1.74 % set(auto2) -> set(quiet). 1.42/1.74 % set(auto2) -> clear(print_initial_clauses). 1.42/1.74 % set(auto2) -> clear(print_given). 1.42/1.74 assign(lrs_ticks,-1). 1.42/1.74 assign(sos_limit,10000). 1.42/1.74 assign(order,kbo). 1.42/1.74 set(lex_order_vars). 1.42/1.74 clear(print_given). 1.42/1.74 1.42/1.74 % formulas(sos). % not echoed (791 formulas) 1.42/1.74 1.42/1.74 ============================== end of input ========================== 1.42/1.74 1.42/1.74 % From the command line: assign(max_seconds, 960). 1.42/1.74 1.42/1.74 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.42/1.74 1.42/1.74 % Formulas that are not ordinary clauses: 1.42/1.74 1 (all A all B (function(B) & relation(B) -> ((all C (in(C,A) -> C = apply(B,C))) & A = relation_dom(B) <-> B = identity_relation(A)))) # label(t34_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 2 (all A all B all C ((all D (in(D,A) & -in(D,B) <-> in(D,C))) <-> C = set_difference(A,B))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 3 (all A (top_str(A) & topological_space(A) & -empty_carrier(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]. 1.42/1.74 4 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 5 (all A all B all C all D (-empty(B) & element(D,B) & element(C,A) & -empty(A) -> 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]. 1.42/1.74 6 (all A (relation(A) & function(A) -> (all B ((all C (in(C,B) <-> (exists D (in(D,relation_dom(A)) & apply(A,D) = C)))) <-> relation_rng(A) = B)))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 7 (all A (one_sorted_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> (is_a_cover_of_carrier(A,B) <-> union_of_subsets(the_carrier(A),B) = cast_as_carrier_subset(A)))))) # label(d8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 8 (all A (lattice(A) & latt_str(A) & upper_bounded_semilattstr(A) & -empty_carrier(A) -> -empty_carrier(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & upper_bounded_relstr(poset_of_lattice(A)) & with_infima_relstr(poset_of_lattice(A)) & with_suprema_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)))) # label(fc2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 9 (all A exists B (relation(B) & A = relation_dom(B) & (all C (in(C,A) -> apply(B,C) = singleton(C))) & function(B))) # label(s3_funct_1__e16_22__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 10 (all A all B (top_str(A) & element(B,powerset(powerset(the_carrier(A)))) & topological_space(A) -> (exists C (element(C,powerset(powerset(the_carrier(A)))) & (all D (element(D,powerset(the_carrier(A))) -> (in(D,C) <-> in(set_difference(cast_as_carrier_subset(A),D),B)))))))) # label(s3_subset_1__e2_37_1_1__pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 11 (all A all B A = set_union2(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 12 (all A (meet_semilatt_str(A) & -empty_carrier(A) -> ((exists B ((all C (element(C,the_carrier(A)) -> meet(A,B,C) = B & B = meet(A,C,B))) & element(B,the_carrier(A)))) <-> lower_bounded_semilattstr(A)))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 13 (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]. 1.42/1.74 14 (all A all B (v1_membered(A) -> v1_membered(set_difference(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 15 (all A all B (v5_membered(A) -> v2_membered(set_difference(A,B)) & v3_membered(set_difference(A,B)) & v5_membered(set_difference(A,B)) & v4_membered(set_difference(A,B)) & v1_membered(set_difference(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 16 (all A (one_sorted_str(A) -> (empty(the_carrier(A)) <-> empty_carrier(A)))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 17 (all A (-empty_carrier(A) & latt_str(A) & lattice(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]. 1.42/1.74 18 (all A all B (ordinal(B) -> ((all C all D all E (C = E & (exists G (ordinal(G) & in(G,A) & G = E)) & (exists F (ordinal(F) & D = F & in(F,A))) & D = C -> E = D)) -> (exists C all D (in(D,C) <-> (exists E (D = E & (exists H (ordinal(H) & H = D & in(H,A))) & in(E,succ(B))))))))) # label(s1_tarski__e8_6__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 19 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_union2(A,B,C) = set_union2(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 20 (all A empty_set = set_difference(empty_set,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 21 (exists A (-empty(A) & v2_membered(A) & v4_membered(A) & v5_membered(A) & v3_membered(A) & v1_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 22 (exists A (latt_str(A) & -empty_carrier(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & upper_bounded_semilattstr(A) & boolean_lattstr(A) & complemented_lattstr(A) & bounded_lattstr(A) & lower_bounded_semilattstr(A) & distributive_lattstr(A) & lattice(A) & meet_commutative(A) & join_associative(A) & join_commutative(A) & strict_latt_str(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 23 (all A all B (finite(A) -> finite(set_intersection2(A,B)))) # label(t15_finset_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 24 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 25 (all A all B all C (-empty_carrier(A) & rel_str(A) & element(C,powerset(B)) & finite(C) & element(B,powerset(the_carrier(A))) & transitive_relstr(A) -> (finite(C) & (all E all F (in(E,C) & subset(F,C) & (exists G (element(G,the_carrier(A)) & relstr_set_smaller(A,F,G) & in(G,B))) -> (exists H (in(H,B) & relstr_set_smaller(A,set_union2(F,singleton(E)),H) & element(H,the_carrier(A)))))) & (exists D (in(D,B) & relstr_set_smaller(A,empty_set,D) & element(D,the_carrier(A)))) -> (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]. 1.42/1.74 26 (all A all B (element(B,A) -> (proper_element(B,A) <-> union(A) != B))) # label(d2_tex_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 27 (all A (meet_semilatt_str(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C (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) # label(non_clause). [assumption]. 1.42/1.74 28 (all A (being_limit_ordinal(A) <-> union(A) = A)) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 29 (all A ((exists B exists C ordered_pair(B,C) = A) -> (all B (B = pair_first(A) <-> (all C all D (A = ordered_pair(C,D) -> C = B)))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 30 (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)))) -> -(finite(C) & is_a_cover_of_carrier(A,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]. 1.42/1.74 31 (all A (ordinal(A) -> -(being_limit_ordinal(A) & (exists B (ordinal(B) & A = succ(B)))) & -(-being_limit_ordinal(A) & (all B (ordinal(B) -> succ(B) != A))))) # label(t42_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 32 (all A all B all C (element(B,the_carrier(A)) & element(C,the_carrier(A)) & meet_semilatt_str(A) & meet_commutative(A) & -empty_carrier(A) -> meet_commut(A,C,B) = meet_commut(A,B,C))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 33 (all A all B all C (relation_of2(C,A,B) -> relation_dom_as_subset(A,B,C) = relation_dom(C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 34 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 35 (all A all B (element(B,powerset(powerset(A))) -> (all C (element(C,powerset(powerset(A))) -> ((all D (element(D,powerset(A)) -> (in(D,C) <-> in(subset_complement(A,D),B)))) <-> C = complements_of_subsets(A,B)))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 36 (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]. 1.42/1.74 37 (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]. 1.42/1.74 38 (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]. 1.42/1.74 39 (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]. 1.42/1.74 40 (all A all B all C (C = unordered_pair(A,B) <-> (all D (D = A | B = D <-> in(D,C))))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 41 (all A (join_semilatt_str(A) -> quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation_of2_as_subset(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]. 1.42/1.74 42 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 43 (all A all B (B = singleton(A) <-> (all C (C = A <-> in(C,B))))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 44 (all A all B (-empty_carrier(B) & lattice(B) & latt_str(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]. 1.42/1.74 45 (all A all B all C (relation(C) -> (in(A,relation_rng(relation_rng_restriction(B,C))) <-> in(A,relation_rng(C)) & in(A,B)))) # label(t115_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 46 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (in(ordered_pair(B,C),the_InternalRel(A)) <-> related(A,B,C)))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 47 (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]. 1.42/1.74 48 (all A (rel_str(A) -> (all B (rel_str(B) -> (subrelstr(B,A) <-> subset(the_carrier(B),the_carrier(A)) & subset(the_InternalRel(B),the_InternalRel(A))))))) # label(d13_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 49 (all A (meet_commutative(A) & meet_semilatt_str(A) & -empty_carrier(A) -> relation(the_L_meet(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)))) # label(fc4_lattice2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 50 (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]. 1.42/1.74 51 (all A (lattice(A) & latt_str(A) & -empty_carrier(A) -> antisymmetric_relstr(poset_of_lattice(A)) & with_infima_relstr(poset_of_lattice(A)) & with_suprema_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)) & -empty_carrier(poset_of_lattice(A)))) # label(fc1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 52 (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]. 1.42/1.74 53 (all A all B (relation(B) -> (well_ordering(B) & subset(A,relation_field(B)) -> A = relation_field(relation_restriction(B,A))))) # label(t39_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 54 (all A (finite(A) -> (all B (element(B,powerset(powerset(A))) -> -((all C -(in(C,B) & (all D (in(D,B) & subset(C,D) -> C = D)))) & B != empty_set))))) # label(t18_finset_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 55 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 56 (all A (function(A) & relation(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)) -> (empty_set = C <-> apply(A,B) = C)))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 57 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) & function(C) -> (relation_isomorphism(A,B,C) -> relation_isomorphism(B,A,function_inverse(C))))))))) # label(t49_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 58 (all A (-empty_carrier(A) & latt_str(A) & lattice(A) -> strict_rel_str(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)))) # label(dt_k3_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 59 (all A (relation(A) & function(A) -> (finite(relation_dom(A)) -> finite(relation_rng(A))))) # label(t26_finset_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 60 (all A all B all C (relation(C) -> (in(A,cartesian_product2(B,B)) & in(A,C) <-> in(A,relation_restriction(C,B))))) # label(t16_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 61 (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]. 1.42/1.74 62 (all A k1_pcomps_1(A) = powerset(A)) # label(redefinition_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 63 (all A (relation(A) -> (all B all C (relation_inverse_image(A,B) = C <-> (all D ((exists E (in(E,B) & in(ordered_pair(D,E),A))) <-> in(D,C))))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 64 (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]. 1.42/1.74 65 (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)))) & (all D (element(D,powerset(the_carrier(A))) -> (subset(B,D) & closed_subset(D,A) <-> in(D,C)))) & meet_of_subsets(the_carrier(A),C) = topstr_closure(A,B))))))) # label(t46_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 66 (all A all B all C (subset(C,cartesian_product2(A,B)) <-> relation_of2(C,A,B))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 67 (all A (top_str(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))))) & (all B (element(B,powerset(the_carrier(A))) -> (all C (element(C,powerset(the_carrier(A))) -> (in(C,the_topology(A)) & in(B,the_topology(A)) -> in(subset_intersection2(the_carrier(A),B,C),the_topology(A))))))) & in(the_carrier(A),the_topology(A)) <-> topological_space(A)))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 68 (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]. 1.42/1.74 69 (all A (relation(A) -> (all B (is_connected_in(A,B) <-> (all C all D -(D != C & -in(ordered_pair(C,D),A) & -in(ordered_pair(D,C),A) & in(D,B) & in(C,B))))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 70 (all A all B (in(B,A) -> apply(identity_relation(A),B) = B)) # label(t35_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.74 71 (all A (rel_str(A) -> (-v1_yellow_3(A) -> -empty_carrier(A)))) # label(cc2_yellow_3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 72 (all A (rel_str(A) -> (all B (subrelstr(B,A) -> rel_str(B))))) # label(dt_m1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 73 (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]. 1.42/1.74 74 (all A all B all C (-empty_carrier(A) & meet_absorbing(A) & latt_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & join_absorbing(A) & meet_commutative(A) -> (below(A,B,C) <-> below_refl(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.74 75 (all A (A != empty_set -> (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]. 1.42/1.74 76 (all A all B (one_sorted_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> ((all C -((all D -(all H (element(H,powerset(the_carrier(A))) -> (C = H -> D = subset_complement(the_carrier(A),H))))) & in(C,B))) & (all C all D all E (in(C,B) & (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))) -> (C = G -> E = subset_complement(the_carrier(A),G)))) -> E = D)) -> (exists C (relation(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)))))) & B = relation_dom(C) & function(C)))))) # label(s2_funct_1__e4_7_2__tops_2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 77 (all A all B all C (relation_of2(C,A,B) -> relation_rng_as_subset(A,B,C) = relation_rng(C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 78 (all A all B (one_sorted_str(A) & element(B,powerset(powerset(the_carrier(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]. 1.42/1.75 79 (all A (one_sorted_str(A) -> (all B (net_str(B,A) & -empty_carrier(B) -> (all C (-empty_carrier(C) & full_subnetstr(C,A,B) & subnetstr(C,A,B) -> (all D (element(D,the_carrier(B)) -> (all E (element(E,the_carrier(B)) -> (all F (element(F,the_carrier(C)) -> (all G (element(G,the_carrier(C)) -> (F = D & related(B,D,E) & G = E -> related(C,F,G)))))))))))))))) # label(t21_yellow_6) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 80 (exists A (latt_str(A) & strict_latt_str(A) & join_associative(A) & upper_bounded_semilattstr(A) & lower_bounded_semilattstr(A) & modular_lattstr(A) & distributive_lattstr(A) & lattice(A) & join_absorbing(A) & meet_absorbing(A) & meet_associative(A) & meet_commutative(A) & join_commutative(A) & -empty_carrier(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 81 (all A in(A,succ(A))) # label(t10_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 82 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 83 (all A (-empty_carrier(A) & latt_str(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]. 1.42/1.75 84 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 85 (exists A (-empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & complete_relstr(A) & trivial_carrier(A) & with_infima_relstr(A) & with_suprema_relstr(A) & antisymmetric_relstr(A) & transitive_relstr(A) & rel_str(A))) # label(rc1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 86 (all A all B (relation(B) -> (transitive(B) -> transitive(relation_restriction(B,A))))) # label(t24_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 87 (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]. 1.42/1.75 88 (all A all B all C (subset(A,C) & subset(A,B) -> subset(A,set_intersection2(B,C)))) # label(t19_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 89 (all A all B all C all D (relation_of2(C,A,B) -> relation_of2_as_subset(relation_dom_restr_as_relation_of(A,B,C,D),A,B))) # label(dt_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 90 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 91 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 92 (exists A (-empty(A) & relation(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 93 (all A relation(identity_relation(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 94 (all A exists B ((all C (in(C,B) -> in(powerset(C),B))) & (all C -(-are_equipotent(C,B) & -in(C,B) & subset(C,B))) & (all C all D (in(C,B) & subset(D,C) -> in(D,B))) & in(A,B))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 95 (all A (rel_str(A) -> (complete_relstr(A) & -empty_carrier(A) -> bounded_relstr(A) & -empty_carrier(A)))) # label(cc3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 96 (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]. 1.42/1.75 97 (all A all B all C (relation(C) & function(C) -> (in(B,relation_dom(C)) & in(B,A) <-> in(B,relation_dom(relation_dom_restriction(C,A)))))) # label(l82_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 98 (all A (-empty_carrier(A) & join_semilatt_str(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]. 1.42/1.75 99 (all A ((all B all C all D (singleton(B) = D & in(B,A) & C = singleton(B) & in(B,A) -> D = C)) -> (exists B (relation(B) & (all C all D (in(C,A) & singleton(C) = D & in(C,A) <-> in(ordered_pair(C,D),B))) & function(B))))) # label(s1_funct_1__e16_22__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 100 (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]. 1.42/1.75 101 (all A exists B (empty(B) & function(B) & epsilon_connected(B) & ordinal(B) & natural(B) & finite(B) & epsilon_transitive(B) & one_to_one(B) & relation(B) & element(B,powerset(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 102 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 103 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 104 (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) -> C = B))))))) # label(t25_orders_2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 105 (all A exists B all C (in(C,B) <-> ordinal(C) & in(C,A))) # label(s1_xboole_0__e6_22__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 106 (all A all B (equipotent(A,B) <-> are_equipotent(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 107 (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]. 1.42/1.75 108 (all A rel_str_of(A,inclusion_order(A)) = incl_POSet(A)) # label(d1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 109 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 110 (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]. 1.42/1.75 111 (all A all B (-(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))) & -(disjoint(A,B) & (exists C in(C,set_intersection2(A,B)))))) # label(t4_xboole_0) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 112 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 113 (all A (-empty_carrier(A) & latt_str(A) -> (meet_absorbing(A) <-> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> C = join(A,meet(A,B,C),C)))))))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 114 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> subset_union2(A,B,C) = subset_union2(A,C,B))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 115 (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]. 1.42/1.75 116 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 117 (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]. 1.42/1.75 118 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 119 (all A (latt_str(A) -> (-empty_carrier(A) & bounded_lattstr(A) -> -empty_carrier(A) & lower_bounded_semilattstr(A) & upper_bounded_semilattstr(A)))) # label(cc4_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 120 (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]. 1.42/1.75 121 (all A all B (v3_membered(A) -> v2_membered(set_intersection2(B,A)) & v3_membered(set_intersection2(B,A)) & v1_membered(set_intersection2(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 122 (all A all B (element(B,powerset(powerset(A))) -> -(B != empty_set & empty_set = complements_of_subsets(A,B)) & -(complements_of_subsets(A,B) != empty_set & empty_set = B))) # label(t10_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 123 (all A (-empty(A) -> (exists B (-empty(B) & finite(B) & element(B,powerset(A)))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 124 (all A all B equipotent(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 125 (all A all B all C all D -(unordered_pair(C,D) = unordered_pair(A,B) & A != C & A != D)) # label(t10_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 126 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 127 (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))) -> (interior(A,C) = C -> open_subset(C,A)) & (open_subset(D,B) -> D = interior(B,D)))))))))) # label(t55_tops_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 128 (all A all B (relation(B) -> -((all C (relation(C) -> -well_orders(C,A))) & equipotent(A,relation_field(B)) & well_ordering(B)))) # label(l30_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 129 (all A (lattice(A) & latt_str(A) & -empty_carrier(A) -> relation_of_lattice(A) = k2_lattice3(A))) # label(redefinition_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 130 (all A (rel_str(A) -> (bounded_relstr(A) -> upper_bounded_relstr(A) & lower_bounded_relstr(A)))) # label(cc4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 131 (all A all B all C (-empty_carrier(B) & latt_str(B) -> ((exists D (latt_set_smaller(B,D,C) & A = D & 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]. 1.42/1.75 132 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 133 (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) <-> meet_on_relstr(A,B) = C)))))) # label(d10_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 134 (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]. 1.42/1.75 135 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 136 (all A (relation_rng(identity_relation(A)) = A & relation_dom(identity_relation(A)) = A)) # label(t71_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 137 (all A (-empty_carrier(A) & latt_str(A) & lower_bounded_semilattstr(A) & lattice(A) -> -empty_carrier(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & lower_bounded_relstr(poset_of_lattice(A)) & with_infima_relstr(poset_of_lattice(A)) & with_suprema_relstr(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)))) # label(fc3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 138 (all A exists B ((all C -(in(C,B) & (all D -((all E (subset(E,C) -> in(E,D))) & in(D,B))))) & (all C -(subset(C,B) & -in(C,B) & -are_equipotent(C,B))) & (all C all D (in(C,B) & subset(D,C) -> in(D,B))) & in(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 139 (all A A = set_union2(A,empty_set)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 140 (all A (ordinal(A) -> (exists B all C (in(C,B) <-> (exists D ((in(D,omega) -> (all E (element(E,powerset(powerset(D))) -> -(E != empty_set & (all F -((all G (in(G,E) & subset(F,G) -> G = F)) & in(F,E))))))) & C = D & ordinal(D))) & in(C,succ(A)))))) # label(s1_xboole_0__e18_27__finset_1__1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 141 (all A (v1_membered(A) -> (all B (element(B,A) -> v1_xcmplx_0(B))))) # label(cc10_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 142 (all A all B (lattice(A) & element(B,the_carrier(poset_of_lattice(A))) & latt_str(A) & -empty_carrier(A) -> element(cast_to_el_of_lattice(A,B),the_carrier(A)))) # label(dt_k5_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 143 (all A (join_associative(A) & join_semilatt_str(A) & -empty_carrier(A) -> relation(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)) & function(the_L_join(A)))) # label(fc3_lattice2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 144 (all A (relation(A) -> (all B (relation(B) -> (all C (function(C) & relation(C) -> (relation_isomorphism(A,B,C) -> (antisymmetric(A) -> antisymmetric(B)) & (well_founded_relation(A) -> well_founded_relation(B)) & (connected(A) -> connected(B)) & (transitive(A) -> transitive(B)) & (reflexive(A) -> reflexive(B))))))))) # label(t53_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 145 (exists A (empty(A) & one_to_one(A) & function(A) & relation(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 146 (exists A (relation(A) & function(A) & relation_empty_yielding(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 147 (all A all B -(in(A,B) & (all C -(in(C,B) & (all D -(in(D,B) & in(D,C))))))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 148 (all A (-empty_carrier(A) & topological_space(A) & top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (all C (element(C,the_carrier(A)) -> (in(C,B) & open_subset(B,A) -> point_neighbourhood(B,A,C)))))))) # label(t5_connsp_2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 149 (exists A (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 150 (all A exists B (function(B) & one_to_one(B) & quasi_total(B,A,A) & onto(B,A,A) & bijective(B,A,A) & relation(B) & relation_of2(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 151 (all A all B (subset(A,singleton(B)) <-> A = singleton(B) | empty_set = A)) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 152 (all A (function(A) & relation(A) -> (all B all C (relation_inverse_image(A,B) = C <-> (all D (in(D,C) <-> in(D,relation_dom(A)) & in(apply(A,D),B))))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 153 (all A (ordinal(A) -> ((all B (ordinal(B) -> (in(B,A) -> in(succ(B),A)))) <-> being_limit_ordinal(A)))) # label(t41_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 154 (all A (-empty_carrier(A) & top_str(A) & topological_space(A) -> (compact_top_space(A) <-> (all B (element(B,powerset(powerset(the_carrier(A)))) -> -(closed_subsets(B,A) & meet_of_subsets(the_carrier(A),B) = empty_set & centered(B))))))) # label(t13_compts_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 155 (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]. 1.42/1.75 156 (all A (meet_semilatt_str(A) -> function(the_L_meet(A)) & relation_of2_as_subset(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)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 157 (all A succ(A) = set_union2(A,singleton(A))) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 158 (all A (one_to_one(A) & function(A) & relation(A) -> relation(relation_inverse(A)) & function(relation_inverse(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 159 (all A all B (v1_membered(A) -> v1_membered(set_intersection2(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 160 (all A (relation(A) -> (is_connected_in(A,relation_field(A)) <-> connected(A)))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 161 (all A (latt_str(A) -> (strict_latt_str(A) -> A = latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A))))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 162 (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]. 1.42/1.75 163 (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]. 1.42/1.75 164 (all A all B all C (-empty_carrier(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & rel_str(A) & reflexive_relstr(A) -> (related_reflexive(A,B,C) <-> related(A,B,C)))) # label(redefinition_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 165 (all A (ordinal(A) -> well_ordering(inclusion_relation(A)))) # label(t7_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 166 (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]. 1.42/1.75 167 (all A all B all C (element(C,powerset(A)) -> -(in(B,C) & in(B,subset_complement(A,C))))) # label(t54_subset_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 168 (all A (-empty(A) -> (exists B (-empty(B) & finite(B) & element(B,powerset(A)))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 169 (exists A (strict_latt_str(A) & meet_commutative(A) & meet_associative(A) & join_absorbing(A) & lattice(A) & upper_bounded_semilattstr(A) & bounded_lattstr(A) & lower_bounded_semilattstr(A) & meet_absorbing(A) & join_associative(A) & join_commutative(A) & -empty_carrier(A) & latt_str(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 170 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 171 (all A (epsilon_transitive(A) & epsilon_connected(A) -> ordinal(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 172 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 173 (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) -> join_commut(A,B,C) = join_commut(A,C,B))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 174 (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]. 1.42/1.75 175 (all A all B (equipotent(A,B) -> equipotent(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 176 (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]. 1.42/1.75 177 (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,B,C) & below(A,C,B) -> B = C))))))) # label(t26_lattices) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 178 (all A all B all C all D (subset(C,D) & subset(A,B) -> subset(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t119_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 179 (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))) & closed_subset(E,A) & subset(B,D) & E = D))))) & element(C,powerset(powerset(the_carrier(A)))))))) # label(s3_subset_1__e1_40__pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 180 (all A all B (relation_of2(B,A,A) -> (function(B) & v1_partfun1(B,A,A) & quasi_total(B,A,A) & reflexive(B) -> function(B) & one_to_one(B) & quasi_total(B,A,A) & onto(B,A,A) & bijective(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 181 (all A (ordinal(A) -> epsilon_transitive(union(A)) & epsilon_connected(union(A)) & ordinal(union(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 182 (all A (rel_str(A) -> (with_infima_relstr(A) -> -empty_carrier(A)))) # label(cc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 183 (all A (rel_str(A) -> (strict_rel_str(A) -> A = rel_str_of(the_carrier(A),the_InternalRel(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 184 (all A all B exists C (relation(C) & quasi_total(C,A,B) & function(C) & relation_of2(C,A,B))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 185 (all A (relation(A) -> ((all B -(subset(B,relation_field(A)) & (all C -(disjoint(fiber(A,C),B) & in(C,B))) & empty_set != B)) <-> well_founded_relation(A)))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 186 (all A bottom_of_relstr(boole_POSet(A)) = empty_set) # label(t18_yellow_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 187 (all A all B (empty(A) & relation(B) -> empty(relation_composition(B,A)) & relation(relation_composition(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 188 (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]. 1.42/1.75 189 (all A relation(inclusion_relation(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 190 (all A (relation(A) -> (all B all C (C = fiber(A,B) <-> (all D (in(D,C) <-> in(ordered_pair(D,B),A) & D != B)))))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 191 (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]. 1.42/1.75 192 (all A all B (lattice(A) & element(B,the_carrier(A)) & latt_str(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]. 1.42/1.75 193 (all A (relation(A) -> ((all B (in(B,relation_field(A)) -> in(ordered_pair(B,B),A))) <-> reflexive(A)))) # label(l1_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 194 (all A (v5_membered(A) -> (all B (element(B,A) -> v1_xreal_0(B) & v1_rat_1(B) & v1_int_1(B) & natural(B) & v1_xcmplx_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 195 (all A all B all C (relation(C) -> ((exists D (in(D,B) & in(ordered_pair(D,A),C) & in(D,relation_dom(C)))) <-> in(A,relation_image(C,B))))) # label(t143_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.75 196 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.75 197 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 198 (exists A (function(A) & one_to_one(A) & relation(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 199 (all A (antisymmetric_relstr(A) & rel_str(A) & lower_bounded_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]. 1.42/1.76 200 (all A (-empty_carrier(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & strict_rel_str(boole_POSet(A)))) # label(fc7_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 201 (all A all B (element(B,the_carrier(A)) & top_str(A) & topological_space(A) & -empty_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]. 1.42/1.76 202 (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]. 1.42/1.76 203 (all A identity_relation(A) = identity_as_relation_of(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 204 (all A all B all C (-empty_carrier(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) & one_sorted_str(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]. 1.42/1.76 205 (all A all B (element(B,powerset(powerset(succ(A)))) & ordinal(A) -> ((all C all D all E ((exists F (in(F,B) & D = set_difference(F,singleton(A)))) & E = C & (exists G (in(G,B) & set_difference(G,singleton(A)) = E)) & C = D -> E = D)) -> (exists C all D ((exists E (in(E,powerset(A)) & D = E & (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]. 1.42/1.76 206 (all A (relation(A) & -empty(A) -> -empty(relation_rng(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 207 (all A all B (strict_latt_str(B) & latt_str(B) -> (powerset(A) = the_carrier(B) & (all C (element(C,powerset(A)) -> (all D (element(D,powerset(A)) -> subset_intersection2(A,C,D) = apply_binary(the_L_meet(B),C,D) & apply_binary(the_L_join(B),C,D) = subset_union2(A,C,D))))) <-> boole_lattice(A) = B))) # label(d1_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 208 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> element(subset_union2(A,B,C),powerset(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 209 (all A element(k1_pcomps_1(A),powerset(powerset(A)))) # label(dt_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 210 (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]. 1.42/1.76 211 (all A all B all C all D (relation_of2_as_subset(D,A,B) & quasi_total(D,A,B) & function(D) -> (all E (function(E) & relation(E) -> (in(C,A) -> apply(relation_composition(D,E),C) = apply(E,apply(D,C)) | empty_set = B))))) # label(t21_funct_2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.76 212 (all A all B (ordinal(B) -> (exists C all D (in(D,C) <-> (exists E (D = E & in(E,A) & ordinal(E))) & in(D,succ(B)))))) # label(s1_xboole_0__e8_6__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.76 213 (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]. 1.42/1.76 214 (all A (relation(A) -> (all B (relation(B) -> (subset(A,B) -> subset(relation_rng(A),relation_rng(B)) & subset(relation_dom(A),relation_dom(B))))))) # label(t25_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.76 215 (exists A (-empty(A) & natural(A) & ordinal(A) & epsilon_connected(A) & epsilon_transitive(A))) # label(rc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 216 (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))) -> (F = C -> subset_complement(the_carrier(A),F) = D))) & (all G (element(G,powerset(the_carrier(A))) -> (G = C -> subset_complement(the_carrier(A),G) = E))) & in(C,B) & in(C,B) -> E = D)) -> (exists C ((all D all E (in(ordered_pair(D,E),C) <-> in(D,B) & (all H (element(H,powerset(the_carrier(A))) -> (D = H -> E = subset_complement(the_carrier(A),H)))) & in(D,B))) & function(C) & relation(C)))))) # label(s1_funct_1__e4_7_2__tops_2__1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.76 217 (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]. 1.42/1.76 218 (all A (function(A) <-> (all B all C all D (in(ordered_pair(B,C),A) & in(ordered_pair(B,D),A) -> C = D)))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 219 (all A (empty(A) & ordinal(A) -> epsilon_connected(A) & natural(A) & ordinal(A) & epsilon_transitive(A))) # label(cc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 220 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 221 (exists A (relation_empty_yielding(A) & relation(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 222 (all A transitive(inclusion_relation(A))) # label(t3_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.76 223 (all A (ordinal(A) -> well_founded_relation(inclusion_relation(A)))) # label(t6_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.76 224 (all A all B (relation(B) -> (identity_relation(A) = B <-> (all C all D (in(ordered_pair(C,D),B) <-> C = D & in(C,A)))))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 225 (all A (rel_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (directed_subset(B,A) <-> (all C (element(C,the_carrier(A)) -> (all D (element(D,the_carrier(A)) -> -(in(C,B) & in(D,B) & (all E (element(E,the_carrier(A)) -> -(in(E,B) & related(A,C,E) & related(A,D,E)))))))))))))) # label(d1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 226 (all A all B (latt_str(B) & lattice(B) & -empty_carrier(B) -> ((exists C exists D (below_refl(B,C,D) & ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D) = A & element(D,the_carrier(B)) & element(C,the_carrier(B)))) <-> in(A,a_1_0_filter_1(B))))) # label(fraenkel_a_1_0_filter_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 227 (all A (lattice(A) & complete_latt_str(A) & latt_str(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C (meet_of_latt_set(A,C) = B <-> (all D (element(D,the_carrier(A)) -> (latt_set_smaller(A,D,C) -> below_refl(A,D,B)))) & latt_set_smaller(A,B,C))))))) # label(t34_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.42/1.76 228 (all A (v1_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B))))) # label(cc16_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 229 (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]. 1.42/1.76 230 (all A all B (element(B,powerset(A)) -> (all C (element(C,powerset(A)) -> (subset(B,subset_complement(A,C)) <-> disjoint(B,C)))))) # label(t43_subset_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.76 231 (all A (v1_partfun1(identity_as_relation_of(A),A,A) & relation_of2_as_subset(identity_as_relation_of(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 232 (all A (relation(A) -> (transitive(A) <-> is_transitive_in(A,relation_field(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 233 (all A (v3_membered(A) -> (all B (element(B,powerset(A)) -> v2_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 234 (all A (rel_str(A) -> (lower_bounded_relstr(A) & upper_bounded_relstr(A) -> bounded_relstr(A)))) # label(cc5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 235 (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]. 1.42/1.76 236 (all A all B (-empty(B) & -empty(A) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 237 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> set_difference(B,C) = subset_difference(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 238 (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]. 1.42/1.76 239 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 240 (all A all B (element(B,powerset(powerset(A))) -> union_of_subsets(A,B) = union(B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 241 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),A) -> in(ordered_pair(C,D),B))) <-> subset(A,B)))))) # label(d3_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 242 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_intersection2(A,B,C) = set_intersection2(B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 243 (all A (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))) # label(dt_k3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.76 244 (all A (v4_membered(A) -> (all B (element(B,A) -> v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) & v1_xcmplx_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 245 (all A all B (finite(A) & finite(B) -> finite(cartesian_product2(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 246 (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]. 1.42/1.77 247 (all A (relation(A) -> (all B (relation_dom(A) = B <-> (all C ((exists D in(ordered_pair(C,D),A)) <-> in(C,B))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 248 (all A (-empty(A) -> -((all B (relation(B) & function(B) -> -(relation_dom(B) = A & (all C (in(C,A) -> in(apply(B,C),C)))))) & (all B -(in(B,A) & empty_set = B))))) # label(t28_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 249 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 250 (all A (rel_str(A) -> (all B ((exists C (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)) -> ((all E (element(E,the_carrier(A)) -> (relstr_element_smaller(A,B,E) -> related(A,E,D)))) & relstr_element_smaller(A,B,D) -> D = C))) & element(C,the_carrier(A)))) <-> ex_inf_of_relstr_set(A,B))))) # label(d8_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 251 (all A all B all C (transitive_relstr(A) & rel_str(A) & finite(C) & element(C,powerset(B)) & element(B,powerset(the_carrier(A))) & -empty_carrier(A) -> ((all D all E all F (D = E & (exists I (F = I & (exists J (element(J,the_carrier(A)) & relstr_set_smaller(A,I,J) & in(J,B))))) & F = D & (exists G (G = E & (exists H (relstr_set_smaller(A,G,H) & in(H,B) & element(H,the_carrier(A)))))) -> F = E)) -> (exists D all E ((exists F (in(F,powerset(C)) & (exists K ((exists L (element(L,the_carrier(A)) & in(L,B) & relstr_set_smaller(A,K,L))) & E = K)) & F = E)) <-> in(E,D)))))) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 252 (all A (top_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> (closed_subsets(B,A) <-> open_subsets(complements_of_subsets(the_carrier(A),B),A)))))) # label(t16_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 253 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 254 (exists A (-empty_carrier(A) & reflexive_relstr(A) & antisymmetric_relstr(A) & transitive_relstr(A) & strict_rel_str(A) & rel_str(A))) # label(rc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 255 (all A (ordinal(A) <-> epsilon_transitive(A) & epsilon_connected(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 256 (all A all B (pair_first(ordered_pair(A,B)) = A & B = pair_second(ordered_pair(A,B)))) # label(t7_mcart_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 257 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),B) <-> in(ordered_pair(C,D),A))) <-> A = B))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 258 (all A (the_carrier(incl_POSet(A)) = A & inclusion_order(A) = the_InternalRel(incl_POSet(A)))) # label(t1_yellow_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 259 (all A all B all C (relation_of2(C,A,B) -> (bijective(C,A,B) & quasi_total(C,A,B) & function(C) -> one_to_one(C) & quasi_total(C,A,B) & onto(C,A,B) & function(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 260 (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 & D = F & related(B,E,F) -> related(A,C,D)))))))))))))) # label(t60_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 261 (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))) -> (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))) & in(C,complements_of_subsets(the_carrier(A),B)) & in(C,complements_of_subsets(the_carrier(A),B)) -> E = D)) -> (exists C all D ((exists E (in(E,complements_of_subsets(the_carrier(A),B)) & (all H (element(H,powerset(the_carrier(A))) -> (H = E -> subset_complement(the_carrier(A),H) = D))) & in(E,complements_of_subsets(the_carrier(A),B)))) <-> in(D,C)))))) # label(s1_tarski__e4_7_1__tops_2__1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 262 (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]. 1.42/1.77 263 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 264 (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]. 1.42/1.77 265 (all A all B all C (relation(C) & function(C) -> (in(B,A) -> apply(C,B) = apply(relation_dom_restriction(C,A),B)))) # label(t72_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 266 (all A (rel_str(A) & antisymmetric_relstr(A) -> (all B (ex_inf_of_relstr_set(A,B) <-> (exists C (relstr_element_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_element_smaller(A,B,D) -> related(A,D,C)))) & element(C,the_carrier(A)))))))) # label(t16_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 267 (all A (relation(A) -> (empty_set = relation_dom(A) | empty_set = relation_rng(A) -> empty_set = A))) # label(t64_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 268 (all A all B all C all D (relation_of2(C,A,B) & element(D,A) & quasi_total(C,A,B) & function(C) & -empty(A) -> element(apply_as_element(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 269 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 270 (exists A (strict_rel_str(A) & rel_str(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 271 (all A all B all C all D (lattice(A) & latt_str(A) & element(C,the_carrier(A)) & element(D,the_carrier(B)) & latt_str(B) & lattice(B) & -empty_carrier(B) & -empty_carrier(A) -> ordered_pair(C,D) = k10_filter_1(A,B,C,D))) # label(redefinition_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 272 (all A all B all C (transitive_relstr(A) & rel_str(A) & element(B,powerset(the_carrier(A))) & finite(C) & element(C,powerset(B)) & -empty_carrier(A) -> (exists D all E (in(E,D) <-> in(E,powerset(C)) & (exists F (E = F & (exists G (element(G,the_carrier(A)) & in(G,B) & relstr_set_smaller(A,F,G))))))))) # label(s1_xboole_0__e11_2_1__waybel_0__1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 273 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> subset_complement(A,meet_of_subsets(A,B)) = union_of_subsets(A,complements_of_subsets(A,B))))) # label(t12_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 274 (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 ((all H (element(H,powerset(the_carrier(A))) -> (H = F -> subset_complement(the_carrier(A),H) = G))) & in(F,complements_of_subsets(the_carrier(A),B)) & E = ordered_pair(F,G))) & 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]. 1.42/1.77 275 (exists A (-empty_carrier(A) & reflexive_relstr(A) & with_suprema_relstr(A) & complete_relstr(A) & lower_bounded_relstr(A) & bounded_relstr(A) & upper_bounded_relstr(A) & with_infima_relstr(A) & antisymmetric_relstr(A) & transitive_relstr(A) & rel_str(A))) # label(rc2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 276 (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]. 1.42/1.77 277 (all A all B all C all D (in(B,D) & in(A,C) <-> in(ordered_pair(A,B),cartesian_product2(C,D)))) # label(l55_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 278 (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)) -> (E = C & D = F & related(A,C,D) & in(E,the_carrier(B)) & in(F,the_carrier(B)) -> related(B,E,F)))))))))))))) # label(t61_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 279 (all A all B (relation(B) -> (well_ordering(B) -> well_ordering(relation_restriction(B,A))))) # label(t32_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 280 (all A all B (ordinal(B) -> -(subset(A,B) & empty_set != A & (all C (ordinal(C) -> -((all D (ordinal(D) -> (in(D,A) -> ordinal_subset(C,D)))) & in(C,A))))))) # label(t32_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 281 (all A (join_semilatt_str(A) & join_commutative(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)) & v1_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(fc2_lattice2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 282 (all A all B exists C all D (in(D,C) <-> (exists E exists F (in(E,A) & F = singleton(E) & 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]. 1.42/1.77 283 (all A all B (-empty(unordered_pair(A,B)) & finite(unordered_pair(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 284 (all A (ordinal(A) -> (all B (ordinal(B) -> -(B != A & -in(B,A) & -in(A,B)))))) # label(t24_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 285 (exists A (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A) & being_limit_ordinal(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 286 (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]. 1.42/1.77 287 (all A all B (function(B) & relation(B) -> subset(relation_image(B,relation_inverse_image(B,A)),A))) # label(t145_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 288 (all A (-empty_carrier(A) & latt_str(A) & lattice(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]. 1.42/1.77 289 (all A all B (v5_membered(A) -> v1_membered(set_intersection2(A,B)) & v4_membered(set_intersection2(A,B)) & v5_membered(set_intersection2(A,B)) & v3_membered(set_intersection2(A,B)) & v2_membered(set_intersection2(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 290 (all A (complete_latt_str(A) & latt_str(A) & lattice(A) & -empty_carrier(A) -> lattice(A) & lower_bounded_semilattstr(A) & bottom_of_semilattstr(A) = join_of_latt_set(A,empty_set) & latt_str(A) & -empty_carrier(A))) # label(t50_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 291 (all A (latt_str(A) -> (-empty_carrier(A) & boolean_lattstr(A) -> upper_bounded_semilattstr(A) & bounded_lattstr(A) & complemented_lattstr(A) & lower_bounded_semilattstr(A) & distributive_lattstr(A) & -empty_carrier(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 292 (all A all B ((exists C (relation_dom(C) = A & B = relation_rng(C) & one_to_one(C) & function(C) & relation(C))) <-> equipotent(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 293 (all A all B (B != A & subset(A,B) <-> proper_subset(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 294 (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) -> apply_as_element(A,B,C,D) = apply(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 295 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (lower_bounded_semilattstr(A) -> (all B (element(B,the_carrier(A)) -> (B = bottom_of_semilattstr(A) <-> (all C (element(C,the_carrier(A)) -> meet(A,B,C) = B & B = meet(A,C,B))))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 296 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> relstr_set_smaller(A,empty_set,B) & relstr_element_smaller(A,empty_set,B))))) # label(t6_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 297 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) <-> closed_subset(B,A)))))) # label(d6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 298 (all A all B (relation(B) -> (connected(B) -> connected(relation_restriction(B,A))))) # label(t23_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 299 (all A exists B (element(B,powerset(A)) & -proper_element(B,powerset(A)))) # label(rc2_tex_2) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 300 (all A all B (element(B,powerset(the_carrier(A))) & top_str(A) & topological_space(A) -> closed_subset(topstr_closure(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 301 (exists A (empty(A) & relation(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 302 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 303 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> element(subset_intersection2(A,B,C),powerset(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 304 (all A all B (element(B,the_carrier(boole_lattice(A))) -> (all C (element(C,the_carrier(boole_lattice(A))) -> (below(boole_lattice(A),B,C) <-> subset(B,C)))))) # label(t2_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 305 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 306 (exists A (epsilon_connected(A) & ordinal(A) & epsilon_transitive(A) & -empty(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 307 (all A (relation(A) -> ((all B all C all D (in(ordered_pair(B,C),A) & in(ordered_pair(C,D),A) -> in(ordered_pair(B,D),A))) <-> transitive(A)))) # label(l2_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 308 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_dom(A),relation_rng(B)) -> relation_rng(relation_composition(B,A)) = relation_rng(A)))))) # label(t47_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 309 (all A all B (relation(B) -> (reflexive(B) -> reflexive(relation_restriction(B,A))))) # label(t22_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 310 (all A all B all C (relation(C) -> (in(A,relation_dom(relation_dom_restriction(C,B))) <-> in(A,relation_dom(C)) & in(A,B)))) # label(t86_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 311 (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]. 1.42/1.77 312 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 313 (all A all B all C ((all D (in(D,A) & in(D,B) <-> in(D,C))) <-> C = set_intersection2(A,B))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 314 (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]. 1.42/1.77 315 (all A all B (relation(B) & function(B) -> (all C (function(C) & relation(C) -> ((all D (in(D,relation_dom(B)) -> apply(C,D) = apply(B,D))) & relation_dom(B) = set_intersection2(relation_dom(C),A) <-> relation_dom_restriction(C,A) = B))))) # label(t68_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 316 (exists A (finite(A) & -empty(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 317 (all A (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A)))) # label(dt_k2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 318 (all A (one_sorted_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> B = subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)))))) # label(t22_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.42/1.77 319 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 320 (all A (epsilon_transitive(A) <-> (all B (in(B,A) -> subset(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 321 (all A all B all C (element(B,powerset(powerset(A))) & function(C) & relation(C) -> ((all D all E all F (D = E & in(relation_image(C,F),B) & D = F & in(relation_image(C,E),B) -> E = F)) -> (exists D all E (in(E,D) <-> (exists F (in(F,powerset(relation_dom(C))) & in(relation_image(C,E),B) & E = F))))))) # label(s1_tarski__e6_27__finset_1__1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 322 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 323 (all A (relation(identity_relation(A)) & reflexive(identity_relation(A)) & transitive(identity_relation(A)) & antisymmetric(identity_relation(A)) & symmetric(identity_relation(A)) & function(identity_relation(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.42/1.77 324 (all A (latt_str(A) -> (lattice(A) & distributive_lattstr(A) & -empty_carrier(A) -> -empty_carrier(A) & meet_commutative(A) & lattice(A) & modular_lattstr(A) & join_absorbing(A) & meet_absorbing(A) & meet_associative(A) & join_associative(A) & join_commutative(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 325 (all A all B (relation(A) & relation(B) -> relation(set_difference(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 326 (all A all B (relation(A) -> relation(relation_restriction(A,B)))) # label(dt_k2_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 327 (all A (-empty_carrier(A) & meet_semilatt_str(A) & meet_associative(A) -> relation(the_L_meet(A)) & v2_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)) & function(the_L_meet(A)))) # label(fc5_lattice2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 328 (all A all B (net_str(B,A) & one_sorted_str(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]. 1.54/1.78 329 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 330 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 331 (all A all B (-empty(A) & relation(B) -> (all C exists D all E (in(E,D) <-> in(E,cartesian_product2(A,C)) & (exists F exists G (in(F,A) & (exists H (in(G,H) & (all I (in(I,H) -> in(ordered_pair(G,I),B))) & F = H)) & E = ordered_pair(F,G))))))) # label(s1_xboole_0__e10_24__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 332 (all A (latt_str(A) -> (lattice(A) & -empty_carrier(A) -> join_associative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & meet_commutative(A) & join_commutative(A) & -empty_carrier(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 333 (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]. 1.54/1.78 334 (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]. 1.54/1.78 335 (all A all B (one_sorted_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> (all C ((all D all E all F (E = D & (exists G exists H (ordered_pair(G,H) = E & in(G,complements_of_subsets(the_carrier(A),B)) & (all I (element(I,powerset(the_carrier(A))) -> (I = G -> subset_complement(the_carrier(A),I) = H))))) & (exists J exists K (ordered_pair(J,K) = F & in(J,complements_of_subsets(the_carrier(A),B)) & (all L (element(L,powerset(the_carrier(A))) -> (L = J -> K = subset_complement(the_carrier(A),L)))))) & F = D -> F = E)) -> (exists D all E (in(E,D) <-> (exists F (in(F,cartesian_product2(complements_of_subsets(the_carrier(A),B),C)) & F = E & (exists M exists N (ordered_pair(M,N) = E & in(M,complements_of_subsets(the_carrier(A),B)) & (all O (element(O,powerset(the_carrier(A))) -> (O = M -> N = subset_complement(the_carrier(A),O)))))))))))))) # label(s1_tarski__e4_7_1__tops_2__2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 336 (exists A (strict_latt_str(A) & -empty_carrier(A) & latt_str(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 337 (all A all B (function(A) & relation(A) -> function(relation_dom_restriction(A,B)) & relation(relation_dom_restriction(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 338 (all A (one_sorted_str(A) -> (all B (net_str(B,A) -> (all C (net_str(C,A) -> (subnetstr(C,A,B) <-> subrelstr(C,B) & the_mapping(A,C) = relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C))))))))) # label(d8_yellow_6) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 339 (all A (centered(A) <-> empty_set != A & (all B -(empty_set != B & empty_set = set_meet(B) & finite(B) & subset(B,A))))) # label(d2_compts_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 340 (all A (empty(A) -> empty(relation_rng(A)) & relation(relation_rng(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 341 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 342 (all A (rel_str(A) -> (lower_bounded_relstr(A) <-> (exists B (element(B,the_carrier(A)) & relstr_element_smaller(A,the_carrier(A),B)))))) # label(d4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 343 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) -> ((all D all E ((exists F (in(ordered_pair(F,E),B) & in(ordered_pair(D,F),A))) <-> in(ordered_pair(D,E),C))) <-> C = relation_composition(A,B)))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 344 (all A (transitive_relstr(A) & antisymmetric_relstr(A) & rel_str(A) & reflexive_relstr(A) -> relation(the_InternalRel(A)) & reflexive(the_InternalRel(A)) & transitive(the_InternalRel(A)) & v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)) & antisymmetric(the_InternalRel(A)))) # label(fc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 345 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 346 (all A all B (subset(A,singleton(B)) <-> singleton(B) = A | empty_set = A)) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 347 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 348 (all A all B (function(A) & finite(B) & relation(A) -> finite(relation_image(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 349 (all A all B all C all D (element(C,A) & element(D,B) & -empty(B) & -empty(A) -> ordered_pair(C,D) = ordered_pair_as_product_element(A,B,C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 350 (all A all B (-empty(B) -> (all C (relation_of2(C,A,B) -> (quasi_total(C,A,B) & function(C) -> v1_partfun1(C,A,B) & quasi_total(C,A,B) & function(C)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 351 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 352 (all A (one_sorted_str(A) & -empty_carrier(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]. 1.54/1.78 353 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 354 (all A all B (element(B,powerset(A)) -> (proper_element(B,powerset(A)) <-> B != A))) # label(t5_tex_2) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 355 (all A (relation(A) -> (empty_set = relation_dom(A) <-> relation_rng(A) = empty_set))) # label(t65_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 356 (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]. 1.54/1.78 357 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 358 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 359 (all A all B all C (relation_of2(B,cartesian_product2(A,A),A) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) & function(C) & quasi_total(B,cartesian_product2(A,A),A) & function(B) -> (all D all E all F (latt_str_of(D,E,F) = latt_str_of(A,B,C) -> A = D & C = F & B = E)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 360 (all A all B (subset(B,A) & subset(A,B) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 361 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 362 (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]. 1.54/1.78 363 (all A (relation(A) -> (all B (relation(B) -> (all C (function(C) & relation(C) -> (relation_isomorphism(A,B,C) <-> relation_dom(C) = relation_field(A) & relation_field(B) = relation_rng(C) & one_to_one(C) & (all D all E (in(ordered_pair(D,E),A) <-> in(D,relation_field(A)) & in(ordered_pair(apply(C,D),apply(C,E)),B) & in(E,relation_field(A))))))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 364 (all A (latt_str(A) & lattice(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> B = cast_to_el_of_LattPOSet(A,B))))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 365 (all A (-empty_carrier(A) & latt_str(A) & lattice(A) -> -empty_carrier(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)))) # label(fc4_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 366 (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]. 1.54/1.78 367 (all A (-empty_carrier(A) & one_sorted_str(A) -> (all B (-empty_carrier(B) & net_str(B,A) -> (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]. 1.54/1.78 368 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 369 (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)) -> ((all D (point_neighbourhood(D,A,C) -> -disjoint(D,B))) <-> in(C,topstr_closure(A,B))))))))) # label(t6_yellow_6) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 370 (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]. 1.54/1.78 371 (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]. 1.54/1.78 372 (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]. 1.54/1.78 373 (all A (one_sorted_str(A) -> (all B (net_str(B,A) -> (all C (subnetstr(C,A,B) -> (subrelstr(C,B) & full_subrelstr(C,B) <-> full_subnetstr(C,A,B)))))))) # label(d9_yellow_6) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 374 (all A (one_sorted_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B)))) # label(t15_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 375 (all A (relation(A) -> (all B all C (relation(C) -> ((all D all E (in(ordered_pair(D,E),A) & in(D,B) <-> in(ordered_pair(D,E),C))) <-> C = relation_dom_restriction(A,B)))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 376 (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]. 1.54/1.78 377 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 378 (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]. 1.54/1.78 379 (all A all B (relation_of2(B,A,A) -> (all C all D (rel_str_of(A,B) = rel_str_of(C,D) -> D = B & C = A)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 380 (all A (latt_str(A) -> (bounded_lattstr(A) & complemented_lattstr(A) & distributive_lattstr(A) & -empty_carrier(A) -> boolean_lattstr(A) & -empty_carrier(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 381 (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]. 1.54/1.78 382 (all A all B (relation(B) -> subset(relation_image(B,A),relation_rng(B)))) # label(t144_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 383 (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]. 1.54/1.78 384 (all A all B ((all C (in(C,B) <-> subset(C,A))) <-> B = powerset(A))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 385 (all A (-empty_carrier(A) & complete_latt_str(A) & latt_str(A) & lattice(A) -> (all B (meet_of_latt_set(A,B) = meet_on_relstr(poset_of_lattice(A),B) & join_on_relstr(poset_of_lattice(A),B) = join_of_latt_set(A,B))))) # label(t29_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 386 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (-empty_carrier(B) & net_str(B,A) -> (all 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)))) <-> is_eventually_in(A,B,C))))))) # label(d11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 387 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> -(B = empty_set & is_a_cover_of_carrier(A,B)))))) # label(t5_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 388 (all A all B (latt_str(A) & -empty_carrier(A) -> element(join_of_latt_set(A,B),the_carrier(A)))) # label(dt_k15_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 389 (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]. 1.54/1.78 390 (all A (one_sorted_str(A) -> empty_carrier_subset(A) = empty_set)) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 391 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (ex_sup_of_relstr_set(A,B) -> ((all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) -> related(A,C,D)))) & relstr_set_smaller(A,B,C) <-> C = join_on_relstr(A,B))))))) # label(d9_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 392 (all A (ordinal(A) -> connected(inclusion_relation(A)))) # label(t4_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.54/1.78 393 (all A (relation(A) -> (all B all C (C = relation_image(A,B) <-> (all D ((exists E (in(ordered_pair(E,D),A) & in(E,B))) <-> in(D,C))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 394 (all A all B all C (-empty_carrier(A) & reflexive_relstr(A) & rel_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) -> related_reflexive(A,B,B))) # label(reflexivity_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 395 (all A (v3_membered(A) -> (all B (element(B,A) -> v1_rat_1(B) & v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 396 (all A (one_sorted_str(A) -> v5_membered(empty_carrier_subset(A)) & v4_membered(empty_carrier_subset(A)) & v3_membered(empty_carrier_subset(A)) & v2_membered(empty_carrier_subset(A)) & v1_membered(empty_carrier_subset(A)) & empty(empty_carrier_subset(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.54/1.78 397 (all A all B all C all D (one_sorted_str(B) & function(C) & quasi_total(C,the_carrier(A),the_carrier(B)) & element(D,the_carrier(A)) & relation_of2(C,the_carrier(A),the_carrier(B)) & -empty_carrier(B) & one_sorted_str(A) & -empty_carrier(A) -> element(apply_on_structs(A,B,C,D),the_carrier(B)))) # label(dt_k1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 398 (all A all B (-in(B,A) <-> A = set_difference(A,singleton(B)))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 399 (all A (ordinal(A) -> ((all B (ordinal(B) -> (in(B,A) -> (in(B,omega) -> (all C (element(C,powerset(powerset(B))) -> -((all D -((all E (subset(D,E) & in(E,C) -> D = E)) & in(D,C))) & empty_set != C))))))) -> (in(A,omega) -> (all F (element(F,powerset(powerset(A))) -> -(empty_set != F & (all G -((all H (subset(G,H) & in(H,F) -> G = H)) & in(G,F)))))))))) -> (all A (ordinal(A) -> (in(A,omega) -> (all I (element(I,powerset(powerset(A))) -> -(I != empty_set & (all J -(in(J,I) & (all K (in(K,I) & subset(J,K) -> K = J)))))))))) # label(s2_ordinal1__e18_27__finset_1__1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 400 (all A ((exists B (ordinal(B) & in(B,A))) -> (exists B (in(B,A) & (all C (ordinal(C) -> (in(C,A) -> ordinal_subset(B,C)))) & ordinal(B))))) # label(s1_ordinal1__e8_6__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 401 (all A (relation(A) -> (all B (relation(B) -> (relation_inverse(A) = B <-> (all C all D (in(ordered_pair(D,C),A) <-> in(ordered_pair(C,D),B)))))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 402 (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]. 1.55/1.78 403 (all A all B all C (relation(C) & function(C) -> (in(ordered_pair(A,B),C) <-> B = apply(C,A) & in(A,relation_dom(C))))) # label(t8_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 404 (all A all B all C all D (latt_str(A) & latt_str(B) & element(C,the_carrier(A)) & element(D,the_carrier(B)) & lattice(B) & -empty_carrier(B) & lattice(A) & -empty_carrier(A) -> 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]. 1.55/1.78 405 (all A (ordinal(A) -> (all B (element(B,A) -> ordinal(B) & epsilon_connected(B) & epsilon_transitive(B))))) # label(cc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 406 (all A all B (element(B,the_carrier(boole_POSet(A))) -> (all C (element(C,the_carrier(boole_POSet(A))) -> (related_reflexive(boole_POSet(A),B,C) <-> subset(B,C)))))) # label(t2_yellow_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 407 (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,B) <-> in(C,subset_complement(the_carrier(A),B))))))))) # label(l40_tops_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 408 (all A all B all C (-empty_carrier(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & meet_semilatt_str(A) & meet_commutative(A) -> element(meet_commut(A,B,C),the_carrier(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 409 (all A (latt_str(A) -> (join_commutative(A) & meet_commutative(A) & meet_associative(A) & join_absorbing(A) & meet_absorbing(A) & join_associative(A) & -empty_carrier(A) -> lattice(A) & -empty_carrier(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 410 (all A all B (relation(B) & function(B) -> (all C (function(C) & relation(C) -> (in(A,relation_dom(B)) -> apply(relation_composition(B,C),A) = apply(C,apply(B,A))))))) # label(t23_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 411 (all A (rel_str(A) -> (is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) <-> antisymmetric_relstr(A)))) # label(d6_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 412 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 413 (all A all B (relation(B) & relation(A) -> relation(set_intersection2(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 414 (all A (rel_str(A) & transitive_relstr(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (all D (element(D,the_carrier(A)) -> (related(A,C,D) & related(A,B,C) -> related(A,B,D)))))))))) # label(t26_orders_2) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 415 (all A (one_sorted_str(A) -> quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A)) & relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A)) & function(identity_on_carrier(A)))) # label(dt_k7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 416 (all A (ordinal(A) & natural(A) -> epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & natural(succ(A)) & ordinal(succ(A)) & -empty(succ(A)))) # label(fc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 417 (all A all B (element(B,powerset(powerset(succ(A)))) & ordinal(A) -> (exists C all D ((exists E (in(E,B) & set_difference(E,singleton(A)) = D)) & in(D,powerset(A)) <-> in(D,C))))) # label(s1_xboole_0__e4_27_3_1__finset_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 418 (all A inclusion_order(A) = inclusion_relation(A)) # label(redefinition_k1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 419 (all A all B (relation(B) -> subset(relation_rng_restriction(A,B),B))) # label(t117_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 420 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 421 (all A all B all C (join_semilatt_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & -empty_carrier(A) -> element(join(A,B,C),the_carrier(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 422 (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]. 1.55/1.78 423 (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]. 1.55/1.78 424 (all A (one_sorted_str(A) -> cast_as_carrier_subset(A) = the_carrier(A))) # label(t12_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 425 (exists A (function(A) & relation_empty_yielding(A) & relation(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 426 (all A (ordinal(A) -> epsilon_connected(A) & epsilon_transitive(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 427 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 428 (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]. 1.55/1.78 429 (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]. 1.55/1.78 430 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 431 (all A all B (element(B,the_carrier(boole_lattice(A))) -> (all C (element(C,the_carrier(boole_lattice(A))) -> set_union2(B,C) = join(boole_lattice(A),B,C) & set_intersection2(B,C) = meet(boole_lattice(A),B,C))))) # label(t1_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 432 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 433 (all A (rel_str(A) & -empty_carrier(A) -> (directed_relstr(A) <-> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (exists D (related(A,C,D) & related(A,B,D) & element(D,the_carrier(A))))))))))) # label(d5_yellow_6) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 434 (all A boole_POSet(A) = poset_of_lattice(boole_lattice(A))) # label(d2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 435 (all A (latt_str(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(A)) -> (all C ((all D (element(D,the_carrier(A)) -> (in(D,C) -> below(A,D,B)))) <-> latt_element_smaller(A,B,C))))))) # label(d17_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 436 (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]. 1.55/1.78 437 (all A (one_sorted_str(A) -> cast_as_carrier_subset(A) = the_carrier(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 438 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 439 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 440 (all A all B all C (element(B,powerset(C)) & in(A,B) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 441 (all A all B (subset(A,B) <-> set_difference(A,B) = empty_set)) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 442 (all A (lattice(A) & latt_str(A) & -empty_carrier(A) -> (all B (element(B,the_carrier(poset_of_lattice(A))) -> B = cast_to_el_of_lattice(A,B))))) # label(d4_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 443 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 444 (all A all B -(proper_subset(B,A) & subset(A,B))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 445 (all A all B all C (-empty_carrier(A) & one_sorted_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> unordered_pair_as_carrier_subset(A,C,B) = unordered_pair_as_carrier_subset(A,B,C))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 446 (all A all B (v5_membered(A) -> v2_membered(set_intersection2(B,A)) & v4_membered(set_intersection2(B,A)) & v5_membered(set_intersection2(B,A)) & v3_membered(set_intersection2(B,A)) & v1_membered(set_intersection2(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 447 (all A all B (finite(B) & subset(A,B) -> finite(A))) # label(t13_finset_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 448 (all A all B all C (relation(B) & function(C) & relation(C) -> ((all D all E all F (E = D & (exists I exists J (ordered_pair(I,J) = F & in(ordered_pair(apply(C,I),apply(C,J)),B))) & D = F & (exists G exists H (ordered_pair(G,H) = E & in(ordered_pair(apply(C,G),apply(C,H)),B))) -> E = F)) -> (exists D all E ((exists F (in(F,cartesian_product2(A,A)) & E = F & (exists K exists L (ordered_pair(K,L) = E & in(ordered_pair(apply(C,K),apply(C,L)),B))))) <-> in(E,D)))))) # label(s1_tarski__e6_21__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 449 (all A all B all C (element(B,powerset(powerset(A))) & function(C) & relation(C) -> (exists D all E (in(E,D) <-> in(E,powerset(relation_dom(C))) & in(relation_image(C,E),B))))) # label(s1_xboole_0__e6_27__finset_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 450 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 451 (all A all B (relation(A) -> relation(relation_dom_restriction(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 452 (all A (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & relation_of2_as_subset(inclusion_order(A),A,A) & v1_partfun1(inclusion_order(A),A,A))) # label(dt_k1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 453 (all A (relation(A) -> relation_image(A,relation_dom(A)) = relation_rng(A))) # label(t146_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.78 454 (all A all B (relation(A) & relation(B) -> relation(relation_composition(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 455 (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_refl(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.55/1.78 456 (all A incl_POSet(powerset(A)) = boole_POSet(A)) # label(t4_yellow_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.79 457 (all A all B (in(A,B) -> B = set_union2(singleton(A),B))) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.79 458 (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]. 1.55/1.79 459 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 460 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> subset_union2(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 461 (all A (-empty_carrier(A) & join_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (C = join(A,B,C) <-> below(A,B,C)))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 462 (all A all B (element(B,powerset(the_carrier(A))) & top_str(A) & topological_space(A) -> ((all C all D all E ((exists F (element(F,powerset(the_carrier(A))) & subset(B,D) & closed_subset(F,A) & F = D)) & E = C & (exists G (element(G,powerset(the_carrier(A))) & subset(B,E) & closed_subset(G,A) & E = G)) & C = D -> E = D)) -> (exists C all D (in(D,C) <-> (exists E (E = D & (exists H (element(H,powerset(the_carrier(A))) & subset(B,D) & closed_subset(H,A) & H = D)) & in(E,powerset(the_carrier(A)))))))))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 463 (all A (rel_str(A) -> join_on_relstr(A,empty_set) = bottom_of_relstr(A))) # label(d11_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 464 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.79 465 (all A all B (relation(B) -> subset(relation_dom_restriction(B,A),B))) # label(t88_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.79 466 (all A (function(A) & relation(A) -> (one_to_one(A) -> (all B (function(B) & relation(B) -> (relation_rng(A) = relation_dom(B) & (all C all D ((C = apply(A,D) & in(D,relation_dom(A)) -> in(C,relation_rng(A)) & D = apply(B,C)) & (D = apply(B,C) & in(C,relation_rng(A)) -> C = apply(A,D) & in(D,relation_dom(A))))) <-> B = function_inverse(A))))))) # label(t54_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.55/1.79 467 (all A all B (v1_membered(A) -> v1_membered(set_intersection2(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 468 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> reflexive(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A)) & antisymmetric(k2_lattice3(A)))) # label(dt_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 469 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 470 (all A (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 471 (all A (relation(A) -> (antisymmetric(A) <-> is_antisymmetric_in(A,relation_field(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 472 (all A (empty(A) -> ordinal(A) & epsilon_connected(A) & epsilon_transitive(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 473 (all A all B (relation(B) & function(B) -> function(relation_rng_restriction(A,B)) & relation(relation_rng_restriction(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 474 (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]. 1.55/1.79 475 (all A all B (B = union(A) <-> (all C ((exists D (in(D,A) & in(C,D))) <-> in(C,B))))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 1.55/1.79 476 (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]. 1.74/2.01 477 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (net_str(B,A) & -empty_carrier(B) -> (all 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))))) <-> is_often_in(A,B,C))))))) # label(d12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 478 (all A (one_sorted_str(A) & -empty_carrier(A) -> -empty(cast_as_carrier_subset(A)))) # label(fc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 479 (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]. 1.74/2.01 480 (all D (ordinal(D) -> ((in(D,omega) -> (all E (element(E,powerset(powerset(D))) -> -((all F -((all G (in(G,E) & subset(F,G) -> 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 -(in(I,H) & (all J (subset(I,J) & in(J,H) -> I = J))))))))))) & (all D (ordinal(D) -> ((all K (ordinal(K) -> (in(K,D) -> (in(K,omega) -> (all L (element(L,powerset(powerset(K))) -> -((all M -((all N (in(N,L) & subset(M,N) -> N = M)) & in(M,L))) & empty_set != L))))))) & being_limit_ordinal(D) -> (in(D,omega) -> (all O (element(O,powerset(powerset(D))) -> -(empty_set != O & (all P -((all Q (in(Q,O) & subset(P,Q) -> Q = P)) & in(P,O))))))) | D = empty_set))) & (in(empty_set,omega) -> (all A (element(A,powerset(powerset(empty_set))) -> -(empty_set != A & (all B -((all C (in(C,A) & subset(B,C) -> B = C)) & in(B,A))))))) -> (all D (ordinal(D) -> (in(D,omega) -> (all R (element(R,powerset(powerset(D))) -> -(R != empty_set & (all S -(in(S,R) & (all T (in(T,R) & subset(S,T) -> T = S)))))))))) # label(s1_ordinal2__e18_27__finset_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 481 (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]. 1.74/2.01 482 (all A all B all C (-empty_carrier(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & one_sorted_str(A) -> unordered_pair(B,C) = unordered_pair_as_carrier_subset(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 483 (all A all B all C (relation_of2(C,A,B) -> (function(C) & one_to_one(C) & quasi_total(C,A,B) & onto(C,A,B) -> bijective(C,A,B) & quasi_total(C,A,B) & function(C)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 484 (all A (top_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> (open_subsets(B,A) <-> (all C (element(C,powerset(the_carrier(A))) -> (in(C,B) -> open_subset(C,A))))))))) # label(d1_tops_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 485 (all A (-empty(A) & relation(A) -> -empty(relation_dom(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 486 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 487 (all A all B all C (meet_semilatt_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) & -empty_carrier(A) -> element(meet(A,B,C),the_carrier(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 488 (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]. 1.74/2.01 489 (all A all B all C all D (ordered_pair(C,D) = ordered_pair(A,B) -> C = A & D = B)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 490 (all A all B (relation(B) -> (antisymmetric(B) -> antisymmetric(relation_restriction(B,A))))) # label(t25_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 491 (all A (-empty_carrier(A) & transitive_relstr(A) & rel_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> ((all C (element(C,powerset(B)) & finite(C) -> (exists D (in(D,B) & relstr_set_smaller(A,C,D) & element(D,the_carrier(A)))))) <-> -empty(B) & directed_subset(B,A)))))) # label(t1_waybel_0) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 492 (all A all B (relation(B) & -empty(A) -> (all C ((all D all E all F ((exists K exists L (F = ordered_pair(K,L) & in(K,A) & (exists M (in(L,M) & (all N (in(N,M) -> in(ordered_pair(L,N),B))) & M = K)))) & D = F & (exists G exists H (ordered_pair(G,H) = E & (exists I (I = G & (all J (in(J,I) -> in(ordered_pair(H,J),B))) & in(H,I))) & in(G,A))) & E = D -> F = E)) -> (exists D all E ((exists F (in(F,cartesian_product2(A,C)) & (exists O exists P (E = ordered_pair(O,P) & (exists Q (O = Q & in(P,Q) & (all R (in(R,Q) -> in(ordered_pair(P,R),B))))) & in(O,A))) & F = E)) <-> in(E,D))))))) # label(s1_tarski__e10_24__wellord2__2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 493 (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)))) & (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)) & 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) <-> (all H (element(H,powerset(the_carrier(A))) -> (H = D -> subset_complement(the_carrier(A),H) = E))) & in(D,complements_of_subsets(the_carrier(A),B)) & in(D,complements_of_subsets(the_carrier(A),B)))) & function(C)))))) # label(s1_funct_1__e4_7_1__tops_2__1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 494 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> ((all C all D all E (D = C & in(set_difference(cast_as_carrier_subset(A),E),B) & C = E & in(set_difference(cast_as_carrier_subset(A),D),B) -> D = E)) -> (exists C all D ((exists E (E = D & in(set_difference(cast_as_carrier_subset(A),D),B) & 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]. 1.74/2.01 495 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 496 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = A)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 497 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 498 (all A all B (v2_membered(A) -> v1_membered(set_difference(A,B)) & v2_membered(set_difference(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 499 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 500 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (closed_subset(B,A) <-> open_subset(subset_complement(the_carrier(A),B),A)))))) # label(t29_tops_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 501 (all A (rel_str(A) -> (with_suprema_relstr(A) -> -empty_carrier(A)))) # label(cc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 502 (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]. 1.74/2.01 503 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 504 (all A (top_str(A) -> one_sorted_str(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 505 (all A all B (relation(B) -> relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A))) # label(t17_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 506 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 507 (all A (empty(A) -> relation(relation_dom(A)) & empty(relation_dom(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 508 (all A (one_sorted_str(A) -> (exists B net_str(B,A)))) # label(existence_l1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 509 (all A all B all C (relation(B) & relation(C) & function(C) -> (exists D ((all E all F (in(E,A) & in(F,A) & in(ordered_pair(apply(C,E),apply(C,F)),B) <-> in(ordered_pair(E,F),D))) & relation(D))))) # label(s1_relat_1__e6_21__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 510 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 511 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 512 (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]. 1.74/2.01 513 (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]. 1.74/2.01 514 (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]. 1.74/2.01 515 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 516 (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]. 1.74/2.01 517 (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]. 1.74/2.01 518 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_field(C)) & in(B,relation_field(C))))) # label(t30_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 519 (all A all B (latt_str(B) & lattice(B) & -empty_carrier(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]. 1.74/2.01 520 (all A all B set_difference(A,B) = set_difference(set_union2(A,B),B)) # label(t40_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 521 (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]. 1.74/2.01 522 (all A exists B (relation_of2(B,A,A) & reflexive(B) & symmetric(B) & v1_partfun1(B,A,A) & transitive(B) & antisymmetric(B) & relation(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 523 (all A all B (relation(B) -> relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A)))) # label(t18_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 524 (all A all B (relation_of2(B,singleton(A),singleton(A)) -> strict_rel_str(rel_str_of(singleton(A),B)) & trivial_carrier(rel_str_of(singleton(A),B)) & -empty_carrier(rel_str_of(singleton(A),B)))) # label(fc1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 525 (all A (-empty_carrier(A) & one_sorted_str(A) -> (exists B (-empty(B) & element(B,powerset(the_carrier(A))))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 526 (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]. 1.74/2.01 527 (all A (latt_str(A) & complete_latt_str(A) & lattice(A) & -empty_carrier(A) -> strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & lower_bounded_relstr(poset_of_lattice(A)) & upper_bounded_relstr(poset_of_lattice(A)) & bounded_relstr(poset_of_lattice(A)) & with_suprema_relstr(poset_of_lattice(A)) & with_infima_relstr(poset_of_lattice(A)) & complete_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & -empty_carrier(poset_of_lattice(A)))) # label(fc4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 528 (all A (element(A,omega) -> ordinal(A) & natural(A) & epsilon_connected(A) & epsilon_transitive(A))) # label(cc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 529 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 530 (all A (rel_str(A) -> (-empty_carrier(A) & trivial_carrier(A) & reflexive_relstr(A) -> -empty_carrier(A) & transitive_relstr(A) & antisymmetric_relstr(A) & complete_relstr(A) & reflexive_relstr(A)))) # label(cc2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 531 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 532 (all A (v5_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 533 (all A ((all B all C -(in(B,A) & in(C,A) & -in(C,B) & B != C & -in(B,C))) <-> epsilon_connected(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 534 (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]. 1.74/2.01 535 (all A (relation(A) -> (all B (is_well_founded_in(A,B) <-> (all C -(subset(C,B) & empty_set != C & (all D -(disjoint(fiber(A,D),C) & in(D,C))))))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 536 (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]. 1.74/2.01 537 (all A (finite(singleton(A)) & -empty(singleton(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 538 (all A (diff_closed(A) & cup_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 539 (all A all B all C (unordered_pair(B,C) = singleton(A) -> C = B)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.01 540 (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]. 1.74/2.01 541 (all A all B (-empty(B) & -empty(A) -> (all C (relation_of2(C,A,B) -> (function(C) & quasi_total(C,A,B) -> function(C) & quasi_total(C,A,B) & v1_partfun1(C,A,B) & -empty(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 542 (all A ((exists B (relation(B) & relation_rng(B) = A & in(relation_dom(B),omega) & function(B))) <-> finite(A))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 543 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 544 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C ((relstr_set_smaller(A,C,B) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,C,D) -> related(A,B,D)))) -> join_on_relstr(A,C) = B & ex_sup_of_relstr_set(A,C)) & (B = join_on_relstr(A,C) & ex_sup_of_relstr_set(A,C) -> (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]. 1.74/2.01 545 (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]. 1.74/2.01 546 (all A (rel_str(A) -> element(bottom_of_relstr(A),the_carrier(A)))) # label(dt_k3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.01 547 (all A (relation(A) -> (all B ((all C all D (in(C,B) & in(D,B) & in(ordered_pair(D,C),A) & in(ordered_pair(C,D),A) -> D = C)) <-> is_antisymmetric_in(A,B))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 548 (all A all B all C all D (unordered_triple(A,B,C) = D <-> (all E (in(E,D) <-> -(E != A & E != B & E != C))))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 549 (all A antisymmetric(inclusion_relation(A))) # label(t5_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 550 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 551 (all A (topological_space(A) & top_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & closed_subset(B,A) & open_subset(B,A))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 552 (exists A (empty(A) & function(A) & relation(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 553 (all A all B ((A != empty_set -> ((all C ((all D (in(D,A) -> in(C,D))) <-> in(C,B))) <-> set_meet(A) = B)) & (empty_set = A -> (B = set_meet(A) <-> B = empty_set)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 554 (all A (topological_space(A) & top_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & open_subset(B,A))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 555 (all A all B (top_str(A) & element(B,powerset(powerset(the_carrier(A)))) & topological_space(A) -> (exists C all D (in(D,C) <-> in(D,powerset(the_carrier(A))) & in(set_difference(cast_as_carrier_subset(A),D),B))))) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 556 (all A (relation(A) -> (all B (B = relation_rng(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(D,C),A)))))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 557 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 558 (all A (reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)) & strict_rel_str(incl_POSet(A)))) # label(fc5_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 559 (all A all B (relation(B) & -empty(A) -> ((all C all D all E ((exists F (F = C & in(D,F) & (all G (in(G,F) -> in(ordered_pair(D,G),B))))) & in(C,A) & (exists H ((all I (in(I,H) -> in(ordered_pair(E,I),B))) & in(E,H) & C = H)) & in(C,A) -> D = E)) -> (exists C (relation(C) & function(C) & (all D all E (in(D,A) & in(D,A) & (exists J ((all K (in(K,J) -> in(ordered_pair(E,K),B))) & in(E,J) & J = D)) <-> in(ordered_pair(D,E),C)))))))) # label(s1_funct_1__e10_24__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 560 (exists A top_str(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 561 (all A all B (v1_partfun1(B,A,A) & relation_of2(B,A,A) & transitive(B) & antisymmetric(B) & reflexive(B) -> strict_rel_str(rel_str_of(A,B)) & antisymmetric_relstr(rel_str_of(A,B)) & transitive_relstr(rel_str_of(A,B)) & reflexive_relstr(rel_str_of(A,B)))) # label(fc3_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 562 (all A (rel_str(A) -> (-empty_carrier(A) & complete_relstr(A) -> with_suprema_relstr(A) & with_infima_relstr(A) & -empty_carrier(A)))) # label(cc1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 563 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 564 (all A all B exists C (relation_of2(C,A,B) & relation(C) & function(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 565 (all A all B (relation(B) -> (all C (relation(C) -> ((all D all E (in(E,A) & in(ordered_pair(D,E),B) <-> in(ordered_pair(D,E),C))) <-> relation_rng_restriction(A,B) = C))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 566 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 567 (all A (relation(A) -> (all B (relation(B) -> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)))))) # label(t160_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 568 (all A (latt_str(A) -> (-empty_carrier(A) & lattice(A) & complete_latt_str(A) -> -empty_carrier(A) & join_commutative(A) & meet_commutative(A) & meet_absorbing(A) & lattice(A) & bounded_lattstr(A) & upper_bounded_semilattstr(A) & lower_bounded_semilattstr(A) & join_absorbing(A) & meet_associative(A) & join_associative(A)))) # label(cc1_knaster) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 569 (all A all B (relation_of2(B,A,A) & -empty(A) -> strict_rel_str(rel_str_of(A,B)) & -empty_carrier(rel_str_of(A,B)))) # label(fc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 570 (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]. 1.74/2.02 571 (all A all B (relation(B) & -empty(A) -> ((all C all D all E ((exists H (H = C & in(E,H) & (all I (in(I,H) -> in(ordered_pair(E,I),B))))) & in(C,A) & (exists F (in(D,F) & (all G (in(G,F) -> in(ordered_pair(D,G),B))) & F = C)) & in(C,A) -> D = E)) -> (exists C all D (in(D,C) <-> (exists E ((exists J (E = J & in(D,J) & (all K (in(K,J) -> in(ordered_pair(D,K),B))))) & in(E,A) & in(E,A)))))))) # label(s1_tarski__e10_24__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 572 (all A (relation(A) -> ((all B all C -(in(B,relation_field(A)) & -in(ordered_pair(C,B),A) & -in(ordered_pair(B,C),A) & B != C & in(C,relation_field(A)))) <-> connected(A)))) # label(l4_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 573 (all A (relation(A) -> relation_inverse(relation_inverse(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 574 (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 G exists H ((all I (element(I,powerset(the_carrier(A))) -> (I = G -> subset_complement(the_carrier(A),I) = H))) & in(G,B) & ordered_pair(G,H) = E)) & (exists J exists K ((all L (element(L,powerset(the_carrier(A))) -> (J = L -> subset_complement(the_carrier(A),L) = K))) & in(J,B) & F = ordered_pair(J,K))) & D = F -> E = F)) -> (exists D all E ((exists F (F = E & (exists M exists N (in(M,B) & (all O (element(O,powerset(the_carrier(A))) -> (O = M -> N = subset_complement(the_carrier(A),O)))) & E = ordered_pair(M,N))) & in(F,cartesian_product2(B,C)))) <-> in(E,D))))))) # label(s1_tarski__e4_7_2__tops_2__2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 575 (exists A (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_connected(A) & ordinal(A) & epsilon_transitive(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 576 (all A (join_commutative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_associative(boole_lattice(A)) & strict_latt_str(boole_lattice(A)) & -empty_carrier(boole_lattice(A)))) # label(fc3_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 577 (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]. 1.74/2.02 578 (all A all B all C (subset(B,C) & subset(A,B) -> subset(A,C))) # label(t1_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 579 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 580 (all A (strict_latt_str(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & lattice(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & join_associative(boole_lattice(A)) & join_commutative(boole_lattice(A)) & -empty_carrier(boole_lattice(A)))) # label(fc1_knaster) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 581 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (-empty_carrier(B) & net_str(B,A) -> (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(lemma) # label(non_clause). [assumption]. 1.74/2.02 582 (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))) -> -(disjoint(B,E) & in(D,E) & open_subset(E,A)))) <-> in(D,C)))) <-> C = topstr_closure(A,B)))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 583 (all A all B all C (-empty_carrier(A) & join_commutative(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) & join_semilatt_str(A) -> element(join_commut(A,B,C),the_carrier(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 584 (all A all B (-((all C -(in(C,B) & in(C,A))) & -disjoint(A,B)) & -(disjoint(A,B) & (exists C (in(C,A) & in(C,B)))))) # label(t3_xboole_0) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 585 (all A all B (ordinal(B) -> (in(A,B) -> ordinal(A)))) # label(t23_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 586 (all A all B ((empty(A) -> (empty(B) <-> element(B,A))) & (-empty(A) -> (in(B,A) <-> element(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 587 (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]. 1.74/2.02 588 (all A ((all B (in(B,A) -> ordinal(B) & subset(B,A))) -> ordinal(A))) # label(t31_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 589 (all A all B all C (in(A,C) & in(B,C) <-> subset(unordered_pair(A,B),C))) # label(t38_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 590 (all A all B all C all D (quasi_total(D,A,B) & relation_of2_as_subset(D,A,B) & function(D) -> (B != empty_set -> (all E (in(E,relation_inverse_image(D,C)) <-> in(apply(D,E),C) & in(E,A)))))) # label(t46_funct_2) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 591 (all A reflexive(inclusion_relation(A))) # label(t2_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 592 (all A (function(A) & relation(A) -> (one_to_one(A) -> function_inverse(A) = relation_inverse(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 593 (all A all B all C (relation(B) & function(C) & relation(C) -> (exists D all E (in(E,D) <-> (exists F exists G (ordered_pair(F,G) = E & in(ordered_pair(apply(C,F),apply(C,G)),B))) & in(E,cartesian_product2(A,A)))))) # label(s1_xboole_0__e6_21__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 594 (all A all B (subset(A,B) -> set_union2(A,set_difference(B,A)) = B)) # label(t45_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 595 (all A all B all C all D (relation_of2(C,A,B) -> relation_dom_restriction(C,D) = relation_dom_restr_as_relation_of(A,B,C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 596 (all A all B (function(B) & relation(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]. 1.74/2.02 597 (all A all B (finite(A) -> finite(set_difference(A,B)))) # label(fc12_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 598 (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]. 1.74/2.02 599 (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]. 1.74/2.02 600 (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]. 1.74/2.02 601 (all A ((all B all C all D (B = C & ordinal(C) & ordinal(D) & B = D -> D = C)) -> (exists B all C (in(C,B) <-> (exists D (C = D & ordinal(C) & in(D,A))))))) # label(s1_tarski__e6_22__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 602 (all A (one_sorted_str(A) -> (all B (net_str(B,A) -> (all C (subnetstr(C,A,B) -> (all D (element(D,the_carrier(B)) -> (all E (element(E,the_carrier(B)) -> (all F (element(F,the_carrier(C)) -> (all G (element(G,the_carrier(C)) -> (F = D & G = E & related(C,F,G) -> related(B,D,E)))))))))))))))) # label(t20_yellow_6) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 603 (all A (latt_str(A) -> (-empty_carrier(A) & upper_bounded_semilattstr(A) & lower_bounded_semilattstr(A) -> bounded_lattstr(A) & -empty_carrier(A)))) # label(cc3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 604 (all A (top_str(A) & topological_space(A) & -empty_carrier(A) -> (exists B (-empty(B) & closed_subset(B,A) & element(B,powerset(the_carrier(A))))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 605 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 606 (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]. 1.74/2.02 607 (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]. 1.74/2.02 608 (all A (relation(A) -> (all B set_intersection2(A,cartesian_product2(B,B)) = relation_restriction(A,B)))) # label(d6_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 609 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 610 (exists A (-empty_carrier(A) & join_absorbing(A) & lattice(A) & meet_absorbing(A) & meet_associative(A) & meet_commutative(A) & join_associative(A) & join_commutative(A) & strict_latt_str(A) & latt_str(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 611 (all A (relation(A) & function(A) -> ((all B all C (apply(A,B) = apply(A,C) & in(C,relation_dom(A)) & in(B,relation_dom(A)) -> C = B)) <-> one_to_one(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 612 (all A all B all C (-empty(A) & relation_of2(B,cartesian_product2(A,A),A) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) & function(C) & quasi_total(B,cartesian_product2(A,A),A) & function(B) -> 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]. 1.74/2.02 613 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 614 (all A all B -(empty(B) & B != A & empty(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 615 (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]. 1.74/2.02 616 (all A (empty(A) -> empty(relation_inverse(A)) & relation(relation_inverse(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 617 (all A (-empty(A) -> -empty_carrier(incl_POSet(A)) & strict_rel_str(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)))) # label(fc6_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 618 (all A (one_sorted_str(A) -> identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))) # label(d11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 619 (all A (relation(A) <-> (all B -((all C all D B != ordered_pair(C,D)) & in(B,A))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 620 (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]. 1.74/2.02 621 (all A all B (relation(B) -> (inclusion_relation(A) = B <-> (all C all D (in(D,A) & in(C,A) -> (subset(C,D) <-> in(ordered_pair(C,D),B)))) & A = relation_field(B)))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 622 (all A all B (ordinal(A) & ordinal(B) -> ordinal_subset(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 623 (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]. 1.74/2.02 624 (all A all B (relation(A) & function(A) & relation(B) & function(B) -> relation(relation_composition(A,B)) & function(relation_composition(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 625 (all A ((all B all C all D (in(B,A) & C = singleton(B) & in(B,A) & singleton(B) = D -> C = D)) -> (exists B all C ((exists D (in(D,A) & C = singleton(D) & in(D,A))) <-> in(C,B))))) # label(s1_tarski__e16_22__wellord2__1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 626 (all A exists B (relation(B) & well_orders(B,A))) # label(t26_wellord2) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 627 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 628 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 629 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 630 (all A all B all C (lattice(B) & complete_latt_str(B) & latt_str(B) & -empty_carrier(B) -> (in(A,a_2_3_lattice3(B,C)) <-> (exists D (A = D & latt_set_smaller(B,D,C) & element(D,the_carrier(B))))))) # label(fraenkel_a_2_3_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 631 (all A all B all C (-empty_carrier(A) & -empty_carrier(B) & net_str(B,A) & element(C,the_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]. 1.74/2.02 632 (all A (in(empty_set,A) & (all B (ordinal(B) -> (being_limit_ordinal(B) & in(empty_set,B) -> subset(A,B)))) & ordinal(A) & being_limit_ordinal(A) <-> omega = A)) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 633 (all A all B (v3_membered(A) -> v1_membered(set_difference(A,B)) & v3_membered(set_difference(A,B)) & v2_membered(set_difference(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 634 (all A (v4_membered(A) -> (all B (element(B,powerset(A)) -> v1_membered(B) & v4_membered(B) & v3_membered(B) & v2_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 635 (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]. 1.74/2.02 636 (all A -empty(succ(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 637 (all A (relation(A) & function(A) -> function(function_inverse(A)) & relation(function_inverse(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 638 (all A all B all C (relation_of2_as_subset(C,A,B) -> ((B = empty_set -> empty_set = A) -> (quasi_total(C,A,B) <-> A = relation_dom_as_subset(A,B,C))) & (empty_set = B -> empty_set = A | (C = empty_set <-> quasi_total(C,A,B))))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 639 (all A (rel_str(A) -> (exists B subrelstr(B,A)))) # label(existence_m1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 640 (exists A (strict_latt_str(A) & latt_str(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 641 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 642 (all A all B all C (relation_of2_as_subset(C,B,A) -> ((all D -((all E -in(ordered_pair(D,E),C)) & in(D,B))) <-> relation_dom_as_subset(B,A,C) = B))) # label(t22_relset_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 643 (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]. 1.74/2.02 644 (all A (diff_closed(powerset(A)) & preboolean(powerset(A)) & cup_closed(powerset(A)) & -empty(powerset(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 645 (all A all B (subset(A,B) <-> set_difference(A,B) = empty_set)) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 646 (all A ((all B all C all D (in(B,A) & singleton(B) = D & C = singleton(B) -> C = D)) & (all B -((all C singleton(B) != C) & in(B,A))) -> (exists B (function(B) & (all C (in(C,A) -> singleton(C) = apply(B,C))) & relation_dom(B) = A & relation(B))))) # label(s2_funct_1__e16_22__wellord2__1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 647 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 648 (exists A (rel_str(A) & -empty_carrier(A) & reflexive_relstr(A) & complete_relstr(A) & antisymmetric_relstr(A) & transitive_relstr(A) & strict_rel_str(A))) # label(rc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 649 (all A all B (finite(A) -> finite(set_intersection2(A,B)))) # label(fc11_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 650 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 651 (all A all B (relation(A) & relation(B) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 652 (all A (relation(A) -> (well_ordering(A) <-> well_orders(A,relation_field(A))))) # label(t8_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 653 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> B = subset_intersection2(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 654 (all A all B (element(B,powerset(powerset(A))) -> B = complements_of_subsets(A,complements_of_subsets(A,B)))) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 655 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 656 (all A exists B (empty(B) & element(B,powerset(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 657 (all A all B (ordinal(B) & ordinal(A) -> (subset(A,B) <-> ordinal_subset(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 658 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) & function(C) -> (well_ordering(A) & relation_isomorphism(A,B,C) -> well_ordering(B)))))))) # label(t54_wellord1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 659 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 660 (all A (top_str(A) -> (all B (element(B,powerset(powerset(the_carrier(A)))) -> (open_subsets(B,A) <-> closed_subsets(complements_of_subsets(the_carrier(A),B),A)))))) # label(t17_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 661 (all A all B all C (function(C) & relation(C) -> (in(B,relation_dom(relation_dom_restriction(C,A))) -> apply(C,B) = apply(relation_dom_restriction(C,A),B)))) # label(t70_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 662 (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]. 1.74/2.02 663 (all A (relation(A) -> relation(relation_inverse(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 664 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 665 (all A (strict_latt_str(boole_lattice(A)) & -empty_carrier(boole_lattice(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 666 (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]. 1.74/2.02 667 (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]. 1.74/2.02 668 (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]. 1.74/2.02 669 (all A all B all C ((all D ((exists E exists F (ordered_pair(E,F) = D & in(F,B) & in(E,A))) <-> in(D,C))) <-> C = cartesian_product2(A,B))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 670 (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]. 1.74/2.02 671 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 672 (all A (relation(A) -> (all B (is_transitive_in(A,B) <-> (all C all D all E (in(D,B) & in(E,B) & in(ordered_pair(D,E),A) & in(ordered_pair(C,D),A) & in(C,B) -> in(ordered_pair(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 673 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 674 (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]. 1.74/2.02 675 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(the_carrier(A))) -> (exists C all D (in(D,powerset(the_carrier(A))) & (exists E (E = D & closed_subset(E,A) & subset(B,D) & element(E,powerset(the_carrier(A))))) <-> in(D,C))))) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 676 (all A all B (one_sorted_str(A) & net_str(B,A) -> (all C (subnetstr(C,A,B) -> net_str(C,A))))) # label(dt_m1_yellow_6) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 677 (all A all B (one_sorted_str(A) & element(B,powerset(powerset(the_carrier(A)))) -> ((all C all D all E (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))) & (all F (element(F,powerset(the_carrier(A))) -> (F = C -> subset_complement(the_carrier(A),F) = D))) -> D = E)) & (all C -((all D -(all H (element(H,powerset(the_carrier(A))) -> (H = C -> subset_complement(the_carrier(A),H) = D)))) & in(C,complements_of_subsets(the_carrier(A),B)))) -> (exists C (relation(C) & complements_of_subsets(the_carrier(A),B) = relation_dom(C) & (all D (in(D,complements_of_subsets(the_carrier(A),B)) -> (all I (element(I,powerset(the_carrier(A))) -> (D = I -> apply(C,D) = subset_complement(the_carrier(A),I)))))) & function(C)))))) # label(s2_funct_1__e4_7_1__tops_2) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 678 (all A all B (v3_membered(A) -> v3_membered(set_intersection2(A,B)) & v2_membered(set_intersection2(A,B)) & v1_membered(set_intersection2(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 1.74/2.02 679 (all A all B all C (relation_of2_as_subset(C,A,B) -> (B = relation_rng_as_subset(A,B,C) <-> (all D -(in(D,B) & (all E -in(ordered_pair(E,D),C))))))) # label(t23_relset_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.02 680 (all A all B all C all D (quasi_total(D,A,B) & relation_of2_as_subset(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]. 1.74/2.03 681 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 682 (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]. 1.74/2.03 683 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 684 (all A (empty(A) & function(A) & relation(A) -> relation(A) & function(A) & one_to_one(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 685 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 686 (all A (relation(A) -> (all B (is_reflexive_in(A,B) & is_antisymmetric_in(A,B) & is_connected_in(A,B) & is_well_founded_in(A,B) & is_transitive_in(A,B) <-> well_orders(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 687 (all A all B (-empty_carrier(B) & latt_str(B) & lattice(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]. 1.74/2.03 688 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 689 (all A (rel_str(A) & lower_bounded_relstr(A) & antisymmetric_relstr(A) & -empty_carrier(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]. 1.74/2.03 690 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (ex_sup_of_relstr_set(A,B) <-> (exists C (element(C,the_carrier(A)) & relstr_set_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) -> related(A,C,D)))))))))) # label(t15_yellow_0) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 691 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 692 (all A (function(A) & relation(A) -> (all B all C (C = relation_image(A,B) <-> (all D (in(D,C) <-> (exists E (in(E,relation_dom(A)) & D = apply(A,E) & in(E,B))))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 693 (exists A (relation(A) & function(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 694 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 695 (all A (relation(identity_relation(A)) & function(identity_relation(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 696 (all A all B (relation(B) & function(B) -> (one_to_one(B) & in(A,relation_rng(B)) -> apply(B,apply(function_inverse(B),A)) = A & A = apply(relation_composition(function_inverse(B),B),A)))) # label(t57_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 697 (all A (empty(A) -> v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v1_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 698 (all A all B all C all D (relation(D) -> (in(A,C) & in(ordered_pair(A,B),D) <-> in(ordered_pair(A,B),relation_composition(identity_relation(C),D))))) # label(t74_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 699 (all A all B (relation(B) -> relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A)))) # label(t145_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 700 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 701 (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]. 1.74/2.03 702 (all A (one_sorted_str(A) -> (all B (net_str(B,A) -> (all C (subnetstr(C,A,B) -> subset(the_carrier(C),the_carrier(B)))))))) # label(t19_yellow_6) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 703 (all A all B (function(B) & relation(B) -> (all C (function(C) & relation(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]. 1.74/2.03 704 (all A A = cast_to_subset(A)) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 705 (all A all B (-empty_carrier(A) & one_sorted_str(A) & -empty_carrier(B) & net_str(B,A) -> -empty(the_mapping(A,B)) & relation(the_mapping(A,B)) & quasi_total(the_mapping(A,B),the_carrier(B),the_carrier(A)) & function(the_mapping(A,B)))) # label(fc15_yellow_6) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 706 (all A (-empty_carrier(A) & latt_str(A) & lattice(A) -> poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)))) # label(d2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 707 (all A all B (relation_empty_yielding(A) & relation(A) -> relation_empty_yielding(relation_dom_restriction(A,B)) & relation(relation_dom_restriction(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 708 (all A (function(A) & relation(A) -> (one_to_one(A) -> relation_dom(function_inverse(A)) = relation_rng(A) & relation_rng(function_inverse(A)) = relation_dom(A)))) # label(t55_funct_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 709 (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]. 1.74/2.03 710 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) & element(C,the_carrier(A)) & element(B,the_carrier(A)) -> meet_commut(A,B,C) = meet(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 711 (all A all B (ordinal(A) & ordinal(B) -> ordinal_subset(A,B) | ordinal_subset(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 712 (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]. 1.74/2.03 713 (all A ((exists B exists C A = ordered_pair(B,C)) -> (all B (B = pair_second(A) <-> (all C all D (ordered_pair(C,D) = A -> D = B)))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 714 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 715 (exists A (-empty_carrier(A) & transitive_relstr(A) & antisymmetric_relstr(A) & complete_relstr(A) & with_infima_relstr(A) & with_suprema_relstr(A) & reflexive_relstr(A) & strict_rel_str(A) & rel_str(A))) # label(rc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 716 (all A (rel_str(A) -> (empty_carrier(A) -> v1_yellow_3(A)))) # label(cc1_yellow_3) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 717 (all A all B (top_str(A) & element(B,the_carrier(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]. 1.74/2.03 718 (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]. 1.74/2.03 719 (all A (strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & -empty_carrier(boole_POSet(A)))) # label(fc8_yellow_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 720 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 721 (all A all B all C all D all E all F (-empty(B) & relation_of2(D,cartesian_product2(A,B),C) & element(E,A) & element(F,B) & quasi_total(D,cartesian_product2(A,B),C) & function(D) & -empty(A) -> element(apply_binary_as_element(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 722 (all A (relation(A) -> (reflexive(A) <-> is_reflexive_in(A,relation_field(A))))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 723 (all A all B all C all D (-empty_carrier(B) & one_sorted_str(B) & quasi_total(C,the_carrier(A),the_carrier(B)) & element(D,the_carrier(A)) & relation_of2(C,the_carrier(A),the_carrier(B)) & function(C) & one_sorted_str(A) & -empty_carrier(A) -> apply(C,D) = apply_on_structs(A,B,C,D))) # label(redefinition_k1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 724 (all A all B all C all D (relation_of2_as_subset(D,A,B) & quasi_total(D,A,B) & function(D) -> (subset(B,C) -> B = empty_set & A != empty_set | quasi_total(D,A,C) & relation_of2_as_subset(D,A,C) & function(D)))) # label(t9_funct_2) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 725 (all A all B (-empty(A) & relation(B) -> ((all C all D all E (in(C,A) & (exists F (F = C & (all G (in(G,F) -> in(ordered_pair(D,G),B))) & in(D,F))) & (exists H (H = C & in(E,H) & (all I (in(I,H) -> in(ordered_pair(E,I),B))))) -> D = E)) & (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 (function(C) & (all D (in(D,A) -> (exists L (D = L & (all M (in(M,L) -> in(ordered_pair(apply(C,D),M),B))) & in(apply(C,D),L))))) & relation_dom(C) = A & relation(C)))))) # label(s2_funct_1__e10_24__wellord2) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 726 (all A all B (finite(B) -> finite(set_intersection2(A,B)))) # label(fc10_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 727 (all A all B (relation(A) -> relation_restriction_as_relation_of(A,B) = relation_restriction(A,B))) # label(redefinition_k1_toler_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 728 (all A all B (set_difference(A,B) = A <-> disjoint(A,B))) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 729 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (B = topstr_closure(A,B) & topological_space(A) -> closed_subset(B,A)) & (closed_subset(B,A) -> B = topstr_closure(A,B)))))) # label(t52_pre_topc) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 730 (all A all B (one_sorted_str(A) & net_str(B,A) -> (exists C subnetstr(C,A,B)))) # label(existence_m1_yellow_6) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 731 (all A (symmetric(A) & transitive(A) & relation(A) -> relation(A) & reflexive(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 732 (all A all B (relation(B) -> relation(relation_rng_restriction(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 733 (all A all B all C ((all D (in(D,A) | in(D,B) <-> in(D,C))) <-> C = set_union2(A,B))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 734 (all A all B (v4_membered(A) -> v3_membered(set_difference(A,B)) & v4_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]. 1.74/2.03 735 (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]. 1.74/2.03 736 (all A all B ((all C all D all E ((exists H exists I (E = ordered_pair(H,I) & in(H,A) & singleton(H) = I)) & C = E & (exists F exists G (ordered_pair(F,G) = D & singleton(F) = G & in(F,A))) & C = D -> E = D)) -> (exists C all D ((exists E (in(E,cartesian_product2(A,B)) & E = D & (exists J exists K (D = ordered_pair(J,K) & in(J,A) & singleton(J) = K)))) <-> in(D,C))))) # label(s1_tarski__e16_22__wellord2__2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 737 (all A empty_set = set_intersection2(A,empty_set)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 738 (all A (ordinal(A) -> ((all B all C all D ((exists E ((in(E,omega) -> (all F (element(F,powerset(powerset(E))) -> -((all G -((all H (subset(G,H) & in(H,F) -> H = G)) & in(G,F))) & F != empty_set)))) & E = C & ordinal(E))) & B = D & (exists I (D = I & (in(I,omega) -> (all J (element(J,powerset(powerset(I))) -> -(empty_set != J & (all K -((all L (in(L,J) & subset(K,L) -> K = L)) & in(K,J))))))) & ordinal(I))) & B = C -> C = D)) -> (exists B all C ((exists D ((exists M (C = M & (in(M,omega) -> (all N (element(N,powerset(powerset(M))) -> -(N != empty_set & (all O -((all P (subset(O,P) & in(P,N) -> P = O)) & in(O,N))))))) & ordinal(M))) & C = D & in(D,succ(A)))) <-> in(C,B)))))) # label(s1_tarski__e18_27__finset_1__1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 739 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_rng(A),relation_dom(B)) -> relation_dom(relation_composition(A,B)) = relation_dom(A)))))) # label(t46_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 740 (all A all B (finite(A) & finite(B) -> finite(set_union2(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 741 (all A (lower_bounded_semilattstr(boole_lattice(A)) & empty_set = bottom_of_semilattstr(boole_lattice(A)))) # label(t3_lattice3) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 742 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 743 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 744 (all A all B (top_str(A) & element(B,powerset(the_carrier(A))) & closed_subset(B,A) & topological_space(A) -> open_subset(subset_complement(the_carrier(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 745 (all A all B all C (function(B) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) & function(C) & relation_of2(B,cartesian_product2(A,A),A) & quasi_total(B,cartesian_product2(A,A),A) -> latt_str(latt_str_of(A,B,C)) & strict_latt_str(latt_str_of(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 746 (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))) -> (C = F -> subset_complement(the_carrier(A),F) = D))) & in(C,B) & (all G (element(G,powerset(the_carrier(A))) -> (C = G -> E = subset_complement(the_carrier(A),G)))) & in(C,B) -> E = D)) -> (exists C all D ((exists E (in(E,B) & (all H (element(H,powerset(the_carrier(A))) -> (H = E -> subset_complement(the_carrier(A),H) = D))) & in(E,B))) <-> in(D,C)))))) # label(s1_tarski__e4_7_2__tops_2__1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 747 (all A all B all C (relation_of2(C,A,B) -> (function(C) & v1_partfun1(C,A,B) -> function(C) & quasi_total(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 748 (all A all B all C -(in(A,B) & in(C,A) & in(B,C))) # label(t3_ordinal1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 749 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 750 (exists A (latt_str(A) & -empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_associative(A) & lower_bounded_semilattstr(A) & bounded_lattstr(A) & complemented_lattstr(A) & upper_bounded_semilattstr(A) & lattice(A) & join_absorbing(A) & meet_absorbing(A) & meet_commutative(A) & strict_latt_str(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 751 (all A all B (relation(B) -> -(empty_set != A & subset(A,relation_rng(B)) & empty_set = relation_inverse_image(B,A)))) # label(t174_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.74/2.03 752 (all A (relation(A) -> (well_ordering(A) <-> reflexive(A) & transitive(A) & well_founded_relation(A) & connected(A) & antisymmetric(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 1.74/2.03 753 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B))))) # label(t11_tops_2) # label(lemma) # label(non_clause). [assumption]. 1.89/2.12 754 (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]. 1.89/2.12 755 (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]. 1.89/2.12 756 (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]. 1.89/2.12 757 (all A all B (-empty_carrier(B) & latt_str(B) & latt_str(A) & -empty_carrier(A) -> latt_str(k8_filter_1(A,B)) & strict_latt_str(k8_filter_1(A,B)))) # label(dt_k8_filter_1) # label(axiom) # label(non_clause). [assumption]. 1.89/2.12 758 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_dom(C)) & in(B,relation_rng(C))))) # label(t20_relat_1) # label(lemma) # label(non_clause). [assumption]. 1.89/2.12 759 (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]. 1.89/2.12 760 (all A all B (top_str(A) & element(B,powerset(the_carrier(A))) & topological_space(A) -> open_subset(interior(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 1.89/2.12 761 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B))))) # label(t47_setfam_1) # label(lemma) # label(non_clause). [assumption]. 1.89/2.12 762 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 1.89/2.12 763 (all A all B all C all D all E all F (-empty(A) & -empty(B) & function(D) & quasi_total(D,cartesian_product2(A,B),C) & relation_of2(D,cartesian_product2(A,B),C) & element(F,B) & element(E,A) -> 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]. 1.89/2.12 764 -(all A (-empty_carrier(A) & one_sorted_str(A) -> (all B (-empty_carrier(B) & net_str(B,A) & directed_relstr(B) & transitive_relstr(B) -> (all C (is_eventually_in(A,B,C) -> is_often_in(A,B,C))))))) # label(t28_yellow_6) # label(negated_conjecture) # label(non_clause). [assumption]. 1.89/2.12 1.89/2.12 ============================== end of process non-clausal formulas === 1.89/2.12 1.89/2.12 ============================== PROCESS INITIAL CLAUSES =============== 1.89/2.12 1.89/2.12 ============================== PREDICATE ELIMINATION ================= 1.89/2.12 765 -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.89/2.12 766 -top_str(A) | -topological_space(A) | empty_carrier(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(3)]. 1.89/2.12 767 -top_str(A) | -topological_space(A) | empty_carrier(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(3)]. 1.89/2.12 768 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -topological_space(A) | element(f7(A,B),powerset(powerset(the_carrier(A)))) # label(s3_subset_1__e2_37_1_1__pre_topc) # label(lemma). [clausify(10)]. 1.89/2.12 769 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -topological_space(A) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s3_subset_1__e2_37_1_1__pre_topc) # label(lemma). [clausify(10)]. 1.89/2.12 770 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -topological_space(A) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s3_subset_1__e2_37_1_1__pre_topc) # label(lemma). [clausify(10)]. 1.89/2.13 771 -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(37)]. 1.89/2.13 772 -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))) # label(t46_pre_topc) # label(lemma). [clausify(65)]. 1.89/2.13 773 -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,f36(A,B)) # label(t46_pre_topc) # label(lemma). [clausify(65)]. 1.89/2.13 774 -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | subset(B,C) | -in(C,f36(A,B)) # label(t46_pre_topc) # label(lemma). [clausify(65)]. 1.89/2.13 775 -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | closed_subset(C,A) | -in(C,f36(A,B)) # label(t46_pre_topc) # label(lemma). [clausify(65)]. 1.89/2.13 776 -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) = meet_of_subsets(the_carrier(A),f36(A,B)) # label(t46_pre_topc) # label(lemma). [clausify(65)]. 1.89/2.13 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(765,e,766,b)]. 1.89/2.13 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(765,e,767,b)]. 1.89/2.13 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(765,e,768,c)]. 1.89/2.13 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(765,e,769,c)]. 1.89/2.13 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(765,e,770,c)]. 1.89/2.13 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(765,e,772,b)]. 1.89/2.13 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),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,f36(A,B)). [resolve(765,e,773,b)]. 1.89/2.13 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),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,f36(A,B)). [resolve(765,e,774,b)]. 1.89/2.13 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),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,f36(A,B)). [resolve(765,e,775,b)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),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),f36(A,B)). [resolve(765,e,776,b)]. 1.90/2.14 777 -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(777,e,766,b)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(777,e,767,b)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(777,e,768,c)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(777,e,769,c)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(777,e,770,c)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(777,e,772,b)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),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,f36(A,B)). [resolve(777,e,773,b)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),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,f36(A,B)). [resolve(777,e,774,b)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),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,f36(A,B)). [resolve(777,e,775,b)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),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),f36(A,B)). [resolve(777,e,776,b)]. 1.90/2.14 778 -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.90/2.14 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(778,e,766,b)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(778,e,767,b)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(778,e,768,c)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(778,e,769,c)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(778,e,770,c)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(778,e,772,b)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(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,f36(A,B)). [resolve(778,e,773,b)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(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,f36(A,B)). [resolve(778,e,774,b)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(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,f36(A,B)). [resolve(778,e,775,b)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(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),f36(A,B)). [resolve(778,e,776,b)]. 1.90/2.15 779 -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(779,e,766,b)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(779,e,767,b)]. 1.90/2.15 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(779,e,768,c)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(779,e,769,c)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(779,e,770,c)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(779,e,772,b)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(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,f36(A,B)). [resolve(779,e,773,b)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(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,f36(A,B)). [resolve(779,e,774,b)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(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,f36(A,B)). [resolve(779,e,775,b)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(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),f36(A,B)). [resolve(779,e,776,b)]. 1.90/2.16 780 -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(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,766,b)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(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,767,b)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(780,e,768,c)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(780,e,769,c)]. 1.90/2.16 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(780,e,770,c)]. 1.90/2.17 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(780,e,772,b)]. 1.90/2.17 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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,f36(A,B)). [resolve(780,e,773,b)]. 1.90/2.17 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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,f36(A,B)). [resolve(780,e,774,b)]. 1.90/2.17 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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,f36(A,B)). [resolve(780,e,775,b)]. 1.90/2.17 Derived: -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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),f36(A,B)). [resolve(780,e,776,b)]. 1.90/2.17 781 -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.90/2.17 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(781,e,766,b)]. 1.90/2.17 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(781,e,767,b)]. 1.90/2.17 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(781,e,768,c)]. 1.90/2.17 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(781,e,769,c)]. 1.90/2.17 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(781,e,770,c)]. 1.90/2.17 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(781,e,772,b)]. 1.90/2.17 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),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,f36(A,B)). [resolve(781,e,773,b)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),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,f36(A,B)). [resolve(781,e,774,b)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),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,f36(A,B)). [resolve(781,e,775,b)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),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),f36(A,B)). [resolve(781,e,776,b)]. 1.90/2.18 782 -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(782,e,766,b)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(782,e,767,b)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(782,e,768,c)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(782,e,769,c)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(782,e,770,c)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(782,e,772,b)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),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,f36(A,B)). [resolve(782,e,773,b)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),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,f36(A,B)). [resolve(782,e,774,b)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),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,f36(A,B)). [resolve(782,e,775,b)]. 1.90/2.18 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),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),f36(A,B)). [resolve(782,e,776,b)]. 1.90/2.19 783 -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(783,e,766,b)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(783,e,767,b)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(783,e,768,c)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(783,e,769,c)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(783,e,770,c)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(783,e,772,b)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(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,f36(A,B)). [resolve(783,e,773,b)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(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,f36(A,B)). [resolve(783,e,774,b)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(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,f36(A,B)). [resolve(783,e,775,b)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(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),f36(A,B)). [resolve(783,e,776,b)]. 1.90/2.19 784 -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(784,e,766,b)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(784,e,767,b)]. 1.90/2.19 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(784,e,768,c)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(784,e,769,c)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(784,e,770,c)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(784,e,772,b)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(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,f36(A,B)). [resolve(784,e,773,b)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(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,f36(A,B)). [resolve(784,e,774,b)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(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,f36(A,B)). [resolve(784,e,775,b)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(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),f36(A,B)). [resolve(784,e,776,b)]. 1.90/2.21 785 -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(785,e,766,b)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(785,e,767,b)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(785,e,768,c)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(785,e,769,c)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(785,e,770,c)]. 1.90/2.21 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(785,e,772,b)]. 1.98/2.22 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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,f36(A,B)). [resolve(785,e,773,b)]. 1.98/2.22 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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,f36(A,B)). [resolve(785,e,774,b)]. 1.98/2.22 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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,f36(A,B)). [resolve(785,e,775,b)]. 1.98/2.22 Derived: -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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),f36(A,B)). [resolve(785,e,776,b)]. 1.98/2.22 786 -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.98/2.22 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(786,e,766,b)]. 1.98/2.22 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(786,e,767,b)]. 1.98/2.22 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(786,e,768,c)]. 1.98/2.22 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(786,e,769,c)]. 1.98/2.22 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(786,e,770,c)]. 1.98/2.22 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(786,e,772,b)]. 1.98/2.22 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),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,f36(A,B)). [resolve(786,e,773,b)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),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,f36(A,B)). [resolve(786,e,774,b)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),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,f36(A,B)). [resolve(786,e,775,b)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),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),f36(A,B)). [resolve(786,e,776,b)]. 1.98/2.23 787 -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(787,e,766,b)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(787,e,767,b)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(787,e,768,c)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(787,e,769,c)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(787,e,770,c)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(787,e,772,b)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),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,f36(A,B)). [resolve(787,e,773,b)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),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,f36(A,B)). [resolve(787,e,774,b)]. 1.98/2.23 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),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,f36(A,B)). [resolve(787,e,775,b)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),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),f36(A,B)). [resolve(787,e,776,b)]. 1.98/2.24 788 -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(788,e,766,b)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(788,e,767,b)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(788,e,768,c)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(788,e,769,c)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(788,e,770,c)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(788,e,772,b)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(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,f36(A,B)). [resolve(788,e,773,b)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(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,f36(A,B)). [resolve(788,e,774,b)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(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,f36(A,B)). [resolve(788,e,775,b)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(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),f36(A,B)). [resolve(788,e,776,b)]. 1.98/2.24 789 -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.98/2.24 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(789,e,766,b)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(789,e,767,b)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(789,e,768,c)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(789,e,769,c)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(789,e,770,c)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(789,e,772,b)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(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,f36(A,B)). [resolve(789,e,773,b)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(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,f36(A,B)). [resolve(789,e,774,b)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(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,f36(A,B)). [resolve(789,e,775,b)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(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),f36(A,B)). [resolve(789,e,776,b)]. 1.98/2.25 790 -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(C,A,B) | in(B,interior(A,C)). [resolve(790,e,766,b)]. 1.98/2.25 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(C,A,B) | -in(B,interior(A,C)). [resolve(790,e,767,b)]. 1.98/2.26 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f7(A,B),powerset(powerset(the_carrier(A)))). [resolve(790,e,768,c)]. 1.98/2.26 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | -in(C,f7(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(790,e,769,c)]. 1.98/2.26 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -element(C,powerset(the_carrier(A))) | in(C,f7(A,B)) | -in(set_difference(cast_as_carrier_subset(A),C),B). [resolve(790,e,770,c)]. 1.98/2.26 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f36(A,B),powerset(powerset(the_carrier(A)))). [resolve(790,e,772,b)]. 1.98/2.26 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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,f36(A,B)). [resolve(790,e,773,b)]. 1.98/2.26 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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,f36(A,B)). [resolve(790,e,774,b)]. 1.98/2.26 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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,f36(A,B)). [resolve(790,e,775,b)]. 1.98/2.26 Derived: -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(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),f36(A,B)). [resolve(790,e,776,b)]. 1.98/2.26 791 -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(67)]. 1.98/2.26 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(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,765,e)]. 1.98/2.26 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(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,777,e)]. 1.98/2.26 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(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,778,e)]. 1.98/2.27 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(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,779,e)]. 1.98/2.27 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(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,780,e)]. 1.98/2.27 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) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,781,e)]. 1.98/2.27 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) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,782,e)]. 1.98/2.27 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) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,783,e)]. 1.98/2.27 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) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,784,e)]. 1.98/2.27 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) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,785,e)]. 1.98/2.27 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,786,e)]. 1.98/2.27 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,787,e)]. 1.98/2.27 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,788,e)]. 1.98/2.27 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,789,e)]. 1.98/2.27 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(791,e,790,e)]. 1.98/2.27 792 -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,765,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,777,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,778,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,779,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,780,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,781,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,782,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,783,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,784,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,785,e)]. 1.98/2.28 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,786,e)]. 2.06/2.30 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,787,e)]. 2.06/2.30 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,788,e)]. 2.06/2.30 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,789,e)]. 2.06/2.30 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(the_carrier(A))) | -in(C,the_topology(A)) | -in(B,the_topology(A)) | in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(792,g,790,e)]. 2.06/2.30 793 -top_str(A) | in(the_carrier(A),the_topology(A)) | -topological_space(A) # label(d1_pre_topc) # label(axiom). [clausify(67)]. 2.06/2.30 794 -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(127)]. 2.06/2.30 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(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,765,e)]. 2.06/2.30 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(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,777,e)]. 2.06/2.30 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(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,778,e)]. 2.06/2.30 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(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,779,e)]. 2.06/2.30 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(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,780,e)]. 2.06/2.30 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) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,781,e)]. 2.06/2.30 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) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,782,e)]. 2.06/2.31 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) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,783,e)]. 2.06/2.31 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) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,784,e)]. 2.06/2.31 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) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,785,e)]. 2.06/2.31 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,786,e)]. 2.06/2.31 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,787,e)]. 2.06/2.31 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,788,e)]. 2.06/2.31 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,789,e)]. 2.06/2.31 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(794,a,790,e)]. 2.06/2.31 795 -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(127)]. 2.06/2.31 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(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,765,e)]. 2.06/2.31 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(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,777,e)]. 2.06/2.31 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(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,778,e)]. 2.06/2.32 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(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,779,e)]. 2.06/2.32 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(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,780,e)]. 2.06/2.32 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) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,781,e)]. 2.06/2.32 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) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,782,e)]. 2.06/2.32 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) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,783,e)]. 2.06/2.32 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) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,784,e)]. 2.06/2.32 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) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,785,e)]. 2.06/2.32 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,786,e)]. 2.06/2.32 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,787,e)]. 2.06/2.32 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,788,e)]. 2.06/2.32 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,789,e)]. 2.06/2.32 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(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(795,a,790,e)]. 2.06/2.32 796 empty_carrier(A) | -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) # label(t5_connsp_2) # label(lemma). [clausify(148)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,765,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,777,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,778,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,779,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,780,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,781,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,782,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,783,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,784,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,785,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,786,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,787,e)]. 2.06/2.34 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,788,e)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,789,e)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -in(C,B) | -open_subset(B,A) | point_neighbourhood(B,A,C) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(796,b,790,e)]. 2.06/2.35 797 empty_carrier(A) | -top_str(A) | -topological_space(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) # label(t13_compts_1) # label(lemma). [clausify(154)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,765,e)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,777,e)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,778,e)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,779,e)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,780,e)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,781,e)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,782,e)]. 2.06/2.35 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,783,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,784,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,785,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,786,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,787,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,788,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,789,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,790,e)]. 2.06/2.36 798 empty_carrier(A) | -top_str(A) | -topological_space(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) # label(t13_compts_1) # label(lemma). [clausify(154)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,765,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,777,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,778,e)]. 2.06/2.36 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,779,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,780,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,781,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,782,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,783,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,784,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,785,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,786,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,787,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,788,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,789,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,790,e)]. 2.06/2.37 799 empty_carrier(A) | -top_str(A) | -topological_space(A) | compact_top_space(A) | closed_subsets(f82(A),A) # label(t13_compts_1) # label(lemma). [clausify(154)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,765,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,777,e)]. 2.06/2.37 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,778,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,779,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,780,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,781,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,782,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,783,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,784,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,785,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,786,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,787,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,788,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,789,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,790,e)]. 2.15/2.38 800 empty_carrier(A) | -top_str(A) | -topological_space(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set # label(t13_compts_1) # label(lemma). [clausify(154)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,765,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,777,e)]. 2.15/2.38 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,778,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,779,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,780,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,781,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,782,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,783,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,784,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,785,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,786,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,787,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,788,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,789,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,790,e)]. 2.15/2.39 801 empty_carrier(A) | -top_str(A) | -topological_space(A) | compact_top_space(A) | centered(f82(A)) # label(t13_compts_1) # label(lemma). [clausify(154)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,765,e)]. 2.15/2.39 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,777,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,778,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,779,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,780,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,781,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,782,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,783,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,784,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,785,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,786,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,787,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,788,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,789,e)]. 2.18/2.40 Derived: empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,790,e)]. 2.18/2.40 802 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f84(A,B)) | element(f85(A,B,C),powerset(the_carrier(A))) # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(179)]. 2.18/2.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,765,e)]. 2.18/2.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,777,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,778,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,779,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,780,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,781,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,782,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,783,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,784,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,785,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,786,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,787,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,788,e)]. 2.18/2.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,789,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | element(f85(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(802,a,790,e)]. 2.20/2.43 803 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f84(A,B)) | closed_subset(f85(A,B,C),A) # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(179)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,765,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,777,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,778,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,779,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,780,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,781,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,782,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,783,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,784,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,785,e)]. 2.20/2.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,786,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,787,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,788,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,789,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | closed_subset(f85(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(803,a,790,e)]. 2.20/2.44 804 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f84(A,B)) | subset(B,C) # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(179)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,765,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,777,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,778,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,779,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,780,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,781,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,782,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,783,e)]. 2.20/2.44 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,784,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,785,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,786,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,787,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,788,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,789,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(804,a,790,e)]. 2.20/2.46 805 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | -in(C,f84(A,B)) | f85(A,B,C) = C # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(179)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,765,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,777,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,778,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,779,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,780,e)]. 2.20/2.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,781,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,782,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,783,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,784,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,785,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,786,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,787,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,788,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,789,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | -in(C,f84(B,A)) | f85(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(805,a,790,e)]. 2.20/2.47 806 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | -element(C,powerset(the_carrier(A))) | in(C,f84(A,B)) | -element(D,powerset(the_carrier(A))) | -closed_subset(D,A) | -subset(B,C) | D != C # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(179)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,765,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,777,e)]. 2.20/2.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,778,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,779,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,780,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,781,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,782,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,783,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,784,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,785,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,786,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,787,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,788,e)]. 2.20/2.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,789,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | -element(C,powerset(the_carrier(B))) | in(C,f84(B,A)) | -element(D,powerset(the_carrier(B))) | -closed_subset(D,B) | -subset(A,C) | D != C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(806,a,790,e)]. 2.20/2.50 807 -topological_space(A) | -element(B,powerset(the_carrier(A))) | -top_str(A) | element(f84(A,B),powerset(powerset(the_carrier(A)))) # label(s3_subset_1__e1_40__pre_topc) # label(lemma). [clausify(179)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,765,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,777,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,778,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,779,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,780,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,781,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,782,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,783,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,784,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,785,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,786,e)]. 2.20/2.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,787,e)]. 2.20/2.51 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,788,e)]. 2.20/2.51 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,789,e)]. 2.20/2.51 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f84(B,A),powerset(powerset(the_carrier(B)))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(807,a,790,e)]. 2.20/2.51 808 -element(A,the_carrier(B)) | -top_str(B) | -topological_space(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) # label(dt_m1_connsp_2) # label(axiom). [clausify(201)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,765,e)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,777,e)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,778,e)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,779,e)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,780,e)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,781,e)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,782,e)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,783,e)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,784,e)]. 2.20/2.51 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,785,e)]. 2.31/2.53 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,786,e)]. 2.31/2.53 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,787,e)]. 2.31/2.53 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,788,e)]. 2.31/2.53 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,789,e)]. 2.31/2.53 Derived: -element(A,the_carrier(B)) | -top_str(B) | empty_carrier(B) | -point_neighbourhood(C,B,A) | element(C,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(808,c,790,e)]. 2.31/2.53 809 -top_str(A) | -topological_space(A) | closed_subset(f110(A),A) # label(rc6_pre_topc) # label(axiom). [clausify(217)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,765,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,777,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,778,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,779,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,780,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,781,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,782,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,783,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,784,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,785,e)]. 2.31/2.53 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,786,e)]. 2.31/2.55 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,787,e)]. 2.31/2.55 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,788,e)]. 2.31/2.55 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,789,e)]. 2.31/2.55 Derived: -top_str(A) | closed_subset(f110(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(809,b,790,e)]. 2.31/2.55 810 -top_str(A) | -topological_space(A) | element(f110(A),powerset(the_carrier(A))) # label(rc6_pre_topc) # label(axiom). [clausify(217)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,765,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,777,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,778,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,779,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,780,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,781,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,782,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,783,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,784,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,785,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,786,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,787,e)]. 2.31/2.55 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,788,e)]. 2.31/2.59 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,789,e)]. 2.31/2.59 Derived: -top_str(A) | element(f110(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(810,b,790,e)]. 2.31/2.59 811 -topological_space(A) | -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) # label(fc5_pre_topc) # label(axiom). [clausify(276)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,765,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,777,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,778,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,779,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,780,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,781,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,782,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,783,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,784,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,785,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,786,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,787,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,788,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,789,e)]. 2.31/2.59 Derived: -top_str(A) | closed_subset(cast_as_carrier_subset(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(811,a,790,e)]. 2.38/2.61 812 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(topstr_closure(B,A),B) # label(fc2_tops_1) # label(axiom). [clausify(300)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,765,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,777,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,778,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,779,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,780,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,781,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,782,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,783,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,784,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,785,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,786,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,787,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,788,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,789,e)]. 2.38/2.61 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(topstr_closure(B,A),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(812,c,790,e)]. 2.38/2.65 813 empty_carrier(A) | -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) # label(t6_yellow_6) # label(lemma). [clausify(369)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,765,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,777,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,778,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,779,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,780,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,781,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,782,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,783,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,784,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,785,e)]. 2.38/2.65 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,786,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,787,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,788,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,789,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | point_neighbourhood(f205(A,B,C),A,C) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(813,c,790,e)]. 2.38/2.66 814 empty_carrier(A) | -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) # label(t6_yellow_6) # label(lemma). [clausify(369)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,765,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,777,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,778,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,779,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,780,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,781,e)]. 2.38/2.66 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,782,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,783,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,784,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,785,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,786,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,787,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,788,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,789,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | disjoint(f205(A,B,C),B) | in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(814,c,790,e)]. 2.46/2.67 815 empty_carrier(A) | -top_str(A) | -topological_space(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) # label(t6_yellow_6) # label(lemma). [clausify(369)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,765,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,777,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,778,e)]. 2.46/2.67 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,779,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,780,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,781,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,782,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,783,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,784,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,785,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,786,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,787,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,788,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,789,e)]. 2.46/2.68 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,the_carrier(A)) | -point_neighbourhood(D,A,C) | -disjoint(D,B) | -in(C,topstr_closure(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(815,c,790,e)]. 2.51/2.72 816 -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(436)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,765,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,777,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,778,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,779,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,780,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,781,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,782,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,783,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,784,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,785,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,786,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,787,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,788,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,789,e)]. 2.51/2.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(816,a,790,e)]. 2.51/2.75 817 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,765,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,777,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,778,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,779,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,780,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,781,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,782,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,783,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,784,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,785,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,786,e)]. 2.51/2.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,787,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,788,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,789,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(817,c,790,e)]. 2.51/2.76 818 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,765,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,777,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,778,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,779,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,780,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,781,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,782,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,783,e)]. 2.51/2.76 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,784,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,785,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,786,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,787,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,788,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,789,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(818,c,790,e)]. 2.51/2.77 819 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,765,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,777,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,778,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,779,e)]. 2.51/2.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,780,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,781,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,782,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,783,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,784,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,785,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,786,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,787,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,788,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,789,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(819,c,790,e)]. 2.51/2.78 820 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,765,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,777,e)]. 2.51/2.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,778,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,779,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,780,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,781,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,782,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,783,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,784,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,785,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,786,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,787,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,788,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,789,e)]. 2.51/2.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(820,c,790,e)]. 2.51/2.80 821 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,765,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,777,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,778,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,779,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,780,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,781,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,782,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,783,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,784,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,785,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,786,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,787,e)]. 2.51/2.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,788,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,789,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(821,c,790,e)]. 2.51/2.81 822 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,765,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,777,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,778,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,779,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,780,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,781,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,782,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,783,e)]. 2.51/2.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,784,e)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,785,e)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,786,e)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,787,e)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,788,e)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,789,e)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(822,c,790,e)]. 2.61/2.82 823 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,765,e)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,777,e)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,778,e)]. 2.61/2.82 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,779,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,780,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,781,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,782,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,783,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,784,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,785,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,786,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,787,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,788,e)]. 2.61/2.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,789,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f248(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(823,c,790,e)]. 2.61/2.84 824 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,765,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,777,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,778,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,779,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,780,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,781,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,782,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,783,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,784,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,785,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,786,e)]. 2.61/2.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,787,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,788,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,789,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(824,c,790,e)]. 2.61/2.85 825 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,765,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,777,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,778,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,779,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,780,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,781,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,782,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,783,e)]. 2.61/2.85 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,784,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,785,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,786,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,787,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,788,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,789,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(825,c,790,e)]. 2.61/2.86 826 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,765,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,777,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,778,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,779,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,780,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,781,e)]. 2.61/2.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,782,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,783,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,784,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,785,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,786,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,787,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,788,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,789,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(826,c,790,e)]. 2.61/2.88 827 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,765,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,777,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,778,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,779,e)]. 2.61/2.88 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,780,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,781,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,782,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,783,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,784,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,785,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,786,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,787,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,788,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,789,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(827,c,790,e)]. 2.61/2.89 828 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,765,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,777,e)]. 2.61/2.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,778,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,779,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,780,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,781,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,782,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,783,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,784,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,785,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,786,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,787,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,788,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,789,e)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(828,c,790,e)]. 2.61/2.90 829 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.61/2.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,765,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,777,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,778,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,779,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,780,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,781,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,782,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,783,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,784,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,785,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,786,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,787,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,788,e)]. 2.71/2.91 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,789,e)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(829,c,790,e)]. 2.71/2.92 830 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,765,e)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,777,e)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,778,e)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,779,e)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,780,e)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,781,e)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,782,e)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,783,e)]. 2.71/2.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,784,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,785,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,786,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,787,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,788,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,789,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f246(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(830,c,790,e)]. 2.71/2.94 831 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,765,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,777,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,778,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,779,e)]. 2.71/2.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,780,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,781,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,782,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,783,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,784,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,785,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,786,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,787,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,788,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,789,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(831,c,790,e)]. 2.71/2.95 832 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,765,e)]. 2.71/2.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,777,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,778,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,779,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,780,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,781,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,782,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,783,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,784,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,785,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,786,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,787,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,788,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,789,e)]. 2.71/2.96 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(832,c,790,e)]. 2.71/2.97 833 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,765,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,777,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,778,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,779,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,780,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,781,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,782,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,783,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,784,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,785,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,786,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,787,e)]. 2.71/2.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,788,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,789,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(833,c,790,e)]. 2.71/2.98 834 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,765,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,777,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,778,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,779,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,780,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,781,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,782,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,783,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,784,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,785,e)]. 2.71/2.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,786,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,787,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,788,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,789,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(834,c,790,e)]. 2.79/2.99 835 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,765,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,777,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,778,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,779,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,780,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,781,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,782,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,783,e)]. 2.79/2.99 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,784,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,785,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,786,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,787,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,788,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,789,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(835,c,790,e)]. 2.80/3.01 836 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,765,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,777,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,778,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,779,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,780,e)]. 2.80/3.01 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,781,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,782,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,783,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,784,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,785,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,786,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,787,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,788,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,789,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(836,c,790,e)]. 2.80/3.02 837 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,765,e)]. 2.80/3.02 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,777,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,778,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,779,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,780,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,781,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,782,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,783,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,784,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,785,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,786,e)]. 2.80/3.03 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,787,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,788,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,789,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f248(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(837,c,790,e)]. 2.80/3.04 838 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,765,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,777,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,778,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,779,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,780,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,781,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,782,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,783,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,784,e)]. 2.80/3.04 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,785,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,786,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,787,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,788,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,789,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(838,c,790,e)]. 2.80/3.06 839 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,765,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,777,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,778,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,779,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,780,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,781,e)]. 2.80/3.06 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,782,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,783,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,784,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,785,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,786,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,787,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,788,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,789,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(839,c,790,e)]. 2.80/3.07 840 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,765,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,777,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,778,e)]. 2.80/3.07 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,779,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,780,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,781,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,782,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,783,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,784,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,785,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,786,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,787,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,788,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,789,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(840,c,790,e)]. 2.80/3.08 841 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,765,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,777,e)]. 2.80/3.08 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,778,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,779,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,780,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,781,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,782,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,783,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,784,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,785,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,786,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,787,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,788,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,789,e)]. 2.80/3.09 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(841,c,790,e)]. 2.80/3.09 842 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,765,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,777,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,778,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,779,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,780,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,781,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,782,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,783,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,784,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,785,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,786,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,787,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,788,e)]. 2.90/3.11 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,789,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(842,c,790,e)]. 2.90/3.12 843 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,765,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,777,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,778,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,779,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,780,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,781,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,782,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,783,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,784,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,785,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,786,e)]. 2.90/3.12 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,787,e)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,788,e)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,789,e)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(843,c,790,e)]. 2.90/3.13 844 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,765,e)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,777,e)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,778,e)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,779,e)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,780,e)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,781,e)]. 2.90/3.13 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,782,e)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,783,e)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,784,e)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,785,e)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,786,e)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,787,e)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,788,e)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,789,e)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f248(B,A) = f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(844,c,790,e)]. 2.90/3.15 845 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,765,e)]. 2.90/3.15 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,777,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,778,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,779,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,780,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,781,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,782,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,783,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,784,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,785,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,786,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,787,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,788,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,789,e)]. 2.90/3.16 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(845,c,790,e)]. 2.90/3.16 846 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,765,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,777,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,778,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,779,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,780,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,781,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,782,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,783,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,784,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,785,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,786,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,787,e)]. 2.90/3.17 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,788,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,789,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(846,c,790,e)]. 2.90/3.18 847 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,765,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,777,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,778,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,779,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,780,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,781,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,782,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,783,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,784,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,785,e)]. 2.90/3.18 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,786,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,787,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,788,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,789,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(847,c,790,e)]. 3.01/3.20 848 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,765,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,777,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,778,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,779,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,780,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,781,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,782,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,783,e)]. 3.01/3.20 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,784,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,785,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,786,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,787,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,788,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,789,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(848,c,790,e)]. 3.01/3.21 849 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,765,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,777,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,778,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,779,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,780,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,781,e)]. 3.01/3.21 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,782,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,783,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,784,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,785,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,786,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,787,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,788,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,789,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(849,c,790,e)]. 3.01/3.22 850 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,765,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,777,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,778,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,779,e)]. 3.01/3.22 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,780,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,781,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,782,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,783,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,784,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,785,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,786,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,787,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,788,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,789,e)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(850,c,790,e)]. 3.01/3.23 851 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.01/3.23 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,765,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,777,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,778,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,779,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,780,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,781,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,782,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,783,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,784,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,785,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,786,e)]. 3.01/3.25 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,787,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,788,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,789,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(851,c,790,e)]. 3.01/3.26 852 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,765,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,777,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,778,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,779,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,780,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,781,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,782,e)]. 3.01/3.26 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,783,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,784,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,785,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,786,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,787,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,788,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,789,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(852,c,790,e)]. 3.01/3.27 853 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,765,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,777,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,778,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,779,e)]. 3.01/3.27 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,780,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,781,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,782,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,783,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,784,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,785,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,786,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,787,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,788,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,789,e)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(853,c,790,e)]. 3.01/3.29 854 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.01/3.29 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,765,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,777,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,778,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,779,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,780,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,781,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,782,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,783,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,784,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,785,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,786,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,787,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,788,e)]. 3.11/3.30 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,789,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(854,c,790,e)]. 3.12/3.31 855 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,765,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,777,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,778,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,779,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,780,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,781,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,782,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,783,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,784,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,785,e)]. 3.12/3.31 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,786,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,787,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,788,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,789,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(855,c,790,e)]. 3.12/3.32 856 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,765,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,777,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,778,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,779,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,780,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,781,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,782,e)]. 3.12/3.32 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,783,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,784,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,785,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,786,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,787,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,788,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,789,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(856,c,790,e)]. 3.12/3.34 857 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,765,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,777,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,778,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,779,e)]. 3.12/3.34 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,780,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,781,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,782,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,783,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,784,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,785,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,786,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,787,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,788,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,789,e)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(857,c,790,e)]. 3.12/3.35 858 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.12/3.35 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,765,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,777,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,778,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,779,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,780,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,781,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,782,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,783,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,784,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,785,e)]. 3.12/3.36 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,786,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,787,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,788,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,789,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | element(f249(B,A),powerset(the_carrier(B))) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(858,c,790,e)]. 3.12/3.38 859 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,765,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,777,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,778,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,779,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,780,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,781,e)]. 3.12/3.38 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,782,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,783,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,784,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,785,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,786,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,787,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,788,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,789,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(859,c,790,e)]. 3.12/3.39 860 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,765,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,777,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,778,e)]. 3.12/3.39 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,779,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,780,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,781,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,782,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,783,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,784,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,785,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,786,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,787,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,788,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,789,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(860,c,790,e)]. 3.12/3.40 861 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,765,e)]. 3.12/3.40 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,777,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,778,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,779,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,780,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,781,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,782,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,783,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,784,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,785,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,786,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,787,e)]. 3.12/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,788,e)]. 3.23/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,789,e)]. 3.23/3.42 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(861,c,790,e)]. 3.23/3.42 862 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,765,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,777,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,778,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,779,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,780,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,781,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,782,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,783,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,784,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,785,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,786,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,787,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,788,e)]. 3.23/3.43 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,789,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(862,c,790,e)]. 3.23/3.45 863 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,765,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,777,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,778,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,779,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,780,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,781,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,782,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,783,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,784,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,785,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,786,e)]. 3.23/3.45 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,787,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,788,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,789,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(863,c,790,e)]. 3.23/3.46 864 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,765,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,777,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,778,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,779,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,780,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,781,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,782,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,783,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,784,e)]. 3.23/3.46 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,785,e)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,786,e)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,787,e)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,788,e)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,789,e)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(864,c,790,e)]. 3.23/3.47 865 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,765,e)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,777,e)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,778,e)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,779,e)]. 3.23/3.47 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,780,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,781,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,782,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,783,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,784,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,785,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,786,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,787,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,788,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,789,e)]. 3.23/3.49 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | subset(A,f247(B,A)) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(865,c,790,e)]. 3.23/3.49 866 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,765,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,777,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,778,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,779,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,780,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,781,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,782,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,783,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,784,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,785,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,786,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,787,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,788,e)]. 3.23/3.50 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,789,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(866,c,790,e)]. 3.34/3.52 867 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,765,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,777,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,778,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,779,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,780,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,781,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,782,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,783,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,784,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,785,e)]. 3.34/3.52 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,786,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,787,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,788,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,789,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(867,c,790,e)]. 3.34/3.53 868 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,765,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,777,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,778,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,779,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,780,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,781,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,782,e)]. 3.34/3.53 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,783,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,784,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,785,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,786,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,787,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,788,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,789,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(868,c,790,e)]. 3.34/3.54 869 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,765,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,777,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,778,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,779,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,780,e)]. 3.34/3.54 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,781,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,782,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,783,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,784,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,785,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,786,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,787,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,788,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,789,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(869,c,790,e)]. 3.34/3.56 870 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,765,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,777,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,778,e)]. 3.34/3.56 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,779,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,780,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,781,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,782,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,783,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,784,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,785,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,786,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,787,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,788,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,789,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(870,c,790,e)]. 3.34/3.57 871 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,765,e)]. 3.34/3.57 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,777,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,778,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,779,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,780,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,781,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,782,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,783,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,784,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,785,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,786,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,787,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,788,e)]. 3.34/3.59 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,789,e)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(871,c,790,e)]. 3.34/3.60 872 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,765,e)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,777,e)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,778,e)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,779,e)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,780,e)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,781,e)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,782,e)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,783,e)]. 3.34/3.60 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,784,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,785,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,786,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,787,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,788,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,789,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | closed_subset(f249(B,A),B) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(872,c,790,e)]. 3.43/3.62 873 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,765,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,777,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,778,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,779,e)]. 3.43/3.62 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,780,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,781,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,782,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,783,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,784,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,785,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,786,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,787,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,788,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,789,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(873,c,790,e)]. 3.43/3.63 874 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,765,e)]. 3.43/3.63 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,777,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,778,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,779,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,780,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,781,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,782,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,783,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,784,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,785,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,786,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,787,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,788,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,789,e)]. 3.43/3.65 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(874,c,790,e)]. 3.43/3.66 875 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,765,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,777,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,778,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,779,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,780,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,781,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,782,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,783,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,784,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,785,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,786,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,787,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,788,e)]. 3.43/3.66 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,789,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(875,c,790,e)]. 3.43/3.68 876 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,765,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,777,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,778,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,779,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,780,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,781,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,782,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,783,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,784,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,785,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,786,e)]. 3.43/3.68 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,787,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,788,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,789,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(876,c,790,e)]. 3.53/3.69 877 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,765,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,777,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,778,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,779,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,780,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,781,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,782,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,783,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,784,e)]. 3.53/3.69 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,785,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,786,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,787,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,788,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,789,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(877,c,790,e)]. 3.53/3.70 878 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,765,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,777,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,778,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,779,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,780,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,781,e)]. 3.53/3.70 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,782,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,783,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,784,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,785,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,786,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,787,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,788,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,789,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(878,c,790,e)]. 3.53/3.72 879 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,765,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,777,e)]. 3.53/3.72 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,778,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,779,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,780,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,781,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,782,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,783,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,784,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,785,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,786,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,787,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,788,e)]. 3.53/3.74 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,789,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f249(B,A) = f247(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(879,c,790,e)]. 3.53/3.75 880 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,765,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,777,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,778,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,779,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,780,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,781,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,782,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,783,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,784,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,785,e)]. 3.53/3.75 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,786,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,787,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,788,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,789,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(880,c,790,e)]. 3.53/3.77 881 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,765,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,777,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,778,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,779,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,780,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,781,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,782,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,783,e)]. 3.53/3.77 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,784,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,785,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,786,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,787,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,788,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,789,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(881,c,790,e)]. 3.53/3.78 882 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,765,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,777,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,778,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,779,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,780,e)]. 3.53/3.78 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,781,e)]. 3.63/3.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,782,e)]. 3.63/3.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,783,e)]. 3.63/3.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,784,e)]. 3.63/3.79 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,785,e)]. 3.63/3.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,786,e)]. 3.63/3.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,787,e)]. 3.63/3.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,788,e)]. 3.63/3.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,789,e)]. 3.63/3.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(882,c,790,e)]. 3.63/3.80 883 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.63/3.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,765,e)]. 3.63/3.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,777,e)]. 3.63/3.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,778,e)]. 3.63/3.80 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,779,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,780,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,781,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,782,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,783,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,784,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,785,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,786,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,787,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,788,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,789,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(883,c,790,e)]. 3.65/3.81 884 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,765,e)]. 3.65/3.81 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,777,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,778,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,779,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,780,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,781,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,782,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,783,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,784,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,785,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,786,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,787,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,788,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,789,e)]. 3.65/3.83 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(884,c,790,e)]. 3.65/3.83 885 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,765,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,777,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,778,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,779,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,780,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,781,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,782,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,783,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,784,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,785,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,786,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,787,e)]. 3.65/3.84 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,788,e)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,789,e)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(885,c,790,e)]. 3.65/3.86 886 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,765,e)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,777,e)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,778,e)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,779,e)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,780,e)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,781,e)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,782,e)]. 3.65/3.86 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,783,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,784,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,785,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,786,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,787,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,788,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,789,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f246(B,A) = f245(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(886,c,790,e)]. 3.65/3.87 887 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,765,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,777,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,778,e)]. 3.65/3.87 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,779,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,780,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,781,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,782,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,783,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,784,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,785,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,786,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,787,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,788,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,789,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f251(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(887,c,790,e)]. 3.65/3.89 888 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,765,e)]. 3.65/3.89 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,777,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,778,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,779,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,780,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,781,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,782,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,783,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,784,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,785,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,786,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,787,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,788,e)]. 3.74/3.90 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,789,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | element(f252(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(888,c,790,e)]. 3.74/3.92 889 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,765,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,777,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,778,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,779,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,780,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,781,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,782,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,783,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,784,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,785,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,786,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,787,e)]. 3.74/3.92 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,788,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,789,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | subset(A,C) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(889,c,790,e)]. 3.74/3.94 890 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,765,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,777,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,778,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,779,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,780,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,781,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,782,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,783,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,784,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,785,e)]. 3.74/3.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,786,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,787,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,788,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,789,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | closed_subset(f252(B,A,C),B) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(890,c,790,e)]. 3.74/3.95 891 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,765,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,777,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,778,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,779,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,780,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,781,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,782,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,783,e)]. 3.74/3.95 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,784,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,785,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,786,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,787,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,788,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,789,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | f252(B,A,C) = C | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(891,c,790,e)]. 3.74/3.97 892 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,765,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,777,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,778,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,779,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,780,e)]. 3.74/3.97 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,781,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,782,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,783,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,784,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,785,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,786,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,787,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,788,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,789,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | -in(C,f250(B,A)) | in(f251(B,A,C),powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(892,c,790,e)]. 3.74/3.98 893 -element(A,powerset(the_carrier(B))) | -top_str(B) | -topological_space(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) # label(s1_tarski__e1_40__pre_topc__1) # label(axiom). [clausify(462)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,765,e)]. 3.74/3.98 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,777,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,778,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,779,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | element(f37(B),powerset(powerset(the_carrier(B)))) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,780,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,781,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,782,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,783,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,784,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | subset(f37(B),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,785,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f38(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,786,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | element(f39(B),powerset(the_carrier(B))) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,787,e)]. 3.83/4.00 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f39(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,788,e)]. 4.73/4.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | in(f38(B),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,789,e)]. 4.73/4.94 Derived: -element(A,powerset(the_carrier(B))) | -top_str(B) | f247(B,A) != f246(B,A) | in(C,f250(B,A)) | D != C | -element(E,powerset(the_carrier(B))) | -subset(A,C) | -closed_subset(E,B) | E != C | -in(D,powerset(the_carrier(B))) | -top_str(B) | -in(union_of_subsets(the_carrier(B),f37(B)),the_topology(B)) | -in(subset_intersection2(the_carrier(B),f38(B),f39(B)),the_topology(B)) | -in(the_carrier(B),the_topology(B)). [resolve(893,c,790,e)]. 4.73/4.94 894 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.73/4.94 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,765,e)]. 4.73/4.94 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,777,e)]. 4.73/4.94 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,778,e)]. 4.73/4.94 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,779,e)]. 4.73/4.94 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,780,e)]. 4.73/4.94 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,781,e)]. 4.73/4.94 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,782,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,783,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,784,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,785,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,786,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,787,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,788,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,789,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(894,a,790,e)]. 4.73/4.95 895 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,765,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,777,e)]. 4.73/4.95 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,778,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,779,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,780,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,781,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,782,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,783,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,784,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,785,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,786,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,787,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,788,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,789,e)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(895,a,790,e)]. 4.80/4.96 896 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.80/4.96 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,765,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,777,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,778,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,779,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,780,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,781,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,782,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,783,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,784,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,785,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,786,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,787,e)]. 4.80/4.97 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,788,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,789,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(896,a,790,e)]. 4.80/4.98 897 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,765,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,777,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,778,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,779,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,780,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,781,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,782,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,783,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,784,e)]. 4.80/4.98 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,785,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,786,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,787,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,788,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,789,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f291(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(897,a,790,e)]. 4.80/4.99 898 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,765,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,777,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,778,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,779,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,780,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,781,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,782,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,783,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,784,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,785,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,786,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,787,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,788,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,789,e)]. 4.80/4.99 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(898,a,790,e)]. 4.85/5.00 899 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,765,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,777,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,778,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,779,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,780,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,781,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,782,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,783,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,784,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,785,e)]. 4.85/5.00 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,786,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,787,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,788,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,789,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(899,a,790,e)]. 4.85/5.01 900 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,765,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,777,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,778,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,779,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,780,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,781,e)]. 4.85/5.01 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,782,e)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,783,e)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,784,e)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,785,e)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,786,e)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,787,e)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,788,e)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,789,e)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(900,a,790,e)]. 4.85/5.02 901 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,765,e)]. 4.85/5.02 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,777,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,778,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,779,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,780,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,781,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,782,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,783,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,784,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,785,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,786,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,787,e)]. 4.85/5.03 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,788,e)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,789,e)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f292(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(901,a,790,e)]. 4.88/5.04 902 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,765,e)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,777,e)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,778,e)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,779,e)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,780,e)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,781,e)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,782,e)]. 4.88/5.04 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,783,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,784,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,785,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,786,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,787,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,788,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,789,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(902,a,790,e)]. 4.88/5.05 903 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,765,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,777,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,778,e)]. 4.88/5.05 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,779,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,780,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,781,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,782,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,783,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,784,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,785,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,786,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,787,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,788,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,789,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(903,a,790,e)]. 4.88/5.06 904 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,765,e)]. 4.88/5.06 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,777,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,778,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,779,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,780,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,781,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,782,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,783,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,784,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,785,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,786,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,787,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,788,e)]. 4.88/5.07 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,789,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(904,a,790,e)]. 4.88/5.08 905 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,765,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,777,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,778,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,779,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,780,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,781,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,782,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,783,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,784,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,785,e)]. 4.88/5.08 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,786,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,787,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,788,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,789,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) = f290(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(905,a,790,e)]. 4.88/5.09 906 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,765,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,777,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,778,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,779,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,780,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,781,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,782,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,783,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,784,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,785,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,786,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,787,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,788,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,789,e)]. 4.88/5.09 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(906,a,790,e)]. 4.88/5.09 907 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,765,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,777,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,778,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,779,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,780,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,781,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,782,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,783,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,784,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,785,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,786,e)]. 4.88/5.10 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,787,e)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,788,e)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,789,e)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(907,a,790,e)]. 4.88/5.11 908 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,765,e)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,777,e)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,778,e)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,779,e)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,780,e)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,781,e)]. 4.88/5.11 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,782,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,783,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,784,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,785,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,786,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,787,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,788,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,789,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(908,a,790,e)]. 4.88/5.12 909 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,765,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,777,e)]. 4.88/5.12 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,778,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,779,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,780,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,781,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,782,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,783,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,784,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,785,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,786,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,787,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,788,e)]. 4.98/5.13 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,789,e)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(set_difference(cast_as_carrier_subset(A),f291(A,B)),B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(909,a,790,e)]. 4.98/5.14 910 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,765,e)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,777,e)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,778,e)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,779,e)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,780,e)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,781,e)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,782,e)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,783,e)]. 4.98/5.14 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,784,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,785,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,786,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,787,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,788,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,789,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | C != D | -in(set_difference(cast_as_carrier_subset(A),D),B) | -in(C,powerset(the_carrier(A))) | in(D,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(910,a,790,e)]. 4.98/5.15 911 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,765,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,777,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,778,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,779,e)]. 4.98/5.15 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,780,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,781,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,782,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,783,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,784,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,785,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,786,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,787,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,788,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,789,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | f294(A,B,C) = C | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(911,a,790,e)]. 4.98/5.16 912 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,765,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,777,e)]. 4.98/5.16 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,778,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,779,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,780,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,781,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,782,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,783,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,784,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,785,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,786,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,787,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,788,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,789,e)]. 4.98/5.17 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(set_difference(cast_as_carrier_subset(A),C),B) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(912,a,790,e)]. 4.98/5.18 913 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) # label(s1_tarski__e2_37_1_1__pre_topc__1) # label(axiom). [clausify(494)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,765,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,777,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,778,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,779,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,780,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,781,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,782,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,783,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,784,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,785,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,786,e)]. 4.98/5.18 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,787,e)]. 5.05/5.25 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,788,e)]. 5.05/5.25 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,789,e)]. 5.05/5.25 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | f292(A,B) != f291(A,B) | in(f294(A,B,C),powerset(the_carrier(A))) | -in(C,f293(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(913,a,790,e)]. 5.05/5.25 914 -topological_space(A) | -top_str(A) | element(f311(A),powerset(the_carrier(A))) # label(rc2_tops_1) # label(axiom). [clausify(551)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,765,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,777,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,778,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,779,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,780,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,781,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,782,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,783,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,784,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,785,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,786,e)]. 5.05/5.25 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,787,e)]. 5.05/5.26 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,788,e)]. 5.05/5.26 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,789,e)]. 5.05/5.26 Derived: -top_str(A) | element(f311(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(914,a,790,e)]. 5.05/5.26 915 -topological_space(A) | -top_str(A) | closed_subset(f311(A),A) # label(rc2_tops_1) # label(axiom). [clausify(551)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,765,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,777,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,778,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,779,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,780,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,781,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,782,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,783,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,784,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,785,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,786,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,787,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,788,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,789,e)]. 5.05/5.26 Derived: -top_str(A) | closed_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(915,a,790,e)]. 5.05/5.27 916 -topological_space(A) | -top_str(A) | open_subset(f311(A),A) # label(rc2_tops_1) # label(axiom). [clausify(551)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,765,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,777,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,778,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,779,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,780,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,781,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,782,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,783,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,784,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,785,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,786,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,787,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,788,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,789,e)]. 5.05/5.27 Derived: -top_str(A) | open_subset(f311(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(916,a,790,e)]. 5.05/5.27 917 -topological_space(A) | -top_str(A) | element(f315(A),powerset(the_carrier(A))) # label(rc1_tops_1) # label(axiom). [clausify(554)]. 5.05/5.27 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,765,e)]. 5.05/5.27 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,777,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,778,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,779,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,780,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,781,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,782,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,783,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,784,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,785,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,786,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,787,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,788,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,789,e)]. 5.14/5.28 Derived: -top_str(A) | element(f315(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(917,a,790,e)]. 5.14/5.28 918 -topological_space(A) | -top_str(A) | open_subset(f315(A),A) # label(rc1_tops_1) # label(axiom). [clausify(554)]. 5.14/5.28 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,765,e)]. 5.14/5.28 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,777,e)]. 5.14/5.28 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,778,e)]. 5.14/5.28 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,779,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,780,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,781,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,782,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,783,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,784,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,785,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,786,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,787,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,788,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,789,e)]. 5.14/5.30 Derived: -top_str(A) | open_subset(f315(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(918,a,790,e)]. 5.14/5.30 919 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -topological_space(A) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(lemma). [clausify(555)]. 5.14/5.30 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,765,e)]. 5.14/5.30 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,777,e)]. 5.14/5.30 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,778,e)]. 5.14/5.30 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,779,e)]. 5.14/5.30 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,780,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,781,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,782,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,783,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,784,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,785,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,786,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,787,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,788,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,789,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(C,powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(919,c,790,e)]. 5.14/5.31 920 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -topological_space(A) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(lemma). [clausify(555)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,765,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,777,e)]. 5.14/5.31 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,778,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,779,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,780,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,781,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,782,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,783,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,784,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,785,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,786,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,787,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,788,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,789,e)]. 5.14/5.32 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -in(C,f316(A,B)) | in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(920,c,790,e)]. 5.14/5.32 921 -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -topological_space(A) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) # label(s1_xboole_0__e2_37_1_1__pre_topc__1) # label(lemma). [clausify(555)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,765,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,777,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,778,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,779,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,780,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,781,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,782,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,783,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,784,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,785,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,786,e)]. 5.18/5.33 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,787,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,788,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,789,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(C,f316(A,B)) | -in(C,powerset(the_carrier(A))) | -in(set_difference(cast_as_carrier_subset(A),C),B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(921,c,790,e)]. 5.33/5.49 922 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) # label(t44_pre_topc) # label(lemma). [clausify(577)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,765,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,777,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,778,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,779,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,780,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,781,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,782,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,783,e)]. 5.33/5.49 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,784,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,785,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,786,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,787,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,788,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,789,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f354(A,B),powerset(the_carrier(A))) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(922,a,790,e)]. 5.33/5.50 923 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) # label(t44_pre_topc) # label(lemma). [clausify(577)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,765,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,777,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,778,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,779,e)]. 5.33/5.50 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,780,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,781,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,782,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,783,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,784,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,785,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,786,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,787,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,788,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,789,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | in(f354(A,B),B) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(923,a,790,e)]. 5.33/5.51 924 -topological_space(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) # label(t44_pre_topc) # label(lemma). [clausify(577)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,765,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,777,e)]. 5.33/5.51 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,778,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,779,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,780,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,781,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,782,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,783,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,784,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,785,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,786,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,787,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,788,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,789,e)]. 5.33/5.52 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subset(f354(A,B),A) | closed_subset(meet_of_subsets(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(924,a,790,e)]. 5.42/5.57 925 -top_str(A) | -topological_space(A) | empty_carrier(A) | -empty(f368(A)) # label(rc7_pre_topc) # label(axiom). [clausify(604)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,765,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,777,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,778,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,779,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,780,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,781,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,782,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,783,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,784,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,785,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,786,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,787,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,788,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,789,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | -empty(f368(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(925,b,790,e)]. 5.42/5.57 926 -top_str(A) | -topological_space(A) | empty_carrier(A) | closed_subset(f368(A),A) # label(rc7_pre_topc) # label(axiom). [clausify(604)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,765,e)]. 5.42/5.57 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,777,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,778,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,779,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,780,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,781,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,782,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,783,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,784,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,785,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,786,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,787,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,788,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,789,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | closed_subset(f368(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(926,b,790,e)]. 5.42/5.58 927 -top_str(A) | -topological_space(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) # label(rc7_pre_topc) # label(axiom). [clausify(604)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,765,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,777,e)]. 5.42/5.58 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,778,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,779,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,780,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,781,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,782,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,783,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,784,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,785,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,786,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,787,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,788,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,789,e)]. 5.50/5.67 Derived: -top_str(A) | empty_carrier(A) | element(f368(A),powerset(the_carrier(A))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(927,b,790,e)]. 5.50/5.67 928 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(675)]. 5.50/5.67 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,765,e)]. 5.50/5.67 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,777,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,778,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,779,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,780,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,781,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,782,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,783,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,784,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,785,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,786,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,787,e)]. 5.50/5.69 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,788,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,789,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,powerset(the_carrier(A))) | D != C | -closed_subset(D,A) | -subset(B,C) | -element(D,powerset(the_carrier(A))) | in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(928,a,790,e)]. 5.50/5.70 929 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(675)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,765,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,777,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,778,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,779,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,780,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,781,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,782,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,783,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,784,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,785,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,786,e)]. 5.50/5.70 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,787,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,788,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,789,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | in(C,powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(929,a,790,e)]. 5.58/5.72 930 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(675)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,765,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,777,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,778,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,779,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,780,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,781,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,782,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,783,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,784,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,785,e)]. 5.58/5.72 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,786,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,787,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,788,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,789,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | f404(A,B,C) = C | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(930,a,790,e)]. 5.58/5.73 931 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(675)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,765,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,777,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,778,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,779,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,780,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,781,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,782,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,783,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,784,e)]. 5.58/5.73 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,785,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,786,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,787,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,788,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,789,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(f404(A,B,C),A) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(931,a,790,e)]. 5.58/5.75 932 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(675)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,765,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,777,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,778,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,779,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,780,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,781,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,782,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,783,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,784,e)]. 5.58/5.75 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,785,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,786,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,787,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,788,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,789,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | subset(B,C) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(932,a,790,e)]. 5.58/5.76 933 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) # label(s1_xboole_0__e1_40__pre_topc__1) # label(lemma). [clausify(675)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,765,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,777,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,778,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,779,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,780,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,781,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,782,e)]. 5.58/5.76 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,783,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,784,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,785,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,786,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,787,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,788,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,789,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | element(f404(A,B,C),powerset(the_carrier(A))) | -in(C,f403(A,B)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(933,a,790,e)]. 5.65/5.86 934 -top_str(A) | -element(B,the_carrier(A)) | -topological_space(A) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) # label(existence_m1_connsp_2) # label(axiom). [clausify(717)]. 5.65/5.86 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,765,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,777,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,778,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,779,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,780,e)]. 5.65/5.86 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,781,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,782,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,783,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,784,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,785,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,786,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,787,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,788,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,789,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | point_neighbourhood(f421(A,B),A,B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(934,c,790,e)]. 5.79/6.01 935 -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(729)]. 5.79/6.01 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,765,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,777,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,778,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,779,e)]. 5.79/6.01 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,780,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,781,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,782,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,783,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,784,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,785,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,786,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,787,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,788,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,789,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | topstr_closure(A,B) != B | closed_subset(B,A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(935,d,790,e)]. 6.04/6.19 936 -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | -topological_space(A) | open_subset(subset_complement(the_carrier(A),B),A) # label(fc3_tops_1) # label(axiom). [clausify(744)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,765,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,777,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,778,e)]. 6.04/6.19 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,779,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,780,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,781,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,782,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,783,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,784,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,785,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,786,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,787,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,788,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,789,e)]. 9.44/9.65 Derived: -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | open_subset(subset_complement(the_carrier(A),B),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(936,d,790,e)]. 9.44/9.65 937 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | open_subset(interior(A,B),A) # label(fc6_tops_1) # label(axiom). [clausify(760)]. 9.44/9.65 938 upper_bounded_semilattstr(c2) # label(rc13_lattices) # label(axiom). [clausify(22)]. 9.44/9.65 939 -lattice(A) | -latt_str(A) | -upper_bounded_semilattstr(A) | empty_carrier(A) | -empty_carrier(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(8)]. 9.44/9.65 940 -lattice(A) | -latt_str(A) | -upper_bounded_semilattstr(A) | empty_carrier(A) | strict_rel_str(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(8)]. 9.44/9.65 941 -lattice(A) | -latt_str(A) | -upper_bounded_semilattstr(A) | empty_carrier(A) | reflexive_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(8)]. 10.59/10.80 942 -lattice(A) | -latt_str(A) | -upper_bounded_semilattstr(A) | empty_carrier(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(8)]. 10.59/10.80 943 -lattice(A) | -latt_str(A) | -upper_bounded_semilattstr(A) | empty_carrier(A) | upper_bounded_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(8)]. 10.59/10.80 944 -lattice(A) | -latt_str(A) | -upper_bounded_semilattstr(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(8)]. 10.59/10.80 945 -lattice(A) | -latt_str(A) | -upper_bounded_semilattstr(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(8)]. 10.59/10.80 946 -lattice(A) | -latt_str(A) | -upper_bounded_semilattstr(A) | empty_carrier(A) | transitive_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(8)]. 10.59/10.80 Derived: -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | upper_bounded_relstr(poset_of_lattice(c2)). [resolve(938,a,943,c)]. 10.59/10.80 947 upper_bounded_semilattstr(c4) # label(rc10_lattices) # label(axiom). [clausify(80)]. 10.59/10.80 Derived: -lattice(c4) | -latt_str(c4) | empty_carrier(c4) | upper_bounded_relstr(poset_of_lattice(c4)). [resolve(947,a,943,c)]. 10.59/10.80 Derived: -lattice(c4) | -latt_str(c4) | empty_carrier(c4) | with_infima_relstr(poset_of_lattice(c4)). [resolve(947,a,944,c)]. 10.59/10.80 Derived: -lattice(c4) | -latt_str(c4) | empty_carrier(c4) | with_suprema_relstr(poset_of_lattice(c4)). [resolve(947,a,945,c)]. 10.59/10.80 948 -latt_str(A) | empty_carrier(A) | -bounded_lattstr(A) | upper_bounded_semilattstr(A) # label(cc4_lattices) # label(axiom). [clausify(119)]. 10.59/10.80 Derived: -latt_str(A) | empty_carrier(A) | -bounded_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | upper_bounded_relstr(poset_of_lattice(A)). [resolve(948,d,943,c)]. 10.59/10.80 Derived: -latt_str(A) | empty_carrier(A) | -bounded_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)). [resolve(948,d,944,c)]. 10.59/10.80 Derived: -latt_str(A) | empty_carrier(A) | -bounded_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)). [resolve(948,d,945,c)]. 10.59/10.80 949 upper_bounded_semilattstr(c11) # label(rc11_lattices) # label(axiom). [clausify(169)]. 10.59/10.80 Derived: -lattice(c11) | -latt_str(c11) | empty_carrier(c11) | upper_bounded_relstr(poset_of_lattice(c11)). [resolve(949,a,943,c)]. 10.59/10.80 Derived: -lattice(c11) | -latt_str(c11) | empty_carrier(c11) | with_infima_relstr(poset_of_lattice(c11)). [resolve(949,a,944,c)]. 10.59/10.80 Derived: -lattice(c11) | -latt_str(c11) | empty_carrier(c11) | with_suprema_relstr(poset_of_lattice(c11)). [resolve(949,a,945,c)]. 10.59/10.80 950 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | upper_bounded_semilattstr(A) # label(cc5_lattices) # label(axiom). [clausify(291)]. 10.59/10.80 Derived: -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | upper_bounded_relstr(poset_of_lattice(A)). [resolve(950,d,943,c)]. 10.59/10.80 Derived: -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)). [resolve(950,d,944,c)]. 10.59/10.80 Derived: -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)). [resolve(950,d,945,c)]. 10.59/10.80 951 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | upper_bounded_semilattstr(A) # label(cc1_knaster) # label(axiom). [clausify(568)]. 10.59/10.80 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -empty_carrier(poset_of_lattice(A)). [resolve(951,e,939,c)]. 10.59/10.80 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | strict_rel_str(poset_of_lattice(A)). [resolve(951,e,940,c)]. 10.59/10.80 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | reflexive_relstr(poset_of_lattice(A)). [resolve(951,e,941,c)]. 11.30/11.43 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | antisymmetric_relstr(poset_of_lattice(A)). [resolve(951,e,942,c)]. 11.30/11.43 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | upper_bounded_relstr(poset_of_lattice(A)). [resolve(951,e,943,c)]. 11.30/11.43 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)). [resolve(951,e,944,c)]. 11.30/11.43 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)). [resolve(951,e,945,c)]. 11.30/11.43 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | transitive_relstr(poset_of_lattice(A)). [resolve(951,e,946,c)]. 11.30/11.43 952 upper_bounded_semilattstr(boole_lattice(A)) # label(fc3_lattice3) # label(axiom). [clausify(576)]. 11.30/11.43 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -empty_carrier(poset_of_lattice(boole_lattice(A))). [resolve(952,a,939,c)]. 11.30/11.43 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | strict_rel_str(poset_of_lattice(boole_lattice(A))). [resolve(952,a,940,c)]. 11.30/11.43 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | reflexive_relstr(poset_of_lattice(boole_lattice(A))). [resolve(952,a,941,c)]. 11.30/11.43 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | antisymmetric_relstr(poset_of_lattice(boole_lattice(A))). [resolve(952,a,942,c)]. 11.30/11.43 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | upper_bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(952,a,943,c)]. 11.30/11.43 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | with_infima_relstr(poset_of_lattice(boole_lattice(A))). [resolve(952,a,944,c)]. 11.30/11.43 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | with_suprema_relstr(poset_of_lattice(boole_lattice(A))). [resolve(952,a,945,c)]. 11.30/11.43 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | transitive_relstr(poset_of_lattice(boole_lattice(A))). [resolve(952,a,946,c)]. 11.30/11.43 953 upper_bounded_semilattstr(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(580)]. 11.30/11.43 954 -latt_str(A) | empty_carrier(A) | -upper_bounded_semilattstr(A) | -lower_bounded_semilattstr(A) | bounded_lattstr(A) # label(cc3_lattices) # label(axiom). [clausify(603)]. 11.30/11.43 Derived: -latt_str(c2) | empty_carrier(c2) | -lower_bounded_semilattstr(c2) | bounded_lattstr(c2). [resolve(954,c,938,a)]. 11.30/11.43 Derived: -latt_str(c4) | empty_carrier(c4) | -lower_bounded_semilattstr(c4) | bounded_lattstr(c4). [resolve(954,c,947,a)]. 11.30/11.43 Derived: -latt_str(c11) | empty_carrier(c11) | -lower_bounded_semilattstr(c11) | bounded_lattstr(c11). [resolve(954,c,949,a)]. 11.30/11.43 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | bounded_lattstr(A) | -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A). [resolve(954,c,950,d)]. 11.30/11.43 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | bounded_lattstr(A) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A). [resolve(954,c,951,e)]. 11.30/11.43 Derived: -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -lower_bounded_semilattstr(boole_lattice(A)) | bounded_lattstr(boole_lattice(A)). [resolve(954,c,952,a)]. 11.30/11.43 955 upper_bounded_semilattstr(c45) # label(rc12_lattices) # label(axiom). [clausify(750)]. 11.30/11.43 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | -empty_carrier(poset_of_lattice(c45)). [resolve(955,a,939,c)]. 14.77/14.93 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | strict_rel_str(poset_of_lattice(c45)). [resolve(955,a,940,c)]. 14.77/14.93 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | reflexive_relstr(poset_of_lattice(c45)). [resolve(955,a,941,c)]. 14.77/14.93 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | antisymmetric_relstr(poset_of_lattice(c45)). [resolve(955,a,942,c)]. 14.77/14.93 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | upper_bounded_relstr(poset_of_lattice(c45)). [resolve(955,a,943,c)]. 14.77/14.93 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | with_infima_relstr(poset_of_lattice(c45)). [resolve(955,a,944,c)]. 14.77/14.93 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | with_suprema_relstr(poset_of_lattice(c45)). [resolve(955,a,945,c)]. 14.77/14.93 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | transitive_relstr(poset_of_lattice(c45)). [resolve(955,a,946,c)]. 14.77/14.93 Derived: -latt_str(c45) | empty_carrier(c45) | -lower_bounded_semilattstr(c45) | bounded_lattstr(c45). [resolve(955,a,954,c)]. 14.77/14.93 956 meet_semilatt_str(c29) # label(existence_l1_lattices) # label(axiom). [clausify(432)]. 14.77/14.93 957 -meet_semilatt_str(A) | empty_carrier(A) | element(f8(A,B),the_carrier(A)) | -element(B,the_carrier(A)) | lower_bounded_semilattstr(A) # label(d13_lattices) # label(axiom). [clausify(12)]. 14.77/14.93 958 -meet_semilatt_str(A) | empty_carrier(A) | meet(A,B,f8(A,B)) != B | meet(A,f8(A,B),B) != B | -element(B,the_carrier(A)) | lower_bounded_semilattstr(A) # label(d13_lattices) # label(axiom). [clausify(12)]. 14.77/14.93 959 -meet_semilatt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | meet(A,f9(A),B) = f9(A) | -lower_bounded_semilattstr(A) # label(d13_lattices) # label(axiom). [clausify(12)]. 14.77/14.93 960 -meet_semilatt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | meet(A,B,f9(A)) = f9(A) | -lower_bounded_semilattstr(A) # label(d13_lattices) # label(axiom). [clausify(12)]. 14.77/14.93 961 -meet_semilatt_str(A) | empty_carrier(A) | element(f9(A),the_carrier(A)) | -lower_bounded_semilattstr(A) # label(d13_lattices) # label(axiom). [clausify(12)]. 14.77/14.93 962 -meet_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_meet(A),B,C) = meet(A,B,C) # label(d2_lattices) # label(axiom). [clausify(27)]. 14.77/14.93 963 -element(A,the_carrier(B)) | -element(C,the_carrier(B)) | -meet_semilatt_str(B) | -meet_commutative(B) | empty_carrier(B) | meet_commut(B,C,A) = meet_commut(B,A,C) # label(commutativity_k4_lattices) # label(axiom). [clausify(32)]. 14.77/14.93 964 -meet_commutative(A) | -meet_semilatt_str(A) | empty_carrier(A) | relation(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(49)]. 14.77/14.93 965 -meet_commutative(A) | -meet_semilatt_str(A) | empty_carrier(A) | function(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(49)]. 14.77/14.93 966 -meet_commutative(A) | -meet_semilatt_str(A) | empty_carrier(A) | v1_binop_1(the_L_meet(A),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(49)]. 14.77/14.93 967 -meet_commutative(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(fc4_lattice2) # label(axiom). [clausify(49)]. 14.77/14.93 968 -meet_commutative(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(fc4_lattice2) # label(axiom). [clausify(49)]. 14.77/14.93 969 -meet_semilatt_str(A) | function(the_L_meet(A)) # label(dt_u1_lattices) # label(axiom). [clausify(156)]. 14.77/14.93 970 -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(156)]. 14.77/14.93 971 -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(156)]. 14.77/14.93 972 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(295)]. 14.77/14.94 973 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(295)]. 14.77/14.94 974 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | element(f166(A,B),the_carrier(A)) # label(d16_lattices) # label(axiom). [clausify(295)]. 14.77/14.94 975 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | meet(A,B,f166(A,B)) != B | meet(A,f166(A,B),B) != B # label(d16_lattices) # label(axiom). [clausify(295)]. 14.77/14.94 976 empty_carrier(A) | -meet_semilatt_str(A) | element(bottom_of_semilattstr(A),the_carrier(A)) # label(dt_k5_lattices) # label(axiom). [clausify(311)]. 14.77/14.94 977 empty_carrier(A) | -meet_semilatt_str(A) | -meet_associative(A) | relation(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(327)]. 14.77/14.94 978 empty_carrier(A) | -meet_semilatt_str(A) | -meet_associative(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(327)]. 14.77/14.94 979 empty_carrier(A) | -meet_semilatt_str(A) | -meet_associative(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(327)]. 14.77/14.94 980 empty_carrier(A) | -meet_semilatt_str(A) | -meet_associative(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(327)]. 14.77/14.94 981 empty_carrier(A) | -meet_semilatt_str(A) | -meet_associative(A) | function(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(327)]. 14.77/14.94 982 empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -meet_semilatt_str(A) | -meet_commutative(A) | element(meet_commut(A,C,B),the_carrier(A)) # label(dt_k4_lattices) # label(axiom). [clausify(408)]. 14.77/14.94 Derived: empty_carrier(c29) | element(f8(c29,A),the_carrier(c29)) | -element(A,the_carrier(c29)) | lower_bounded_semilattstr(c29). [resolve(956,a,957,a)]. 14.77/14.94 Derived: empty_carrier(c29) | meet(c29,A,f8(c29,A)) != A | meet(c29,f8(c29,A),A) != A | -element(A,the_carrier(c29)) | lower_bounded_semilattstr(c29). [resolve(956,a,958,a)]. 14.77/14.94 Derived: empty_carrier(c29) | -element(A,the_carrier(c29)) | meet(c29,f9(c29),A) = f9(c29) | -lower_bounded_semilattstr(c29). [resolve(956,a,959,a)]. 14.77/14.94 Derived: empty_carrier(c29) | -element(A,the_carrier(c29)) | meet(c29,A,f9(c29)) = f9(c29) | -lower_bounded_semilattstr(c29). [resolve(956,a,960,a)]. 14.77/14.94 Derived: empty_carrier(c29) | element(f9(c29),the_carrier(c29)) | -lower_bounded_semilattstr(c29). [resolve(956,a,961,a)]. 14.77/14.94 Derived: empty_carrier(c29) | -element(A,the_carrier(c29)) | -element(B,the_carrier(c29)) | apply_binary_as_element(the_carrier(c29),the_carrier(c29),the_carrier(c29),the_L_meet(c29),A,B) = meet(c29,A,B). [resolve(956,a,962,a)]. 14.77/14.94 Derived: -element(A,the_carrier(c29)) | -element(B,the_carrier(c29)) | -meet_commutative(c29) | empty_carrier(c29) | meet_commut(c29,B,A) = meet_commut(c29,A,B). [resolve(956,a,963,c)]. 14.77/14.94 Derived: -meet_commutative(c29) | empty_carrier(c29) | relation(the_L_meet(c29)). [resolve(956,a,964,b)]. 14.77/14.94 Derived: -meet_commutative(c29) | empty_carrier(c29) | function(the_L_meet(c29)). [resolve(956,a,965,b)]. 14.77/14.94 Derived: -meet_commutative(c29) | empty_carrier(c29) | v1_binop_1(the_L_meet(c29),the_carrier(c29)). [resolve(956,a,966,b)]. 14.77/14.94 Derived: -meet_commutative(c29) | empty_carrier(c29) | v1_partfun1(the_L_meet(c29),cartesian_product2(the_carrier(c29),the_carrier(c29)),the_carrier(c29)). [resolve(956,a,967,b)]. 14.77/14.94 Derived: -meet_commutative(c29) | empty_carrier(c29) | quasi_total(the_L_meet(c29),cartesian_product2(the_carrier(c29),the_carrier(c29)),the_carrier(c29)). [resolve(956,a,968,b)]. 14.77/14.94 Derived: function(the_L_meet(c29)). [resolve(956,a,969,a)]. 14.77/14.94 Derived: relation_of2_as_subset(the_L_meet(c29),cartesian_product2(the_carrier(c29),the_carrier(c29)),the_carrier(c29)). [resolve(956,a,970,a)]. 16.26/16.40 Derived: quasi_total(the_L_meet(c29),cartesian_product2(the_carrier(c29),the_carrier(c29)),the_carrier(c29)). [resolve(956,a,971,a)]. 16.26/16.40 Derived: empty_carrier(c29) | -lower_bounded_semilattstr(c29) | -element(A,the_carrier(c29)) | bottom_of_semilattstr(c29) != A | -element(B,the_carrier(c29)) | meet(c29,A,B) = A. [resolve(956,a,972,b)]. 16.26/16.40 Derived: empty_carrier(c29) | -lower_bounded_semilattstr(c29) | -element(A,the_carrier(c29)) | bottom_of_semilattstr(c29) != A | -element(B,the_carrier(c29)) | meet(c29,B,A) = A. [resolve(956,a,973,b)]. 16.26/16.40 Derived: empty_carrier(c29) | -lower_bounded_semilattstr(c29) | -element(A,the_carrier(c29)) | bottom_of_semilattstr(c29) = A | element(f166(c29,A),the_carrier(c29)). [resolve(956,a,974,b)]. 16.26/16.40 Derived: empty_carrier(c29) | -lower_bounded_semilattstr(c29) | -element(A,the_carrier(c29)) | bottom_of_semilattstr(c29) = A | meet(c29,A,f166(c29,A)) != A | meet(c29,f166(c29,A),A) != A. [resolve(956,a,975,b)]. 16.26/16.40 Derived: empty_carrier(c29) | element(bottom_of_semilattstr(c29),the_carrier(c29)). [resolve(956,a,976,b)]. 16.26/16.40 Derived: empty_carrier(c29) | -meet_associative(c29) | relation(the_L_meet(c29)). [resolve(956,a,977,b)]. 16.26/16.40 Derived: empty_carrier(c29) | -meet_associative(c29) | v2_binop_1(the_L_meet(c29),the_carrier(c29)). [resolve(956,a,978,b)]. 16.26/16.40 Derived: empty_carrier(c29) | -meet_associative(c29) | v1_partfun1(the_L_meet(c29),cartesian_product2(the_carrier(c29),the_carrier(c29)),the_carrier(c29)). [resolve(956,a,979,b)]. 16.26/16.40 Derived: empty_carrier(c29) | -element(A,the_carrier(c29)) | -element(B,the_carrier(c29)) | -meet_commutative(c29) | element(meet_commut(c29,B,A),the_carrier(c29)). [resolve(956,a,982,d)]. 16.26/16.40 983 -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | empty_carrier(A) | element(meet(A,C,B),the_carrier(A)) # label(dt_k2_lattices) # label(axiom). [clausify(487)]. 16.26/16.40 Derived: -element(A,the_carrier(c29)) | -element(B,the_carrier(c29)) | empty_carrier(c29) | element(meet(c29,B,A),the_carrier(c29)). [resolve(983,a,956,a)]. 16.26/16.40 984 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(664)]. 16.26/16.40 Derived: -latt_str(A) | empty_carrier(A) | element(f8(A,B),the_carrier(A)) | -element(B,the_carrier(A)) | lower_bounded_semilattstr(A). [resolve(984,b,957,a)]. 16.26/16.40 Derived: -latt_str(A) | empty_carrier(A) | meet(A,B,f8(A,B)) != B | meet(A,f8(A,B),B) != B | -element(B,the_carrier(A)) | lower_bounded_semilattstr(A). [resolve(984,b,958,a)]. 16.26/16.40 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | meet(A,f9(A),B) = f9(A) | -lower_bounded_semilattstr(A). [resolve(984,b,959,a)]. 16.26/16.40 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | meet(A,B,f9(A)) = f9(A) | -lower_bounded_semilattstr(A). [resolve(984,b,960,a)]. 16.26/16.40 Derived: -latt_str(A) | empty_carrier(A) | element(f9(A),the_carrier(A)) | -lower_bounded_semilattstr(A). [resolve(984,b,961,a)]. 16.26/16.40 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(984,b,962,a)]. 16.26/16.40 Derived: -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -meet_commutative(A) | empty_carrier(A) | meet_commut(A,C,B) = meet_commut(A,B,C). [resolve(984,b,963,c)]. 16.26/16.40 Derived: -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | relation(the_L_meet(A)). [resolve(984,b,964,b)]. 16.26/16.40 Derived: -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | function(the_L_meet(A)). [resolve(984,b,965,b)]. 16.26/16.40 Derived: -latt_str(A) | -meet_commutative(A) | empty_carrier(A) | v1_binop_1(the_L_meet(A),the_carrier(A)). [resolve(984,b,966,b)]. 16.26/16.40 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(984,b,967,b)]. 16.26/16.40 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(984,b,968,b)]. 20.31/20.46 Derived: -latt_str(A) | function(the_L_meet(A)). [resolve(984,b,969,a)]. 20.31/20.46 Derived: -latt_str(A) | relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(984,b,970,a)]. 20.31/20.46 Derived: -latt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(984,b,971,a)]. 20.31/20.46 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(984,b,972,b)]. 20.31/20.46 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(984,b,973,b)]. 20.31/20.46 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | element(f166(A,B),the_carrier(A)). [resolve(984,b,974,b)]. 20.31/20.46 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | meet(A,B,f166(A,B)) != B | meet(A,f166(A,B),B) != B. [resolve(984,b,975,b)]. 20.31/20.46 Derived: -latt_str(A) | empty_carrier(A) | element(bottom_of_semilattstr(A),the_carrier(A)). [resolve(984,b,976,b)]. 20.31/20.46 Derived: -latt_str(A) | empty_carrier(A) | -meet_associative(A) | relation(the_L_meet(A)). [resolve(984,b,977,b)]. 20.31/20.46 Derived: -latt_str(A) | empty_carrier(A) | -meet_associative(A) | v2_binop_1(the_L_meet(A),the_carrier(A)). [resolve(984,b,978,b)]. 20.31/20.46 Derived: -latt_str(A) | empty_carrier(A) | -meet_associative(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(984,b,979,b)]. 20.31/20.46 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -meet_commutative(A) | element(meet_commut(A,C,B),the_carrier(A)). [resolve(984,b,982,d)]. 20.31/20.46 Derived: -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | empty_carrier(A) | element(meet(A,C,B),the_carrier(A)). [resolve(984,b,983,a)]. 20.31/20.46 985 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(688)]. 20.31/20.46 Derived: one_sorted_str(c29). [resolve(985,a,956,a)]. 20.31/20.46 Derived: one_sorted_str(A) | -latt_str(A). [resolve(985,a,984,b)]. 20.31/20.46 986 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet_commut(A,C,B) = meet(A,C,B) # label(redefinition_k4_lattices) # label(axiom). [clausify(710)]. 20.31/20.46 Derived: empty_carrier(c29) | -meet_commutative(c29) | -element(A,the_carrier(c29)) | -element(B,the_carrier(c29)) | meet_commut(c29,B,A) = meet(c29,B,A). [resolve(986,c,956,a)]. 20.31/20.46 Derived: empty_carrier(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet_commut(A,C,B) = meet(A,C,B) | -latt_str(A). [resolve(986,c,984,b)]. 20.31/20.46 987 empty_carrier(A) | -meet_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | -below(A,C,B) | below_refl(A,C,B) # label(redefinition_r3_lattices) # label(axiom). [clausify(74)]. 20.31/20.46 988 meet_absorbing(c2) # label(rc13_lattices) # label(axiom). [clausify(22)]. 20.31/20.46 Derived: empty_carrier(c2) | -latt_str(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | -join_absorbing(c2) | -meet_commutative(c2) | -below(c2,B,A) | below_refl(c2,B,A). [resolve(987,b,988,a)]. 20.31/20.46 989 empty_carrier(A) | -meet_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | below(A,C,B) | -below_refl(A,C,B) # label(redefinition_r3_lattices) # label(axiom). [clausify(74)]. 20.31/20.46 Derived: empty_carrier(c2) | -latt_str(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | -join_absorbing(c2) | -meet_commutative(c2) | below(c2,B,A) | -below_refl(c2,B,A). [resolve(989,b,988,a)]. 20.31/20.46 990 meet_absorbing(c4) # label(rc10_lattices) # label(axiom). [clausify(80)]. 20.31/20.46 Derived: empty_carrier(c4) | -latt_str(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | -join_absorbing(c4) | -meet_commutative(c4) | -below(c4,B,A) | below_refl(c4,B,A). [resolve(990,a,987,b)]. 20.31/20.48 Derived: empty_carrier(c4) | -latt_str(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | -join_absorbing(c4) | -meet_commutative(c4) | below(c4,B,A) | -below_refl(c4,B,A). [resolve(990,a,989,b)]. 20.31/20.48 991 empty_carrier(A) | -latt_str(A) | -meet_absorbing(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,meet(A,B,C),C) = C # label(d8_lattices) # label(axiom). [clausify(113)]. 20.31/20.48 Derived: empty_carrier(c2) | -latt_str(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | join(c2,meet(c2,A,B),B) = B. [resolve(991,c,988,a)]. 20.31/20.48 Derived: empty_carrier(c4) | -latt_str(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | join(c4,meet(c4,A,B),B) = B. [resolve(991,c,990,a)]. 20.31/20.48 992 empty_carrier(A) | -latt_str(A) | meet_absorbing(A) | element(f62(A),the_carrier(A)) # label(d8_lattices) # label(axiom). [clausify(113)]. 20.31/20.48 Derived: empty_carrier(A) | -latt_str(A) | element(f62(A),the_carrier(A)) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | -below(A,C,B) | below_refl(A,C,B). [resolve(992,c,987,b)]. 20.31/20.48 Derived: empty_carrier(A) | -latt_str(A) | element(f62(A),the_carrier(A)) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | below(A,C,B) | -below_refl(A,C,B). [resolve(992,c,989,b)]. 20.31/20.48 Derived: empty_carrier(A) | -latt_str(A) | element(f62(A),the_carrier(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(992,c,991,c)]. 20.31/20.48 993 empty_carrier(A) | -latt_str(A) | meet_absorbing(A) | element(f63(A),the_carrier(A)) # label(d8_lattices) # label(axiom). [clausify(113)]. 20.31/20.48 Derived: empty_carrier(A) | -latt_str(A) | element(f63(A),the_carrier(A)) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | -below(A,C,B) | below_refl(A,C,B). [resolve(993,c,987,b)]. 20.31/20.48 Derived: empty_carrier(A) | -latt_str(A) | element(f63(A),the_carrier(A)) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | below(A,C,B) | -below_refl(A,C,B). [resolve(993,c,989,b)]. 20.31/20.48 Derived: empty_carrier(A) | -latt_str(A) | element(f63(A),the_carrier(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(993,c,991,c)]. 20.31/20.48 994 empty_carrier(A) | -latt_str(A) | meet_absorbing(A) | join(A,meet(A,f62(A),f63(A)),f63(A)) != f63(A) # label(d8_lattices) # label(axiom). [clausify(113)]. 20.31/20.48 Derived: empty_carrier(A) | -latt_str(A) | join(A,meet(A,f62(A),f63(A)),f63(A)) != f63(A) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | -below(A,C,B) | below_refl(A,C,B). [resolve(994,c,987,b)]. 20.31/20.48 Derived: empty_carrier(A) | -latt_str(A) | join(A,meet(A,f62(A),f63(A)),f63(A)) != f63(A) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | below(A,C,B) | -below_refl(A,C,B). [resolve(994,c,989,b)]. 20.31/20.48 Derived: empty_carrier(A) | -latt_str(A) | join(A,meet(A,f62(A),f63(A)),f63(A)) != f63(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(994,c,991,c)]. 20.31/20.48 995 meet_absorbing(c11) # label(rc11_lattices) # label(axiom). [clausify(169)]. 20.31/20.48 Derived: empty_carrier(c11) | -latt_str(c11) | -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | -join_absorbing(c11) | -meet_commutative(c11) | -below(c11,B,A) | below_refl(c11,B,A). [resolve(995,a,987,b)]. 20.31/20.48 Derived: empty_carrier(c11) | -latt_str(c11) | -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | -join_absorbing(c11) | -meet_commutative(c11) | below(c11,B,A) | -below_refl(c11,B,A). [resolve(995,a,989,b)]. 20.39/20.59 Derived: empty_carrier(c11) | -latt_str(c11) | -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | join(c11,meet(c11,A,B),B) = B. [resolve(995,a,991,c)]. 20.39/20.59 996 -latt_str(A) | -lattice(A) | -distributive_lattstr(A) | empty_carrier(A) | meet_absorbing(A) # label(cc7_lattices) # label(axiom). [clausify(324)]. 20.39/20.59 Derived: -latt_str(A) | -lattice(A) | -distributive_lattstr(A) | empty_carrier(A) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | -below(A,C,B) | below_refl(A,C,B). [resolve(996,e,987,b)]. 20.39/20.59 Derived: -latt_str(A) | -lattice(A) | -distributive_lattstr(A) | empty_carrier(A) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | below(A,C,B) | -below_refl(A,C,B). [resolve(996,e,989,b)]. 20.39/20.59 Derived: -latt_str(A) | -lattice(A) | -distributive_lattstr(A) | empty_carrier(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(996,e,991,c)]. 20.39/20.59 997 -latt_str(A) | -lattice(A) | empty_carrier(A) | meet_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(332)]. 20.39/20.59 Derived: -latt_str(A) | -lattice(A) | empty_carrier(A) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | -below(A,C,B) | below_refl(A,C,B). [resolve(997,d,987,b)]. 20.39/20.59 Derived: -latt_str(A) | -lattice(A) | empty_carrier(A) | empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_absorbing(A) | -meet_commutative(A) | below(A,C,B) | -below_refl(A,C,B). [resolve(997,d,989,b)]. 20.39/20.59 Derived: -latt_str(A) | -lattice(A) | empty_carrier(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(997,d,991,c)]. 20.39/20.59 998 meet_absorbing(boole_lattice(A)) # label(fc2_lattice3) # label(axiom). [clausify(376)]. 20.39/20.59 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_absorbing(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -below(boole_lattice(A),C,B) | below_refl(boole_lattice(A),C,B). [resolve(998,a,987,b)]. 20.39/20.59 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_absorbing(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | below(boole_lattice(A),C,B) | -below_refl(boole_lattice(A),C,B). [resolve(998,a,989,b)]. 20.39/20.59 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(998,a,991,c)]. 20.39/20.59 999 -latt_str(A) | -join_commutative(A) | -meet_commutative(A) | -meet_associative(A) | -join_absorbing(A) | -meet_absorbing(A) | -join_associative(A) | empty_carrier(A) | lattice(A) # label(cc2_lattices) # label(axiom). [clausify(409)]. 20.39/20.59 Derived: -latt_str(c2) | -join_commutative(c2) | -meet_commutative(c2) | -meet_associative(c2) | -join_absorbing(c2) | -join_associative(c2) | empty_carrier(c2) | lattice(c2). [resolve(999,f,988,a)]. 20.39/20.59 Derived: -latt_str(c4) | -join_commutative(c4) | -meet_commutative(c4) | -meet_associative(c4) | -join_absorbing(c4) | -join_associative(c4) | empty_carrier(c4) | lattice(c4). [resolve(999,f,990,a)]. 20.39/20.59 Derived: -latt_str(A) | -join_commutative(A) | -meet_commutative(A) | -meet_associative(A) | -join_absorbing(A) | -join_associative(A) | empty_carrier(A) | lattice(A) | empty_carrier(A) | -latt_str(A) | element(f62(A),the_carrier(A)). [resolve(999,f,992,c)]. 20.39/20.59 Derived: -latt_str(A) | -join_commutative(A) | -meet_commutative(A) | -meet_associative(A) | -join_absorbing(A) | -join_associative(A) | empty_carrier(A) | lattice(A) | empty_carrier(A) | -latt_str(A) | element(f63(A),the_carrier(A)). [resolve(999,f,993,c)]. 21.38/21.51 Derived: -latt_str(A) | -join_commutative(A) | -meet_commutative(A) | -meet_associative(A) | -join_absorbing(A) | -join_associative(A) | empty_carrier(A) | lattice(A) | empty_carrier(A) | -latt_str(A) | join(A,meet(A,f62(A),f63(A)),f63(A)) != f63(A). [resolve(999,f,994,c)]. 21.38/21.51 Derived: -latt_str(c11) | -join_commutative(c11) | -meet_commutative(c11) | -meet_associative(c11) | -join_absorbing(c11) | -join_associative(c11) | empty_carrier(c11) | lattice(c11). [resolve(999,f,995,a)]. 21.38/21.51 1000 -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_refl(B,A,A) # label(reflexivity_r3_lattices) # label(axiom). [clausify(455)]. 21.38/21.51 Derived: -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | -latt_str(c2) | -join_absorbing(c2) | -meet_commutative(c2) | empty_carrier(c2) | below_refl(c2,A,A). [resolve(1000,e,988,a)]. 21.38/21.51 Derived: -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | -latt_str(c4) | -join_absorbing(c4) | -meet_commutative(c4) | empty_carrier(c4) | below_refl(c4,A,A). [resolve(1000,e,990,a)]. 21.38/21.51 Derived: -element(A,the_carrier(B)) | -element(C,the_carrier(B)) | -latt_str(B) | -join_absorbing(B) | -meet_commutative(B) | empty_carrier(B) | below_refl(B,A,A) | empty_carrier(B) | -latt_str(B) | element(f62(B),the_carrier(B)). [resolve(1000,e,992,c)]. 21.38/21.51 Derived: -element(A,the_carrier(B)) | -element(C,the_carrier(B)) | -latt_str(B) | -join_absorbing(B) | -meet_commutative(B) | empty_carrier(B) | below_refl(B,A,A) | empty_carrier(B) | -latt_str(B) | element(f63(B),the_carrier(B)). [resolve(1000,e,993,c)]. 21.38/21.51 Derived: -element(A,the_carrier(B)) | -element(C,the_carrier(B)) | -latt_str(B) | -join_absorbing(B) | -meet_commutative(B) | empty_carrier(B) | below_refl(B,A,A) | empty_carrier(B) | -latt_str(B) | join(B,meet(B,f62(B),f63(B)),f63(B)) != f63(B). [resolve(1000,e,994,c)]. 21.38/21.51 Derived: -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | -latt_str(c11) | -join_absorbing(c11) | -meet_commutative(c11) | empty_carrier(c11) | below_refl(c11,A,A). [resolve(1000,e,995,a)]. 21.38/21.51 Derived: -element(A,the_carrier(B)) | -element(C,the_carrier(B)) | -latt_str(B) | -join_absorbing(B) | -meet_commutative(B) | empty_carrier(B) | below_refl(B,A,A) | -latt_str(B) | -lattice(B) | -distributive_lattstr(B) | empty_carrier(B). [resolve(1000,e,996,e)]. 21.38/21.51 Derived: -element(A,the_carrier(B)) | -element(C,the_carrier(B)) | -latt_str(B) | -join_absorbing(B) | -meet_commutative(B) | empty_carrier(B) | below_refl(B,A,A) | -latt_str(B) | -lattice(B) | empty_carrier(B). [resolve(1000,e,997,d)]. 21.38/21.51 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_refl(boole_lattice(B),A,A). [resolve(1000,e,998,a)]. 21.38/21.51 1001 -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(521)]. 21.38/21.51 Derived: -latt_str(c2) | -meet_commutative(c2) | empty_carrier(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | below(c2,meet_commut(c2,A,B),A). [resolve(1001,a,988,a)]. 21.38/21.51 Derived: -latt_str(c4) | -meet_commutative(c4) | empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | below(c4,meet_commut(c4,A,B),A). [resolve(1001,a,990,a)]. 21.38/21.51 Derived: -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) | empty_carrier(A) | -latt_str(A) | element(f62(A),the_carrier(A)). [resolve(1001,a,992,c)]. 21.38/21.51 Derived: -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) | empty_carrier(A) | -latt_str(A) | element(f63(A),the_carrier(A)). [resolve(1001,a,993,c)]. 22.09/22.23 Derived: -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) | empty_carrier(A) | -latt_str(A) | join(A,meet(A,f62(A),f63(A)),f63(A)) != f63(A). [resolve(1001,a,994,c)]. 22.09/22.23 Derived: -latt_str(c11) | -meet_commutative(c11) | empty_carrier(c11) | -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | below(c11,meet_commut(c11,A,B),A). [resolve(1001,a,995,a)]. 22.09/22.23 Derived: -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) | -latt_str(A) | -lattice(A) | -distributive_lattstr(A) | empty_carrier(A). [resolve(1001,a,996,e)]. 22.09/22.23 Derived: -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) | -latt_str(A) | -lattice(A) | empty_carrier(A). [resolve(1001,a,997,d)]. 22.09/22.23 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(1001,a,998,a)]. 22.09/22.23 1002 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | meet_absorbing(A) # label(cc1_knaster) # label(axiom). [clausify(568)]. 22.09/22.23 1003 meet_absorbing(boole_lattice(A)) # label(fc3_lattice3) # label(axiom). [clausify(576)]. 22.09/22.23 1004 meet_absorbing(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(580)]. 22.09/22.23 1005 meet_absorbing(c40) # label(rc9_lattices) # label(axiom). [clausify(610)]. 22.09/22.23 Derived: empty_carrier(c40) | -latt_str(c40) | -element(A,the_carrier(c40)) | -element(B,the_carrier(c40)) | -join_absorbing(c40) | -meet_commutative(c40) | -below(c40,B,A) | below_refl(c40,B,A). [resolve(1005,a,987,b)]. 22.09/22.23 Derived: empty_carrier(c40) | -latt_str(c40) | -element(A,the_carrier(c40)) | -element(B,the_carrier(c40)) | -join_absorbing(c40) | -meet_commutative(c40) | below(c40,B,A) | -below_refl(c40,B,A). [resolve(1005,a,989,b)]. 22.09/22.23 Derived: empty_carrier(c40) | -latt_str(c40) | -element(A,the_carrier(c40)) | -element(B,the_carrier(c40)) | join(c40,meet(c40,A,B),B) = B. [resolve(1005,a,991,c)]. 22.09/22.23 Derived: -latt_str(c40) | -join_commutative(c40) | -meet_commutative(c40) | -meet_associative(c40) | -join_absorbing(c40) | -join_associative(c40) | empty_carrier(c40) | lattice(c40). [resolve(1005,a,999,f)]. 22.09/22.23 Derived: -element(A,the_carrier(c40)) | -element(B,the_carrier(c40)) | -latt_str(c40) | -join_absorbing(c40) | -meet_commutative(c40) | empty_carrier(c40) | below_refl(c40,A,A). [resolve(1005,a,1000,e)]. 22.09/22.23 Derived: -latt_str(c40) | -meet_commutative(c40) | empty_carrier(c40) | -element(A,the_carrier(c40)) | -element(B,the_carrier(c40)) | below(c40,meet_commut(c40,A,B),A). [resolve(1005,a,1001,a)]. 22.09/22.23 1006 meet_absorbing(c45) # label(rc12_lattices) # label(axiom). [clausify(750)]. 22.09/22.23 Derived: empty_carrier(c45) | -latt_str(c45) | -element(A,the_carrier(c45)) | -element(B,the_carrier(c45)) | -join_absorbing(c45) | -meet_commutative(c45) | -below(c45,B,A) | below_refl(c45,B,A). [resolve(1006,a,987,b)]. 22.09/22.23 Derived: empty_carrier(c45) | -latt_str(c45) | -element(A,the_carrier(c45)) | -element(B,the_carrier(c45)) | -join_absorbing(c45) | -meet_commutative(c45) | below(c45,B,A) | -below_refl(c45,B,A). [resolve(1006,a,989,b)]. 22.09/22.23 Derived: empty_carrier(c45) | -latt_str(c45) | -element(A,the_carrier(c45)) | -element(B,the_carrier(c45)) | join(c45,meet(c45,A,B),B) = B. [resolve(1006,a,991,c)]. 22.09/22.23 Derived: -latt_str(c45) | -join_commutative(c45) | -meet_commutative(c45) | -meet_associative(c45) | -join_absorbing(c45) | -join_associative(c45) | empty_carrier(c45) | lattice(c45). [resolve(1006,a,999,f)]. 22.09/22.23 Derived: -element(A,the_carrier(c45)) | -element(B,the_carrier(c45)) | -latt_str(c45) | -join_absorbing(c45) | -meet_commutative(c45) | empty_carrier(c45) | below_refl(c45,A,A). [resolve(1006,a,1000,e)]. 22.09/22.23 Derived: -latt_str(c45) | -meet_commutative(c45) | empty_carrier(c45) | -element(A,the_carrier(c45)) | -element(B,the_carrier(c45)) | below(c45,meet_commut(c45,A,B),A). [resolve(1006,a,1001,a)]. 35.58/35.80 1007 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | bounded_lattstr(A) # label(cc5_lattices) # label(axiom). [clausify(291)]. 35.58/35.80 1008 boolean_lattstr(c2) # label(rc13_lattices) # label(axiom). [clausify(22)]. 35.58/35.80 Derived: -latt_str(c2) | empty_carrier(c2) | bounded_lattstr(c2). [resolve(1007,c,1008,a)]. 35.58/35.80 1009 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | complemented_lattstr(A) # label(cc5_lattices) # label(axiom). [clausify(291)]. 35.58/35.80 Derived: -latt_str(c2) | empty_carrier(c2) | complemented_lattstr(c2). [resolve(1009,c,1008,a)]. 35.58/35.80 1010 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | lower_bounded_semilattstr(A) # label(cc5_lattices) # label(axiom). [clausify(291)]. 35.58/35.80 Derived: -latt_str(c2) | empty_carrier(c2) | lower_bounded_semilattstr(c2). [resolve(1010,c,1008,a)]. 35.58/35.80 1011 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | distributive_lattstr(A) # label(cc5_lattices) # label(axiom). [clausify(291)]. 35.58/35.80 Derived: -latt_str(c2) | empty_carrier(c2) | distributive_lattstr(c2). [resolve(1011,c,1008,a)]. 35.58/35.80 1012 -latt_str(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | -distributive_lattstr(A) | empty_carrier(A) | boolean_lattstr(A) # label(cc6_lattices) # label(axiom). [clausify(380)]. 35.58/35.80 Derived: -latt_str(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | -distributive_lattstr(A) | empty_carrier(A) | -latt_str(A) | empty_carrier(A) | lower_bounded_semilattstr(A). [resolve(1012,f,1010,c)]. 35.58/35.80 1013 boolean_lattstr(boole_lattice(A)) # label(fc3_lattice3) # label(axiom). [clausify(576)]. 35.58/35.80 1014 boolean_lattstr(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(580)]. 35.58/35.80 Derived: -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | bounded_lattstr(boole_lattice(A)). [resolve(1014,a,1007,c)]. 35.58/35.80 Derived: -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | distributive_lattstr(boole_lattice(A)). [resolve(1014,a,1011,c)]. 35.58/35.80 1015 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | upper_bounded_relstr(poset_of_lattice(A)). [resolve(950,d,943,c)]. 35.58/35.80 Derived: -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | upper_bounded_relstr(poset_of_lattice(c2)). [resolve(1015,c,1008,a)]. 35.58/35.80 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | upper_bounded_relstr(poset_of_lattice(A)) | -latt_str(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | -distributive_lattstr(A) | empty_carrier(A). [resolve(1015,c,1012,f)]. 35.58/35.80 1016 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)). [resolve(950,d,944,c)]. 35.58/35.80 Derived: -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | with_infima_relstr(poset_of_lattice(c2)). [resolve(1016,c,1008,a)]. 35.58/35.80 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)) | -latt_str(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | -distributive_lattstr(A) | empty_carrier(A). [resolve(1016,c,1012,f)]. 35.58/35.80 1017 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)). [resolve(950,d,945,c)]. 35.58/35.80 Derived: -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | with_suprema_relstr(poset_of_lattice(c2)). [resolve(1017,c,1008,a)]. 35.58/35.80 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)) | -latt_str(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | -distributive_lattstr(A) | empty_carrier(A). [resolve(1017,c,1012,f)]. 35.58/35.80 1018 -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | bounded_lattstr(A) | -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A). [resolve(954,c,950,d)]. 35.58/35.80 1019 -latt_str(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | -distributive_lattstr(A) | empty_carrier(A) | -latt_str(A) | empty_carrier(A) | lower_bounded_semilattstr(A). [resolve(1012,f,1010,c)]. 35.68/35.81 1020 complemented_lattstr(c2) # label(rc13_lattices) # label(axiom). [clausify(22)]. 35.68/35.81 1021 complemented_lattstr(boole_lattice(A)) # label(fc3_lattice3) # label(axiom). [clausify(576)]. 35.68/35.81 1022 complemented_lattstr(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(580)]. 35.68/35.81 1023 complemented_lattstr(c45) # label(rc12_lattices) # label(axiom). [clausify(750)]. 35.68/35.81 1024 -latt_str(c2) | empty_carrier(c2) | complemented_lattstr(c2). [resolve(1009,c,1008,a)]. 35.68/35.81 Derived: -latt_str(c2) | -bounded_lattstr(c2) | -distributive_lattstr(c2) | empty_carrier(c2) | -latt_str(c2) | empty_carrier(c2) | lower_bounded_semilattstr(c2). [resolve(1019,c,1020,a)]. 35.68/35.81 Derived: -latt_str(boole_lattice(A)) | -bounded_lattstr(boole_lattice(A)) | -distributive_lattstr(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | lower_bounded_semilattstr(boole_lattice(A)). [resolve(1019,c,1021,a)]. 35.68/35.81 Derived: -latt_str(c45) | -bounded_lattstr(c45) | -distributive_lattstr(c45) | empty_carrier(c45) | -latt_str(c45) | empty_carrier(c45) | lower_bounded_semilattstr(c45). [resolve(1019,c,1023,a)]. 35.68/35.81 1025 -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | upper_bounded_relstr(poset_of_lattice(A)) | -latt_str(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | -distributive_lattstr(A) | empty_carrier(A). [resolve(1015,c,1012,f)]. 35.68/35.81 Derived: -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | upper_bounded_relstr(poset_of_lattice(c2)) | -latt_str(c2) | -bounded_lattstr(c2) | -distributive_lattstr(c2) | empty_carrier(c2). [resolve(1025,i,1020,a)]. 35.68/35.81 Derived: -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | upper_bounded_relstr(poset_of_lattice(boole_lattice(A))) | -latt_str(boole_lattice(A)) | -bounded_lattstr(boole_lattice(A)) | -distributive_lattstr(boole_lattice(A)) | empty_carrier(boole_lattice(A)). [resolve(1025,i,1021,a)]. 35.68/35.81 Derived: -latt_str(c45) | empty_carrier(c45) | -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | upper_bounded_relstr(poset_of_lattice(c45)) | -latt_str(c45) | -bounded_lattstr(c45) | -distributive_lattstr(c45) | empty_carrier(c45). [resolve(1025,i,1023,a)]. 35.68/35.81 1026 -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)) | -latt_str(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | -distributive_lattstr(A) | empty_carrier(A). [resolve(1016,c,1012,f)]. 35.68/35.81 Derived: -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | with_infima_relstr(poset_of_lattice(c2)) | -latt_str(c2) | -bounded_lattstr(c2) | -distributive_lattstr(c2) | empty_carrier(c2). [resolve(1026,i,1020,a)]. 35.68/35.81 Derived: -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | with_infima_relstr(poset_of_lattice(boole_lattice(A))) | -latt_str(boole_lattice(A)) | -bounded_lattstr(boole_lattice(A)) | -distributive_lattstr(boole_lattice(A)) | empty_carrier(boole_lattice(A)). [resolve(1026,i,1021,a)]. 35.68/35.81 Derived: -latt_str(c45) | empty_carrier(c45) | -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | with_infima_relstr(poset_of_lattice(c45)) | -latt_str(c45) | -bounded_lattstr(c45) | -distributive_lattstr(c45) | empty_carrier(c45). [resolve(1026,i,1023,a)]. 35.68/35.81 1027 -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)) | -latt_str(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | -distributive_lattstr(A) | empty_carrier(A). [resolve(1017,c,1012,f)]. 35.68/35.81 Derived: -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | with_suprema_relstr(poset_of_lattice(c2)) | -latt_str(c2) | -bounded_lattstr(c2) | -distributive_lattstr(c2) | empty_carrier(c2). [resolve(1027,i,1020,a)]. 35.97/36.14 Derived: -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | with_suprema_relstr(poset_of_lattice(boole_lattice(A))) | -latt_str(boole_lattice(A)) | -bounded_lattstr(boole_lattice(A)) | -distributive_lattstr(boole_lattice(A)) | empty_carrier(boole_lattice(A)). [resolve(1027,i,1021,a)]. 35.97/36.14 Derived: -latt_str(c45) | empty_carrier(c45) | -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | with_suprema_relstr(poset_of_lattice(c45)) | -latt_str(c45) | -bounded_lattstr(c45) | -distributive_lattstr(c45) | empty_carrier(c45). [resolve(1027,i,1023,a)]. 35.97/36.14 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(161)]. 35.97/36.14 1029 strict_latt_str(c2) # label(rc13_lattices) # label(axiom). [clausify(22)]. 35.97/36.14 1030 strict_latt_str(c4) # label(rc10_lattices) # label(axiom). [clausify(80)]. 35.97/36.14 Derived: -latt_str(c2) | latt_str_of(the_carrier(c2),the_L_join(c2),the_L_meet(c2)) = c2. [resolve(1028,b,1029,a)]. 35.97/36.14 Derived: -latt_str(c4) | latt_str_of(the_carrier(c4),the_L_join(c4),the_L_meet(c4)) = c4. [resolve(1028,b,1030,a)]. 35.97/36.14 1031 strict_latt_str(c11) # label(rc11_lattices) # label(axiom). [clausify(169)]. 35.97/36.14 Derived: -latt_str(c11) | latt_str_of(the_carrier(c11),the_L_join(c11),the_L_meet(c11)) = c11. [resolve(1031,a,1028,b)]. 35.97/36.14 1032 -strict_latt_str(A) | -latt_str(A) | powerset(B) != the_carrier(A) | element(f101(B,A),powerset(B)) | boole_lattice(B) = A # label(d1_lattice3) # label(axiom). [clausify(207)]. 35.97/36.14 Derived: -latt_str(c2) | powerset(A) != the_carrier(c2) | element(f101(A,c2),powerset(A)) | boole_lattice(A) = c2. [resolve(1032,a,1029,a)]. 35.97/36.14 Derived: -latt_str(c4) | powerset(A) != the_carrier(c4) | element(f101(A,c4),powerset(A)) | boole_lattice(A) = c4. [resolve(1032,a,1030,a)]. 35.97/36.14 Derived: -latt_str(c11) | powerset(A) != the_carrier(c11) | element(f101(A,c11),powerset(A)) | boole_lattice(A) = c11. [resolve(1032,a,1031,a)]. 35.97/36.14 1033 -strict_latt_str(A) | -latt_str(A) | powerset(B) != the_carrier(A) | element(f102(B,A),powerset(B)) | boole_lattice(B) = A # label(d1_lattice3) # label(axiom). [clausify(207)]. 35.97/36.14 Derived: -latt_str(c2) | powerset(A) != the_carrier(c2) | element(f102(A,c2),powerset(A)) | boole_lattice(A) = c2. [resolve(1033,a,1029,a)]. 35.97/36.14 Derived: -latt_str(c4) | powerset(A) != the_carrier(c4) | element(f102(A,c4),powerset(A)) | boole_lattice(A) = c4. [resolve(1033,a,1030,a)]. 35.97/36.14 Derived: -latt_str(c11) | powerset(A) != the_carrier(c11) | element(f102(A,c11),powerset(A)) | boole_lattice(A) = c11. [resolve(1033,a,1031,a)]. 35.97/36.14 1034 -strict_latt_str(A) | -latt_str(A) | powerset(B) != the_carrier(A) | apply_binary(the_L_meet(A),f101(B,A),f102(B,A)) != subset_intersection2(B,f101(B,A),f102(B,A)) | apply_binary(the_L_join(A),f101(B,A),f102(B,A)) != subset_union2(B,f101(B,A),f102(B,A)) | boole_lattice(B) = A # label(d1_lattice3) # label(axiom). [clausify(207)]. 35.97/36.14 Derived: -latt_str(c2) | powerset(A) != the_carrier(c2) | apply_binary(the_L_meet(c2),f101(A,c2),f102(A,c2)) != subset_intersection2(A,f101(A,c2),f102(A,c2)) | apply_binary(the_L_join(c2),f101(A,c2),f102(A,c2)) != subset_union2(A,f101(A,c2),f102(A,c2)) | boole_lattice(A) = c2. [resolve(1034,a,1029,a)]. 35.97/36.14 Derived: -latt_str(c4) | powerset(A) != the_carrier(c4) | apply_binary(the_L_meet(c4),f101(A,c4),f102(A,c4)) != subset_intersection2(A,f101(A,c4),f102(A,c4)) | apply_binary(the_L_join(c4),f101(A,c4),f102(A,c4)) != subset_union2(A,f101(A,c4),f102(A,c4)) | boole_lattice(A) = c4. [resolve(1034,a,1030,a)]. 35.97/36.14 Derived: -latt_str(c11) | powerset(A) != the_carrier(c11) | apply_binary(the_L_meet(c11),f101(A,c11),f102(A,c11)) != subset_intersection2(A,f101(A,c11),f102(A,c11)) | apply_binary(the_L_join(c11),f101(A,c11),f102(A,c11)) != subset_union2(A,f101(A,c11),f102(A,c11)) | boole_lattice(A) = c11. [resolve(1034,a,1031,a)]. 35.97/36.14 1035 -strict_latt_str(A) | -latt_str(A) | powerset(B) = the_carrier(A) | boole_lattice(B) != A # label(d1_lattice3) # label(axiom). [clausify(207)]. 36.08/36.23 Derived: -latt_str(c2) | powerset(A) = the_carrier(c2) | boole_lattice(A) != c2. [resolve(1035,a,1029,a)]. 36.08/36.23 Derived: -latt_str(c4) | powerset(A) = the_carrier(c4) | boole_lattice(A) != c4. [resolve(1035,a,1030,a)]. 36.08/36.23 Derived: -latt_str(c11) | powerset(A) = the_carrier(c11) | boole_lattice(A) != c11. [resolve(1035,a,1031,a)]. 36.08/36.23 1036 -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(207)]. 36.08/36.23 Derived: -latt_str(c2) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c2),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c2. [resolve(1036,a,1029,a)]. 36.08/36.23 Derived: -latt_str(c4) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c4),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c4. [resolve(1036,a,1030,a)]. 36.08/36.23 Derived: -latt_str(c11) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c11),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c11. [resolve(1036,a,1031,a)]. 36.08/36.23 1037 -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(207)]. 36.08/36.23 Derived: -latt_str(c2) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c2),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c2. [resolve(1037,a,1029,a)]. 36.08/36.23 Derived: -latt_str(c4) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c4),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c4. [resolve(1037,a,1030,a)]. 36.08/36.23 Derived: -latt_str(c11) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c11),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c11. [resolve(1037,a,1031,a)]. 36.08/36.23 1038 strict_latt_str(c25) # label(rc6_lattices) # label(axiom). [clausify(336)]. 36.08/36.23 Derived: -latt_str(c25) | latt_str_of(the_carrier(c25),the_L_join(c25),the_L_meet(c25)) = c25. [resolve(1038,a,1028,b)]. 36.08/36.23 Derived: -latt_str(c25) | powerset(A) != the_carrier(c25) | element(f101(A,c25),powerset(A)) | boole_lattice(A) = c25. [resolve(1038,a,1032,a)]. 36.08/36.23 Derived: -latt_str(c25) | powerset(A) != the_carrier(c25) | element(f102(A,c25),powerset(A)) | boole_lattice(A) = c25. [resolve(1038,a,1033,a)]. 36.08/36.23 Derived: -latt_str(c25) | powerset(A) != the_carrier(c25) | apply_binary(the_L_meet(c25),f101(A,c25),f102(A,c25)) != subset_intersection2(A,f101(A,c25),f102(A,c25)) | apply_binary(the_L_join(c25),f101(A,c25),f102(A,c25)) != subset_union2(A,f101(A,c25),f102(A,c25)) | boole_lattice(A) = c25. [resolve(1038,a,1034,a)]. 36.08/36.23 Derived: -latt_str(c25) | powerset(A) = the_carrier(c25) | boole_lattice(A) != c25. [resolve(1038,a,1035,a)]. 36.08/36.23 Derived: -latt_str(c25) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c25),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c25. [resolve(1038,a,1036,a)]. 36.08/36.23 Derived: -latt_str(c25) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c25),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c25. [resolve(1038,a,1037,a)]. 36.08/36.23 1039 strict_latt_str(boole_lattice(A)) # label(fc2_lattice3) # label(axiom). [clausify(376)]. 36.08/36.23 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(1039,a,1028,b)]. 36.08/36.23 Derived: -latt_str(boole_lattice(A)) | powerset(B) != the_carrier(boole_lattice(A)) | element(f101(B,boole_lattice(A)),powerset(B)) | boole_lattice(B) = boole_lattice(A). [resolve(1039,a,1032,a)]. 36.08/36.23 Derived: -latt_str(boole_lattice(A)) | powerset(B) != the_carrier(boole_lattice(A)) | element(f102(B,boole_lattice(A)),powerset(B)) | boole_lattice(B) = boole_lattice(A). [resolve(1039,a,1033,a)]. 36.08/36.23 Derived: -latt_str(boole_lattice(A)) | powerset(B) != the_carrier(boole_lattice(A)) | apply_binary(the_L_meet(boole_lattice(A)),f101(B,boole_lattice(A)),f102(B,boole_lattice(A))) != subset_intersection2(B,f101(B,boole_lattice(A)),f102(B,boole_lattice(A))) | apply_binary(the_L_join(boole_lattice(A)),f101(B,boole_lattice(A)),f102(B,boole_lattice(A))) != subset_union2(B,f101(B,boole_lattice(A)),f102(B,boole_lattice(A))) | boole_lattice(B) = boole_lattice(A). [resolve(1039,a,1034,a)]. 37.29/37.44 Derived: -latt_str(boole_lattice(A)) | powerset(B) = the_carrier(boole_lattice(A)) | boole_lattice(B) != boole_lattice(A). [resolve(1039,a,1035,a)]. 37.29/37.44 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(1039,a,1036,a)]. 37.29/37.44 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(1039,a,1037,a)]. 37.29/37.44 1040 strict_latt_str(boole_lattice(A)) # label(dt_k1_lattice3) # label(axiom). [clausify(470)]. 37.29/37.44 1041 strict_latt_str(boole_lattice(A)) # label(fc3_lattice3) # label(axiom). [clausify(576)]. 37.29/37.44 1042 strict_latt_str(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(580)]. 37.29/37.44 1043 strict_latt_str(c40) # label(rc9_lattices) # label(axiom). [clausify(610)]. 37.29/37.44 Derived: -latt_str(c40) | latt_str_of(the_carrier(c40),the_L_join(c40),the_L_meet(c40)) = c40. [resolve(1043,a,1028,b)]. 37.29/37.44 Derived: -latt_str(c40) | powerset(A) != the_carrier(c40) | element(f101(A,c40),powerset(A)) | boole_lattice(A) = c40. [resolve(1043,a,1032,a)]. 37.29/37.44 Derived: -latt_str(c40) | powerset(A) != the_carrier(c40) | element(f102(A,c40),powerset(A)) | boole_lattice(A) = c40. [resolve(1043,a,1033,a)]. 37.29/37.44 Derived: -latt_str(c40) | powerset(A) != the_carrier(c40) | apply_binary(the_L_meet(c40),f101(A,c40),f102(A,c40)) != subset_intersection2(A,f101(A,c40),f102(A,c40)) | apply_binary(the_L_join(c40),f101(A,c40),f102(A,c40)) != subset_union2(A,f101(A,c40),f102(A,c40)) | boole_lattice(A) = c40. [resolve(1043,a,1034,a)]. 37.29/37.44 Derived: -latt_str(c40) | powerset(A) = the_carrier(c40) | boole_lattice(A) != c40. [resolve(1043,a,1035,a)]. 37.29/37.44 Derived: -latt_str(c40) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c40),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c40. [resolve(1043,a,1036,a)]. 37.29/37.44 Derived: -latt_str(c40) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c40),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c40. [resolve(1043,a,1037,a)]. 37.29/37.44 1044 empty(A) | -relation_of2(B,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -function(C) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B) | strict_latt_str(latt_str_of(A,B,C)) # label(fc3_lattices) # label(axiom). [clausify(612)]. 37.29/37.44 Derived: empty(A) | -relation_of2(B,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -function(C) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B) | -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). [resolve(1044,h,1028,b)]. 37.29/37.44 Derived: empty(A) | -relation_of2(B,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -function(C) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B) | -latt_str(latt_str_of(A,B,C)) | powerset(D) != the_carrier(latt_str_of(A,B,C)) | element(f101(D,latt_str_of(A,B,C)),powerset(D)) | boole_lattice(D) = latt_str_of(A,B,C). [resolve(1044,h,1032,a)]. 37.29/37.44 Derived: empty(A) | -relation_of2(B,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -function(C) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B) | -latt_str(latt_str_of(A,B,C)) | powerset(D) != the_carrier(latt_str_of(A,B,C)) | element(f102(D,latt_str_of(A,B,C)),powerset(D)) | boole_lattice(D) = latt_str_of(A,B,C). [resolve(1044,h,1033,a)]. 37.75/37.91 Derived: empty(A) | -relation_of2(B,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -function(C) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B) | -latt_str(latt_str_of(A,B,C)) | powerset(D) != the_carrier(latt_str_of(A,B,C)) | apply_binary(the_L_meet(latt_str_of(A,B,C)),f101(D,latt_str_of(A,B,C)),f102(D,latt_str_of(A,B,C))) != subset_intersection2(D,f101(D,latt_str_of(A,B,C)),f102(D,latt_str_of(A,B,C))) | apply_binary(the_L_join(latt_str_of(A,B,C)),f101(D,latt_str_of(A,B,C)),f102(D,latt_str_of(A,B,C))) != subset_union2(D,f101(D,latt_str_of(A,B,C)),f102(D,latt_str_of(A,B,C))) | boole_lattice(D) = latt_str_of(A,B,C). [resolve(1044,h,1034,a)]. 37.75/37.91 Derived: empty(A) | -relation_of2(B,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -function(C) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B) | -latt_str(latt_str_of(A,B,C)) | powerset(D) = the_carrier(latt_str_of(A,B,C)) | boole_lattice(D) != latt_str_of(A,B,C). [resolve(1044,h,1035,a)]. 37.75/37.91 Derived: empty(A) | -relation_of2(B,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -function(C) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B) | -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). [resolve(1044,h,1036,a)]. 37.75/37.91 Derived: empty(A) | -relation_of2(B,cartesian_product2(A,A),A) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -function(C) | -quasi_total(B,cartesian_product2(A,A),A) | -function(B) | -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). [resolve(1044,h,1037,a)]. 37.75/37.91 1045 strict_latt_str(c41) # label(rc3_lattices) # label(axiom). [clausify(640)]. 37.75/37.91 Derived: -latt_str(c41) | latt_str_of(the_carrier(c41),the_L_join(c41),the_L_meet(c41)) = c41. [resolve(1045,a,1028,b)]. 37.75/37.91 Derived: -latt_str(c41) | powerset(A) != the_carrier(c41) | element(f101(A,c41),powerset(A)) | boole_lattice(A) = c41. [resolve(1045,a,1032,a)]. 37.75/37.91 Derived: -latt_str(c41) | powerset(A) != the_carrier(c41) | element(f102(A,c41),powerset(A)) | boole_lattice(A) = c41. [resolve(1045,a,1033,a)]. 37.75/37.91 Derived: -latt_str(c41) | powerset(A) != the_carrier(c41) | apply_binary(the_L_meet(c41),f101(A,c41),f102(A,c41)) != subset_intersection2(A,f101(A,c41),f102(A,c41)) | apply_binary(the_L_join(c41),f101(A,c41),f102(A,c41)) != subset_union2(A,f101(A,c41),f102(A,c41)) | boole_lattice(A) = c41. [resolve(1045,a,1034,a)]. 37.75/37.91 Derived: -latt_str(c41) | powerset(A) = the_carrier(c41) | boole_lattice(A) != c41. [resolve(1045,a,1035,a)]. 37.75/37.91 Derived: -latt_str(c41) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c41),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c41. [resolve(1045,a,1036,a)]. 37.75/37.91 Derived: -latt_str(c41) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c41),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c41. [resolve(1045,a,1037,a)]. 37.75/37.91 1046 strict_latt_str(boole_lattice(A)) # label(fc1_lattice3) # label(axiom). [clausify(665)]. 37.75/37.91 1047 -function(A) | -quasi_total(B,cartesian_product2(C,C),C) | -relation_of2(B,cartesian_product2(C,C),C) | -function(B) | -relation_of2(A,cartesian_product2(C,C),C) | -quasi_total(A,cartesian_product2(C,C),C) | strict_latt_str(latt_str_of(C,A,B)) # label(dt_g3_lattices) # label(axiom). [clausify(745)]. 37.75/37.91 Derived: -function(A) | -quasi_total(B,cartesian_product2(C,C),C) | -relation_of2(B,cartesian_product2(C,C),C) | -function(B) | -relation_of2(A,cartesian_product2(C,C),C) | -quasi_total(A,cartesian_product2(C,C),C) | -latt_str(latt_str_of(C,A,B)) | latt_str_of(the_carrier(latt_str_of(C,A,B)),the_L_join(latt_str_of(C,A,B)),the_L_meet(latt_str_of(C,A,B))) = latt_str_of(C,A,B). [resolve(1047,g,1028,b)]. 37.75/37.94 Derived: -function(A) | -quasi_total(B,cartesian_product2(C,C),C) | -relation_of2(B,cartesian_product2(C,C),C) | -function(B) | -relation_of2(A,cartesian_product2(C,C),C) | -quasi_total(A,cartesian_product2(C,C),C) | -latt_str(latt_str_of(C,A,B)) | powerset(D) != the_carrier(latt_str_of(C,A,B)) | element(f101(D,latt_str_of(C,A,B)),powerset(D)) | boole_lattice(D) = latt_str_of(C,A,B). [resolve(1047,g,1032,a)]. 37.75/37.94 Derived: -function(A) | -quasi_total(B,cartesian_product2(C,C),C) | -relation_of2(B,cartesian_product2(C,C),C) | -function(B) | -relation_of2(A,cartesian_product2(C,C),C) | -quasi_total(A,cartesian_product2(C,C),C) | -latt_str(latt_str_of(C,A,B)) | powerset(D) != the_carrier(latt_str_of(C,A,B)) | element(f102(D,latt_str_of(C,A,B)),powerset(D)) | boole_lattice(D) = latt_str_of(C,A,B). [resolve(1047,g,1033,a)]. 37.75/37.94 Derived: -function(A) | -quasi_total(B,cartesian_product2(C,C),C) | -relation_of2(B,cartesian_product2(C,C),C) | -function(B) | -relation_of2(A,cartesian_product2(C,C),C) | -quasi_total(A,cartesian_product2(C,C),C) | -latt_str(latt_str_of(C,A,B)) | powerset(D) != the_carrier(latt_str_of(C,A,B)) | apply_binary(the_L_meet(latt_str_of(C,A,B)),f101(D,latt_str_of(C,A,B)),f102(D,latt_str_of(C,A,B))) != subset_intersection2(D,f101(D,latt_str_of(C,A,B)),f102(D,latt_str_of(C,A,B))) | apply_binary(the_L_join(latt_str_of(C,A,B)),f101(D,latt_str_of(C,A,B)),f102(D,latt_str_of(C,A,B))) != subset_union2(D,f101(D,latt_str_of(C,A,B)),f102(D,latt_str_of(C,A,B))) | boole_lattice(D) = latt_str_of(C,A,B). [resolve(1047,g,1034,a)]. 37.75/37.94 Derived: -function(A) | -quasi_total(B,cartesian_product2(C,C),C) | -relation_of2(B,cartesian_product2(C,C),C) | -function(B) | -relation_of2(A,cartesian_product2(C,C),C) | -quasi_total(A,cartesian_product2(C,C),C) | -latt_str(latt_str_of(C,A,B)) | powerset(D) = the_carrier(latt_str_of(C,A,B)) | boole_lattice(D) != latt_str_of(C,A,B). [resolve(1047,g,1035,a)]. 37.75/37.94 Derived: -function(A) | -quasi_total(B,cartesian_product2(C,C),C) | -relation_of2(B,cartesian_product2(C,C),C) | -function(B) | -relation_of2(A,cartesian_product2(C,C),C) | -quasi_total(A,cartesian_product2(C,C),C) | -latt_str(latt_str_of(C,A,B)) | -element(D,powerset(E)) | -element(F,powerset(E)) | apply_binary(the_L_meet(latt_str_of(C,A,B)),D,F) = subset_intersection2(E,D,F) | boole_lattice(E) != latt_str_of(C,A,B). [resolve(1047,g,1036,a)]. 37.75/37.94 Derived: -function(A) | -quasi_total(B,cartesian_product2(C,C),C) | -relation_of2(B,cartesian_product2(C,C),C) | -function(B) | -relation_of2(A,cartesian_product2(C,C),C) | -quasi_total(A,cartesian_product2(C,C),C) | -latt_str(latt_str_of(C,A,B)) | -element(D,powerset(E)) | -element(F,powerset(E)) | apply_binary(the_L_join(latt_str_of(C,A,B)),D,F) = subset_union2(E,D,F) | boole_lattice(E) != latt_str_of(C,A,B). [resolve(1047,g,1037,a)]. 37.75/37.94 1048 strict_latt_str(c45) # label(rc12_lattices) # label(axiom). [clausify(750)]. 37.75/37.94 Derived: -latt_str(c45) | latt_str_of(the_carrier(c45),the_L_join(c45),the_L_meet(c45)) = c45. [resolve(1048,a,1028,b)]. 37.75/37.94 Derived: -latt_str(c45) | powerset(A) != the_carrier(c45) | element(f101(A,c45),powerset(A)) | boole_lattice(A) = c45. [resolve(1048,a,1032,a)]. 37.75/37.94 Derived: -latt_str(c45) | powerset(A) != the_carrier(c45) | element(f102(A,c45),powerset(A)) | boole_lattice(A) = c45. [resolve(1048,a,1033,a)]. 37.75/37.94 Derived: -latt_str(c45) | powerset(A) != the_carrier(c45) | apply_binary(the_L_meet(c45),f101(A,c45),f102(A,c45)) != subset_intersection2(A,f101(A,c45),f102(A,c45)) | apply_binary(the_L_join(c45),f101(A,c45),f102(A,c45)) != subset_union2(A,f101(A,c45),f102(A,c45)) | boole_lattice(A) = c45. [resolve(1048,a,1034,a)]. 37.75/37.94 Derived: -latt_str(c45) | powerset(A) = the_carrier(c45) | boole_lattice(A) != c45. [resolve(1048,a,1035,a)]. 37.75/37.94 Derived: -latt_str(c45) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_meet(c45),A,C) = subset_intersection2(B,A,C) | boole_lattice(B) != c45. [resolve(1048,a,1036,a)]. 37.75/37.94 Derived: -latt_str(c45) | -element(A,powerset(B)) | -element(C,powerset(B)) | apply_binary(the_L_join(c45),A,C) = subset_union2(B,A,C) | boole_lattice(B) != c45. [resolve(1048,a,1037,a)]. 41.47/41.60 1049 empty_carrier(A) | -latt_str(A) | -latt_str(B) | empty_carrier(B) | strict_latt_str(k8_filter_1(B,A)) # label(dt_k8_filter_1) # label(axiom). [clausify(757)]. 41.47/41.60 Derived: empty_carrier(A) | -latt_str(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(1049,e,1028,b)]. 41.47/41.60 Derived: empty_carrier(A) | -latt_str(A) | -latt_str(B) | empty_carrier(B) | -latt_str(k8_filter_1(B,A)) | powerset(C) != the_carrier(k8_filter_1(B,A)) | element(f101(C,k8_filter_1(B,A)),powerset(C)) | boole_lattice(C) = k8_filter_1(B,A). [resolve(1049,e,1032,a)]. 41.47/41.60 Derived: empty_carrier(A) | -latt_str(A) | -latt_str(B) | empty_carrier(B) | -latt_str(k8_filter_1(B,A)) | powerset(C) != the_carrier(k8_filter_1(B,A)) | element(f102(C,k8_filter_1(B,A)),powerset(C)) | boole_lattice(C) = k8_filter_1(B,A). [resolve(1049,e,1033,a)]. 41.47/41.60 Derived: empty_carrier(A) | -latt_str(A) | -latt_str(B) | empty_carrier(B) | -latt_str(k8_filter_1(B,A)) | powerset(C) != the_carrier(k8_filter_1(B,A)) | apply_binary(the_L_meet(k8_filter_1(B,A)),f101(C,k8_filter_1(B,A)),f102(C,k8_filter_1(B,A))) != subset_intersection2(C,f101(C,k8_filter_1(B,A)),f102(C,k8_filter_1(B,A))) | apply_binary(the_L_join(k8_filter_1(B,A)),f101(C,k8_filter_1(B,A)),f102(C,k8_filter_1(B,A))) != subset_union2(C,f101(C,k8_filter_1(B,A)),f102(C,k8_filter_1(B,A))) | boole_lattice(C) = k8_filter_1(B,A). [resolve(1049,e,1034,a)]. 41.47/41.60 Derived: empty_carrier(A) | -latt_str(A) | -latt_str(B) | empty_carrier(B) | -latt_str(k8_filter_1(B,A)) | powerset(C) = the_carrier(k8_filter_1(B,A)) | boole_lattice(C) != k8_filter_1(B,A). [resolve(1049,e,1035,a)]. 41.47/41.60 Derived: empty_carrier(A) | -latt_str(A) | -latt_str(B) | empty_carrier(B) | -latt_str(k8_filter_1(B,A)) | -element(C,powerset(D)) | -element(E,powerset(D)) | apply_binary(the_L_meet(k8_filter_1(B,A)),C,E) = subset_intersection2(D,C,E) | boole_lattice(D) != k8_filter_1(B,A). [resolve(1049,e,1036,a)]. 41.47/41.60 Derived: empty_carrier(A) | -latt_str(A) | -latt_str(B) | empty_carrier(B) | -latt_str(k8_filter_1(B,A)) | -element(C,powerset(D)) | -element(E,powerset(D)) | apply_binary(the_L_join(k8_filter_1(B,A)),C,E) = subset_union2(D,C,E) | boole_lattice(D) != k8_filter_1(B,A). [resolve(1049,e,1037,a)]. 41.47/41.60 1050 -lattice(A) | -latt_str(A) | empty_carrier(A) | transitive_relstr(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(51)]. 41.47/41.60 1051 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | in(f19(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1052 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | in(f19(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1053 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | in(f19(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1054 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | subset(f20(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1055 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | subset(f20(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1056 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | subset(f20(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1057 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | element(f21(A,C,B),the_carrier(A)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1058 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | element(f21(A,C,B),the_carrier(A)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1059 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | element(f21(A,C,B),the_carrier(A)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1060 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | relstr_set_smaller(A,f20(A,C,B),f21(A,C,B)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1061 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | relstr_set_smaller(A,f20(A,C,B),f21(A,C,B)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1062 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | relstr_set_smaller(A,f20(A,C,B),f21(A,C,B)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1063 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | in(f21(A,C,B),C) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1064 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | in(f21(A,C,B),C) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1065 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | in(f21(A,C,B),C) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.60 1066 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | -in(D,C) | -relstr_set_smaller(A,set_union2(f20(A,C,B),singleton(f19(A,C,B))),D) | -element(D,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,empty_set,E) | -element(E,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.61 1067 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | -in(D,C) | -relstr_set_smaller(A,set_union2(f20(A,C,B),singleton(f19(A,C,B))),D) | -element(D,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,empty_set,E) | -element(E,the_carrier(A)) | in(f22(A,C,B),C) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.61 1068 empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -transitive_relstr(A) | -in(D,C) | -relstr_set_smaller(A,set_union2(f20(A,C,B),singleton(f19(A,C,B))),D) | -element(D,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,empty_set,E) | -element(E,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)) # label(s2_finset_1__e11_2_1__waybel_0) # label(lemma). [clausify(25)]. 41.47/41.61 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | in(f19(poset_of_lattice(A),C,B),B) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),B,f22(poset_of_lattice(A),C,B)). [resolve(1050,d,1051,f)]. 41.47/41.61 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | in(f19(poset_of_lattice(A),C,B),B) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | in(f22(poset_of_lattice(A),C,B),C). [resolve(1050,d,1052,f)]. 41.47/41.61 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | in(f19(poset_of_lattice(A),C,B),B) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | element(f22(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))). [resolve(1050,d,1053,f)]. 41.47/41.61 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | subset(f20(poset_of_lattice(A),C,B),B) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),B,f22(poset_of_lattice(A),C,B)). [resolve(1050,d,1054,f)]. 41.47/41.61 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | subset(f20(poset_of_lattice(A),C,B),B) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | in(f22(poset_of_lattice(A),C,B),C). [resolve(1050,d,1055,f)]. 41.47/41.61 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | subset(f20(poset_of_lattice(A),C,B),B) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | element(f22(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))). [resolve(1050,d,1056,f)]. 41.47/41.61 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | element(f21(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),B,f22(poset_of_lattice(A),C,B)). [resolve(1050,d,1057,f)]. 41.47/41.63 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | element(f21(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | in(f22(poset_of_lattice(A),C,B),C). [resolve(1050,d,1058,f)]. 41.47/41.63 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | element(f21(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | element(f22(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))). [resolve(1050,d,1059,f)]. 41.47/41.63 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | relstr_set_smaller(poset_of_lattice(A),f20(poset_of_lattice(A),C,B),f21(poset_of_lattice(A),C,B)) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),B,f22(poset_of_lattice(A),C,B)). [resolve(1050,d,1060,f)]. 41.47/41.63 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | relstr_set_smaller(poset_of_lattice(A),f20(poset_of_lattice(A),C,B),f21(poset_of_lattice(A),C,B)) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | in(f22(poset_of_lattice(A),C,B),C). [resolve(1050,d,1061,f)]. 41.47/41.63 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | relstr_set_smaller(poset_of_lattice(A),f20(poset_of_lattice(A),C,B),f21(poset_of_lattice(A),C,B)) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | element(f22(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))). [resolve(1050,d,1062,f)]. 41.47/41.63 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | in(f21(poset_of_lattice(A),C,B),C) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),B,f22(poset_of_lattice(A),C,B)). [resolve(1050,d,1063,f)]. 41.47/41.63 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | in(f21(poset_of_lattice(A),C,B),C) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | in(f22(poset_of_lattice(A),C,B),C). [resolve(1050,d,1064,f)]. 41.47/41.63 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | in(f21(poset_of_lattice(A),C,B),C) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,D) | -element(D,the_carrier(poset_of_lattice(A))) | element(f22(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))). [resolve(1050,d,1065,f)]. 41.47/41.63 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),set_union2(f20(poset_of_lattice(A),C,B),singleton(f19(poset_of_lattice(A),C,B))),D) | -element(D,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,E) | -element(E,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),B,f22(poset_of_lattice(A),C,B)). [resolve(1050,d,1066,f)]. 41.47/41.67 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),set_union2(f20(poset_of_lattice(A),C,B),singleton(f19(poset_of_lattice(A),C,B))),D) | -element(D,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,E) | -element(E,the_carrier(poset_of_lattice(A))) | in(f22(poset_of_lattice(A),C,B),C). [resolve(1050,d,1067,f)]. 41.47/41.67 Derived: -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | -in(D,C) | -relstr_set_smaller(poset_of_lattice(A),set_union2(f20(poset_of_lattice(A),C,B),singleton(f19(poset_of_lattice(A),C,B))),D) | -element(D,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),empty_set,E) | -element(E,the_carrier(poset_of_lattice(A))) | element(f22(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))). [resolve(1050,d,1068,f)]. 41.47/41.67 1069 empty_carrier(A) | -latt_str(A) | -lattice(A) | transitive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(58)]. 41.47/41.67 1070 transitive_relstr(c6) # label(rc1_yellow_0) # label(axiom). [clausify(85)]. 41.47/41.67 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | in(f19(c6,B,A),A) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | relstr_set_smaller(c6,A,f22(c6,B,A)). [resolve(1070,a,1051,f)]. 41.47/41.67 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | in(f19(c6,B,A),A) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | in(f22(c6,B,A),B). [resolve(1070,a,1052,f)]. 41.47/41.67 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | in(f19(c6,B,A),A) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | element(f22(c6,B,A),the_carrier(c6)). [resolve(1070,a,1053,f)]. 41.47/41.67 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | subset(f20(c6,B,A),A) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | relstr_set_smaller(c6,A,f22(c6,B,A)). [resolve(1070,a,1054,f)]. 41.47/41.67 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | subset(f20(c6,B,A),A) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | in(f22(c6,B,A),B). [resolve(1070,a,1055,f)]. 41.47/41.67 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | subset(f20(c6,B,A),A) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | element(f22(c6,B,A),the_carrier(c6)). [resolve(1070,a,1056,f)]. 41.47/41.67 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | element(f21(c6,B,A),the_carrier(c6)) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | relstr_set_smaller(c6,A,f22(c6,B,A)). [resolve(1070,a,1057,f)]. 41.47/41.67 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | element(f21(c6,B,A),the_carrier(c6)) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | in(f22(c6,B,A),B). [resolve(1070,a,1058,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | element(f21(c6,B,A),the_carrier(c6)) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | element(f22(c6,B,A),the_carrier(c6)). [resolve(1070,a,1059,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | relstr_set_smaller(c6,f20(c6,B,A),f21(c6,B,A)) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | relstr_set_smaller(c6,A,f22(c6,B,A)). [resolve(1070,a,1060,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | relstr_set_smaller(c6,f20(c6,B,A),f21(c6,B,A)) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | in(f22(c6,B,A),B). [resolve(1070,a,1061,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | relstr_set_smaller(c6,f20(c6,B,A),f21(c6,B,A)) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | element(f22(c6,B,A),the_carrier(c6)). [resolve(1070,a,1062,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | in(f21(c6,B,A),B) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | relstr_set_smaller(c6,A,f22(c6,B,A)). [resolve(1070,a,1063,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | in(f21(c6,B,A),B) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | in(f22(c6,B,A),B). [resolve(1070,a,1064,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | in(f21(c6,B,A),B) | -in(C,B) | -relstr_set_smaller(c6,empty_set,C) | -element(C,the_carrier(c6)) | element(f22(c6,B,A),the_carrier(c6)). [resolve(1070,a,1065,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | -in(C,B) | -relstr_set_smaller(c6,set_union2(f20(c6,B,A),singleton(f19(c6,B,A))),C) | -element(C,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,empty_set,D) | -element(D,the_carrier(c6)) | relstr_set_smaller(c6,A,f22(c6,B,A)). [resolve(1070,a,1066,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | -in(C,B) | -relstr_set_smaller(c6,set_union2(f20(c6,B,A),singleton(f19(c6,B,A))),C) | -element(C,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,empty_set,D) | -element(D,the_carrier(c6)) | in(f22(c6,B,A),B). [resolve(1070,a,1067,f)]. 41.59/41.72 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c6))) | -in(C,B) | -relstr_set_smaller(c6,set_union2(f20(c6,B,A),singleton(f19(c6,B,A))),C) | -element(C,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,empty_set,D) | -element(D,the_carrier(c6)) | element(f22(c6,B,A),the_carrier(c6)). [resolve(1070,a,1068,f)]. 41.59/41.72 1071 empty_carrier(A) | -latt_str(A) | -lower_bounded_semilattstr(A) | -lattice(A) | transitive_relstr(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(137)]. 41.59/41.72 1072 transitive_relstr(boole_POSet(A)) # label(fc7_yellow_1) # label(axiom). [clausify(200)]. 41.59/41.72 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | in(f19(boole_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | relstr_set_smaller(boole_POSet(A),B,f22(boole_POSet(A),C,B)). [resolve(1072,a,1051,f)]. 41.59/41.72 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | in(f19(boole_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | in(f22(boole_POSet(A),C,B),C). [resolve(1072,a,1052,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | in(f19(boole_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | element(f22(boole_POSet(A),C,B),the_carrier(boole_POSet(A))). [resolve(1072,a,1053,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | subset(f20(boole_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | relstr_set_smaller(boole_POSet(A),B,f22(boole_POSet(A),C,B)). [resolve(1072,a,1054,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | subset(f20(boole_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | in(f22(boole_POSet(A),C,B),C). [resolve(1072,a,1055,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | subset(f20(boole_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | element(f22(boole_POSet(A),C,B),the_carrier(boole_POSet(A))). [resolve(1072,a,1056,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | element(f21(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | relstr_set_smaller(boole_POSet(A),B,f22(boole_POSet(A),C,B)). [resolve(1072,a,1057,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | element(f21(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | in(f22(boole_POSet(A),C,B),C). [resolve(1072,a,1058,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | element(f21(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | element(f22(boole_POSet(A),C,B),the_carrier(boole_POSet(A))). [resolve(1072,a,1059,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | relstr_set_smaller(boole_POSet(A),f20(boole_POSet(A),C,B),f21(boole_POSet(A),C,B)) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | relstr_set_smaller(boole_POSet(A),B,f22(boole_POSet(A),C,B)). [resolve(1072,a,1060,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | relstr_set_smaller(boole_POSet(A),f20(boole_POSet(A),C,B),f21(boole_POSet(A),C,B)) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | in(f22(boole_POSet(A),C,B),C). [resolve(1072,a,1061,f)]. 41.59/41.73 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | relstr_set_smaller(boole_POSet(A),f20(boole_POSet(A),C,B),f21(boole_POSet(A),C,B)) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | element(f22(boole_POSet(A),C,B),the_carrier(boole_POSet(A))). [resolve(1072,a,1062,f)]. 41.59/41.76 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | in(f21(boole_POSet(A),C,B),C) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | relstr_set_smaller(boole_POSet(A),B,f22(boole_POSet(A),C,B)). [resolve(1072,a,1063,f)]. 41.59/41.76 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | in(f21(boole_POSet(A),C,B),C) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | in(f22(boole_POSet(A),C,B),C). [resolve(1072,a,1064,f)]. 41.59/41.76 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | in(f21(boole_POSet(A),C,B),C) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),empty_set,D) | -element(D,the_carrier(boole_POSet(A))) | element(f22(boole_POSet(A),C,B),the_carrier(boole_POSet(A))). [resolve(1072,a,1065,f)]. 41.59/41.76 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),set_union2(f20(boole_POSet(A),C,B),singleton(f19(boole_POSet(A),C,B))),D) | -element(D,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),empty_set,E) | -element(E,the_carrier(boole_POSet(A))) | relstr_set_smaller(boole_POSet(A),B,f22(boole_POSet(A),C,B)). [resolve(1072,a,1066,f)]. 41.59/41.76 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),set_union2(f20(boole_POSet(A),C,B),singleton(f19(boole_POSet(A),C,B))),D) | -element(D,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),empty_set,E) | -element(E,the_carrier(boole_POSet(A))) | in(f22(boole_POSet(A),C,B),C). [resolve(1072,a,1067,f)]. 41.59/41.76 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(boole_POSet(A)))) | -in(D,C) | -relstr_set_smaller(boole_POSet(A),set_union2(f20(boole_POSet(A),C,B),singleton(f19(boole_POSet(A),C,B))),D) | -element(D,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),empty_set,E) | -element(E,the_carrier(boole_POSet(A))) | element(f22(boole_POSet(A),C,B),the_carrier(boole_POSet(A))). [resolve(1072,a,1068,f)]. 41.59/41.76 1073 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.59/41.76 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f134(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1073,a,1050,d)]. 41.59/41.76 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f134(c6,B,A) = f133(c6,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1073,a,1070,a)]. 41.59/41.76 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f134(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1073,a,1072,a)]. 41.59/41.78 1074 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.59/41.78 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f134(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1074,a,1050,d)]. 41.59/41.78 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f134(c6,B,A) = f133(c6,B,A) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1074,a,1070,a)]. 41.59/41.78 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f134(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1074,a,1072,a)]. 41.59/41.78 1075 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.59/41.78 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f134(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1075,a,1050,d)]. 41.59/41.78 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f134(c6,B,A) = f133(c6,B,A) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1075,a,1070,a)]. 41.59/41.78 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f134(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1075,a,1072,a)]. 41.59/41.78 1076 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.59/41.78 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f134(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1076,a,1050,d)]. 41.59/41.78 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f134(c6,B,A) = f133(c6,B,A) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1076,a,1070,a)]. 41.59/41.78 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f134(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1076,a,1072,a)]. 41.59/41.78 1077 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.59/41.80 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f134(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1077,a,1050,d)]. 41.59/41.80 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f134(c6,B,A) = f133(c6,B,A) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1077,a,1070,a)]. 41.59/41.80 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f134(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1077,a,1072,a)]. 41.59/41.80 1078 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.59/41.80 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f134(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1078,a,1050,d)]. 41.59/41.80 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f134(c6,B,A) = f133(c6,B,A) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1078,a,1070,a)]. 41.59/41.80 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f134(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1078,a,1072,a)]. 41.59/41.80 1079 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.59/41.80 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f134(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1079,a,1050,d)]. 41.59/41.80 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f134(c6,B,A) = f133(c6,B,A) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1079,a,1070,a)]. 41.59/41.80 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f134(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1079,a,1072,a)]. 41.59/41.80 1080 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.82 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f136(poset_of_lattice(A),C,B) = f135(poset_of_lattice(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1080,a,1050,d)]. 41.67/41.82 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f136(c6,B,A) = f135(c6,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1080,a,1070,a)]. 41.67/41.82 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f136(boole_POSet(A),C,B) = f135(boole_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1080,a,1072,a)]. 41.67/41.82 1081 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.82 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f136(poset_of_lattice(A),C,B) = f135(poset_of_lattice(A),C,B) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1081,a,1050,d)]. 41.67/41.82 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f136(c6,B,A) = f135(c6,B,A) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1081,a,1070,a)]. 41.67/41.82 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f136(boole_POSet(A),C,B) = f135(boole_POSet(A),C,B) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1081,a,1072,a)]. 41.67/41.82 1082 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.82 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f136(poset_of_lattice(A),C,B) = f135(poset_of_lattice(A),C,B) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1082,a,1050,d)]. 41.67/41.82 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f136(c6,B,A) = f135(c6,B,A) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1082,a,1070,a)]. 41.67/41.82 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f136(boole_POSet(A),C,B) = f135(boole_POSet(A),C,B) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1082,a,1072,a)]. 41.67/41.82 1083 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.82 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f136(poset_of_lattice(A),C,B) = f135(poset_of_lattice(A),C,B) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1083,a,1050,d)]. 41.67/41.84 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f136(c6,B,A) = f135(c6,B,A) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1083,a,1070,a)]. 41.67/41.84 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f136(boole_POSet(A),C,B) = f135(boole_POSet(A),C,B) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1083,a,1072,a)]. 41.67/41.84 1084 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.84 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f136(poset_of_lattice(A),C,B) = f135(poset_of_lattice(A),C,B) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1084,a,1050,d)]. 41.67/41.84 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f136(c6,B,A) = f135(c6,B,A) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1084,a,1070,a)]. 41.67/41.84 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f136(boole_POSet(A),C,B) = f135(boole_POSet(A),C,B) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1084,a,1072,a)]. 41.67/41.84 1085 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.84 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f136(poset_of_lattice(A),C,B) = f135(poset_of_lattice(A),C,B) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1085,a,1050,d)]. 41.67/41.84 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f136(c6,B,A) = f135(c6,B,A) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1085,a,1070,a)]. 41.67/41.84 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f136(boole_POSet(A),C,B) = f135(boole_POSet(A),C,B) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1085,a,1072,a)]. 41.67/41.84 1086 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.84 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f136(poset_of_lattice(A),C,B) = f135(poset_of_lattice(A),C,B) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1086,a,1050,d)]. 41.67/41.86 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f136(c6,B,A) = f135(c6,B,A) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1086,a,1070,a)]. 41.67/41.86 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f136(boole_POSet(A),C,B) = f135(boole_POSet(A),C,B) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1086,a,1072,a)]. 41.67/41.86 1087 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.86 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f137(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1087,a,1050,d)]. 41.67/41.86 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f137(c6,B,A),the_carrier(c6)) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1087,a,1070,a)]. 41.67/41.86 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f137(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1087,a,1072,a)]. 41.67/41.86 1088 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.86 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f137(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1088,a,1050,d)]. 41.67/41.86 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f137(c6,B,A),the_carrier(c6)) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1088,a,1070,a)]. 41.67/41.86 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f137(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1088,a,1072,a)]. 41.67/41.86 1089 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.86 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f137(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1089,a,1050,d)]. 41.67/41.88 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f137(c6,B,A),the_carrier(c6)) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1089,a,1070,a)]. 41.67/41.88 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f137(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1089,a,1072,a)]. 41.67/41.88 1090 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.88 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f137(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1090,a,1050,d)]. 41.67/41.88 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f137(c6,B,A),the_carrier(c6)) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1090,a,1070,a)]. 41.67/41.88 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f137(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1090,a,1072,a)]. 41.67/41.88 1091 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.88 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f137(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1091,a,1050,d)]. 41.67/41.88 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f137(c6,B,A),the_carrier(c6)) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1091,a,1070,a)]. 41.67/41.88 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f137(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1091,a,1072,a)]. 41.67/41.88 1092 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.67/41.88 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f137(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1092,a,1050,d)]. 41.75/41.90 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f137(c6,B,A),the_carrier(c6)) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1092,a,1070,a)]. 41.75/41.90 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f137(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1092,a,1072,a)]. 41.75/41.90 1093 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.90 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f137(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1093,a,1050,d)]. 41.75/41.90 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f137(c6,B,A),the_carrier(c6)) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1093,a,1070,a)]. 41.75/41.90 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f137(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1093,a,1072,a)]. 41.75/41.90 1094 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.90 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f136(poset_of_lattice(A),C,B),f137(poset_of_lattice(A),C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1094,a,1050,d)]. 41.75/41.90 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f136(c6,B,A),f137(c6,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1094,a,1070,a)]. 41.75/41.90 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f136(boole_POSet(A),C,B),f137(boole_POSet(A),C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1094,a,1072,a)]. 41.75/41.90 1095 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.90 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f136(poset_of_lattice(A),C,B),f137(poset_of_lattice(A),C,B)) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1095,a,1050,d)]. 41.75/41.91 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f136(c6,B,A),f137(c6,B,A)) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1095,a,1070,a)]. 41.75/41.91 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f136(boole_POSet(A),C,B),f137(boole_POSet(A),C,B)) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1095,a,1072,a)]. 41.75/41.91 1096 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.91 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f136(poset_of_lattice(A),C,B),f137(poset_of_lattice(A),C,B)) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1096,a,1050,d)]. 41.75/41.91 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f136(c6,B,A),f137(c6,B,A)) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1096,a,1070,a)]. 41.75/41.91 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f136(boole_POSet(A),C,B),f137(boole_POSet(A),C,B)) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1096,a,1072,a)]. 41.75/41.91 1097 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.91 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f136(poset_of_lattice(A),C,B),f137(poset_of_lattice(A),C,B)) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1097,a,1050,d)]. 41.75/41.91 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f136(c6,B,A),f137(c6,B,A)) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1097,a,1070,a)]. 41.75/41.91 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f136(boole_POSet(A),C,B),f137(boole_POSet(A),C,B)) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1097,a,1072,a)]. 41.75/41.91 1098 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.91 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f136(poset_of_lattice(A),C,B),f137(poset_of_lattice(A),C,B)) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1098,a,1050,d)]. 41.75/41.93 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f136(c6,B,A),f137(c6,B,A)) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1098,a,1070,a)]. 41.75/41.93 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f136(boole_POSet(A),C,B),f137(boole_POSet(A),C,B)) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1098,a,1072,a)]. 41.75/41.93 1099 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.93 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f136(poset_of_lattice(A),C,B),f137(poset_of_lattice(A),C,B)) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1099,a,1050,d)]. 41.75/41.93 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f136(c6,B,A),f137(c6,B,A)) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1099,a,1070,a)]. 41.75/41.93 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f136(boole_POSet(A),C,B),f137(boole_POSet(A),C,B)) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1099,a,1072,a)]. 41.75/41.93 1100 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.93 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f136(poset_of_lattice(A),C,B),f137(poset_of_lattice(A),C,B)) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1100,a,1050,d)]. 41.75/41.93 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f136(c6,B,A),f137(c6,B,A)) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1100,a,1070,a)]. 41.75/41.93 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f136(boole_POSet(A),C,B),f137(boole_POSet(A),C,B)) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1100,a,1072,a)]. 41.75/41.93 1101 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.93 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f137(poset_of_lattice(A),C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1101,a,1050,d)]. 41.75/41.95 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f137(c6,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1101,a,1070,a)]. 41.75/41.95 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f137(boole_POSet(A),C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1101,a,1072,a)]. 41.75/41.95 1102 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.95 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f137(poset_of_lattice(A),C,B),C) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1102,a,1050,d)]. 41.75/41.95 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f137(c6,B,A),B) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1102,a,1070,a)]. 41.75/41.95 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f137(boole_POSet(A),C,B),C) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1102,a,1072,a)]. 41.75/41.95 1103 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.95 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f137(poset_of_lattice(A),C,B),C) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1103,a,1050,d)]. 41.75/41.95 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f137(c6,B,A),B) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1103,a,1070,a)]. 41.75/41.95 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f137(boole_POSet(A),C,B),C) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1103,a,1072,a)]. 41.75/41.95 1104 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.75/41.95 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f137(poset_of_lattice(A),C,B),C) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1104,a,1050,d)]. 41.75/41.95 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f137(c6,B,A),B) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1104,a,1070,a)]. 41.85/41.98 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f137(boole_POSet(A),C,B),C) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1104,a,1072,a)]. 41.85/41.98 1105 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.85/41.98 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f137(poset_of_lattice(A),C,B),C) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1105,a,1050,d)]. 41.85/41.98 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f137(c6,B,A),B) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1105,a,1070,a)]. 41.85/41.98 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f137(boole_POSet(A),C,B),C) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1105,a,1072,a)]. 41.85/41.98 1106 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.85/41.98 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f137(poset_of_lattice(A),C,B),C) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1106,a,1050,d)]. 41.85/41.98 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f137(c6,B,A),B) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1106,a,1070,a)]. 41.85/41.98 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f137(boole_POSet(A),C,B),C) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1106,a,1072,a)]. 41.85/41.98 1107 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.85/41.98 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f137(poset_of_lattice(A),C,B),C) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1107,a,1050,d)]. 41.85/41.98 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f137(c6,B,A),B) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1107,a,1070,a)]. 41.85/41.98 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f137(boole_POSet(A),C,B),C) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1107,a,1072,a)]. 41.85/41.98 1108 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.87/42.00 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1108,a,1050,d)]. 41.87/42.00 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) = f133(c6,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1108,a,1070,a)]. 41.87/42.00 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1108,a,1072,a)]. 41.87/42.00 1109 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.87/42.00 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1109,a,1050,d)]. 41.87/42.00 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) = f133(c6,B,A) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1109,a,1070,a)]. 41.87/42.00 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1109,a,1072,a)]. 41.87/42.00 1110 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.87/42.00 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1110,a,1050,d)]. 41.87/42.00 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) = f133(c6,B,A) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1110,a,1070,a)]. 41.87/42.00 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1110,a,1072,a)]. 41.87/42.01 1111 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.87/42.01 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1111,a,1050,d)]. 41.87/42.01 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) = f133(c6,B,A) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1111,a,1070,a)]. 41.87/42.01 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1111,a,1072,a)]. 41.87/42.01 1112 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.87/42.01 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1112,a,1050,d)]. 41.87/42.01 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) = f133(c6,B,A) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1112,a,1070,a)]. 41.87/42.01 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1112,a,1072,a)]. 41.87/42.01 1113 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.87/42.01 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1113,a,1050,d)]. 41.87/42.01 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) = f133(c6,B,A) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1113,a,1070,a)]. 41.87/42.01 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1113,a,1072,a)]. 41.87/42.01 1114 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.04 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) = f133(poset_of_lattice(A),C,B) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1114,a,1050,d)]. 41.89/42.04 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) = f133(c6,B,A) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1114,a,1070,a)]. 41.89/42.04 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) = f133(boole_POSet(A),C,B) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1114,a,1072,a)]. 41.89/42.04 1115 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.04 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f138(poset_of_lattice(A),C,B) = f134(poset_of_lattice(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1115,a,1050,d)]. 41.89/42.04 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f138(c6,B,A) = f134(c6,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1115,a,1070,a)]. 41.89/42.04 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f138(boole_POSet(A),C,B) = f134(boole_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1115,a,1072,a)]. 41.89/42.04 1116 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.04 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f138(poset_of_lattice(A),C,B) = f134(poset_of_lattice(A),C,B) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1116,a,1050,d)]. 41.89/42.04 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f138(c6,B,A) = f134(c6,B,A) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1116,a,1070,a)]. 41.89/42.04 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f138(boole_POSet(A),C,B) = f134(boole_POSet(A),C,B) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1116,a,1072,a)]. 41.89/42.04 1117 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.04 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f138(poset_of_lattice(A),C,B) = f134(poset_of_lattice(A),C,B) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1117,a,1050,d)]. 41.89/42.06 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f138(c6,B,A) = f134(c6,B,A) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1117,a,1070,a)]. 41.89/42.06 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f138(boole_POSet(A),C,B) = f134(boole_POSet(A),C,B) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1117,a,1072,a)]. 41.89/42.06 1118 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.06 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f138(poset_of_lattice(A),C,B) = f134(poset_of_lattice(A),C,B) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1118,a,1050,d)]. 41.89/42.06 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f138(c6,B,A) = f134(c6,B,A) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1118,a,1070,a)]. 41.89/42.06 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f138(boole_POSet(A),C,B) = f134(boole_POSet(A),C,B) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1118,a,1072,a)]. 41.89/42.06 1119 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.06 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f138(poset_of_lattice(A),C,B) = f134(poset_of_lattice(A),C,B) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1119,a,1050,d)]. 41.89/42.06 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f138(c6,B,A) = f134(c6,B,A) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1119,a,1070,a)]. 41.89/42.06 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f138(boole_POSet(A),C,B) = f134(boole_POSet(A),C,B) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1119,a,1072,a)]. 41.89/42.06 1120 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.06 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f138(poset_of_lattice(A),C,B) = f134(poset_of_lattice(A),C,B) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1120,a,1050,d)]. 41.89/42.08 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f138(c6,B,A) = f134(c6,B,A) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1120,a,1070,a)]. 41.89/42.08 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f138(boole_POSet(A),C,B) = f134(boole_POSet(A),C,B) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1120,a,1072,a)]. 41.89/42.08 1121 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.08 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f138(poset_of_lattice(A),C,B) = f134(poset_of_lattice(A),C,B) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1121,a,1050,d)]. 41.89/42.08 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f138(c6,B,A) = f134(c6,B,A) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1121,a,1070,a)]. 41.89/42.08 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f138(boole_POSet(A),C,B) = f134(boole_POSet(A),C,B) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1121,a,1072,a)]. 41.89/42.08 1122 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.08 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f138(poset_of_lattice(A),C,B),f139(poset_of_lattice(A),C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1122,a,1050,d)]. 41.89/42.08 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f138(c6,B,A),f139(c6,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1122,a,1070,a)]. 41.89/42.08 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f138(boole_POSet(A),C,B),f139(boole_POSet(A),C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1122,a,1072,a)]. 41.89/42.08 1123 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.08 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f138(poset_of_lattice(A),C,B),f139(poset_of_lattice(A),C,B)) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1123,a,1050,d)]. 41.89/42.10 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f138(c6,B,A),f139(c6,B,A)) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1123,a,1070,a)]. 41.89/42.10 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f138(boole_POSet(A),C,B),f139(boole_POSet(A),C,B)) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1123,a,1072,a)]. 41.89/42.10 1124 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.10 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f138(poset_of_lattice(A),C,B),f139(poset_of_lattice(A),C,B)) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1124,a,1050,d)]. 41.89/42.10 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f138(c6,B,A),f139(c6,B,A)) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1124,a,1070,a)]. 41.89/42.10 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f138(boole_POSet(A),C,B),f139(boole_POSet(A),C,B)) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1124,a,1072,a)]. 41.89/42.10 1125 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.10 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f138(poset_of_lattice(A),C,B),f139(poset_of_lattice(A),C,B)) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1125,a,1050,d)]. 41.89/42.10 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f138(c6,B,A),f139(c6,B,A)) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1125,a,1070,a)]. 41.89/42.10 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f138(boole_POSet(A),C,B),f139(boole_POSet(A),C,B)) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1125,a,1072,a)]. 41.89/42.10 1126 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.89/42.10 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f138(poset_of_lattice(A),C,B),f139(poset_of_lattice(A),C,B)) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1126,a,1050,d)]. 41.97/42.12 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f138(c6,B,A),f139(c6,B,A)) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1126,a,1070,a)]. 41.97/42.12 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f138(boole_POSet(A),C,B),f139(boole_POSet(A),C,B)) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1126,a,1072,a)]. 41.97/42.12 1127 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.12 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f138(poset_of_lattice(A),C,B),f139(poset_of_lattice(A),C,B)) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1127,a,1050,d)]. 41.97/42.12 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f138(c6,B,A),f139(c6,B,A)) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1127,a,1070,a)]. 41.97/42.12 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f138(boole_POSet(A),C,B),f139(boole_POSet(A),C,B)) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1127,a,1072,a)]. 41.97/42.12 1128 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.12 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | relstr_set_smaller(poset_of_lattice(A),f138(poset_of_lattice(A),C,B),f139(poset_of_lattice(A),C,B)) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1128,a,1050,d)]. 41.97/42.12 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | relstr_set_smaller(c6,f138(c6,B,A),f139(c6,B,A)) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1128,a,1070,a)]. 41.97/42.12 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | relstr_set_smaller(boole_POSet(A),f138(boole_POSet(A),C,B),f139(boole_POSet(A),C,B)) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1128,a,1072,a)]. 41.97/42.12 1129 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.12 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f139(poset_of_lattice(A),C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1129,a,1050,d)]. 41.97/42.14 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f139(c6,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1129,a,1070,a)]. 41.97/42.14 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f139(boole_POSet(A),C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1129,a,1072,a)]. 41.97/42.14 1130 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.14 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f139(poset_of_lattice(A),C,B),C) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1130,a,1050,d)]. 41.97/42.14 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f139(c6,B,A),B) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1130,a,1070,a)]. 41.97/42.14 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f139(boole_POSet(A),C,B),C) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1130,a,1072,a)]. 41.97/42.14 1131 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.14 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f139(poset_of_lattice(A),C,B),C) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1131,a,1050,d)]. 41.97/42.14 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f139(c6,B,A),B) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1131,a,1070,a)]. 41.97/42.14 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f139(boole_POSet(A),C,B),C) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1131,a,1072,a)]. 41.97/42.14 1132 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.14 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f139(poset_of_lattice(A),C,B),C) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1132,a,1050,d)]. 41.97/42.16 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f139(c6,B,A),B) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1132,a,1070,a)]. 41.97/42.16 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f139(boole_POSet(A),C,B),C) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1132,a,1072,a)]. 41.97/42.16 1133 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.16 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f139(poset_of_lattice(A),C,B),C) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1133,a,1050,d)]. 41.97/42.16 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f139(c6,B,A),B) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1133,a,1070,a)]. 41.97/42.16 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f139(boole_POSet(A),C,B),C) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1133,a,1072,a)]. 41.97/42.16 1134 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.16 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f139(poset_of_lattice(A),C,B),C) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1134,a,1050,d)]. 41.97/42.16 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f139(c6,B,A),B) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1134,a,1070,a)]. 41.97/42.16 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f139(boole_POSet(A),C,B),C) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1134,a,1072,a)]. 41.97/42.16 1135 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.16 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | in(f139(poset_of_lattice(A),C,B),C) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1135,a,1050,d)]. 41.97/42.16 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | in(f139(c6,B,A),B) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1135,a,1070,a)]. 41.97/42.16 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | in(f139(boole_POSet(A),C,B),C) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1135,a,1072,a)]. 41.97/42.18 1136 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.18 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f139(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1136,a,1050,d)]. 41.97/42.18 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f139(c6,B,A),the_carrier(c6)) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1136,a,1070,a)]. 41.97/42.18 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f139(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1136,a,1072,a)]. 41.97/42.18 1137 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.18 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f139(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1137,a,1050,d)]. 41.97/42.18 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f139(c6,B,A),the_carrier(c6)) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1137,a,1070,a)]. 41.97/42.18 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f139(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1137,a,1072,a)]. 41.97/42.18 1138 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 41.97/42.18 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f139(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1138,a,1050,d)]. 41.97/42.18 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f139(c6,B,A),the_carrier(c6)) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1138,a,1070,a)]. 41.97/42.18 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f139(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1138,a,1072,a)]. 42.07/42.20 1139 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.20 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f139(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1139,a,1050,d)]. 42.07/42.20 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f139(c6,B,A),the_carrier(c6)) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1139,a,1070,a)]. 42.07/42.20 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f139(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1139,a,1072,a)]. 42.07/42.20 1140 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.20 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f139(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1140,a,1050,d)]. 42.07/42.20 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f139(c6,B,A),the_carrier(c6)) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1140,a,1070,a)]. 42.07/42.20 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f139(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1140,a,1072,a)]. 42.07/42.20 1141 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.20 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f139(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1141,a,1050,d)]. 42.07/42.20 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f139(c6,B,A),the_carrier(c6)) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1141,a,1070,a)]. 42.07/42.20 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f139(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1141,a,1072,a)]. 42.07/42.22 1142 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.22 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | element(f139(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1142,a,1050,d)]. 42.07/42.22 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | element(f139(c6,B,A),the_carrier(c6)) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1142,a,1070,a)]. 42.07/42.22 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | element(f139(boole_POSet(A),C,B),the_carrier(boole_POSet(A))) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1142,a,1072,a)]. 42.07/42.22 1143 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.22 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) != f134(poset_of_lattice(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(poset_of_lattice(A))) | -in(E,C) | -relstr_set_smaller(poset_of_lattice(A),F,E) | F != V6 | D != V6 | in(V6,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1143,a,1050,d)]. 42.07/42.22 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) != f134(c6,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c6)) | -in(D,B) | -relstr_set_smaller(c6,E,D) | E != F | C != F | in(F,f140(c6,B,A)). [resolve(1143,a,1070,a)]. 42.07/42.22 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) != f134(boole_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(boole_POSet(A))) | -in(E,C) | -relstr_set_smaller(boole_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(boole_POSet(A),C,B)). [resolve(1143,a,1072,a)]. 42.07/42.22 1144 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.22 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) != f134(poset_of_lattice(A),C,B) | in(f141(poset_of_lattice(A),C,B,D),powerset(B)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1144,a,1050,d)]. 42.07/42.22 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) != f134(c6,B,A) | in(f141(c6,B,A,C),powerset(A)) | -in(C,f140(c6,B,A)). [resolve(1144,a,1070,a)]. 42.07/42.22 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) != f134(boole_POSet(A),C,B) | in(f141(boole_POSet(A),C,B,D),powerset(B)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1144,a,1072,a)]. 42.07/42.22 1145 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.24 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) != f134(poset_of_lattice(A),C,B) | element(f143(poset_of_lattice(A),C,B,D),the_carrier(poset_of_lattice(A))) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1145,a,1050,d)]. 42.07/42.24 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) != f134(c6,B,A) | element(f143(c6,B,A,C),the_carrier(c6)) | -in(C,f140(c6,B,A)). [resolve(1145,a,1070,a)]. 42.07/42.24 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) != f134(boole_POSet(A),C,B) | element(f143(boole_POSet(A),C,B,D),the_carrier(boole_POSet(A))) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1145,a,1072,a)]. 42.07/42.24 1146 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.24 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) != f134(poset_of_lattice(A),C,B) | in(f143(poset_of_lattice(A),C,B,D),C) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1146,a,1050,d)]. 42.07/42.24 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) != f134(c6,B,A) | in(f143(c6,B,A,C),B) | -in(C,f140(c6,B,A)). [resolve(1146,a,1070,a)]. 42.07/42.24 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) != f134(boole_POSet(A),C,B) | in(f143(boole_POSet(A),C,B,D),C) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1146,a,1072,a)]. 42.07/42.24 1147 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.24 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) != f134(poset_of_lattice(A),C,B) | relstr_set_smaller(poset_of_lattice(A),f142(poset_of_lattice(A),C,B,D),f143(poset_of_lattice(A),C,B,D)) | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1147,a,1050,d)]. 42.07/42.24 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) != f134(c6,B,A) | relstr_set_smaller(c6,f142(c6,B,A,C),f143(c6,B,A,C)) | -in(C,f140(c6,B,A)). [resolve(1147,a,1070,a)]. 42.07/42.24 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) != f134(boole_POSet(A),C,B) | relstr_set_smaller(boole_POSet(A),f142(boole_POSet(A),C,B,D),f143(boole_POSet(A),C,B,D)) | -in(D,f140(boole_POSet(A),C,B)). [resolve(1147,a,1072,a)]. 42.07/42.24 1148 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.26 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) != f134(poset_of_lattice(A),C,B) | f142(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1148,a,1050,d)]. 42.07/42.26 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) != f134(c6,B,A) | f142(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1148,a,1070,a)]. 42.07/42.26 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) != f134(boole_POSet(A),C,B) | f142(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1148,a,1072,a)]. 42.07/42.26 1149 -transitive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)) # label(s1_tarski__e11_2_1__waybel_0__1) # label(axiom). [clausify(251)]. 42.07/42.26 Derived: -rel_str(poset_of_lattice(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(poset_of_lattice(A)))) | empty_carrier(poset_of_lattice(A)) | f135(poset_of_lattice(A),C,B) != f134(poset_of_lattice(A),C,B) | f141(poset_of_lattice(A),C,B,D) = D | -in(D,f140(poset_of_lattice(A),C,B)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1149,a,1050,d)]. 42.07/42.26 Derived: -rel_str(c6) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c6))) | empty_carrier(c6) | f135(c6,B,A) != f134(c6,B,A) | f141(c6,B,A,C) = C | -in(C,f140(c6,B,A)). [resolve(1149,a,1070,a)]. 42.07/42.26 Derived: -rel_str(boole_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(boole_POSet(A)))) | empty_carrier(boole_POSet(A)) | f135(boole_POSet(A),C,B) != f134(boole_POSet(A),C,B) | f141(boole_POSet(A),C,B,D) = D | -in(D,f140(boole_POSet(A),C,B)). [resolve(1149,a,1072,a)]. 42.07/42.26 1150 transitive_relstr(c15) # label(rc2_orders_2) # label(axiom). [clausify(254)]. 42.07/42.26 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | in(f19(c15,B,A),A) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | relstr_set_smaller(c15,A,f22(c15,B,A)). [resolve(1150,a,1051,f)]. 42.07/42.26 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | in(f19(c15,B,A),A) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | in(f22(c15,B,A),B). [resolve(1150,a,1052,f)]. 42.07/42.26 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | in(f19(c15,B,A),A) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | element(f22(c15,B,A),the_carrier(c15)). [resolve(1150,a,1053,f)]. 42.07/42.26 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | subset(f20(c15,B,A),A) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | relstr_set_smaller(c15,A,f22(c15,B,A)). [resolve(1150,a,1054,f)]. 42.07/42.26 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | subset(f20(c15,B,A),A) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | in(f22(c15,B,A),B). [resolve(1150,a,1055,f)]. 42.07/42.26 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | subset(f20(c15,B,A),A) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | element(f22(c15,B,A),the_carrier(c15)). [resolve(1150,a,1056,f)]. 42.07/42.26 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | element(f21(c15,B,A),the_carrier(c15)) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | relstr_set_smaller(c15,A,f22(c15,B,A)). [resolve(1150,a,1057,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | element(f21(c15,B,A),the_carrier(c15)) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | in(f22(c15,B,A),B). [resolve(1150,a,1058,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | element(f21(c15,B,A),the_carrier(c15)) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | element(f22(c15,B,A),the_carrier(c15)). [resolve(1150,a,1059,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | relstr_set_smaller(c15,f20(c15,B,A),f21(c15,B,A)) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | relstr_set_smaller(c15,A,f22(c15,B,A)). [resolve(1150,a,1060,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | relstr_set_smaller(c15,f20(c15,B,A),f21(c15,B,A)) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | in(f22(c15,B,A),B). [resolve(1150,a,1061,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | relstr_set_smaller(c15,f20(c15,B,A),f21(c15,B,A)) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | element(f22(c15,B,A),the_carrier(c15)). [resolve(1150,a,1062,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | in(f21(c15,B,A),B) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | relstr_set_smaller(c15,A,f22(c15,B,A)). [resolve(1150,a,1063,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | in(f21(c15,B,A),B) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | in(f22(c15,B,A),B). [resolve(1150,a,1064,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | in(f21(c15,B,A),B) | -in(C,B) | -relstr_set_smaller(c15,empty_set,C) | -element(C,the_carrier(c15)) | element(f22(c15,B,A),the_carrier(c15)). [resolve(1150,a,1065,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | -in(C,B) | -relstr_set_smaller(c15,set_union2(f20(c15,B,A),singleton(f19(c15,B,A))),C) | -element(C,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,empty_set,D) | -element(D,the_carrier(c15)) | relstr_set_smaller(c15,A,f22(c15,B,A)). [resolve(1150,a,1066,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | -in(C,B) | -relstr_set_smaller(c15,set_union2(f20(c15,B,A),singleton(f19(c15,B,A))),C) | -element(C,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,empty_set,D) | -element(D,the_carrier(c15)) | in(f22(c15,B,A),B). [resolve(1150,a,1067,f)]. 42.07/42.28 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c15))) | -in(C,B) | -relstr_set_smaller(c15,set_union2(f20(c15,B,A),singleton(f19(c15,B,A))),C) | -element(C,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,empty_set,D) | -element(D,the_carrier(c15)) | element(f22(c15,B,A),the_carrier(c15)). [resolve(1150,a,1068,f)]. 42.07/42.28 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f134(c15,B,A) = f133(c15,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1073,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f134(c15,B,A) = f133(c15,B,A) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1074,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f134(c15,B,A) = f133(c15,B,A) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1075,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f134(c15,B,A) = f133(c15,B,A) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1076,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f134(c15,B,A) = f133(c15,B,A) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1077,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f134(c15,B,A) = f133(c15,B,A) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1078,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f134(c15,B,A) = f133(c15,B,A) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1079,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f136(c15,B,A) = f135(c15,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1080,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f136(c15,B,A) = f135(c15,B,A) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1081,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f136(c15,B,A) = f135(c15,B,A) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1082,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f136(c15,B,A) = f135(c15,B,A) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1083,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f136(c15,B,A) = f135(c15,B,A) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1084,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f136(c15,B,A) = f135(c15,B,A) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1085,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f136(c15,B,A) = f135(c15,B,A) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1086,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f137(c15,B,A),the_carrier(c15)) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1087,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f137(c15,B,A),the_carrier(c15)) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1088,a)]. 42.16/42.30 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f137(c15,B,A),the_carrier(c15)) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1089,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f137(c15,B,A),the_carrier(c15)) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1090,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f137(c15,B,A),the_carrier(c15)) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1091,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f137(c15,B,A),the_carrier(c15)) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1092,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f137(c15,B,A),the_carrier(c15)) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1093,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f136(c15,B,A),f137(c15,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1094,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f136(c15,B,A),f137(c15,B,A)) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1095,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f136(c15,B,A),f137(c15,B,A)) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1096,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f136(c15,B,A),f137(c15,B,A)) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1097,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f136(c15,B,A),f137(c15,B,A)) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1098,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f136(c15,B,A),f137(c15,B,A)) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1099,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f136(c15,B,A),f137(c15,B,A)) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1100,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f137(c15,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1101,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f137(c15,B,A),B) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1102,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f137(c15,B,A),B) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1103,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f137(c15,B,A),B) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1104,a)]. 42.19/42.32 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f137(c15,B,A),B) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1105,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f137(c15,B,A),B) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1106,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f137(c15,B,A),B) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1107,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) = f133(c15,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1108,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) = f133(c15,B,A) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1109,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) = f133(c15,B,A) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1110,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) = f133(c15,B,A) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1111,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) = f133(c15,B,A) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1112,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) = f133(c15,B,A) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1113,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) = f133(c15,B,A) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1114,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f138(c15,B,A) = f134(c15,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1115,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f138(c15,B,A) = f134(c15,B,A) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1116,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f138(c15,B,A) = f134(c15,B,A) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1117,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f138(c15,B,A) = f134(c15,B,A) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1118,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f138(c15,B,A) = f134(c15,B,A) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1119,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f138(c15,B,A) = f134(c15,B,A) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1120,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f138(c15,B,A) = f134(c15,B,A) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1121,a)]. 42.19/42.34 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f138(c15,B,A),f139(c15,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1122,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f138(c15,B,A),f139(c15,B,A)) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1123,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f138(c15,B,A),f139(c15,B,A)) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1124,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f138(c15,B,A),f139(c15,B,A)) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1125,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f138(c15,B,A),f139(c15,B,A)) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1126,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f138(c15,B,A),f139(c15,B,A)) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1127,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | relstr_set_smaller(c15,f138(c15,B,A),f139(c15,B,A)) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1128,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f139(c15,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1129,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f139(c15,B,A),B) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1130,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f139(c15,B,A),B) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1131,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f139(c15,B,A),B) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1132,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f139(c15,B,A),B) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1133,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f139(c15,B,A),B) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1134,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | in(f139(c15,B,A),B) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1135,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f139(c15,B,A),the_carrier(c15)) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1136,a)]. 42.19/42.35 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f139(c15,B,A),the_carrier(c15)) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1137,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f139(c15,B,A),the_carrier(c15)) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1138,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f139(c15,B,A),the_carrier(c15)) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1139,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f139(c15,B,A),the_carrier(c15)) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1140,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f139(c15,B,A),the_carrier(c15)) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1141,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | element(f139(c15,B,A),the_carrier(c15)) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1142,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) != f134(c15,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c15)) | -in(D,B) | -relstr_set_smaller(c15,E,D) | E != F | C != F | in(F,f140(c15,B,A)). [resolve(1150,a,1143,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) != f134(c15,B,A) | in(f141(c15,B,A,C),powerset(A)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1144,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) != f134(c15,B,A) | element(f143(c15,B,A,C),the_carrier(c15)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1145,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) != f134(c15,B,A) | in(f143(c15,B,A,C),B) | -in(C,f140(c15,B,A)). [resolve(1150,a,1146,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) != f134(c15,B,A) | relstr_set_smaller(c15,f142(c15,B,A,C),f143(c15,B,A,C)) | -in(C,f140(c15,B,A)). [resolve(1150,a,1147,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) != f134(c15,B,A) | f142(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1148,a)]. 42.19/42.38 Derived: -rel_str(c15) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c15))) | empty_carrier(c15) | f135(c15,B,A) != f134(c15,B,A) | f141(c15,B,A,C) = C | -in(C,f140(c15,B,A)). [resolve(1150,a,1149,a)]. 42.19/42.38 1151 -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | in(D,powerset(C)) # label(s1_xboole_0__e11_2_1__waybel_0__1) # label(lemma). [clausify(272)]. 42.19/42.38 Derived: -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(poset_of_lattice(A)) | -in(D,f154(poset_of_lattice(A),B,C)) | in(D,powerset(C)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1151,a,1050,d)]. 42.19/42.38 Derived: -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c6) | -in(C,f154(c6,A,B)) | in(C,powerset(B)). [resolve(1151,a,1070,a)]. 42.19/42.38 Derived: -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(boole_POSet(A)) | -in(D,f154(boole_POSet(A),B,C)) | in(D,powerset(C)). [resolve(1151,a,1072,a)]. 42.19/42.38 Derived: -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c15) | -in(C,f154(c15,A,B)) | in(C,powerset(B)). [resolve(1151,a,1150,a)]. 42.28/42.40 1152 -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | f155(A,B,C,D) = D # label(s1_xboole_0__e11_2_1__waybel_0__1) # label(lemma). [clausify(272)]. 42.28/42.40 Derived: -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(poset_of_lattice(A)) | -in(D,f154(poset_of_lattice(A),B,C)) | f155(poset_of_lattice(A),B,C,D) = D | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1152,a,1050,d)]. 42.28/42.40 Derived: -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c6) | -in(C,f154(c6,A,B)) | f155(c6,A,B,C) = C. [resolve(1152,a,1070,a)]. 42.28/42.40 Derived: -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(boole_POSet(A)) | -in(D,f154(boole_POSet(A),B,C)) | f155(boole_POSet(A),B,C,D) = D. [resolve(1152,a,1072,a)]. 42.28/42.40 Derived: -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c15) | -in(C,f154(c15,A,B)) | f155(c15,A,B,C) = C. [resolve(1152,a,1150,a)]. 42.28/42.40 1153 -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | element(f156(A,B,C,D),the_carrier(A)) # label(s1_xboole_0__e11_2_1__waybel_0__1) # label(lemma). [clausify(272)]. 42.28/42.40 Derived: -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(poset_of_lattice(A)) | -in(D,f154(poset_of_lattice(A),B,C)) | element(f156(poset_of_lattice(A),B,C,D),the_carrier(poset_of_lattice(A))) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1153,a,1050,d)]. 42.28/42.40 Derived: -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c6) | -in(C,f154(c6,A,B)) | element(f156(c6,A,B,C),the_carrier(c6)). [resolve(1153,a,1070,a)]. 42.28/42.40 Derived: -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(boole_POSet(A)) | -in(D,f154(boole_POSet(A),B,C)) | element(f156(boole_POSet(A),B,C,D),the_carrier(boole_POSet(A))). [resolve(1153,a,1072,a)]. 42.28/42.40 Derived: -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c15) | -in(C,f154(c15,A,B)) | element(f156(c15,A,B,C),the_carrier(c15)). [resolve(1153,a,1150,a)]. 42.28/42.40 1154 -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | in(f156(A,B,C,D),B) # label(s1_xboole_0__e11_2_1__waybel_0__1) # label(lemma). [clausify(272)]. 42.28/42.40 Derived: -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(poset_of_lattice(A)) | -in(D,f154(poset_of_lattice(A),B,C)) | in(f156(poset_of_lattice(A),B,C,D),B) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1154,a,1050,d)]. 42.28/42.40 Derived: -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c6) | -in(C,f154(c6,A,B)) | in(f156(c6,A,B,C),A). [resolve(1154,a,1070,a)]. 42.28/42.40 Derived: -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(boole_POSet(A)) | -in(D,f154(boole_POSet(A),B,C)) | in(f156(boole_POSet(A),B,C,D),B). [resolve(1154,a,1072,a)]. 42.28/42.40 Derived: -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c15) | -in(C,f154(c15,A,B)) | in(f156(c15,A,B,C),A). [resolve(1154,a,1150,a)]. 42.28/42.40 1155 -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | relstr_set_smaller(A,f155(A,B,C,D),f156(A,B,C,D)) # label(s1_xboole_0__e11_2_1__waybel_0__1) # label(lemma). [clausify(272)]. 42.28/42.43 Derived: -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(poset_of_lattice(A)) | -in(D,f154(poset_of_lattice(A),B,C)) | relstr_set_smaller(poset_of_lattice(A),f155(poset_of_lattice(A),B,C,D),f156(poset_of_lattice(A),B,C,D)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1155,a,1050,d)]. 42.28/42.43 Derived: -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c6) | -in(C,f154(c6,A,B)) | relstr_set_smaller(c6,f155(c6,A,B,C),f156(c6,A,B,C)). [resolve(1155,a,1070,a)]. 42.28/42.43 Derived: -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(boole_POSet(A)) | -in(D,f154(boole_POSet(A),B,C)) | relstr_set_smaller(boole_POSet(A),f155(boole_POSet(A),B,C,D),f156(boole_POSet(A),B,C,D)). [resolve(1155,a,1072,a)]. 42.28/42.43 Derived: -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c15) | -in(C,f154(c15,A,B)) | relstr_set_smaller(c15,f155(c15,A,B,C),f156(c15,A,B,C)). [resolve(1155,a,1150,a)]. 42.28/42.43 1156 -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | in(D,f154(A,B,C)) | -in(D,powerset(C)) | E != D | -element(F,the_carrier(A)) | -in(F,B) | -relstr_set_smaller(A,E,F) # label(s1_xboole_0__e11_2_1__waybel_0__1) # label(lemma). [clausify(272)]. 42.28/42.43 Derived: -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(poset_of_lattice(A)) | in(D,f154(poset_of_lattice(A),B,C)) | -in(D,powerset(C)) | E != D | -element(F,the_carrier(poset_of_lattice(A))) | -in(F,B) | -relstr_set_smaller(poset_of_lattice(A),E,F) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1156,a,1050,d)]. 42.28/42.43 Derived: -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c6) | in(C,f154(c6,A,B)) | -in(C,powerset(B)) | D != C | -element(E,the_carrier(c6)) | -in(E,A) | -relstr_set_smaller(c6,D,E). [resolve(1156,a,1070,a)]. 42.28/42.43 Derived: -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(boole_POSet(A)) | in(D,f154(boole_POSet(A),B,C)) | -in(D,powerset(C)) | E != D | -element(F,the_carrier(boole_POSet(A))) | -in(F,B) | -relstr_set_smaller(boole_POSet(A),E,F). [resolve(1156,a,1072,a)]. 42.28/42.43 Derived: -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c15) | in(C,f154(c15,A,B)) | -in(C,powerset(B)) | D != C | -element(E,the_carrier(c15)) | -in(E,A) | -relstr_set_smaller(c15,D,E). [resolve(1156,a,1150,a)]. 42.28/42.43 1157 transitive_relstr(c18) # label(rc2_yellow_0) # label(axiom). [clausify(275)]. 42.28/42.43 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | in(f19(c18,B,A),A) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | relstr_set_smaller(c18,A,f22(c18,B,A)). [resolve(1157,a,1051,f)]. 42.28/42.43 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | in(f19(c18,B,A),A) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | in(f22(c18,B,A),B). [resolve(1157,a,1052,f)]. 42.28/42.43 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | in(f19(c18,B,A),A) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | element(f22(c18,B,A),the_carrier(c18)). [resolve(1157,a,1053,f)]. 42.28/42.43 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | subset(f20(c18,B,A),A) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | relstr_set_smaller(c18,A,f22(c18,B,A)). [resolve(1157,a,1054,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | subset(f20(c18,B,A),A) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | in(f22(c18,B,A),B). [resolve(1157,a,1055,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | subset(f20(c18,B,A),A) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | element(f22(c18,B,A),the_carrier(c18)). [resolve(1157,a,1056,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | element(f21(c18,B,A),the_carrier(c18)) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | relstr_set_smaller(c18,A,f22(c18,B,A)). [resolve(1157,a,1057,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | element(f21(c18,B,A),the_carrier(c18)) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | in(f22(c18,B,A),B). [resolve(1157,a,1058,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | element(f21(c18,B,A),the_carrier(c18)) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | element(f22(c18,B,A),the_carrier(c18)). [resolve(1157,a,1059,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | relstr_set_smaller(c18,f20(c18,B,A),f21(c18,B,A)) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | relstr_set_smaller(c18,A,f22(c18,B,A)). [resolve(1157,a,1060,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | relstr_set_smaller(c18,f20(c18,B,A),f21(c18,B,A)) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | in(f22(c18,B,A),B). [resolve(1157,a,1061,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | relstr_set_smaller(c18,f20(c18,B,A),f21(c18,B,A)) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | element(f22(c18,B,A),the_carrier(c18)). [resolve(1157,a,1062,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | in(f21(c18,B,A),B) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | relstr_set_smaller(c18,A,f22(c18,B,A)). [resolve(1157,a,1063,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | in(f21(c18,B,A),B) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | in(f22(c18,B,A),B). [resolve(1157,a,1064,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | in(f21(c18,B,A),B) | -in(C,B) | -relstr_set_smaller(c18,empty_set,C) | -element(C,the_carrier(c18)) | element(f22(c18,B,A),the_carrier(c18)). [resolve(1157,a,1065,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | -in(C,B) | -relstr_set_smaller(c18,set_union2(f20(c18,B,A),singleton(f19(c18,B,A))),C) | -element(C,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,empty_set,D) | -element(D,the_carrier(c18)) | relstr_set_smaller(c18,A,f22(c18,B,A)). [resolve(1157,a,1066,f)]. 42.28/42.44 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | -in(C,B) | -relstr_set_smaller(c18,set_union2(f20(c18,B,A),singleton(f19(c18,B,A))),C) | -element(C,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,empty_set,D) | -element(D,the_carrier(c18)) | in(f22(c18,B,A),B). [resolve(1157,a,1067,f)]. 42.28/42.46 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c18))) | -in(C,B) | -relstr_set_smaller(c18,set_union2(f20(c18,B,A),singleton(f19(c18,B,A))),C) | -element(C,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,empty_set,D) | -element(D,the_carrier(c18)) | element(f22(c18,B,A),the_carrier(c18)). [resolve(1157,a,1068,f)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f134(c18,B,A) = f133(c18,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1073,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f134(c18,B,A) = f133(c18,B,A) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1074,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f134(c18,B,A) = f133(c18,B,A) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1075,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f134(c18,B,A) = f133(c18,B,A) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1076,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f134(c18,B,A) = f133(c18,B,A) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1077,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f134(c18,B,A) = f133(c18,B,A) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1078,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f134(c18,B,A) = f133(c18,B,A) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1079,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f136(c18,B,A) = f135(c18,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1080,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f136(c18,B,A) = f135(c18,B,A) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1081,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f136(c18,B,A) = f135(c18,B,A) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1082,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f136(c18,B,A) = f135(c18,B,A) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1083,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f136(c18,B,A) = f135(c18,B,A) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1084,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f136(c18,B,A) = f135(c18,B,A) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1085,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f136(c18,B,A) = f135(c18,B,A) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1086,a)]. 42.28/42.46 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f137(c18,B,A),the_carrier(c18)) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1087,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f137(c18,B,A),the_carrier(c18)) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1088,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f137(c18,B,A),the_carrier(c18)) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1089,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f137(c18,B,A),the_carrier(c18)) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1090,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f137(c18,B,A),the_carrier(c18)) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1091,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f137(c18,B,A),the_carrier(c18)) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1092,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f137(c18,B,A),the_carrier(c18)) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1093,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f136(c18,B,A),f137(c18,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1094,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f136(c18,B,A),f137(c18,B,A)) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1095,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f136(c18,B,A),f137(c18,B,A)) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1096,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f136(c18,B,A),f137(c18,B,A)) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1097,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f136(c18,B,A),f137(c18,B,A)) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1098,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f136(c18,B,A),f137(c18,B,A)) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1099,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f136(c18,B,A),f137(c18,B,A)) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1100,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f137(c18,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1101,a)]. 42.36/42.48 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f137(c18,B,A),B) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1102,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f137(c18,B,A),B) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1103,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f137(c18,B,A),B) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1104,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f137(c18,B,A),B) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1105,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f137(c18,B,A),B) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1106,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f137(c18,B,A),B) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1107,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) = f133(c18,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1108,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) = f133(c18,B,A) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1109,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) = f133(c18,B,A) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1110,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) = f133(c18,B,A) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1111,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) = f133(c18,B,A) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1112,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) = f133(c18,B,A) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1113,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) = f133(c18,B,A) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1114,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f138(c18,B,A) = f134(c18,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1115,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f138(c18,B,A) = f134(c18,B,A) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1116,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f138(c18,B,A) = f134(c18,B,A) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1117,a)]. 42.36/42.50 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f138(c18,B,A) = f134(c18,B,A) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1118,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f138(c18,B,A) = f134(c18,B,A) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1119,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f138(c18,B,A) = f134(c18,B,A) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1120,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f138(c18,B,A) = f134(c18,B,A) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1121,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f138(c18,B,A),f139(c18,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1122,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f138(c18,B,A),f139(c18,B,A)) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1123,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f138(c18,B,A),f139(c18,B,A)) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1124,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f138(c18,B,A),f139(c18,B,A)) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1125,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f138(c18,B,A),f139(c18,B,A)) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1126,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f138(c18,B,A),f139(c18,B,A)) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1127,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | relstr_set_smaller(c18,f138(c18,B,A),f139(c18,B,A)) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1128,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f139(c18,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1129,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f139(c18,B,A),B) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1130,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f139(c18,B,A),B) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1131,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f139(c18,B,A),B) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1132,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f139(c18,B,A),B) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1133,a)]. 42.36/42.52 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f139(c18,B,A),B) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1134,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | in(f139(c18,B,A),B) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1135,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f139(c18,B,A),the_carrier(c18)) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1136,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f139(c18,B,A),the_carrier(c18)) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1137,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f139(c18,B,A),the_carrier(c18)) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1138,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f139(c18,B,A),the_carrier(c18)) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1139,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f139(c18,B,A),the_carrier(c18)) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1140,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f139(c18,B,A),the_carrier(c18)) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1141,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | element(f139(c18,B,A),the_carrier(c18)) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1142,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) != f134(c18,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c18)) | -in(D,B) | -relstr_set_smaller(c18,E,D) | E != F | C != F | in(F,f140(c18,B,A)). [resolve(1157,a,1143,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) != f134(c18,B,A) | in(f141(c18,B,A,C),powerset(A)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1144,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) != f134(c18,B,A) | element(f143(c18,B,A,C),the_carrier(c18)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1145,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) != f134(c18,B,A) | in(f143(c18,B,A,C),B) | -in(C,f140(c18,B,A)). [resolve(1157,a,1146,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) != f134(c18,B,A) | relstr_set_smaller(c18,f142(c18,B,A,C),f143(c18,B,A,C)) | -in(C,f140(c18,B,A)). [resolve(1157,a,1147,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) != f134(c18,B,A) | f142(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1148,a)]. 42.36/42.54 Derived: -rel_str(c18) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c18))) | empty_carrier(c18) | f135(c18,B,A) != f134(c18,B,A) | f141(c18,B,A,C) = C | -in(C,f140(c18,B,A)). [resolve(1157,a,1149,a)]. 42.36/42.54 Derived: -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c18) | -in(C,f154(c18,A,B)) | in(C,powerset(B)). [resolve(1157,a,1151,a)]. 42.36/42.54 Derived: -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c18) | -in(C,f154(c18,A,B)) | f155(c18,A,B,C) = C. [resolve(1157,a,1152,a)]. 42.46/42.60 Derived: -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c18) | -in(C,f154(c18,A,B)) | element(f156(c18,A,B,C),the_carrier(c18)). [resolve(1157,a,1153,a)]. 42.46/42.60 Derived: -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c18) | -in(C,f154(c18,A,B)) | in(f156(c18,A,B,C),A). [resolve(1157,a,1154,a)]. 42.46/42.60 Derived: -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c18) | -in(C,f154(c18,A,B)) | relstr_set_smaller(c18,f155(c18,A,B,C),f156(c18,A,B,C)). [resolve(1157,a,1155,a)]. 42.46/42.60 Derived: -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c18) | in(C,f154(c18,A,B)) | -in(C,powerset(B)) | D != C | -element(E,the_carrier(c18)) | -in(E,A) | -relstr_set_smaller(c18,D,E). [resolve(1157,a,1156,a)]. 42.46/42.60 1158 -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | relation(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(344)]. 42.46/42.60 Derived: -antisymmetric_relstr(poset_of_lattice(A)) | -rel_str(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(1158,a,1050,d)]. 42.46/42.60 Derived: -antisymmetric_relstr(c6) | -rel_str(c6) | -reflexive_relstr(c6) | relation(the_InternalRel(c6)). [resolve(1158,a,1070,a)]. 42.46/42.60 Derived: -antisymmetric_relstr(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | relation(the_InternalRel(boole_POSet(A))). [resolve(1158,a,1072,a)]. 42.46/42.60 Derived: -antisymmetric_relstr(c15) | -rel_str(c15) | -reflexive_relstr(c15) | relation(the_InternalRel(c15)). [resolve(1158,a,1150,a)]. 42.46/42.60 Derived: -antisymmetric_relstr(c18) | -rel_str(c18) | -reflexive_relstr(c18) | relation(the_InternalRel(c18)). [resolve(1158,a,1157,a)]. 42.46/42.60 1159 -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | reflexive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(344)]. 42.46/42.60 Derived: -antisymmetric_relstr(poset_of_lattice(A)) | -rel_str(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(1159,a,1050,d)]. 42.46/42.60 Derived: -antisymmetric_relstr(c6) | -rel_str(c6) | -reflexive_relstr(c6) | reflexive(the_InternalRel(c6)). [resolve(1159,a,1070,a)]. 42.46/42.60 Derived: -antisymmetric_relstr(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | reflexive(the_InternalRel(boole_POSet(A))). [resolve(1159,a,1072,a)]. 42.46/42.60 Derived: -antisymmetric_relstr(c15) | -rel_str(c15) | -reflexive_relstr(c15) | reflexive(the_InternalRel(c15)). [resolve(1159,a,1150,a)]. 42.46/42.60 Derived: -antisymmetric_relstr(c18) | -rel_str(c18) | -reflexive_relstr(c18) | reflexive(the_InternalRel(c18)). [resolve(1159,a,1157,a)]. 42.46/42.60 1160 -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | transitive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(344)]. 42.46/42.60 Derived: -antisymmetric_relstr(poset_of_lattice(A)) | -rel_str(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(1160,a,1050,d)]. 42.46/42.60 Derived: -antisymmetric_relstr(c6) | -rel_str(c6) | -reflexive_relstr(c6) | transitive(the_InternalRel(c6)). [resolve(1160,a,1070,a)]. 42.46/42.60 Derived: -antisymmetric_relstr(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | transitive(the_InternalRel(boole_POSet(A))). [resolve(1160,a,1072,a)]. 42.46/42.60 Derived: -antisymmetric_relstr(c15) | -rel_str(c15) | -reflexive_relstr(c15) | transitive(the_InternalRel(c15)). [resolve(1160,a,1150,a)]. 42.46/42.60 Derived: -antisymmetric_relstr(c18) | -rel_str(c18) | -reflexive_relstr(c18) | transitive(the_InternalRel(c18)). [resolve(1160,a,1157,a)]. 43.39/43.57 1161 -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(fc2_orders_2) # label(axiom). [clausify(344)]. 43.39/43.57 Derived: -antisymmetric_relstr(poset_of_lattice(A)) | -rel_str(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(1161,a,1050,d)]. 43.39/43.57 Derived: -antisymmetric_relstr(c6) | -rel_str(c6) | -reflexive_relstr(c6) | v1_partfun1(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(1161,a,1070,a)]. 43.39/43.57 Derived: -antisymmetric_relstr(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | v1_partfun1(the_InternalRel(boole_POSet(A)),the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))). [resolve(1161,a,1072,a)]. 43.39/43.57 Derived: -antisymmetric_relstr(c15) | -rel_str(c15) | -reflexive_relstr(c15) | v1_partfun1(the_InternalRel(c15),the_carrier(c15),the_carrier(c15)). [resolve(1161,a,1150,a)]. 43.39/43.57 Derived: -antisymmetric_relstr(c18) | -rel_str(c18) | -reflexive_relstr(c18) | v1_partfun1(the_InternalRel(c18),the_carrier(c18),the_carrier(c18)). [resolve(1161,a,1157,a)]. 43.39/43.57 1162 -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | antisymmetric(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(344)]. 43.39/43.57 Derived: -antisymmetric_relstr(poset_of_lattice(A)) | -rel_str(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(1162,a,1050,d)]. 43.39/43.57 Derived: -antisymmetric_relstr(c6) | -rel_str(c6) | -reflexive_relstr(c6) | antisymmetric(the_InternalRel(c6)). [resolve(1162,a,1070,a)]. 43.39/43.57 Derived: -antisymmetric_relstr(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | antisymmetric(the_InternalRel(boole_POSet(A))). [resolve(1162,a,1072,a)]. 43.39/43.57 Derived: -antisymmetric_relstr(c15) | -rel_str(c15) | -reflexive_relstr(c15) | antisymmetric(the_InternalRel(c15)). [resolve(1162,a,1150,a)]. 43.39/43.57 Derived: -antisymmetric_relstr(c18) | -rel_str(c18) | -reflexive_relstr(c18) | antisymmetric(the_InternalRel(c18)). [resolve(1162,a,1157,a)]. 43.39/43.57 1163 empty_carrier(A) | -latt_str(A) | -lattice(A) | transitive_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(365)]. 43.39/43.57 1164 -rel_str(A) | -transitive_relstr(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -related(A,C,D) | -related(A,B,C) | related(A,B,D) # label(t26_orders_2) # label(lemma). [clausify(414)]. 43.39/43.57 Derived: -rel_str(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -element(D,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),C,D) | -related(poset_of_lattice(A),B,C) | related(poset_of_lattice(A),B,D) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1164,b,1050,d)]. 43.39/43.57 Derived: -rel_str(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | -element(C,the_carrier(c6)) | -related(c6,B,C) | -related(c6,A,B) | related(c6,A,C). [resolve(1164,b,1070,a)]. 43.39/43.57 Derived: -rel_str(boole_POSet(A)) | -element(B,the_carrier(boole_POSet(A))) | -element(C,the_carrier(boole_POSet(A))) | -element(D,the_carrier(boole_POSet(A))) | -related(boole_POSet(A),C,D) | -related(boole_POSet(A),B,C) | related(boole_POSet(A),B,D). [resolve(1164,b,1072,a)]. 43.39/43.57 Derived: -rel_str(c15) | -element(A,the_carrier(c15)) | -element(B,the_carrier(c15)) | -element(C,the_carrier(c15)) | -related(c15,B,C) | -related(c15,A,B) | related(c15,A,C). [resolve(1164,b,1150,a)]. 43.39/43.57 Derived: -rel_str(c18) | -element(A,the_carrier(c18)) | -element(B,the_carrier(c18)) | -element(C,the_carrier(c18)) | -related(c18,B,C) | -related(c18,A,B) | related(c18,A,C). [resolve(1164,b,1157,a)]. 43.39/43.57 1165 empty_carrier(A) | -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f268(A,B),powerset(B)) | -empty(B) # label(t1_waybel_0) # label(lemma). [clausify(491)]. 43.39/43.60 Derived: empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | element(f268(poset_of_lattice(A),B),powerset(B)) | -empty(B) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1165,b,1050,d)]. 43.39/43.60 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | element(f268(c6,A),powerset(A)) | -empty(A). [resolve(1165,b,1070,a)]. 43.39/43.60 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | element(f268(boole_POSet(A),B),powerset(B)) | -empty(B). [resolve(1165,b,1072,a)]. 43.39/43.60 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | element(f268(c15,A),powerset(A)) | -empty(A). [resolve(1165,b,1150,a)]. 43.39/43.60 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | element(f268(c18,A),powerset(A)) | -empty(A). [resolve(1165,b,1157,a)]. 43.39/43.60 1166 empty_carrier(A) | -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f268(A,B),powerset(B)) | directed_subset(B,A) # label(t1_waybel_0) # label(lemma). [clausify(491)]. 43.39/43.60 Derived: empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | element(f268(poset_of_lattice(A),B),powerset(B)) | directed_subset(B,poset_of_lattice(A)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1166,b,1050,d)]. 43.39/43.60 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | element(f268(c6,A),powerset(A)) | directed_subset(A,c6). [resolve(1166,b,1070,a)]. 43.39/43.60 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | element(f268(boole_POSet(A),B),powerset(B)) | directed_subset(B,boole_POSet(A)). [resolve(1166,b,1072,a)]. 43.39/43.60 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | element(f268(c15,A),powerset(A)) | directed_subset(A,c15). [resolve(1166,b,1150,a)]. 43.39/43.60 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | element(f268(c18,A),powerset(A)) | directed_subset(A,c18). [resolve(1166,b,1157,a)]. 43.39/43.60 1167 empty_carrier(A) | -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | finite(f268(A,B)) | -empty(B) # label(t1_waybel_0) # label(lemma). [clausify(491)]. 43.39/43.60 Derived: empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | finite(f268(poset_of_lattice(A),B)) | -empty(B) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1167,b,1050,d)]. 43.39/43.60 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | finite(f268(c6,A)) | -empty(A). [resolve(1167,b,1070,a)]. 43.39/43.60 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | finite(f268(boole_POSet(A),B)) | -empty(B). [resolve(1167,b,1072,a)]. 43.39/43.60 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | finite(f268(c15,A)) | -empty(A). [resolve(1167,b,1150,a)]. 43.39/43.60 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | finite(f268(c18,A)) | -empty(A). [resolve(1167,b,1157,a)]. 43.39/43.60 1168 empty_carrier(A) | -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | finite(f268(A,B)) | directed_subset(B,A) # label(t1_waybel_0) # label(lemma). [clausify(491)]. 43.39/43.60 Derived: empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | finite(f268(poset_of_lattice(A),B)) | directed_subset(B,poset_of_lattice(A)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1168,b,1050,d)]. 43.39/43.60 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | finite(f268(c6,A)) | directed_subset(A,c6). [resolve(1168,b,1070,a)]. 43.39/43.60 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | finite(f268(boole_POSet(A),B)) | directed_subset(B,boole_POSet(A)). [resolve(1168,b,1072,a)]. 43.48/43.62 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | finite(f268(c15,A)) | directed_subset(A,c15). [resolve(1168,b,1150,a)]. 43.48/43.62 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | finite(f268(c18,A)) | directed_subset(A,c18). [resolve(1168,b,1157,a)]. 43.48/43.62 1169 empty_carrier(A) | -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,B) | -relstr_set_smaller(A,f268(A,B),C) | -element(C,the_carrier(A)) | -empty(B) # label(t1_waybel_0) # label(lemma). [clausify(491)]. 43.48/43.62 1170 empty_carrier(A) | -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,B) | -relstr_set_smaller(A,f268(A,B),C) | -element(C,the_carrier(A)) | directed_subset(B,A) # label(t1_waybel_0) # label(lemma). [clausify(491)]. 43.48/43.62 Derived: empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -in(C,B) | -relstr_set_smaller(poset_of_lattice(A),f268(poset_of_lattice(A),B),C) | -element(C,the_carrier(poset_of_lattice(A))) | directed_subset(B,poset_of_lattice(A)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1170,b,1050,d)]. 43.48/43.62 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -in(B,A) | -relstr_set_smaller(c6,f268(c6,A),B) | -element(B,the_carrier(c6)) | directed_subset(A,c6). [resolve(1170,b,1070,a)]. 43.48/43.62 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -in(C,B) | -relstr_set_smaller(boole_POSet(A),f268(boole_POSet(A),B),C) | -element(C,the_carrier(boole_POSet(A))) | directed_subset(B,boole_POSet(A)). [resolve(1170,b,1072,a)]. 43.48/43.62 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -in(B,A) | -relstr_set_smaller(c15,f268(c15,A),B) | -element(B,the_carrier(c15)) | directed_subset(A,c15). [resolve(1170,b,1150,a)]. 43.48/43.62 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -in(B,A) | -relstr_set_smaller(c18,f268(c18,A),B) | -element(B,the_carrier(c18)) | directed_subset(A,c18). [resolve(1170,b,1157,a)]. 43.48/43.62 1171 empty_carrier(A) | -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(B)) | -finite(C) | in(f269(A,B,C),B) | empty(B) | -directed_subset(B,A) # label(t1_waybel_0) # label(lemma). [clausify(491)]. 43.48/43.62 Derived: empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -element(C,powerset(B)) | -finite(C) | in(f269(poset_of_lattice(A),B,C),B) | empty(B) | -directed_subset(B,poset_of_lattice(A)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1171,b,1050,d)]. 43.48/43.62 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -element(B,powerset(A)) | -finite(B) | in(f269(c6,A,B),A) | empty(A) | -directed_subset(A,c6). [resolve(1171,b,1070,a)]. 43.48/43.62 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -element(C,powerset(B)) | -finite(C) | in(f269(boole_POSet(A),B,C),B) | empty(B) | -directed_subset(B,boole_POSet(A)). [resolve(1171,b,1072,a)]. 43.48/43.62 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -element(B,powerset(A)) | -finite(B) | in(f269(c15,A,B),A) | empty(A) | -directed_subset(A,c15). [resolve(1171,b,1150,a)]. 43.48/43.62 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -element(B,powerset(A)) | -finite(B) | in(f269(c18,A,B),A) | empty(A) | -directed_subset(A,c18). [resolve(1171,b,1157,a)]. 43.48/43.62 1172 empty_carrier(A) | -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f269(A,B,C)) | empty(B) | -directed_subset(B,A) # label(t1_waybel_0) # label(lemma). [clausify(491)]. 43.48/43.62 Derived: empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(poset_of_lattice(A),C,f269(poset_of_lattice(A),B,C)) | empty(B) | -directed_subset(B,poset_of_lattice(A)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1172,b,1050,d)]. 43.57/43.74 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -element(B,powerset(A)) | -finite(B) | relstr_set_smaller(c6,B,f269(c6,A,B)) | empty(A) | -directed_subset(A,c6). [resolve(1172,b,1070,a)]. 43.57/43.74 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(boole_POSet(A),C,f269(boole_POSet(A),B,C)) | empty(B) | -directed_subset(B,boole_POSet(A)). [resolve(1172,b,1072,a)]. 43.57/43.74 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -element(B,powerset(A)) | -finite(B) | relstr_set_smaller(c15,B,f269(c15,A,B)) | empty(A) | -directed_subset(A,c15). [resolve(1172,b,1150,a)]. 43.57/43.74 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -element(B,powerset(A)) | -finite(B) | relstr_set_smaller(c18,B,f269(c18,A,B)) | empty(A) | -directed_subset(A,c18). [resolve(1172,b,1157,a)]. 43.57/43.74 1173 empty_carrier(A) | -transitive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(B)) | -finite(C) | element(f269(A,B,C),the_carrier(A)) | empty(B) | -directed_subset(B,A) # label(t1_waybel_0) # label(lemma). [clausify(491)]. 43.57/43.74 Derived: empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -element(C,powerset(B)) | -finite(C) | element(f269(poset_of_lattice(A),B,C),the_carrier(poset_of_lattice(A))) | empty(B) | -directed_subset(B,poset_of_lattice(A)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1173,b,1050,d)]. 43.57/43.74 Derived: empty_carrier(c6) | -rel_str(c6) | -element(A,powerset(the_carrier(c6))) | -element(B,powerset(A)) | -finite(B) | element(f269(c6,A,B),the_carrier(c6)) | empty(A) | -directed_subset(A,c6). [resolve(1173,b,1070,a)]. 43.57/43.74 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -element(C,powerset(B)) | -finite(C) | element(f269(boole_POSet(A),B,C),the_carrier(boole_POSet(A))) | empty(B) | -directed_subset(B,boole_POSet(A)). [resolve(1173,b,1072,a)]. 43.57/43.74 Derived: empty_carrier(c15) | -rel_str(c15) | -element(A,powerset(the_carrier(c15))) | -element(B,powerset(A)) | -finite(B) | element(f269(c15,A,B),the_carrier(c15)) | empty(A) | -directed_subset(A,c15). [resolve(1173,b,1150,a)]. 43.57/43.74 Derived: empty_carrier(c18) | -rel_str(c18) | -element(A,powerset(the_carrier(c18))) | -element(B,powerset(A)) | -finite(B) | element(f269(c18,A,B),the_carrier(c18)) | empty(A) | -directed_subset(A,c18). [resolve(1173,b,1157,a)]. 43.57/43.74 1174 -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | transitive_relstr(A) # label(d5_orders_2) # label(axiom). [clausify(517)]. 43.57/43.74 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f19(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1174,c,1051,f)]. 43.57/43.74 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f19(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1174,c,1052,f)]. 43.57/43.74 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f19(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1174,c,1053,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | subset(f20(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1174,c,1054,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | subset(f20(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1174,c,1055,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | subset(f20(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1174,c,1056,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | element(f21(A,C,B),the_carrier(A)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1174,c,1057,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | element(f21(A,C,B),the_carrier(A)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1174,c,1058,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | element(f21(A,C,B),the_carrier(A)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1174,c,1059,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | relstr_set_smaller(A,f20(A,C,B),f21(A,C,B)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1174,c,1060,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | relstr_set_smaller(A,f20(A,C,B),f21(A,C,B)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1174,c,1061,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | relstr_set_smaller(A,f20(A,C,B),f21(A,C,B)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1174,c,1062,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f21(A,C,B),C) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1174,c,1063,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f21(A,C,B),C) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1174,c,1064,f)]. 43.57/43.75 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f21(A,C,B),C) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1174,c,1065,f)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -in(D,C) | -relstr_set_smaller(A,set_union2(f20(A,C,B),singleton(f19(A,C,B))),D) | -element(D,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,empty_set,E) | -element(E,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1174,c,1066,f)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -in(D,C) | -relstr_set_smaller(A,set_union2(f20(A,C,B),singleton(f19(A,C,B))),D) | -element(D,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,empty_set,E) | -element(E,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1174,c,1067,f)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -in(D,C) | -relstr_set_smaller(A,set_union2(f20(A,C,B),singleton(f19(A,C,B))),D) | -element(D,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,empty_set,E) | -element(E,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1174,c,1068,f)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1073,a)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1074,a)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1075,a)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1076,a)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1077,a)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1078,a)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1079,a)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1080,a)]. 43.57/43.76 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1081,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1082,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1083,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1084,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1085,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1086,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1087,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1088,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1089,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1090,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1091,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1092,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1093,a)]. 43.57/43.77 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1094,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1095,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1096,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1097,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1098,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1099,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1100,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1101,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1102,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1103,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1104,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1105,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1106,a)]. 43.66/43.79 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1107,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1108,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1109,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1110,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1111,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1112,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1113,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1114,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1115,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1116,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1117,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1118,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1119,a)]. 43.68/43.80 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1120,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1121,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1122,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1123,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1124,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1125,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1126,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1127,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1128,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1129,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1130,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1131,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1132,a)]. 43.69/43.82 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1133,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1134,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1135,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1136,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1137,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1138,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1139,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1140,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1141,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1142,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1174,c,1143,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1174,c,1144,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1174,c,1145,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1174,c,1146,a)]. 43.69/43.83 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1174,c,1147,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1148,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1174,c,1149,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | in(D,powerset(C)). [resolve(1174,c,1151,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | f155(A,B,C,D) = D. [resolve(1174,c,1152,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | element(f156(A,B,C,D),the_carrier(A)). [resolve(1174,c,1153,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | in(f156(A,B,C,D),B). [resolve(1174,c,1154,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | relstr_set_smaller(A,f155(A,B,C,D),f156(A,B,C,D)). [resolve(1174,c,1155,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | in(D,f154(A,B,C)) | -in(D,powerset(C)) | E != D | -element(F,the_carrier(A)) | -in(F,B) | -relstr_set_smaller(A,E,F). [resolve(1174,c,1156,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | relation(the_InternalRel(A)). [resolve(1174,c,1158,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | reflexive(the_InternalRel(A)). [resolve(1174,c,1159,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | transitive(the_InternalRel(A)). [resolve(1174,c,1160,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)). [resolve(1174,c,1161,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | antisymmetric(the_InternalRel(A)). [resolve(1174,c,1162,a)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -related(A,C,D) | -related(A,B,C) | related(A,B,D). [resolve(1174,c,1164,b)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f268(A,B),powerset(B)) | -empty(B). [resolve(1174,c,1165,b)]. 43.69/43.85 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f268(A,B),powerset(B)) | directed_subset(B,A). [resolve(1174,c,1166,b)]. 43.78/43.98 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | finite(f268(A,B)) | -empty(B). [resolve(1174,c,1167,b)]. 43.78/43.98 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | finite(f268(A,B)) | directed_subset(B,A). [resolve(1174,c,1168,b)]. 43.78/43.98 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,B) | -relstr_set_smaller(A,f268(A,B),C) | -element(C,the_carrier(A)) | directed_subset(B,A). [resolve(1174,c,1170,b)]. 43.78/43.98 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(B)) | -finite(C) | in(f269(A,B,C),B) | empty(B) | -directed_subset(B,A). [resolve(1174,c,1171,b)]. 43.78/43.98 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f269(A,B,C)) | empty(B) | -directed_subset(B,A). [resolve(1174,c,1172,b)]. 43.78/43.98 Derived: -rel_str(A) | -is_transitive_in(the_InternalRel(A),the_carrier(A)) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(B)) | -finite(C) | element(f269(A,B,C),the_carrier(A)) | empty(B) | -directed_subset(B,A). [resolve(1174,c,1173,b)]. 43.78/43.98 1175 -rel_str(A) | is_transitive_in(the_InternalRel(A),the_carrier(A)) | -transitive_relstr(A) # label(d5_orders_2) # label(axiom). [clausify(517)]. 43.78/43.98 Derived: -rel_str(poset_of_lattice(A)) | is_transitive_in(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1175,c,1050,d)]. 43.78/43.98 Derived: -rel_str(c6) | is_transitive_in(the_InternalRel(c6),the_carrier(c6)). [resolve(1175,c,1070,a)]. 43.78/43.98 Derived: -rel_str(boole_POSet(A)) | is_transitive_in(the_InternalRel(boole_POSet(A)),the_carrier(boole_POSet(A))). [resolve(1175,c,1072,a)]. 43.78/43.98 Derived: -rel_str(c15) | is_transitive_in(the_InternalRel(c15),the_carrier(c15)). [resolve(1175,c,1150,a)]. 43.78/43.98 Derived: -rel_str(c18) | is_transitive_in(the_InternalRel(c18),the_carrier(c18)). [resolve(1175,c,1157,a)]. 43.78/43.98 1176 -latt_str(A) | -complete_latt_str(A) | -lattice(A) | empty_carrier(A) | transitive_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(527)]. 43.78/43.98 1177 -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | transitive_relstr(A) # label(cc2_yellow_0) # label(axiom). [clausify(530)]. 43.78/43.98 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f19(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1177,e,1051,f)]. 43.78/43.98 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f19(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1177,e,1052,f)]. 43.78/43.98 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f19(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1177,e,1053,f)]. 43.78/43.98 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | subset(f20(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1177,e,1054,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | subset(f20(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1177,e,1055,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | subset(f20(A,C,B),B) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1177,e,1056,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | element(f21(A,C,B),the_carrier(A)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1177,e,1057,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | element(f21(A,C,B),the_carrier(A)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1177,e,1058,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | element(f21(A,C,B),the_carrier(A)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1177,e,1059,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | relstr_set_smaller(A,f20(A,C,B),f21(A,C,B)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1177,e,1060,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | relstr_set_smaller(A,f20(A,C,B),f21(A,C,B)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1177,e,1061,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | relstr_set_smaller(A,f20(A,C,B),f21(A,C,B)) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1177,e,1062,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f21(A,C,B),C) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1177,e,1063,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f21(A,C,B),C) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1177,e,1064,f)]. 43.87/44.00 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | in(f21(A,C,B),C) | -in(D,C) | -relstr_set_smaller(A,empty_set,D) | -element(D,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1177,e,1065,f)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -in(D,C) | -relstr_set_smaller(A,set_union2(f20(A,C,B),singleton(f19(A,C,B))),D) | -element(D,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,empty_set,E) | -element(E,the_carrier(A)) | relstr_set_smaller(A,B,f22(A,C,B)). [resolve(1177,e,1066,f)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -in(D,C) | -relstr_set_smaller(A,set_union2(f20(A,C,B),singleton(f19(A,C,B))),D) | -element(D,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,empty_set,E) | -element(E,the_carrier(A)) | in(f22(A,C,B),C). [resolve(1177,e,1067,f)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(A))) | -in(D,C) | -relstr_set_smaller(A,set_union2(f20(A,C,B),singleton(f19(A,C,B))),D) | -element(D,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,empty_set,E) | -element(E,the_carrier(A)) | element(f22(A,C,B),the_carrier(A)). [resolve(1177,e,1068,f)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1073,a)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1074,a)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1075,a)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1076,a)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1077,a)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1078,a)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f134(A,C,B) = f133(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1079,a)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1080,a)]. 43.87/44.01 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1081,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1082,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1083,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1084,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1085,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f136(A,C,B) = f135(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1086,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1087,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1088,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1089,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1090,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1091,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1092,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f137(A,C,B),the_carrier(A)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1093,a)]. 43.87/44.03 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1094,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1095,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1096,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1097,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1098,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1099,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f136(A,C,B),f137(A,C,B)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1100,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1101,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1102,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1103,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1104,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1105,a)]. 43.87/44.04 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1106,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f137(A,C,B),C) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1107,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1108,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1109,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1110,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1111,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1112,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1113,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) = f133(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1114,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1115,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1116,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1117,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1118,a)]. 43.87/44.06 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1119,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1120,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f138(A,C,B) = f134(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1121,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1122,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1123,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1124,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1125,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1126,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1127,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | relstr_set_smaller(A,f138(A,C,B),f139(A,C,B)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1128,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1129,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1130,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1131,a)]. 43.87/44.08 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1132,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1133,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1134,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | in(f139(A,C,B),C) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1135,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1136,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1137,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1138,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1139,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1140,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1141,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | element(f139(A,C,B),the_carrier(A)) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1142,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | -in(D,powerset(B)) | -element(E,the_carrier(A)) | -in(E,C) | -relstr_set_smaller(A,F,E) | F != V6 | D != V6 | in(V6,f140(A,C,B)). [resolve(1177,e,1143,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | in(f141(A,C,B,D),powerset(B)) | -in(D,f140(A,C,B)). [resolve(1177,e,1144,a)]. 43.97/44.10 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | element(f143(A,C,B,D),the_carrier(A)) | -in(D,f140(A,C,B)). [resolve(1177,e,1145,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | in(f143(A,C,B,D),C) | -in(D,f140(A,C,B)). [resolve(1177,e,1146,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | relstr_set_smaller(A,f142(A,C,B,D),f143(A,C,B,D)) | -in(D,f140(A,C,B)). [resolve(1177,e,1147,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | f142(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1148,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(A))) | empty_carrier(A) | f135(A,C,B) != f134(A,C,B) | f141(A,C,B,D) = D | -in(D,f140(A,C,B)). [resolve(1177,e,1149,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | in(D,powerset(C)). [resolve(1177,e,1151,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | f155(A,B,C,D) = D. [resolve(1177,e,1152,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | element(f156(A,B,C,D),the_carrier(A)). [resolve(1177,e,1153,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | in(f156(A,B,C,D),B). [resolve(1177,e,1154,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | -in(D,f154(A,B,C)) | relstr_set_smaller(A,f155(A,B,C,D),f156(A,B,C,D)). [resolve(1177,e,1155,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(A) | in(D,f154(A,B,C)) | -in(D,powerset(C)) | E != D | -element(F,the_carrier(A)) | -in(F,B) | -relstr_set_smaller(A,E,F). [resolve(1177,e,1156,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | relation(the_InternalRel(A)). [resolve(1177,e,1158,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | reflexive(the_InternalRel(A)). [resolve(1177,e,1159,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | transitive(the_InternalRel(A)). [resolve(1177,e,1160,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)). [resolve(1177,e,1161,a)]. 43.99/44.12 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | -reflexive_relstr(A) | antisymmetric(the_InternalRel(A)). [resolve(1177,e,1162,a)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -element(D,the_carrier(A)) | -related(A,C,D) | -related(A,B,C) | related(A,B,D). [resolve(1177,e,1164,b)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f268(A,B),powerset(B)) | -empty(B). [resolve(1177,e,1165,b)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | element(f268(A,B),powerset(B)) | directed_subset(B,A). [resolve(1177,e,1166,b)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | finite(f268(A,B)) | -empty(B). [resolve(1177,e,1167,b)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | finite(f268(A,B)) | directed_subset(B,A). [resolve(1177,e,1168,b)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -in(C,B) | -relstr_set_smaller(A,f268(A,B),C) | -element(C,the_carrier(A)) | directed_subset(B,A). [resolve(1177,e,1170,b)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(B)) | -finite(C) | in(f269(A,B,C),B) | empty(B) | -directed_subset(B,A). [resolve(1177,e,1171,b)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(A,C,f269(A,B,C)) | empty(B) | -directed_subset(B,A). [resolve(1177,e,1172,b)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | empty_carrier(A) | -rel_str(A) | -element(B,powerset(the_carrier(A))) | -element(C,powerset(B)) | -finite(C) | element(f269(A,B,C),the_carrier(A)) | empty(B) | -directed_subset(B,A). [resolve(1177,e,1173,b)]. 43.99/44.17 Derived: -rel_str(A) | empty_carrier(A) | -trivial_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | is_transitive_in(the_InternalRel(A),the_carrier(A)). [resolve(1177,e,1175,c)]. 43.99/44.17 1178 transitive_relstr(incl_POSet(A)) # label(fc5_yellow_1) # label(axiom). [clausify(558)]. 43.99/44.17 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | in(f19(incl_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | relstr_set_smaller(incl_POSet(A),B,f22(incl_POSet(A),C,B)). [resolve(1178,a,1051,f)]. 43.99/44.17 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | in(f19(incl_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | in(f22(incl_POSet(A),C,B),C). [resolve(1178,a,1052,f)]. 43.99/44.17 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | in(f19(incl_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | element(f22(incl_POSet(A),C,B),the_carrier(incl_POSet(A))). [resolve(1178,a,1053,f)]. 43.99/44.17 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | subset(f20(incl_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | relstr_set_smaller(incl_POSet(A),B,f22(incl_POSet(A),C,B)). [resolve(1178,a,1054,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | subset(f20(incl_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | in(f22(incl_POSet(A),C,B),C). [resolve(1178,a,1055,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | subset(f20(incl_POSet(A),C,B),B) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | element(f22(incl_POSet(A),C,B),the_carrier(incl_POSet(A))). [resolve(1178,a,1056,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | element(f21(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | relstr_set_smaller(incl_POSet(A),B,f22(incl_POSet(A),C,B)). [resolve(1178,a,1057,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | element(f21(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | in(f22(incl_POSet(A),C,B),C). [resolve(1178,a,1058,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | element(f21(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | element(f22(incl_POSet(A),C,B),the_carrier(incl_POSet(A))). [resolve(1178,a,1059,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | relstr_set_smaller(incl_POSet(A),f20(incl_POSet(A),C,B),f21(incl_POSet(A),C,B)) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | relstr_set_smaller(incl_POSet(A),B,f22(incl_POSet(A),C,B)). [resolve(1178,a,1060,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | relstr_set_smaller(incl_POSet(A),f20(incl_POSet(A),C,B),f21(incl_POSet(A),C,B)) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | in(f22(incl_POSet(A),C,B),C). [resolve(1178,a,1061,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | relstr_set_smaller(incl_POSet(A),f20(incl_POSet(A),C,B),f21(incl_POSet(A),C,B)) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | element(f22(incl_POSet(A),C,B),the_carrier(incl_POSet(A))). [resolve(1178,a,1062,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | in(f21(incl_POSet(A),C,B),C) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | relstr_set_smaller(incl_POSet(A),B,f22(incl_POSet(A),C,B)). [resolve(1178,a,1063,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | in(f21(incl_POSet(A),C,B),C) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | in(f22(incl_POSet(A),C,B),C). [resolve(1178,a,1064,f)]. 43.99/44.18 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | in(f21(incl_POSet(A),C,B),C) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),empty_set,D) | -element(D,the_carrier(incl_POSet(A))) | element(f22(incl_POSet(A),C,B),the_carrier(incl_POSet(A))). [resolve(1178,a,1065,f)]. 43.99/44.19 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),set_union2(f20(incl_POSet(A),C,B),singleton(f19(incl_POSet(A),C,B))),D) | -element(D,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),empty_set,E) | -element(E,the_carrier(incl_POSet(A))) | relstr_set_smaller(incl_POSet(A),B,f22(incl_POSet(A),C,B)). [resolve(1178,a,1066,f)]. 43.99/44.19 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),set_union2(f20(incl_POSet(A),C,B),singleton(f19(incl_POSet(A),C,B))),D) | -element(D,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),empty_set,E) | -element(E,the_carrier(incl_POSet(A))) | in(f22(incl_POSet(A),C,B),C). [resolve(1178,a,1067,f)]. 43.99/44.19 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(C)) | -finite(B) | -element(C,powerset(the_carrier(incl_POSet(A)))) | -in(D,C) | -relstr_set_smaller(incl_POSet(A),set_union2(f20(incl_POSet(A),C,B),singleton(f19(incl_POSet(A),C,B))),D) | -element(D,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),empty_set,E) | -element(E,the_carrier(incl_POSet(A))) | element(f22(incl_POSet(A),C,B),the_carrier(incl_POSet(A))). [resolve(1178,a,1068,f)]. 43.99/44.19 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f134(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1073,a)]. 43.99/44.19 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f134(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1074,a)]. 43.99/44.19 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f134(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1075,a)]. 43.99/44.19 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f134(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1076,a)]. 43.99/44.19 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f134(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1077,a)]. 43.99/44.19 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f134(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1078,a)]. 43.99/44.19 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f134(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1079,a)]. 43.99/44.19 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f136(incl_POSet(A),C,B) = f135(incl_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1080,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f136(incl_POSet(A),C,B) = f135(incl_POSet(A),C,B) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1081,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f136(incl_POSet(A),C,B) = f135(incl_POSet(A),C,B) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1082,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f136(incl_POSet(A),C,B) = f135(incl_POSet(A),C,B) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1083,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f136(incl_POSet(A),C,B) = f135(incl_POSet(A),C,B) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1084,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f136(incl_POSet(A),C,B) = f135(incl_POSet(A),C,B) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1085,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f136(incl_POSet(A),C,B) = f135(incl_POSet(A),C,B) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1086,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f137(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1087,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f137(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1088,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f137(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1089,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f137(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1090,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f137(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1091,a)]. 43.99/44.20 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f137(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1092,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f137(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1093,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f136(incl_POSet(A),C,B),f137(incl_POSet(A),C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1094,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f136(incl_POSet(A),C,B),f137(incl_POSet(A),C,B)) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1095,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f136(incl_POSet(A),C,B),f137(incl_POSet(A),C,B)) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1096,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f136(incl_POSet(A),C,B),f137(incl_POSet(A),C,B)) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1097,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f136(incl_POSet(A),C,B),f137(incl_POSet(A),C,B)) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1098,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f136(incl_POSet(A),C,B),f137(incl_POSet(A),C,B)) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1099,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f136(incl_POSet(A),C,B),f137(incl_POSet(A),C,B)) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1100,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f137(incl_POSet(A),C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1101,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f137(incl_POSet(A),C,B),C) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1102,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f137(incl_POSet(A),C,B),C) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1103,a)]. 44.10/44.21 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f137(incl_POSet(A),C,B),C) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1104,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f137(incl_POSet(A),C,B),C) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1105,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f137(incl_POSet(A),C,B),C) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1106,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f137(incl_POSet(A),C,B),C) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1107,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1108,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1109,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1110,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1111,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1112,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1113,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) = f133(incl_POSet(A),C,B) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1114,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f138(incl_POSet(A),C,B) = f134(incl_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1115,a)]. 44.10/44.23 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f138(incl_POSet(A),C,B) = f134(incl_POSet(A),C,B) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1116,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f138(incl_POSet(A),C,B) = f134(incl_POSet(A),C,B) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1117,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f138(incl_POSet(A),C,B) = f134(incl_POSet(A),C,B) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1118,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f138(incl_POSet(A),C,B) = f134(incl_POSet(A),C,B) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1119,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f138(incl_POSet(A),C,B) = f134(incl_POSet(A),C,B) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1120,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f138(incl_POSet(A),C,B) = f134(incl_POSet(A),C,B) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1121,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f138(incl_POSet(A),C,B),f139(incl_POSet(A),C,B)) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1122,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f138(incl_POSet(A),C,B),f139(incl_POSet(A),C,B)) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1123,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f138(incl_POSet(A),C,B),f139(incl_POSet(A),C,B)) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1124,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f138(incl_POSet(A),C,B),f139(incl_POSet(A),C,B)) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1125,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f138(incl_POSet(A),C,B),f139(incl_POSet(A),C,B)) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1126,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f138(incl_POSet(A),C,B),f139(incl_POSet(A),C,B)) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1127,a)]. 44.10/44.24 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | relstr_set_smaller(incl_POSet(A),f138(incl_POSet(A),C,B),f139(incl_POSet(A),C,B)) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1128,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f139(incl_POSet(A),C,B),C) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1129,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f139(incl_POSet(A),C,B),C) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1130,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f139(incl_POSet(A),C,B),C) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1131,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f139(incl_POSet(A),C,B),C) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1132,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f139(incl_POSet(A),C,B),C) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1133,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f139(incl_POSet(A),C,B),C) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1134,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | in(f139(incl_POSet(A),C,B),C) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1135,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f139(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1136,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f139(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1137,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f139(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1138,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f139(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1139,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f139(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1140,a)]. 44.10/44.25 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f139(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1141,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | element(f139(incl_POSet(A),C,B),the_carrier(incl_POSet(A))) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1142,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) != f134(incl_POSet(A),C,B) | -in(D,powerset(B)) | -element(E,the_carrier(incl_POSet(A))) | -in(E,C) | -relstr_set_smaller(incl_POSet(A),F,E) | F != V6 | D != V6 | in(V6,f140(incl_POSet(A),C,B)). [resolve(1178,a,1143,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) != f134(incl_POSet(A),C,B) | in(f141(incl_POSet(A),C,B,D),powerset(B)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1144,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) != f134(incl_POSet(A),C,B) | element(f143(incl_POSet(A),C,B,D),the_carrier(incl_POSet(A))) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1145,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) != f134(incl_POSet(A),C,B) | in(f143(incl_POSet(A),C,B,D),C) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1146,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) != f134(incl_POSet(A),C,B) | relstr_set_smaller(incl_POSet(A),f142(incl_POSet(A),C,B,D),f143(incl_POSet(A),C,B,D)) | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1147,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) != f134(incl_POSet(A),C,B) | f142(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1148,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -finite(B) | -element(B,powerset(C)) | -element(C,powerset(the_carrier(incl_POSet(A)))) | empty_carrier(incl_POSet(A)) | f135(incl_POSet(A),C,B) != f134(incl_POSet(A),C,B) | f141(incl_POSet(A),C,B,D) = D | -in(D,f140(incl_POSet(A),C,B)). [resolve(1178,a,1149,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(incl_POSet(A)) | -in(D,f154(incl_POSet(A),B,C)) | in(D,powerset(C)). [resolve(1178,a,1151,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(incl_POSet(A)) | -in(D,f154(incl_POSet(A),B,C)) | f155(incl_POSet(A),B,C,D) = D. [resolve(1178,a,1152,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(incl_POSet(A)) | -in(D,f154(incl_POSet(A),B,C)) | element(f156(incl_POSet(A),B,C,D),the_carrier(incl_POSet(A))). [resolve(1178,a,1153,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(incl_POSet(A)) | -in(D,f154(incl_POSet(A),B,C)) | in(f156(incl_POSet(A),B,C,D),B). [resolve(1178,a,1154,a)]. 44.10/44.26 Derived: -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(incl_POSet(A)) | -in(D,f154(incl_POSet(A),B,C)) | relstr_set_smaller(incl_POSet(A),f155(incl_POSet(A),B,C,D),f156(incl_POSet(A),B,C,D)). [resolve(1178,a,1155,a)]. 44.18/44.32 Derived: -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -finite(C) | -element(C,powerset(B)) | empty_carrier(incl_POSet(A)) | in(D,f154(incl_POSet(A),B,C)) | -in(D,powerset(C)) | E != D | -element(F,the_carrier(incl_POSet(A))) | -in(F,B) | -relstr_set_smaller(incl_POSet(A),E,F). [resolve(1178,a,1156,a)]. 44.18/44.32 Derived: -antisymmetric_relstr(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | relation(the_InternalRel(incl_POSet(A))). [resolve(1178,a,1158,a)]. 44.18/44.32 Derived: -antisymmetric_relstr(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | reflexive(the_InternalRel(incl_POSet(A))). [resolve(1178,a,1159,a)]. 44.18/44.32 Derived: -antisymmetric_relstr(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | transitive(the_InternalRel(incl_POSet(A))). [resolve(1178,a,1160,a)]. 44.18/44.32 Derived: -antisymmetric_relstr(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | v1_partfun1(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))). [resolve(1178,a,1161,a)]. 44.18/44.32 Derived: -antisymmetric_relstr(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | antisymmetric(the_InternalRel(incl_POSet(A))). [resolve(1178,a,1162,a)]. 44.18/44.32 Derived: -rel_str(incl_POSet(A)) | -element(B,the_carrier(incl_POSet(A))) | -element(C,the_carrier(incl_POSet(A))) | -element(D,the_carrier(incl_POSet(A))) | -related(incl_POSet(A),C,D) | -related(incl_POSet(A),B,C) | related(incl_POSet(A),B,D). [resolve(1178,a,1164,b)]. 44.18/44.32 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | element(f268(incl_POSet(A),B),powerset(B)) | -empty(B). [resolve(1178,a,1165,b)]. 44.18/44.32 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | element(f268(incl_POSet(A),B),powerset(B)) | directed_subset(B,incl_POSet(A)). [resolve(1178,a,1166,b)]. 44.18/44.32 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | finite(f268(incl_POSet(A),B)) | -empty(B). [resolve(1178,a,1167,b)]. 44.18/44.32 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | finite(f268(incl_POSet(A),B)) | directed_subset(B,incl_POSet(A)). [resolve(1178,a,1168,b)]. 44.18/44.32 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -in(C,B) | -relstr_set_smaller(incl_POSet(A),f268(incl_POSet(A),B),C) | -element(C,the_carrier(incl_POSet(A))) | directed_subset(B,incl_POSet(A)). [resolve(1178,a,1170,b)]. 44.18/44.32 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -element(C,powerset(B)) | -finite(C) | in(f269(incl_POSet(A),B,C),B) | empty(B) | -directed_subset(B,incl_POSet(A)). [resolve(1178,a,1171,b)]. 44.18/44.32 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -element(C,powerset(B)) | -finite(C) | relstr_set_smaller(incl_POSet(A),C,f269(incl_POSet(A),B,C)) | empty(B) | -directed_subset(B,incl_POSet(A)). [resolve(1178,a,1172,b)]. 44.18/44.32 Derived: empty_carrier(incl_POSet(A)) | -rel_str(incl_POSet(A)) | -element(B,powerset(the_carrier(incl_POSet(A)))) | -element(C,powerset(B)) | -finite(C) | element(f269(incl_POSet(A),B,C),the_carrier(incl_POSet(A))) | empty(B) | -directed_subset(B,incl_POSet(A)). [resolve(1178,a,1173,b)]. 44.18/44.32 Derived: -rel_str(incl_POSet(A)) | is_transitive_in(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A))). [resolve(1178,a,1175,c)]. 44.18/44.32 1179 -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | transitive_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(561)]. 44.18/44.32 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | in(f19(rel_str_of(B,A),D,C),C) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),C,f22(rel_str_of(B,A),D,C)). [resolve(1179,f,1051,f)]. 44.18/44.33 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | in(f19(rel_str_of(B,A),D,C),C) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | in(f22(rel_str_of(B,A),D,C),D). [resolve(1179,f,1052,f)]. 44.18/44.33 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | in(f19(rel_str_of(B,A),D,C),C) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | element(f22(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))). [resolve(1179,f,1053,f)]. 44.18/44.33 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | subset(f20(rel_str_of(B,A),D,C),C) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),C,f22(rel_str_of(B,A),D,C)). [resolve(1179,f,1054,f)]. 44.18/44.33 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | subset(f20(rel_str_of(B,A),D,C),C) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | in(f22(rel_str_of(B,A),D,C),D). [resolve(1179,f,1055,f)]. 44.18/44.33 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | subset(f20(rel_str_of(B,A),D,C),C) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | element(f22(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))). [resolve(1179,f,1056,f)]. 44.18/44.33 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | element(f21(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),C,f22(rel_str_of(B,A),D,C)). [resolve(1179,f,1057,f)]. 44.18/44.33 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | element(f21(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | in(f22(rel_str_of(B,A),D,C),D). [resolve(1179,f,1058,f)]. 44.18/44.33 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | element(f21(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | element(f22(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))). [resolve(1179,f,1059,f)]. 44.18/44.34 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | relstr_set_smaller(rel_str_of(B,A),f20(rel_str_of(B,A),D,C),f21(rel_str_of(B,A),D,C)) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),C,f22(rel_str_of(B,A),D,C)). [resolve(1179,f,1060,f)]. 44.18/44.34 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | relstr_set_smaller(rel_str_of(B,A),f20(rel_str_of(B,A),D,C),f21(rel_str_of(B,A),D,C)) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | in(f22(rel_str_of(B,A),D,C),D). [resolve(1179,f,1061,f)]. 44.18/44.34 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | relstr_set_smaller(rel_str_of(B,A),f20(rel_str_of(B,A),D,C),f21(rel_str_of(B,A),D,C)) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | element(f22(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))). [resolve(1179,f,1062,f)]. 44.18/44.34 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | in(f21(rel_str_of(B,A),D,C),D) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),C,f22(rel_str_of(B,A),D,C)). [resolve(1179,f,1063,f)]. 44.18/44.34 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | in(f21(rel_str_of(B,A),D,C),D) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | in(f22(rel_str_of(B,A),D,C),D). [resolve(1179,f,1064,f)]. 44.18/44.34 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | in(f21(rel_str_of(B,A),D,C),D) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,E) | -element(E,the_carrier(rel_str_of(B,A))) | element(f22(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))). [resolve(1179,f,1065,f)]. 44.18/44.34 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),set_union2(f20(rel_str_of(B,A),D,C),singleton(f19(rel_str_of(B,A),D,C))),E) | -element(E,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,F) | -element(F,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),C,f22(rel_str_of(B,A),D,C)). [resolve(1179,f,1066,f)]. 44.18/44.34 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),set_union2(f20(rel_str_of(B,A),D,C),singleton(f19(rel_str_of(B,A),D,C))),E) | -element(E,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,F) | -element(F,the_carrier(rel_str_of(B,A))) | in(f22(rel_str_of(B,A),D,C),D). [resolve(1179,f,1067,f)]. 44.18/44.35 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(D)) | -finite(C) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | -in(E,D) | -relstr_set_smaller(rel_str_of(B,A),set_union2(f20(rel_str_of(B,A),D,C),singleton(f19(rel_str_of(B,A),D,C))),E) | -element(E,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),empty_set,F) | -element(F,the_carrier(rel_str_of(B,A))) | element(f22(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))). [resolve(1179,f,1068,f)]. 44.18/44.35 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f134(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1073,a)]. 44.18/44.35 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f134(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1074,a)]. 44.18/44.35 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f134(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1075,a)]. 44.18/44.35 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f134(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1076,a)]. 44.18/44.35 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f134(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1077,a)]. 44.18/44.35 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f134(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1078,a)]. 44.18/44.35 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f134(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1079,a)]. 44.18/44.35 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f136(rel_str_of(B,A),D,C) = f135(rel_str_of(B,A),D,C) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1080,a)]. 44.18/44.36 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f136(rel_str_of(B,A),D,C) = f135(rel_str_of(B,A),D,C) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1081,a)]. 44.18/44.36 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f136(rel_str_of(B,A),D,C) = f135(rel_str_of(B,A),D,C) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1082,a)]. 44.18/44.36 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f136(rel_str_of(B,A),D,C) = f135(rel_str_of(B,A),D,C) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1083,a)]. 44.18/44.36 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f136(rel_str_of(B,A),D,C) = f135(rel_str_of(B,A),D,C) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1084,a)]. 44.18/44.36 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f136(rel_str_of(B,A),D,C) = f135(rel_str_of(B,A),D,C) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1085,a)]. 44.18/44.36 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f136(rel_str_of(B,A),D,C) = f135(rel_str_of(B,A),D,C) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1086,a)]. 44.18/44.36 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f137(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1087,a)]. 44.18/44.36 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f137(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1088,a)]. 44.18/44.36 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f137(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1089,a)]. 44.18/44.37 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f137(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1090,a)]. 44.18/44.37 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f137(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1091,a)]. 44.18/44.37 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f137(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1092,a)]. 44.18/44.37 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f137(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1093,a)]. 44.18/44.37 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f136(rel_str_of(B,A),D,C),f137(rel_str_of(B,A),D,C)) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1094,a)]. 44.18/44.37 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f136(rel_str_of(B,A),D,C),f137(rel_str_of(B,A),D,C)) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1095,a)]. 44.18/44.37 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f136(rel_str_of(B,A),D,C),f137(rel_str_of(B,A),D,C)) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1096,a)]. 44.18/44.37 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f136(rel_str_of(B,A),D,C),f137(rel_str_of(B,A),D,C)) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1097,a)]. 44.18/44.37 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f136(rel_str_of(B,A),D,C),f137(rel_str_of(B,A),D,C)) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1098,a)]. 44.26/44.38 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f136(rel_str_of(B,A),D,C),f137(rel_str_of(B,A),D,C)) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1099,a)]. 44.26/44.38 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f136(rel_str_of(B,A),D,C),f137(rel_str_of(B,A),D,C)) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1100,a)]. 44.26/44.38 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f137(rel_str_of(B,A),D,C),D) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1101,a)]. 44.26/44.38 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f137(rel_str_of(B,A),D,C),D) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1102,a)]. 44.26/44.38 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f137(rel_str_of(B,A),D,C),D) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1103,a)]. 44.26/44.38 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f137(rel_str_of(B,A),D,C),D) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1104,a)]. 44.26/44.38 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f137(rel_str_of(B,A),D,C),D) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1105,a)]. 44.26/44.38 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f137(rel_str_of(B,A),D,C),D) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1106,a)]. 44.26/44.38 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f137(rel_str_of(B,A),D,C),D) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1107,a)]. 44.26/44.39 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1108,a)]. 44.26/44.39 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1109,a)]. 44.26/44.39 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1110,a)]. 44.26/44.39 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1111,a)]. 44.26/44.39 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1112,a)]. 44.26/44.39 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1113,a)]. 44.26/44.39 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) = f133(rel_str_of(B,A),D,C) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1114,a)]. 44.26/44.39 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f138(rel_str_of(B,A),D,C) = f134(rel_str_of(B,A),D,C) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1115,a)]. 44.26/44.39 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f138(rel_str_of(B,A),D,C) = f134(rel_str_of(B,A),D,C) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1116,a)]. 44.26/44.40 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f138(rel_str_of(B,A),D,C) = f134(rel_str_of(B,A),D,C) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1117,a)]. 44.26/44.40 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f138(rel_str_of(B,A),D,C) = f134(rel_str_of(B,A),D,C) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1118,a)]. 44.26/44.40 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f138(rel_str_of(B,A),D,C) = f134(rel_str_of(B,A),D,C) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1119,a)]. 44.26/44.40 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f138(rel_str_of(B,A),D,C) = f134(rel_str_of(B,A),D,C) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1120,a)]. 44.26/44.40 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f138(rel_str_of(B,A),D,C) = f134(rel_str_of(B,A),D,C) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1121,a)]. 44.26/44.40 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f138(rel_str_of(B,A),D,C),f139(rel_str_of(B,A),D,C)) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1122,a)]. 44.26/44.40 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f138(rel_str_of(B,A),D,C),f139(rel_str_of(B,A),D,C)) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1123,a)]. 44.26/44.40 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f138(rel_str_of(B,A),D,C),f139(rel_str_of(B,A),D,C)) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1124,a)]. 44.26/44.40 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f138(rel_str_of(B,A),D,C),f139(rel_str_of(B,A),D,C)) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1125,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f138(rel_str_of(B,A),D,C),f139(rel_str_of(B,A),D,C)) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1126,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f138(rel_str_of(B,A),D,C),f139(rel_str_of(B,A),D,C)) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1127,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | relstr_set_smaller(rel_str_of(B,A),f138(rel_str_of(B,A),D,C),f139(rel_str_of(B,A),D,C)) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1128,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f139(rel_str_of(B,A),D,C),D) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1129,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f139(rel_str_of(B,A),D,C),D) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1130,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f139(rel_str_of(B,A),D,C),D) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1131,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f139(rel_str_of(B,A),D,C),D) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1132,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f139(rel_str_of(B,A),D,C),D) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1133,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f139(rel_str_of(B,A),D,C),D) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1134,a)]. 44.29/44.41 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | in(f139(rel_str_of(B,A),D,C),D) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1135,a)]. 44.30/44.42 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f139(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1136,a)]. 44.30/44.42 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f139(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1137,a)]. 44.30/44.42 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f139(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1138,a)]. 44.30/44.42 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f139(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1139,a)]. 44.30/44.42 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f139(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1140,a)]. 44.30/44.42 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f139(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1141,a)]. 44.30/44.42 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | element(f139(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1142,a)]. 44.30/44.42 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) != f134(rel_str_of(B,A),D,C) | -in(E,powerset(C)) | -element(F,the_carrier(rel_str_of(B,A))) | -in(F,D) | -relstr_set_smaller(rel_str_of(B,A),V6,F) | V6 != V7 | E != V7 | in(V7,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1143,a)]. 44.30/44.42 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) != f134(rel_str_of(B,A),D,C) | in(f141(rel_str_of(B,A),D,C,E),powerset(C)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1144,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) != f134(rel_str_of(B,A),D,C) | element(f143(rel_str_of(B,A),D,C,E),the_carrier(rel_str_of(B,A))) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1145,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) != f134(rel_str_of(B,A),D,C) | in(f143(rel_str_of(B,A),D,C,E),D) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1146,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) != f134(rel_str_of(B,A),D,C) | relstr_set_smaller(rel_str_of(B,A),f142(rel_str_of(B,A),D,C,E),f143(rel_str_of(B,A),D,C,E)) | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1147,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) != f134(rel_str_of(B,A),D,C) | f142(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1148,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -finite(C) | -element(C,powerset(D)) | -element(D,powerset(the_carrier(rel_str_of(B,A)))) | empty_carrier(rel_str_of(B,A)) | f135(rel_str_of(B,A),D,C) != f134(rel_str_of(B,A),D,C) | f141(rel_str_of(B,A),D,C,E) = E | -in(E,f140(rel_str_of(B,A),D,C)). [resolve(1179,f,1149,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -finite(D) | -element(D,powerset(C)) | empty_carrier(rel_str_of(B,A)) | -in(E,f154(rel_str_of(B,A),C,D)) | in(E,powerset(D)). [resolve(1179,f,1151,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -finite(D) | -element(D,powerset(C)) | empty_carrier(rel_str_of(B,A)) | -in(E,f154(rel_str_of(B,A),C,D)) | f155(rel_str_of(B,A),C,D,E) = E. [resolve(1179,f,1152,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -finite(D) | -element(D,powerset(C)) | empty_carrier(rel_str_of(B,A)) | -in(E,f154(rel_str_of(B,A),C,D)) | element(f156(rel_str_of(B,A),C,D,E),the_carrier(rel_str_of(B,A))). [resolve(1179,f,1153,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -finite(D) | -element(D,powerset(C)) | empty_carrier(rel_str_of(B,A)) | -in(E,f154(rel_str_of(B,A),C,D)) | in(f156(rel_str_of(B,A),C,D,E),C). [resolve(1179,f,1154,a)]. 44.30/44.43 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -finite(D) | -element(D,powerset(C)) | empty_carrier(rel_str_of(B,A)) | -in(E,f154(rel_str_of(B,A),C,D)) | relstr_set_smaller(rel_str_of(B,A),f155(rel_str_of(B,A),C,D,E),f156(rel_str_of(B,A),C,D,E)). [resolve(1179,f,1155,a)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -finite(D) | -element(D,powerset(C)) | empty_carrier(rel_str_of(B,A)) | in(E,f154(rel_str_of(B,A),C,D)) | -in(E,powerset(D)) | F != E | -element(V6,the_carrier(rel_str_of(B,A))) | -in(V6,C) | -relstr_set_smaller(rel_str_of(B,A),F,V6). [resolve(1179,f,1156,a)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -antisymmetric_relstr(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | relation(the_InternalRel(rel_str_of(B,A))). [resolve(1179,f,1158,a)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -antisymmetric_relstr(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | reflexive(the_InternalRel(rel_str_of(B,A))). [resolve(1179,f,1159,a)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -antisymmetric_relstr(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | transitive(the_InternalRel(rel_str_of(B,A))). [resolve(1179,f,1160,a)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -antisymmetric_relstr(rel_str_of(B,A)) | -rel_str(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(1179,f,1161,a)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -antisymmetric_relstr(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | antisymmetric(the_InternalRel(rel_str_of(B,A))). [resolve(1179,f,1162,a)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(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))) | -element(E,the_carrier(rel_str_of(B,A))) | -related(rel_str_of(B,A),D,E) | -related(rel_str_of(B,A),C,D) | related(rel_str_of(B,A),C,E). [resolve(1179,f,1164,b)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | element(f268(rel_str_of(B,A),C),powerset(C)) | -empty(C). [resolve(1179,f,1165,b)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | element(f268(rel_str_of(B,A),C),powerset(C)) | directed_subset(C,rel_str_of(B,A)). [resolve(1179,f,1166,b)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | finite(f268(rel_str_of(B,A),C)) | -empty(C). [resolve(1179,f,1167,b)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | finite(f268(rel_str_of(B,A),C)) | directed_subset(C,rel_str_of(B,A)). [resolve(1179,f,1168,b)]. 44.30/44.44 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -in(D,C) | -relstr_set_smaller(rel_str_of(B,A),f268(rel_str_of(B,A),C),D) | -element(D,the_carrier(rel_str_of(B,A))) | directed_subset(C,rel_str_of(B,A)). [resolve(1179,f,1170,b)]. 44.60/44.75 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -element(D,powerset(C)) | -finite(D) | in(f269(rel_str_of(B,A),C,D),C) | empty(C) | -directed_subset(C,rel_str_of(B,A)). [resolve(1179,f,1171,b)]. 44.60/44.75 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -element(D,powerset(C)) | -finite(D) | relstr_set_smaller(rel_str_of(B,A),D,f269(rel_str_of(B,A),C,D)) | empty(C) | -directed_subset(C,rel_str_of(B,A)). [resolve(1179,f,1172,b)]. 44.60/44.75 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | empty_carrier(rel_str_of(B,A)) | -rel_str(rel_str_of(B,A)) | -element(C,powerset(the_carrier(rel_str_of(B,A)))) | -element(D,powerset(C)) | -finite(D) | element(f269(rel_str_of(B,A),C,D),the_carrier(rel_str_of(B,A))) | empty(C) | -directed_subset(C,rel_str_of(B,A)). [resolve(1179,f,1173,b)]. 44.60/44.75 Derived: -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | -transitive(A) | -antisymmetric(A) | -reflexive(A) | -rel_str(rel_str_of(B,A)) | is_transitive_in(the_InternalRel(rel_str_of(B,A)),the_carrier(rel_str_of(B,A))). [resolve(1179,f,1175,c)]. 44.60/44.75 1180 empty(A) | transitive_relstr(incl_POSet(A)) # label(fc6_yellow_1) # label(axiom). [clausify(617)]. 44.60/44.75 1181 transitive_relstr(c42) # label(rc1_lattice3) # label(axiom). [clausify(648)]. 44.60/44.75 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | in(f19(c42,B,A),A) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | relstr_set_smaller(c42,A,f22(c42,B,A)). [resolve(1181,a,1051,f)]. 44.60/44.75 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | in(f19(c42,B,A),A) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | in(f22(c42,B,A),B). [resolve(1181,a,1052,f)]. 44.60/44.75 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | in(f19(c42,B,A),A) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | element(f22(c42,B,A),the_carrier(c42)). [resolve(1181,a,1053,f)]. 44.60/44.75 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | subset(f20(c42,B,A),A) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | relstr_set_smaller(c42,A,f22(c42,B,A)). [resolve(1181,a,1054,f)]. 44.60/44.75 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | subset(f20(c42,B,A),A) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | in(f22(c42,B,A),B). [resolve(1181,a,1055,f)]. 44.60/44.75 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | subset(f20(c42,B,A),A) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | element(f22(c42,B,A),the_carrier(c42)). [resolve(1181,a,1056,f)]. 44.60/44.75 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | element(f21(c42,B,A),the_carrier(c42)) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | relstr_set_smaller(c42,A,f22(c42,B,A)). [resolve(1181,a,1057,f)]. 44.60/44.75 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | element(f21(c42,B,A),the_carrier(c42)) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | in(f22(c42,B,A),B). [resolve(1181,a,1058,f)]. 44.60/44.75 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | element(f21(c42,B,A),the_carrier(c42)) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | element(f22(c42,B,A),the_carrier(c42)). [resolve(1181,a,1059,f)]. 44.60/44.76 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | relstr_set_smaller(c42,f20(c42,B,A),f21(c42,B,A)) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | relstr_set_smaller(c42,A,f22(c42,B,A)). [resolve(1181,a,1060,f)]. 44.60/44.76 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | relstr_set_smaller(c42,f20(c42,B,A),f21(c42,B,A)) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | in(f22(c42,B,A),B). [resolve(1181,a,1061,f)]. 44.60/44.76 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | relstr_set_smaller(c42,f20(c42,B,A),f21(c42,B,A)) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | element(f22(c42,B,A),the_carrier(c42)). [resolve(1181,a,1062,f)]. 44.60/44.76 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | in(f21(c42,B,A),B) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | relstr_set_smaller(c42,A,f22(c42,B,A)). [resolve(1181,a,1063,f)]. 44.60/44.76 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | in(f21(c42,B,A),B) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | in(f22(c42,B,A),B). [resolve(1181,a,1064,f)]. 44.60/44.76 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | in(f21(c42,B,A),B) | -in(C,B) | -relstr_set_smaller(c42,empty_set,C) | -element(C,the_carrier(c42)) | element(f22(c42,B,A),the_carrier(c42)). [resolve(1181,a,1065,f)]. 44.60/44.76 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | -in(C,B) | -relstr_set_smaller(c42,set_union2(f20(c42,B,A),singleton(f19(c42,B,A))),C) | -element(C,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,empty_set,D) | -element(D,the_carrier(c42)) | relstr_set_smaller(c42,A,f22(c42,B,A)). [resolve(1181,a,1066,f)]. 44.60/44.76 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | -in(C,B) | -relstr_set_smaller(c42,set_union2(f20(c42,B,A),singleton(f19(c42,B,A))),C) | -element(C,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,empty_set,D) | -element(D,the_carrier(c42)) | in(f22(c42,B,A),B). [resolve(1181,a,1067,f)]. 44.60/44.76 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c42))) | -in(C,B) | -relstr_set_smaller(c42,set_union2(f20(c42,B,A),singleton(f19(c42,B,A))),C) | -element(C,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,empty_set,D) | -element(D,the_carrier(c42)) | element(f22(c42,B,A),the_carrier(c42)). [resolve(1181,a,1068,f)]. 44.60/44.76 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f134(c42,B,A) = f133(c42,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1073,a)]. 44.60/44.76 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f134(c42,B,A) = f133(c42,B,A) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1074,a)]. 44.60/44.76 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f134(c42,B,A) = f133(c42,B,A) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1075,a)]. 44.60/44.76 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f134(c42,B,A) = f133(c42,B,A) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1076,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f134(c42,B,A) = f133(c42,B,A) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1077,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f134(c42,B,A) = f133(c42,B,A) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1078,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f134(c42,B,A) = f133(c42,B,A) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1079,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f136(c42,B,A) = f135(c42,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1080,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f136(c42,B,A) = f135(c42,B,A) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1081,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f136(c42,B,A) = f135(c42,B,A) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1082,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f136(c42,B,A) = f135(c42,B,A) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1083,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f136(c42,B,A) = f135(c42,B,A) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1084,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f136(c42,B,A) = f135(c42,B,A) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1085,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f136(c42,B,A) = f135(c42,B,A) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1086,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f137(c42,B,A),the_carrier(c42)) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1087,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f137(c42,B,A),the_carrier(c42)) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1088,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f137(c42,B,A),the_carrier(c42)) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1089,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f137(c42,B,A),the_carrier(c42)) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1090,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f137(c42,B,A),the_carrier(c42)) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1091,a)]. 44.60/44.78 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f137(c42,B,A),the_carrier(c42)) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1092,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f137(c42,B,A),the_carrier(c42)) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1093,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f136(c42,B,A),f137(c42,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1094,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f136(c42,B,A),f137(c42,B,A)) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1095,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f136(c42,B,A),f137(c42,B,A)) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1096,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f136(c42,B,A),f137(c42,B,A)) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1097,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f136(c42,B,A),f137(c42,B,A)) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1098,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f136(c42,B,A),f137(c42,B,A)) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1099,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f136(c42,B,A),f137(c42,B,A)) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1100,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f137(c42,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1101,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f137(c42,B,A),B) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1102,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f137(c42,B,A),B) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1103,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f137(c42,B,A),B) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1104,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f137(c42,B,A),B) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1105,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f137(c42,B,A),B) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1106,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f137(c42,B,A),B) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1107,a)]. 44.60/44.79 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) = f133(c42,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1108,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) = f133(c42,B,A) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1109,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) = f133(c42,B,A) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1110,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) = f133(c42,B,A) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1111,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) = f133(c42,B,A) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1112,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) = f133(c42,B,A) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1113,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) = f133(c42,B,A) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1114,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f138(c42,B,A) = f134(c42,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1115,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f138(c42,B,A) = f134(c42,B,A) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1116,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f138(c42,B,A) = f134(c42,B,A) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1117,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f138(c42,B,A) = f134(c42,B,A) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1118,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f138(c42,B,A) = f134(c42,B,A) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1119,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f138(c42,B,A) = f134(c42,B,A) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1120,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f138(c42,B,A) = f134(c42,B,A) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1121,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f138(c42,B,A),f139(c42,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1122,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f138(c42,B,A),f139(c42,B,A)) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1123,a)]. 44.69/44.81 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f138(c42,B,A),f139(c42,B,A)) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1124,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f138(c42,B,A),f139(c42,B,A)) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1125,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f138(c42,B,A),f139(c42,B,A)) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1126,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f138(c42,B,A),f139(c42,B,A)) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1127,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | relstr_set_smaller(c42,f138(c42,B,A),f139(c42,B,A)) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1128,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f139(c42,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1129,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f139(c42,B,A),B) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1130,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f139(c42,B,A),B) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1131,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f139(c42,B,A),B) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1132,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f139(c42,B,A),B) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1133,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f139(c42,B,A),B) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1134,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | in(f139(c42,B,A),B) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1135,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f139(c42,B,A),the_carrier(c42)) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1136,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f139(c42,B,A),the_carrier(c42)) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1137,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f139(c42,B,A),the_carrier(c42)) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1138,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f139(c42,B,A),the_carrier(c42)) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1139,a)]. 44.69/44.82 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f139(c42,B,A),the_carrier(c42)) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1140,a)]. 44.69/44.84 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f139(c42,B,A),the_carrier(c42)) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1141,a)]. 44.69/44.84 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | element(f139(c42,B,A),the_carrier(c42)) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1142,a)]. 44.69/44.84 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) != f134(c42,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c42)) | -in(D,B) | -relstr_set_smaller(c42,E,D) | E != F | C != F | in(F,f140(c42,B,A)). [resolve(1181,a,1143,a)]. 44.69/44.84 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) != f134(c42,B,A) | in(f141(c42,B,A,C),powerset(A)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1144,a)]. 44.69/44.84 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) != f134(c42,B,A) | element(f143(c42,B,A,C),the_carrier(c42)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1145,a)]. 44.69/44.84 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) != f134(c42,B,A) | in(f143(c42,B,A,C),B) | -in(C,f140(c42,B,A)). [resolve(1181,a,1146,a)]. 44.69/44.84 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) != f134(c42,B,A) | relstr_set_smaller(c42,f142(c42,B,A,C),f143(c42,B,A,C)) | -in(C,f140(c42,B,A)). [resolve(1181,a,1147,a)]. 44.69/44.84 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) != f134(c42,B,A) | f142(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1148,a)]. 44.69/44.84 Derived: -rel_str(c42) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c42))) | empty_carrier(c42) | f135(c42,B,A) != f134(c42,B,A) | f141(c42,B,A,C) = C | -in(C,f140(c42,B,A)). [resolve(1181,a,1149,a)]. 44.69/44.84 Derived: -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c42) | -in(C,f154(c42,A,B)) | in(C,powerset(B)). [resolve(1181,a,1151,a)]. 44.69/44.84 Derived: -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c42) | -in(C,f154(c42,A,B)) | f155(c42,A,B,C) = C. [resolve(1181,a,1152,a)]. 44.69/44.84 Derived: -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c42) | -in(C,f154(c42,A,B)) | element(f156(c42,A,B,C),the_carrier(c42)). [resolve(1181,a,1153,a)]. 44.69/44.84 Derived: -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c42) | -in(C,f154(c42,A,B)) | in(f156(c42,A,B,C),A). [resolve(1181,a,1154,a)]. 44.69/44.84 Derived: -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c42) | -in(C,f154(c42,A,B)) | relstr_set_smaller(c42,f155(c42,A,B,C),f156(c42,A,B,C)). [resolve(1181,a,1155,a)]. 44.69/44.84 Derived: -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c42) | in(C,f154(c42,A,B)) | -in(C,powerset(B)) | D != C | -element(E,the_carrier(c42)) | -in(E,A) | -relstr_set_smaller(c42,D,E). [resolve(1181,a,1156,a)]. 44.69/44.84 Derived: -antisymmetric_relstr(c42) | -rel_str(c42) | -reflexive_relstr(c42) | relation(the_InternalRel(c42)). [resolve(1181,a,1158,a)]. 44.69/44.84 Derived: -antisymmetric_relstr(c42) | -rel_str(c42) | -reflexive_relstr(c42) | reflexive(the_InternalRel(c42)). [resolve(1181,a,1159,a)]. 44.69/44.84 Derived: -antisymmetric_relstr(c42) | -rel_str(c42) | -reflexive_relstr(c42) | transitive(the_InternalRel(c42)). [resolve(1181,a,1160,a)]. 44.77/44.95 Derived: -antisymmetric_relstr(c42) | -rel_str(c42) | -reflexive_relstr(c42) | v1_partfun1(the_InternalRel(c42),the_carrier(c42),the_carrier(c42)). [resolve(1181,a,1161,a)]. 44.77/44.95 Derived: -antisymmetric_relstr(c42) | -rel_str(c42) | -reflexive_relstr(c42) | antisymmetric(the_InternalRel(c42)). [resolve(1181,a,1162,a)]. 44.77/44.95 Derived: -rel_str(c42) | -element(A,the_carrier(c42)) | -element(B,the_carrier(c42)) | -element(C,the_carrier(c42)) | -related(c42,B,C) | -related(c42,A,B) | related(c42,A,C). [resolve(1181,a,1164,b)]. 44.77/44.95 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | element(f268(c42,A),powerset(A)) | -empty(A). [resolve(1181,a,1165,b)]. 44.77/44.95 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | element(f268(c42,A),powerset(A)) | directed_subset(A,c42). [resolve(1181,a,1166,b)]. 44.77/44.95 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | finite(f268(c42,A)) | -empty(A). [resolve(1181,a,1167,b)]. 44.77/44.95 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | finite(f268(c42,A)) | directed_subset(A,c42). [resolve(1181,a,1168,b)]. 44.77/44.95 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -in(B,A) | -relstr_set_smaller(c42,f268(c42,A),B) | -element(B,the_carrier(c42)) | directed_subset(A,c42). [resolve(1181,a,1170,b)]. 44.77/44.95 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -element(B,powerset(A)) | -finite(B) | in(f269(c42,A,B),A) | empty(A) | -directed_subset(A,c42). [resolve(1181,a,1171,b)]. 44.77/44.95 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -element(B,powerset(A)) | -finite(B) | relstr_set_smaller(c42,B,f269(c42,A,B)) | empty(A) | -directed_subset(A,c42). [resolve(1181,a,1172,b)]. 44.77/44.95 Derived: empty_carrier(c42) | -rel_str(c42) | -element(A,powerset(the_carrier(c42))) | -element(B,powerset(A)) | -finite(B) | element(f269(c42,A,B),the_carrier(c42)) | empty(A) | -directed_subset(A,c42). [resolve(1181,a,1173,b)]. 44.77/44.95 Derived: -rel_str(c42) | is_transitive_in(the_InternalRel(c42),the_carrier(c42)). [resolve(1181,a,1175,c)]. 44.77/44.95 1182 transitive_relstr(c44) # label(rc2_lattice3) # label(axiom). [clausify(715)]. 44.77/44.95 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | in(f19(c44,B,A),A) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | relstr_set_smaller(c44,A,f22(c44,B,A)). [resolve(1182,a,1051,f)]. 44.77/44.95 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | in(f19(c44,B,A),A) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | in(f22(c44,B,A),B). [resolve(1182,a,1052,f)]. 44.77/44.95 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | in(f19(c44,B,A),A) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | element(f22(c44,B,A),the_carrier(c44)). [resolve(1182,a,1053,f)]. 44.77/44.95 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | subset(f20(c44,B,A),A) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | relstr_set_smaller(c44,A,f22(c44,B,A)). [resolve(1182,a,1054,f)]. 44.77/44.95 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | subset(f20(c44,B,A),A) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | in(f22(c44,B,A),B). [resolve(1182,a,1055,f)]. 44.77/44.95 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | subset(f20(c44,B,A),A) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | element(f22(c44,B,A),the_carrier(c44)). [resolve(1182,a,1056,f)]. 44.77/44.95 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | element(f21(c44,B,A),the_carrier(c44)) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | relstr_set_smaller(c44,A,f22(c44,B,A)). [resolve(1182,a,1057,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | element(f21(c44,B,A),the_carrier(c44)) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | in(f22(c44,B,A),B). [resolve(1182,a,1058,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | element(f21(c44,B,A),the_carrier(c44)) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | element(f22(c44,B,A),the_carrier(c44)). [resolve(1182,a,1059,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | relstr_set_smaller(c44,f20(c44,B,A),f21(c44,B,A)) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | relstr_set_smaller(c44,A,f22(c44,B,A)). [resolve(1182,a,1060,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | relstr_set_smaller(c44,f20(c44,B,A),f21(c44,B,A)) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | in(f22(c44,B,A),B). [resolve(1182,a,1061,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | relstr_set_smaller(c44,f20(c44,B,A),f21(c44,B,A)) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | element(f22(c44,B,A),the_carrier(c44)). [resolve(1182,a,1062,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | in(f21(c44,B,A),B) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | relstr_set_smaller(c44,A,f22(c44,B,A)). [resolve(1182,a,1063,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | in(f21(c44,B,A),B) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | in(f22(c44,B,A),B). [resolve(1182,a,1064,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | in(f21(c44,B,A),B) | -in(C,B) | -relstr_set_smaller(c44,empty_set,C) | -element(C,the_carrier(c44)) | element(f22(c44,B,A),the_carrier(c44)). [resolve(1182,a,1065,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | -in(C,B) | -relstr_set_smaller(c44,set_union2(f20(c44,B,A),singleton(f19(c44,B,A))),C) | -element(C,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,empty_set,D) | -element(D,the_carrier(c44)) | relstr_set_smaller(c44,A,f22(c44,B,A)). [resolve(1182,a,1066,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | -in(C,B) | -relstr_set_smaller(c44,set_union2(f20(c44,B,A),singleton(f19(c44,B,A))),C) | -element(C,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,empty_set,D) | -element(D,the_carrier(c44)) | in(f22(c44,B,A),B). [resolve(1182,a,1067,f)]. 44.77/44.96 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c44))) | -in(C,B) | -relstr_set_smaller(c44,set_union2(f20(c44,B,A),singleton(f19(c44,B,A))),C) | -element(C,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,empty_set,D) | -element(D,the_carrier(c44)) | element(f22(c44,B,A),the_carrier(c44)). [resolve(1182,a,1068,f)]. 44.77/44.96 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f134(c44,B,A) = f133(c44,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1073,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f134(c44,B,A) = f133(c44,B,A) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1074,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f134(c44,B,A) = f133(c44,B,A) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1075,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f134(c44,B,A) = f133(c44,B,A) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1076,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f134(c44,B,A) = f133(c44,B,A) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1077,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f134(c44,B,A) = f133(c44,B,A) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1078,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f134(c44,B,A) = f133(c44,B,A) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1079,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f136(c44,B,A) = f135(c44,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1080,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f136(c44,B,A) = f135(c44,B,A) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1081,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f136(c44,B,A) = f135(c44,B,A) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1082,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f136(c44,B,A) = f135(c44,B,A) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1083,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f136(c44,B,A) = f135(c44,B,A) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1084,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f136(c44,B,A) = f135(c44,B,A) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1085,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f136(c44,B,A) = f135(c44,B,A) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1086,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f137(c44,B,A),the_carrier(c44)) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1087,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f137(c44,B,A),the_carrier(c44)) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1088,a)]. 44.87/44.98 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f137(c44,B,A),the_carrier(c44)) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1089,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f137(c44,B,A),the_carrier(c44)) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1090,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f137(c44,B,A),the_carrier(c44)) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1091,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f137(c44,B,A),the_carrier(c44)) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1092,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f137(c44,B,A),the_carrier(c44)) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1093,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f136(c44,B,A),f137(c44,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1094,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f136(c44,B,A),f137(c44,B,A)) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1095,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f136(c44,B,A),f137(c44,B,A)) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1096,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f136(c44,B,A),f137(c44,B,A)) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1097,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f136(c44,B,A),f137(c44,B,A)) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1098,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f136(c44,B,A),f137(c44,B,A)) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1099,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f136(c44,B,A),f137(c44,B,A)) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1100,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f137(c44,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1101,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f137(c44,B,A),B) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1102,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f137(c44,B,A),B) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1103,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f137(c44,B,A),B) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1104,a)]. 44.87/44.99 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f137(c44,B,A),B) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1105,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f137(c44,B,A),B) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1106,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f137(c44,B,A),B) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1107,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) = f133(c44,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1108,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) = f133(c44,B,A) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1109,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) = f133(c44,B,A) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1110,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) = f133(c44,B,A) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1111,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) = f133(c44,B,A) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1112,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) = f133(c44,B,A) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1113,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) = f133(c44,B,A) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1114,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f138(c44,B,A) = f134(c44,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1115,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f138(c44,B,A) = f134(c44,B,A) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1116,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f138(c44,B,A) = f134(c44,B,A) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1117,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f138(c44,B,A) = f134(c44,B,A) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1118,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f138(c44,B,A) = f134(c44,B,A) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1119,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f138(c44,B,A) = f134(c44,B,A) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1120,a)]. 44.89/45.01 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f138(c44,B,A) = f134(c44,B,A) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1121,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f138(c44,B,A),f139(c44,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1122,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f138(c44,B,A),f139(c44,B,A)) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1123,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f138(c44,B,A),f139(c44,B,A)) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1124,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f138(c44,B,A),f139(c44,B,A)) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1125,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f138(c44,B,A),f139(c44,B,A)) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1126,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f138(c44,B,A),f139(c44,B,A)) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1127,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | relstr_set_smaller(c44,f138(c44,B,A),f139(c44,B,A)) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1128,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f139(c44,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1129,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f139(c44,B,A),B) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1130,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f139(c44,B,A),B) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1131,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f139(c44,B,A),B) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1132,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f139(c44,B,A),B) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1133,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f139(c44,B,A),B) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1134,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | in(f139(c44,B,A),B) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1135,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f139(c44,B,A),the_carrier(c44)) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1136,a)]. 44.91/45.02 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f139(c44,B,A),the_carrier(c44)) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1137,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f139(c44,B,A),the_carrier(c44)) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1138,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f139(c44,B,A),the_carrier(c44)) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1139,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f139(c44,B,A),the_carrier(c44)) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1140,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f139(c44,B,A),the_carrier(c44)) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1141,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | element(f139(c44,B,A),the_carrier(c44)) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1142,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) != f134(c44,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c44)) | -in(D,B) | -relstr_set_smaller(c44,E,D) | E != F | C != F | in(F,f140(c44,B,A)). [resolve(1182,a,1143,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) != f134(c44,B,A) | in(f141(c44,B,A,C),powerset(A)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1144,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) != f134(c44,B,A) | element(f143(c44,B,A,C),the_carrier(c44)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1145,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) != f134(c44,B,A) | in(f143(c44,B,A,C),B) | -in(C,f140(c44,B,A)). [resolve(1182,a,1146,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) != f134(c44,B,A) | relstr_set_smaller(c44,f142(c44,B,A,C),f143(c44,B,A,C)) | -in(C,f140(c44,B,A)). [resolve(1182,a,1147,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) != f134(c44,B,A) | f142(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1148,a)]. 44.91/45.04 Derived: -rel_str(c44) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c44))) | empty_carrier(c44) | f135(c44,B,A) != f134(c44,B,A) | f141(c44,B,A,C) = C | -in(C,f140(c44,B,A)). [resolve(1182,a,1149,a)]. 44.91/45.04 Derived: -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c44) | -in(C,f154(c44,A,B)) | in(C,powerset(B)). [resolve(1182,a,1151,a)]. 44.91/45.04 Derived: -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c44) | -in(C,f154(c44,A,B)) | f155(c44,A,B,C) = C. [resolve(1182,a,1152,a)]. 44.91/45.04 Derived: -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c44) | -in(C,f154(c44,A,B)) | element(f156(c44,A,B,C),the_carrier(c44)). [resolve(1182,a,1153,a)]. 44.91/45.04 Derived: -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c44) | -in(C,f154(c44,A,B)) | in(f156(c44,A,B,C),A). [resolve(1182,a,1154,a)]. 44.91/45.04 Derived: -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c44) | -in(C,f154(c44,A,B)) | relstr_set_smaller(c44,f155(c44,A,B,C),f156(c44,A,B,C)). [resolve(1182,a,1155,a)]. 45.30/45.46 Derived: -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c44) | in(C,f154(c44,A,B)) | -in(C,powerset(B)) | D != C | -element(E,the_carrier(c44)) | -in(E,A) | -relstr_set_smaller(c44,D,E). [resolve(1182,a,1156,a)]. 45.30/45.46 Derived: -antisymmetric_relstr(c44) | -rel_str(c44) | -reflexive_relstr(c44) | relation(the_InternalRel(c44)). [resolve(1182,a,1158,a)]. 45.30/45.46 Derived: -antisymmetric_relstr(c44) | -rel_str(c44) | -reflexive_relstr(c44) | reflexive(the_InternalRel(c44)). [resolve(1182,a,1159,a)]. 45.30/45.46 Derived: -antisymmetric_relstr(c44) | -rel_str(c44) | -reflexive_relstr(c44) | transitive(the_InternalRel(c44)). [resolve(1182,a,1160,a)]. 45.30/45.46 Derived: -antisymmetric_relstr(c44) | -rel_str(c44) | -reflexive_relstr(c44) | v1_partfun1(the_InternalRel(c44),the_carrier(c44),the_carrier(c44)). [resolve(1182,a,1161,a)]. 45.30/45.46 Derived: -antisymmetric_relstr(c44) | -rel_str(c44) | -reflexive_relstr(c44) | antisymmetric(the_InternalRel(c44)). [resolve(1182,a,1162,a)]. 45.30/45.46 Derived: -rel_str(c44) | -element(A,the_carrier(c44)) | -element(B,the_carrier(c44)) | -element(C,the_carrier(c44)) | -related(c44,B,C) | -related(c44,A,B) | related(c44,A,C). [resolve(1182,a,1164,b)]. 45.30/45.46 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | element(f268(c44,A),powerset(A)) | -empty(A). [resolve(1182,a,1165,b)]. 45.30/45.46 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | element(f268(c44,A),powerset(A)) | directed_subset(A,c44). [resolve(1182,a,1166,b)]. 45.30/45.46 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | finite(f268(c44,A)) | -empty(A). [resolve(1182,a,1167,b)]. 45.30/45.46 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | finite(f268(c44,A)) | directed_subset(A,c44). [resolve(1182,a,1168,b)]. 45.30/45.46 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -in(B,A) | -relstr_set_smaller(c44,f268(c44,A),B) | -element(B,the_carrier(c44)) | -empty(A). [resolve(1182,a,1169,b)]. 45.30/45.46 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -in(B,A) | -relstr_set_smaller(c44,f268(c44,A),B) | -element(B,the_carrier(c44)) | directed_subset(A,c44). [resolve(1182,a,1170,b)]. 45.30/45.46 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -element(B,powerset(A)) | -finite(B) | in(f269(c44,A,B),A) | empty(A) | -directed_subset(A,c44). [resolve(1182,a,1171,b)]. 45.30/45.46 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -element(B,powerset(A)) | -finite(B) | relstr_set_smaller(c44,B,f269(c44,A,B)) | empty(A) | -directed_subset(A,c44). [resolve(1182,a,1172,b)]. 45.30/45.46 Derived: empty_carrier(c44) | -rel_str(c44) | -element(A,powerset(the_carrier(c44))) | -element(B,powerset(A)) | -finite(B) | element(f269(c44,A,B),the_carrier(c44)) | empty(A) | -directed_subset(A,c44). [resolve(1182,a,1173,b)]. 45.30/45.46 Derived: -rel_str(c44) | is_transitive_in(the_InternalRel(c44),the_carrier(c44)). [resolve(1182,a,1175,c)]. 45.30/45.46 1183 transitive_relstr(boole_POSet(A)) # label(fc8_yellow_1) # label(axiom). [clausify(719)]. 45.30/45.46 Derived: empty_carrier(boole_POSet(A)) | -rel_str(boole_POSet(A)) | -element(B,powerset(the_carrier(boole_POSet(A)))) | -in(C,B) | -relstr_set_smaller(boole_POSet(A),f268(boole_POSet(A),B),C) | -element(C,the_carrier(boole_POSet(A))) | -empty(B). [resolve(1183,a,1169,b)]. 45.30/45.46 1184 transitive_relstr(c47) # label(t28_yellow_6) # label(negated_conjecture). [clausify(764)]. 45.30/45.46 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | in(f19(c47,B,A),A) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | relstr_set_smaller(c47,A,f22(c47,B,A)). [resolve(1184,a,1051,f)]. 45.30/45.46 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | in(f19(c47,B,A),A) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | in(f22(c47,B,A),B). [resolve(1184,a,1052,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | in(f19(c47,B,A),A) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | element(f22(c47,B,A),the_carrier(c47)). [resolve(1184,a,1053,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | subset(f20(c47,B,A),A) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | relstr_set_smaller(c47,A,f22(c47,B,A)). [resolve(1184,a,1054,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | subset(f20(c47,B,A),A) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | in(f22(c47,B,A),B). [resolve(1184,a,1055,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | subset(f20(c47,B,A),A) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | element(f22(c47,B,A),the_carrier(c47)). [resolve(1184,a,1056,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | element(f21(c47,B,A),the_carrier(c47)) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | relstr_set_smaller(c47,A,f22(c47,B,A)). [resolve(1184,a,1057,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | element(f21(c47,B,A),the_carrier(c47)) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | in(f22(c47,B,A),B). [resolve(1184,a,1058,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | element(f21(c47,B,A),the_carrier(c47)) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | element(f22(c47,B,A),the_carrier(c47)). [resolve(1184,a,1059,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | relstr_set_smaller(c47,f20(c47,B,A),f21(c47,B,A)) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | relstr_set_smaller(c47,A,f22(c47,B,A)). [resolve(1184,a,1060,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | relstr_set_smaller(c47,f20(c47,B,A),f21(c47,B,A)) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | in(f22(c47,B,A),B). [resolve(1184,a,1061,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | relstr_set_smaller(c47,f20(c47,B,A),f21(c47,B,A)) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | element(f22(c47,B,A),the_carrier(c47)). [resolve(1184,a,1062,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | in(f21(c47,B,A),B) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | relstr_set_smaller(c47,A,f22(c47,B,A)). [resolve(1184,a,1063,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | in(f21(c47,B,A),B) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | in(f22(c47,B,A),B). [resolve(1184,a,1064,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | in(f21(c47,B,A),B) | -in(C,B) | -relstr_set_smaller(c47,empty_set,C) | -element(C,the_carrier(c47)) | element(f22(c47,B,A),the_carrier(c47)). [resolve(1184,a,1065,f)]. 45.30/45.47 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | -in(C,B) | -relstr_set_smaller(c47,set_union2(f20(c47,B,A),singleton(f19(c47,B,A))),C) | -element(C,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,empty_set,D) | -element(D,the_carrier(c47)) | relstr_set_smaller(c47,A,f22(c47,B,A)). [resolve(1184,a,1066,f)]. 45.38/45.48 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | -in(C,B) | -relstr_set_smaller(c47,set_union2(f20(c47,B,A),singleton(f19(c47,B,A))),C) | -element(C,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,empty_set,D) | -element(D,the_carrier(c47)) | in(f22(c47,B,A),B). [resolve(1184,a,1067,f)]. 45.38/45.48 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(B)) | -finite(A) | -element(B,powerset(the_carrier(c47))) | -in(C,B) | -relstr_set_smaller(c47,set_union2(f20(c47,B,A),singleton(f19(c47,B,A))),C) | -element(C,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,empty_set,D) | -element(D,the_carrier(c47)) | element(f22(c47,B,A),the_carrier(c47)). [resolve(1184,a,1068,f)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f134(c47,B,A) = f133(c47,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1073,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f134(c47,B,A) = f133(c47,B,A) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1074,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f134(c47,B,A) = f133(c47,B,A) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1075,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f134(c47,B,A) = f133(c47,B,A) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1076,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f134(c47,B,A) = f133(c47,B,A) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1077,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f134(c47,B,A) = f133(c47,B,A) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1078,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f134(c47,B,A) = f133(c47,B,A) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1079,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f136(c47,B,A) = f135(c47,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1080,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f136(c47,B,A) = f135(c47,B,A) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1081,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f136(c47,B,A) = f135(c47,B,A) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1082,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f136(c47,B,A) = f135(c47,B,A) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1083,a)]. 45.38/45.48 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f136(c47,B,A) = f135(c47,B,A) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1084,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f136(c47,B,A) = f135(c47,B,A) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1085,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f136(c47,B,A) = f135(c47,B,A) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1086,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f137(c47,B,A),the_carrier(c47)) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1087,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f137(c47,B,A),the_carrier(c47)) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1088,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f137(c47,B,A),the_carrier(c47)) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1089,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f137(c47,B,A),the_carrier(c47)) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1090,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f137(c47,B,A),the_carrier(c47)) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1091,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f137(c47,B,A),the_carrier(c47)) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1092,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f137(c47,B,A),the_carrier(c47)) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1093,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f136(c47,B,A),f137(c47,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1094,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f136(c47,B,A),f137(c47,B,A)) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1095,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f136(c47,B,A),f137(c47,B,A)) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1096,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f136(c47,B,A),f137(c47,B,A)) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1097,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f136(c47,B,A),f137(c47,B,A)) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1098,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f136(c47,B,A),f137(c47,B,A)) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1099,a)]. 45.38/45.50 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f136(c47,B,A),f137(c47,B,A)) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1100,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f137(c47,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1101,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f137(c47,B,A),B) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1102,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f137(c47,B,A),B) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1103,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f137(c47,B,A),B) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1104,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f137(c47,B,A),B) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1105,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f137(c47,B,A),B) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1106,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f137(c47,B,A),B) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1107,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) = f133(c47,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1108,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) = f133(c47,B,A) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1109,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) = f133(c47,B,A) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1110,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) = f133(c47,B,A) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1111,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) = f133(c47,B,A) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1112,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) = f133(c47,B,A) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1113,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) = f133(c47,B,A) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1114,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f138(c47,B,A) = f134(c47,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1115,a)]. 45.38/45.51 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f138(c47,B,A) = f134(c47,B,A) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1116,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f138(c47,B,A) = f134(c47,B,A) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1117,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f138(c47,B,A) = f134(c47,B,A) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1118,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f138(c47,B,A) = f134(c47,B,A) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1119,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f138(c47,B,A) = f134(c47,B,A) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1120,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f138(c47,B,A) = f134(c47,B,A) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1121,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f138(c47,B,A),f139(c47,B,A)) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1122,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f138(c47,B,A),f139(c47,B,A)) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1123,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f138(c47,B,A),f139(c47,B,A)) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1124,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f138(c47,B,A),f139(c47,B,A)) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1125,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f138(c47,B,A),f139(c47,B,A)) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1126,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f138(c47,B,A),f139(c47,B,A)) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1127,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | relstr_set_smaller(c47,f138(c47,B,A),f139(c47,B,A)) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1128,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f139(c47,B,A),B) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1129,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f139(c47,B,A),B) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1130,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f139(c47,B,A),B) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1131,a)]. 45.38/45.53 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f139(c47,B,A),B) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1132,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f139(c47,B,A),B) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1133,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f139(c47,B,A),B) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1134,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | in(f139(c47,B,A),B) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1135,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f139(c47,B,A),the_carrier(c47)) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1136,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f139(c47,B,A),the_carrier(c47)) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1137,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f139(c47,B,A),the_carrier(c47)) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1138,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f139(c47,B,A),the_carrier(c47)) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1139,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f139(c47,B,A),the_carrier(c47)) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1140,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f139(c47,B,A),the_carrier(c47)) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1141,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | element(f139(c47,B,A),the_carrier(c47)) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1142,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) != f134(c47,B,A) | -in(C,powerset(A)) | -element(D,the_carrier(c47)) | -in(D,B) | -relstr_set_smaller(c47,E,D) | E != F | C != F | in(F,f140(c47,B,A)). [resolve(1184,a,1143,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) != f134(c47,B,A) | in(f141(c47,B,A,C),powerset(A)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1144,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) != f134(c47,B,A) | element(f143(c47,B,A,C),the_carrier(c47)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1145,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) != f134(c47,B,A) | in(f143(c47,B,A,C),B) | -in(C,f140(c47,B,A)). [resolve(1184,a,1146,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) != f134(c47,B,A) | relstr_set_smaller(c47,f142(c47,B,A,C),f143(c47,B,A,C)) | -in(C,f140(c47,B,A)). [resolve(1184,a,1147,a)]. 45.38/45.54 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) != f134(c47,B,A) | f142(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1148,a)]. 45.38/45.55 Derived: -rel_str(c47) | -finite(A) | -element(A,powerset(B)) | -element(B,powerset(the_carrier(c47))) | empty_carrier(c47) | f135(c47,B,A) != f134(c47,B,A) | f141(c47,B,A,C) = C | -in(C,f140(c47,B,A)). [resolve(1184,a,1149,a)]. 45.38/45.55 Derived: -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c47) | -in(C,f154(c47,A,B)) | in(C,powerset(B)). [resolve(1184,a,1151,a)]. 45.38/45.55 Derived: -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c47) | -in(C,f154(c47,A,B)) | f155(c47,A,B,C) = C. [resolve(1184,a,1152,a)]. 45.38/45.55 Derived: -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c47) | -in(C,f154(c47,A,B)) | element(f156(c47,A,B,C),the_carrier(c47)). [resolve(1184,a,1153,a)]. 45.38/45.55 Derived: -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c47) | -in(C,f154(c47,A,B)) | in(f156(c47,A,B,C),A). [resolve(1184,a,1154,a)]. 45.38/45.55 Derived: -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c47) | -in(C,f154(c47,A,B)) | relstr_set_smaller(c47,f155(c47,A,B,C),f156(c47,A,B,C)). [resolve(1184,a,1155,a)]. 45.38/45.55 Derived: -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -finite(B) | -element(B,powerset(A)) | empty_carrier(c47) | in(C,f154(c47,A,B)) | -in(C,powerset(B)) | D != C | -element(E,the_carrier(c47)) | -in(E,A) | -relstr_set_smaller(c47,D,E). [resolve(1184,a,1156,a)]. 45.38/45.55 Derived: -antisymmetric_relstr(c47) | -rel_str(c47) | -reflexive_relstr(c47) | relation(the_InternalRel(c47)). [resolve(1184,a,1158,a)]. 45.38/45.55 Derived: -antisymmetric_relstr(c47) | -rel_str(c47) | -reflexive_relstr(c47) | reflexive(the_InternalRel(c47)). [resolve(1184,a,1159,a)]. 45.38/45.55 Derived: -antisymmetric_relstr(c47) | -rel_str(c47) | -reflexive_relstr(c47) | transitive(the_InternalRel(c47)). [resolve(1184,a,1160,a)]. 45.38/45.55 Derived: -antisymmetric_relstr(c47) | -rel_str(c47) | -reflexive_relstr(c47) | v1_partfun1(the_InternalRel(c47),the_carrier(c47),the_carrier(c47)). [resolve(1184,a,1161,a)]. 45.38/45.55 Derived: -antisymmetric_relstr(c47) | -rel_str(c47) | -reflexive_relstr(c47) | antisymmetric(the_InternalRel(c47)). [resolve(1184,a,1162,a)]. 45.38/45.55 Derived: -rel_str(c47) | -element(A,the_carrier(c47)) | -element(B,the_carrier(c47)) | -element(C,the_carrier(c47)) | -related(c47,B,C) | -related(c47,A,B) | related(c47,A,C). [resolve(1184,a,1164,b)]. 45.38/45.55 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | element(f268(c47,A),powerset(A)) | -empty(A). [resolve(1184,a,1165,b)]. 45.38/45.55 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | element(f268(c47,A),powerset(A)) | directed_subset(A,c47). [resolve(1184,a,1166,b)]. 45.38/45.55 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | finite(f268(c47,A)) | -empty(A). [resolve(1184,a,1167,b)]. 45.38/45.55 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | finite(f268(c47,A)) | directed_subset(A,c47). [resolve(1184,a,1168,b)]. 45.38/45.55 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -in(B,A) | -relstr_set_smaller(c47,f268(c47,A),B) | -element(B,the_carrier(c47)) | -empty(A). [resolve(1184,a,1169,b)]. 45.38/45.55 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -in(B,A) | -relstr_set_smaller(c47,f268(c47,A),B) | -element(B,the_carrier(c47)) | directed_subset(A,c47). [resolve(1184,a,1170,b)]. 45.38/45.55 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -element(B,powerset(A)) | -finite(B) | in(f269(c47,A,B),A) | empty(A) | -directed_subset(A,c47). [resolve(1184,a,1171,b)]. 45.38/45.55 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -element(B,powerset(A)) | -finite(B) | relstr_set_smaller(c47,B,f269(c47,A,B)) | empty(A) | -directed_subset(A,c47). [resolve(1184,a,1172,b)]. 45.38/45.55 Derived: empty_carrier(c47) | -rel_str(c47) | -element(A,powerset(the_carrier(c47))) | -element(B,powerset(A)) | -finite(B) | element(f269(c47,A,B),the_carrier(c47)) | empty(A) | -directed_subset(A,c47). [resolve(1184,a,1173,b)]. 51.61/51.79 Derived: -rel_str(c47) | is_transitive_in(the_InternalRel(c47),the_carrier(c47)). [resolve(1184,a,1175,c)]. 51.61/51.79 1185 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | transitive_relstr(poset_of_lattice(A)). [resolve(951,e,946,c)]. 51.61/51.79 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | empty_carrier(poset_of_lattice(A)) | -rel_str(poset_of_lattice(A)) | -element(B,powerset(the_carrier(poset_of_lattice(A)))) | -in(C,B) | -relstr_set_smaller(poset_of_lattice(A),f268(poset_of_lattice(A),B),C) | -element(C,the_carrier(poset_of_lattice(A))) | -empty(B). [resolve(1185,h,1169,b)]. 51.61/51.79 1186 -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | transitive_relstr(poset_of_lattice(boole_lattice(A))). [resolve(952,a,946,c)]. 51.61/51.79 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | empty_carrier(poset_of_lattice(boole_lattice(A))) | -rel_str(poset_of_lattice(boole_lattice(A))) | -element(B,powerset(the_carrier(poset_of_lattice(boole_lattice(A))))) | -in(C,B) | -relstr_set_smaller(poset_of_lattice(boole_lattice(A)),f268(poset_of_lattice(boole_lattice(A)),B),C) | -element(C,the_carrier(poset_of_lattice(boole_lattice(A)))) | -empty(B). [resolve(1186,d,1169,b)]. 51.61/51.79 1187 -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | transitive_relstr(poset_of_lattice(c45)). [resolve(955,a,946,c)]. 51.61/51.79 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | empty_carrier(poset_of_lattice(c45)) | -rel_str(poset_of_lattice(c45)) | -element(A,powerset(the_carrier(poset_of_lattice(c45)))) | -in(B,A) | -relstr_set_smaller(poset_of_lattice(c45),f268(poset_of_lattice(c45),A),B) | -element(B,the_carrier(poset_of_lattice(c45))) | -empty(A). [resolve(1187,d,1169,b)]. 51.61/51.79 1188 -top_str(A) | compact_top_space(A) | element(f26(A),powerset(powerset(the_carrier(A)))) # label(d3_compts_1) # label(axiom). [clausify(30)]. 51.61/51.79 1189 -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B) # label(d3_compts_1) # label(axiom). [clausify(30)]. 51.61/51.79 1190 -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B) # label(d3_compts_1) # label(axiom). [clausify(30)]. 51.61/51.79 1191 -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B) # label(d3_compts_1) # label(axiom). [clausify(30)]. 51.61/51.79 1192 -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B) # label(d3_compts_1) # label(axiom). [clausify(30)]. 51.61/51.79 Derived: -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1188,b,1189,b)]. 51.61/51.79 Derived: -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1188,b,1190,b)]. 51.61/51.79 Derived: -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1188,b,1191,b)]. 51.61/51.79 Derived: -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1188,b,1192,b)]. 53.61/53.75 1193 -top_str(A) | compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -finite(B) | -is_a_cover_of_carrier(A,B) | -subset(B,f26(A)) # label(d3_compts_1) # label(axiom). [clausify(30)]. 53.61/53.75 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -finite(B) | -is_a_cover_of_carrier(A,B) | -subset(B,f26(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | element(f25(A,C),powerset(powerset(the_carrier(A)))) | -open_subsets(C,A) | -is_a_cover_of_carrier(A,C). [resolve(1193,b,1189,b)]. 53.61/53.75 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -finite(B) | -is_a_cover_of_carrier(A,B) | -subset(B,f26(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | finite(f25(A,C)) | -open_subsets(C,A) | -is_a_cover_of_carrier(A,C). [resolve(1193,b,1190,b)]. 53.61/53.75 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -finite(B) | -is_a_cover_of_carrier(A,B) | -subset(B,f26(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,C)) | -open_subsets(C,A) | -is_a_cover_of_carrier(A,C). [resolve(1193,b,1191,b)]. 53.61/53.75 Derived: -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -finite(B) | -is_a_cover_of_carrier(A,B) | -subset(B,f26(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | subset(f25(A,C),C) | -open_subsets(C,A) | -is_a_cover_of_carrier(A,C). [resolve(1193,b,1192,b)]. 53.61/53.75 1194 -top_str(A) | compact_top_space(A) | open_subsets(f26(A),A) # label(d3_compts_1) # label(axiom). [clausify(30)]. 53.61/53.75 Derived: -top_str(A) | open_subsets(f26(A),A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1194,b,1189,b)]. 53.61/53.75 Derived: -top_str(A) | open_subsets(f26(A),A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1194,b,1190,b)]. 53.61/53.75 Derived: -top_str(A) | open_subsets(f26(A),A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1194,b,1191,b)]. 53.61/53.75 Derived: -top_str(A) | open_subsets(f26(A),A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1194,b,1192,b)]. 53.61/53.75 1195 -top_str(A) | compact_top_space(A) | is_a_cover_of_carrier(A,f26(A)) # label(d3_compts_1) # label(axiom). [clausify(30)]. 53.61/53.75 Derived: -top_str(A) | is_a_cover_of_carrier(A,f26(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1195,b,1189,b)]. 53.61/53.75 Derived: -top_str(A) | is_a_cover_of_carrier(A,f26(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1195,b,1190,b)]. 53.61/53.75 Derived: -top_str(A) | is_a_cover_of_carrier(A,f26(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1195,b,1191,b)]. 53.61/53.75 Derived: -top_str(A) | is_a_cover_of_carrier(A,f26(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1195,b,1192,b)]. 53.61/53.75 1196 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,765,e)]. 53.61/53.75 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1196,c,1188,b)]. 53.61/53.76 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1196,c,1193,b)]. 53.61/53.76 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1196,c,1194,b)]. 53.61/53.76 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1196,c,1195,b)]. 53.61/53.76 1197 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,777,e)]. 53.61/53.76 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1197,c,1188,b)]. 53.61/53.76 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1197,c,1193,b)]. 53.61/53.76 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1197,c,1194,b)]. 53.61/53.76 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1197,c,1195,b)]. 53.61/53.76 1198 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,778,e)]. 53.61/53.76 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1198,c,1188,b)]. 53.61/53.77 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1198,c,1193,b)]. 53.61/53.77 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1198,c,1194,b)]. 53.61/53.77 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1198,c,1195,b)]. 53.61/53.77 1199 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,779,e)]. 53.61/53.77 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1199,c,1188,b)]. 53.61/53.77 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1199,c,1193,b)]. 53.61/53.77 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1199,c,1194,b)]. 53.61/53.77 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1199,c,1195,b)]. 53.61/53.77 1200 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,780,e)]. 53.61/53.77 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1200,c,1188,b)]. 53.61/53.78 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1200,c,1193,b)]. 53.61/53.78 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1200,c,1194,b)]. 53.61/53.78 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1200,c,1195,b)]. 53.61/53.78 1201 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,781,e)]. 53.61/53.78 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1201,c,1188,b)]. 53.61/53.78 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1201,c,1193,b)]. 53.61/53.78 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1201,c,1194,b)]. 53.61/53.78 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1201,c,1195,b)]. 53.61/53.78 1202 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,782,e)]. 53.61/53.78 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1202,c,1188,b)]. 53.61/53.79 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1202,c,1193,b)]. 53.61/53.79 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1202,c,1194,b)]. 53.61/53.79 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1202,c,1195,b)]. 53.61/53.79 1203 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,783,e)]. 53.61/53.79 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1203,c,1188,b)]. 53.61/53.79 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1203,c,1193,b)]. 53.61/53.79 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1203,c,1194,b)]. 53.61/53.79 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1203,c,1195,b)]. 53.61/53.79 1204 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,784,e)]. 53.61/53.79 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1204,c,1188,b)]. 53.61/53.79 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1204,c,1193,b)]. 53.70/53.81 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1204,c,1194,b)]. 53.70/53.81 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1204,c,1195,b)]. 53.70/53.81 1205 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,785,e)]. 53.70/53.81 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1205,c,1188,b)]. 53.70/53.81 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1205,c,1193,b)]. 53.70/53.81 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1205,c,1194,b)]. 53.70/53.81 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1205,c,1195,b)]. 53.70/53.81 1206 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,786,e)]. 53.70/53.81 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1206,c,1188,b)]. 53.70/53.81 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1206,c,1193,b)]. 53.70/53.82 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1206,c,1194,b)]. 53.70/53.82 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1206,c,1195,b)]. 53.70/53.82 1207 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,787,e)]. 53.70/53.82 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1207,c,1188,b)]. 53.70/53.82 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1207,c,1193,b)]. 53.70/53.82 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1207,c,1194,b)]. 53.70/53.82 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1207,c,1195,b)]. 53.70/53.82 1208 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,788,e)]. 53.70/53.82 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1208,c,1188,b)]. 53.70/53.82 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1208,c,1193,b)]. 53.70/53.83 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1208,c,1194,b)]. 53.70/53.83 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1208,c,1195,b)]. 53.70/53.83 1209 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,789,e)]. 53.70/53.83 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1209,c,1188,b)]. 53.70/53.83 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1209,c,1193,b)]. 53.70/53.83 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1209,c,1194,b)]. 53.70/53.83 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1209,c,1195,b)]. 53.70/53.83 1210 empty_carrier(A) | -top_str(A) | -compact_top_space(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(797,c,790,e)]. 53.70/53.83 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | element(f26(A),powerset(powerset(the_carrier(A)))). [resolve(1210,c,1188,b)]. 53.70/53.88 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(C,powerset(powerset(the_carrier(A)))) | -finite(C) | -is_a_cover_of_carrier(A,C) | -subset(C,f26(A)). [resolve(1210,c,1193,b)]. 53.70/53.88 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | open_subsets(f26(A),A). [resolve(1210,c,1194,b)]. 53.70/53.88 Derived: empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | is_a_cover_of_carrier(A,f26(A)). [resolve(1210,c,1195,b)]. 53.70/53.88 1211 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,765,e)]. 53.70/53.88 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1211,c,1189,b)]. 53.70/53.88 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1211,c,1190,b)]. 53.70/53.88 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1211,c,1191,b)]. 53.70/53.88 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1211,c,1192,b)]. 53.70/53.88 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1211,c,1196,c)]. 53.70/53.88 1212 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,777,e)]. 53.80/53.93 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1212,c,1189,b)]. 53.80/53.93 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1212,c,1190,b)]. 53.80/53.93 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1212,c,1191,b)]. 53.80/53.93 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1212,c,1192,b)]. 53.80/53.93 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1212,c,1197,c)]. 53.80/53.93 1213 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,778,e)]. 53.80/53.93 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1213,c,1189,b)]. 53.80/53.93 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1213,c,1190,b)]. 53.80/53.93 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1213,c,1191,b)]. 53.80/53.93 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1213,c,1192,b)]. 53.91/54.02 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1213,c,1198,c)]. 53.91/54.02 1214 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,779,e)]. 53.91/54.02 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1214,c,1189,b)]. 53.91/54.02 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1214,c,1190,b)]. 53.91/54.02 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1214,c,1191,b)]. 53.91/54.02 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1214,c,1192,b)]. 53.91/54.02 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1214,c,1199,c)]. 53.91/54.02 1215 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,780,e)]. 53.91/54.02 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1215,c,1189,b)]. 53.91/54.02 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1215,c,1190,b)]. 53.91/54.09 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1215,c,1191,b)]. 53.91/54.09 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1215,c,1192,b)]. 53.91/54.09 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1215,c,1200,c)]. 53.91/54.09 1216 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,781,e)]. 53.91/54.09 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1216,c,1189,b)]. 53.91/54.09 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1216,c,1190,b)]. 53.91/54.09 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1216,c,1191,b)]. 53.91/54.09 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1216,c,1192,b)]. 53.91/54.09 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1216,c,1201,c)]. 54.00/54.18 1217 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,782,e)]. 54.00/54.18 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1217,c,1189,b)]. 54.00/54.18 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1217,c,1190,b)]. 54.00/54.18 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1217,c,1191,b)]. 54.00/54.18 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1217,c,1192,b)]. 54.00/54.18 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1217,c,1202,c)]. 54.00/54.18 1218 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,783,e)]. 54.00/54.18 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1218,c,1189,b)]. 54.00/54.18 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1218,c,1190,b)]. 54.00/54.18 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1218,c,1191,b)]. 54.00/54.18 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1218,c,1192,b)]. 54.09/54.27 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1218,c,1203,c)]. 54.09/54.27 1219 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,784,e)]. 54.09/54.27 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1219,c,1189,b)]. 54.09/54.27 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1219,c,1190,b)]. 54.09/54.27 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1219,c,1191,b)]. 54.09/54.27 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1219,c,1192,b)]. 54.09/54.27 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1219,c,1204,c)]. 54.09/54.27 1220 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,785,e)]. 54.09/54.27 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1220,c,1189,b)]. 54.09/54.27 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1220,c,1190,b)]. 54.21/54.35 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1220,c,1191,b)]. 54.21/54.35 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1220,c,1192,b)]. 54.21/54.35 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1220,c,1205,c)]. 54.21/54.35 1221 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,786,e)]. 54.21/54.35 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1221,c,1189,b)]. 54.21/54.35 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1221,c,1190,b)]. 54.21/54.35 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1221,c,1191,b)]. 54.21/54.35 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1221,c,1192,b)]. 54.21/54.35 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1221,c,1206,c)]. 54.30/54.42 1222 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,787,e)]. 54.30/54.42 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1222,c,1189,b)]. 54.30/54.42 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1222,c,1190,b)]. 54.30/54.42 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1222,c,1191,b)]. 54.30/54.42 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1222,c,1192,b)]. 54.30/54.42 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1222,c,1207,c)]. 54.30/54.42 1223 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,788,e)]. 54.30/54.42 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1223,c,1189,b)]. 54.30/54.42 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1223,c,1190,b)]. 54.30/54.42 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1223,c,1191,b)]. 54.40/54.51 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1223,c,1192,b)]. 54.40/54.51 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1223,c,1208,c)]. 54.40/54.51 1224 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,789,e)]. 54.40/54.51 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1224,c,1189,b)]. 54.40/54.51 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1224,c,1190,b)]. 54.40/54.51 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1224,c,1191,b)]. 54.40/54.51 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1224,c,1192,b)]. 54.40/54.51 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1224,c,1209,c)]. 54.40/54.51 1225 empty_carrier(A) | -top_str(A) | compact_top_space(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(798,c,790,e)]. 54.40/54.51 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1225,c,1189,b)]. 54.40/54.56 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1225,c,1190,b)]. 54.40/54.56 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1225,c,1191,b)]. 54.40/54.56 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1225,c,1192,b)]. 54.40/54.56 Derived: empty_carrier(A) | -top_str(A) | element(f82(A),powerset(powerset(the_carrier(A)))) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1225,c,1210,c)]. 54.40/54.56 1226 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,765,e)]. 54.40/54.56 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1226,c,1189,b)]. 54.40/54.56 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1226,c,1190,b)]. 54.40/54.56 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1226,c,1191,b)]. 54.40/54.56 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1226,c,1192,b)]. 54.51/54.66 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1226,c,1196,c)]. 54.51/54.66 1227 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,777,e)]. 54.51/54.66 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1227,c,1189,b)]. 54.51/54.66 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1227,c,1190,b)]. 54.51/54.66 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1227,c,1191,b)]. 54.51/54.66 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1227,c,1192,b)]. 54.51/54.66 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1227,c,1197,c)]. 54.51/54.66 1228 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,778,e)]. 54.51/54.66 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1228,c,1189,b)]. 54.51/54.66 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1228,c,1190,b)]. 54.51/54.66 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1228,c,1191,b)]. 54.61/54.75 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1228,c,1192,b)]. 54.61/54.75 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1228,c,1198,c)]. 54.61/54.75 1229 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,779,e)]. 54.61/54.75 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1229,c,1189,b)]. 54.61/54.75 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1229,c,1190,b)]. 54.61/54.75 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1229,c,1191,b)]. 54.61/54.75 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1229,c,1192,b)]. 54.61/54.75 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1229,c,1199,c)]. 54.61/54.75 1230 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,780,e)]. 54.61/54.75 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1230,c,1189,b)]. 54.70/54.83 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1230,c,1190,b)]. 54.70/54.83 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1230,c,1191,b)]. 54.70/54.83 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1230,c,1192,b)]. 54.70/54.83 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1230,c,1200,c)]. 54.70/54.83 1231 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,781,e)]. 54.70/54.83 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1231,c,1189,b)]. 54.70/54.83 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1231,c,1190,b)]. 54.70/54.83 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1231,c,1191,b)]. 54.70/54.83 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1231,c,1192,b)]. 54.70/54.83 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1231,c,1201,c)]. 54.81/54.93 1232 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,782,e)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1232,c,1189,b)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1232,c,1190,b)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1232,c,1191,b)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1232,c,1192,b)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1232,c,1202,c)]. 54.81/54.93 1233 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,783,e)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1233,c,1189,b)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1233,c,1190,b)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1233,c,1191,b)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1233,c,1192,b)]. 54.81/54.93 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1233,c,1203,c)]. 54.81/55.00 1234 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,784,e)]. 54.81/55.00 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1234,c,1189,b)]. 54.81/55.00 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1234,c,1190,b)]. 54.81/55.00 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1234,c,1191,b)]. 54.81/55.00 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1234,c,1192,b)]. 54.81/55.00 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1234,c,1204,c)]. 54.81/55.00 1235 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,785,e)]. 54.81/55.00 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1235,c,1189,b)]. 54.81/55.00 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1235,c,1190,b)]. 54.81/55.00 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1235,c,1191,b)]. 54.81/55.00 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1235,c,1192,b)]. 55.00/55.10 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1235,c,1205,c)]. 55.00/55.10 1236 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,786,e)]. 55.00/55.10 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1236,c,1189,b)]. 55.00/55.10 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1236,c,1190,b)]. 55.00/55.10 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1236,c,1191,b)]. 55.00/55.10 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1236,c,1192,b)]. 55.00/55.10 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1236,c,1206,c)]. 55.00/55.10 1237 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,787,e)]. 55.00/55.10 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1237,c,1189,b)]. 55.00/55.10 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1237,c,1190,b)]. 55.00/55.19 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1237,c,1191,b)]. 55.00/55.19 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1237,c,1192,b)]. 55.00/55.19 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1237,c,1207,c)]. 55.00/55.19 1238 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,788,e)]. 55.00/55.19 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1238,c,1189,b)]. 55.00/55.19 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1238,c,1190,b)]. 55.00/55.19 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1238,c,1191,b)]. 55.00/55.19 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1238,c,1192,b)]. 55.00/55.19 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1238,c,1208,c)]. 55.00/55.19 1239 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,789,e)]. 55.13/55.25 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1239,c,1189,b)]. 55.13/55.25 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1239,c,1190,b)]. 55.13/55.25 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1239,c,1191,b)]. 55.13/55.25 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1239,c,1192,b)]. 55.13/55.25 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1239,c,1209,c)]. 55.13/55.25 1240 empty_carrier(A) | -top_str(A) | compact_top_space(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(799,c,790,e)]. 55.13/55.25 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1240,c,1189,b)]. 55.13/55.25 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1240,c,1190,b)]. 55.13/55.25 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1240,c,1191,b)]. 55.13/55.25 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1240,c,1192,b)]. 55.22/55.34 Derived: empty_carrier(A) | -top_str(A) | closed_subsets(f82(A),A) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1240,c,1210,c)]. 55.22/55.34 1241 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,765,e)]. 55.22/55.34 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1241,c,1189,b)]. 55.22/55.34 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1241,c,1190,b)]. 55.22/55.34 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1241,c,1191,b)]. 55.22/55.34 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1241,c,1192,b)]. 55.22/55.34 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1241,c,1196,c)]. 55.22/55.34 1242 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,777,e)]. 55.22/55.34 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1242,c,1189,b)]. 55.31/55.40 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1242,c,1190,b)]. 55.31/55.40 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1242,c,1191,b)]. 55.31/55.40 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1242,c,1192,b)]. 55.31/55.40 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1242,c,1197,c)]. 55.31/55.40 1243 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,778,e)]. 55.31/55.40 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1243,c,1189,b)]. 55.31/55.40 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1243,c,1190,b)]. 55.31/55.40 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1243,c,1191,b)]. 55.31/55.40 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1243,c,1192,b)]. 55.31/55.40 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1243,c,1198,c)]. 55.40/55.49 1244 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,779,e)]. 55.40/55.49 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1244,c,1189,b)]. 55.40/55.49 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1244,c,1190,b)]. 55.40/55.49 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1244,c,1191,b)]. 55.40/55.49 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1244,c,1192,b)]. 55.40/55.49 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1244,c,1199,c)]. 55.40/55.49 1245 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,780,e)]. 55.40/55.49 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1245,c,1189,b)]. 55.40/55.49 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1245,c,1190,b)]. 55.40/55.49 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1245,c,1191,b)]. 55.43/55.58 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1245,c,1192,b)]. 55.43/55.58 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1245,c,1200,c)]. 55.43/55.58 1246 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,781,e)]. 55.43/55.58 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1246,c,1189,b)]. 55.43/55.58 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1246,c,1190,b)]. 55.43/55.58 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1246,c,1191,b)]. 55.43/55.58 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1246,c,1192,b)]. 55.43/55.58 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1246,c,1201,c)]. 55.43/55.58 1247 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,782,e)]. 55.43/55.58 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1247,c,1189,b)]. 55.52/55.65 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1247,c,1190,b)]. 55.52/55.65 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1247,c,1191,b)]. 55.52/55.65 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1247,c,1192,b)]. 55.52/55.65 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1247,c,1202,c)]. 55.52/55.65 1248 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,783,e)]. 55.52/55.65 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1248,c,1189,b)]. 55.52/55.65 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1248,c,1190,b)]. 55.52/55.65 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1248,c,1191,b)]. 55.52/55.65 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1248,c,1192,b)]. 55.52/55.65 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1248,c,1203,c)]. 55.61/55.73 1249 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,784,e)]. 55.61/55.73 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1249,c,1189,b)]. 55.61/55.73 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1249,c,1190,b)]. 55.61/55.73 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1249,c,1191,b)]. 55.61/55.73 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1249,c,1192,b)]. 55.61/55.73 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1249,c,1204,c)]. 55.61/55.73 1250 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,785,e)]. 55.61/55.73 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1250,c,1189,b)]. 55.61/55.73 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1250,c,1190,b)]. 55.61/55.73 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1250,c,1191,b)]. 55.61/55.73 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1250,c,1192,b)]. 55.73/55.82 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1250,c,1205,c)]. 55.73/55.82 1251 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,786,e)]. 55.73/55.82 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1251,c,1189,b)]. 55.73/55.82 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1251,c,1190,b)]. 55.73/55.82 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1251,c,1191,b)]. 55.73/55.82 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1251,c,1192,b)]. 55.73/55.82 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1251,c,1206,c)]. 55.73/55.82 1252 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,787,e)]. 55.73/55.82 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1252,c,1189,b)]. 55.84/55.91 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1252,c,1190,b)]. 55.84/55.91 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1252,c,1191,b)]. 55.84/55.91 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1252,c,1192,b)]. 55.84/55.91 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1252,c,1207,c)]. 55.84/55.91 1253 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,788,e)]. 55.84/55.91 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1253,c,1189,b)]. 55.84/55.91 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1253,c,1190,b)]. 55.84/55.91 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1253,c,1191,b)]. 55.84/55.91 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1253,c,1192,b)]. 55.84/55.91 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1253,c,1208,c)]. 55.84/55.97 1254 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,789,e)]. 55.84/55.97 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1254,c,1189,b)]. 55.84/55.97 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1254,c,1190,b)]. 55.84/55.97 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1254,c,1191,b)]. 55.84/55.97 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1254,c,1192,b)]. 55.84/55.97 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1254,c,1209,c)]. 55.84/55.97 1255 empty_carrier(A) | -top_str(A) | compact_top_space(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(800,c,790,e)]. 55.84/55.97 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1255,c,1189,b)]. 55.84/55.97 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1255,c,1190,b)]. 55.92/56.07 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1255,c,1191,b)]. 55.92/56.07 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1255,c,1192,b)]. 55.92/56.07 Derived: empty_carrier(A) | -top_str(A) | meet_of_subsets(the_carrier(A),f82(A)) = empty_set | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1255,c,1210,c)]. 55.92/56.07 1256 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,765,e)]. 55.92/56.07 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1256,c,1189,b)]. 55.92/56.07 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1256,c,1190,b)]. 55.92/56.07 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1256,c,1191,b)]. 55.92/56.07 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1256,c,1192,b)]. 55.92/56.07 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1256,c,1196,c)]. 55.92/56.07 1257 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,777,e)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1257,c,1189,b)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1257,c,1190,b)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1257,c,1191,b)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1257,c,1192,b)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1257,c,1197,c)]. 56.00/56.13 1258 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,778,e)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1258,c,1189,b)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1258,c,1190,b)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1258,c,1191,b)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1258,c,1192,b)]. 56.00/56.13 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1258,c,1198,c)]. 56.14/56.22 1259 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,779,e)]. 56.14/56.22 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1259,c,1189,b)]. 56.14/56.22 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1259,c,1190,b)]. 56.14/56.22 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1259,c,1191,b)]. 56.14/56.22 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1259,c,1192,b)]. 56.14/56.22 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1259,c,1199,c)]. 56.14/56.22 1260 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,780,e)]. 56.14/56.22 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1260,c,1189,b)]. 56.14/56.22 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1260,c,1190,b)]. 56.14/56.22 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1260,c,1191,b)]. 56.24/56.31 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1260,c,1192,b)]. 56.24/56.31 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | element(f37(A),powerset(powerset(the_carrier(A)))) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1260,c,1200,c)]. 56.24/56.31 1261 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,781,e)]. 56.24/56.31 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1261,c,1189,b)]. 56.24/56.31 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1261,c,1190,b)]. 56.24/56.31 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1261,c,1191,b)]. 56.24/56.31 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1261,c,1192,b)]. 56.24/56.31 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1261,c,1201,c)]. 56.24/56.31 1262 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,782,e)]. 56.24/56.31 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1262,c,1189,b)]. 56.24/56.31 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1262,c,1190,b)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1262,c,1191,b)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1262,c,1192,b)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1262,c,1202,c)]. 56.32/56.41 1263 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,783,e)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1263,c,1189,b)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1263,c,1190,b)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1263,c,1191,b)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1263,c,1192,b)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1263,c,1203,c)]. 56.32/56.41 1264 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,784,e)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1264,c,1189,b)]. 56.32/56.41 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1264,c,1190,b)]. 56.42/56.51 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1264,c,1191,b)]. 56.42/56.51 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1264,c,1192,b)]. 56.42/56.51 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1264,c,1204,c)]. 56.42/56.51 1265 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,785,e)]. 56.42/56.51 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1265,c,1189,b)]. 56.42/56.51 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1265,c,1190,b)]. 56.42/56.51 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1265,c,1191,b)]. 56.42/56.51 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1265,c,1192,b)]. 56.42/56.51 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | subset(f37(A),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1265,c,1205,c)]. 56.42/56.51 1266 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,786,e)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1266,c,1189,b)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1266,c,1190,b)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1266,c,1191,b)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1266,c,1192,b)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f38(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1266,c,1206,c)]. 56.52/56.60 1267 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,787,e)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1267,c,1189,b)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1267,c,1190,b)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1267,c,1191,b)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1267,c,1192,b)]. 56.52/56.60 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | element(f39(A),powerset(the_carrier(A))) | -in(the_carrier(A),the_topology(A)). [resolve(1267,c,1207,c)]. 56.54/56.66 1268 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,788,e)]. 56.54/56.66 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1268,c,1189,b)]. 56.54/56.66 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1268,c,1190,b)]. 56.54/56.66 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1268,c,1191,b)]. 56.54/56.66 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1268,c,1192,b)]. 56.54/56.66 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f39(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1268,c,1208,c)]. 56.54/56.66 1269 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,789,e)]. 56.54/56.66 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1269,c,1189,b)]. 56.54/56.66 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1269,c,1190,b)]. 56.54/56.66 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1269,c,1191,b)]. 63.21/63.33 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1269,c,1192,b)]. 63.21/63.33 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | in(f38(A),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1269,c,1209,c)]. 63.21/63.33 1270 empty_carrier(A) | -top_str(A) | compact_top_space(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(801,c,790,e)]. 63.21/63.33 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | element(f25(A,B),powerset(powerset(the_carrier(A)))) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1270,c,1189,b)]. 63.21/63.33 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | finite(f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1270,c,1190,b)]. 63.21/63.33 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | is_a_cover_of_carrier(A,f25(A,B)) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1270,c,1191,b)]. 63.21/63.33 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | subset(f25(A,B),B) | -open_subsets(B,A) | -is_a_cover_of_carrier(A,B). [resolve(1270,c,1192,b)]. 63.21/63.33 Derived: empty_carrier(A) | -top_str(A) | centered(f82(A)) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)) | empty_carrier(A) | -top_str(A) | -element(B,powerset(powerset(the_carrier(A)))) | -closed_subsets(B,A) | meet_of_subsets(the_carrier(A),B) != empty_set | -centered(B) | -top_str(A) | -in(union_of_subsets(the_carrier(A),f37(A)),the_topology(A)) | -in(subset_intersection2(the_carrier(A),f38(A),f39(A)),the_topology(A)) | -in(the_carrier(A),the_topology(A)). [resolve(1270,c,1210,c)]. 63.21/63.33 1271 join_semilatt_str(c21) # label(existence_l2_lattices) # label(axiom). [clausify(302)]. 63.21/63.33 1272 -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(41)]. 63.21/63.33 1273 -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(41)]. 63.21/63.33 1274 -join_semilatt_str(A) | function(the_L_join(A)) # label(dt_u2_lattices) # label(axiom). [clausify(41)]. 63.21/63.34 1275 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -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). [clausify(98)]. 63.21/63.34 1276 -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(115)]. 63.21/63.34 1277 -join_associative(A) | -join_semilatt_str(A) | empty_carrier(A) | relation(the_L_join(A)) # label(fc3_lattice2) # label(axiom). [clausify(143)]. 63.21/63.34 1278 -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(143)]. 63.21/63.34 1279 -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(143)]. 63.21/63.34 1280 -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(143)]. 63.21/63.34 1281 -join_associative(A) | -join_semilatt_str(A) | empty_carrier(A) | function(the_L_join(A)) # label(fc3_lattice2) # label(axiom). [clausify(143)]. 63.21/63.34 1282 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(170)]. 63.21/63.34 1283 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_commutative(A) | join_commut(A,B,C) = join_commut(A,C,B) # label(commutativity_k3_lattices) # label(axiom). [clausify(173)]. 63.21/63.34 1284 -join_semilatt_str(A) | -join_commutative(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | -below(A,C,B) | C = B # label(t26_lattices) # label(lemma). [clausify(177)]. 63.21/63.34 1285 -join_semilatt_str(A) | -join_commutative(A) | empty_carrier(A) | relation(the_L_join(A)) # label(fc2_lattice2) # label(axiom). [clausify(281)]. 63.21/63.34 1286 -join_semilatt_str(A) | -join_commutative(A) | empty_carrier(A) | function(the_L_join(A)) # label(fc2_lattice2) # label(axiom). [clausify(281)]. 63.21/63.34 1287 -join_semilatt_str(A) | -join_commutative(A) | empty_carrier(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(281)]. 63.21/63.34 1288 -join_semilatt_str(A) | -join_commutative(A) | empty_carrier(A) | v1_binop_1(the_L_join(A),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(281)]. 63.21/63.34 1289 -join_semilatt_str(A) | -join_commutative(A) | empty_carrier(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(281)]. 63.21/63.34 Derived: quasi_total(the_L_join(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(1271,a,1272,a)]. 63.21/63.34 Derived: relation_of2_as_subset(the_L_join(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(1271,a,1273,a)]. 63.21/63.34 Derived: function(the_L_join(c21)). [resolve(1271,a,1274,a)]. 63.21/63.34 Derived: empty_carrier(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | join(c21,A,B) = apply_binary_as_element(the_carrier(c21),the_carrier(c21),the_carrier(c21),the_L_join(c21),A,B). [resolve(1271,a,1275,b)]. 63.21/63.34 Derived: -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | -join_commutative(c21) | empty_carrier(c21) | join_commut(c21,A,B) = join(c21,A,B). [resolve(1271,a,1276,c)]. 63.21/63.34 Derived: -join_associative(c21) | empty_carrier(c21) | relation(the_L_join(c21)). [resolve(1271,a,1277,b)]. 63.21/63.34 Derived: -join_associative(c21) | empty_carrier(c21) | v1_partfun1(the_L_join(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(1271,a,1278,b)]. 63.21/63.34 Derived: -join_associative(c21) | empty_carrier(c21) | v2_binop_1(the_L_join(c21),the_carrier(c21)). [resolve(1271,a,1279,b)]. 64.41/64.49 Derived: one_sorted_str(c21). [resolve(1271,a,1282,a)]. 64.41/64.49 Derived: empty_carrier(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | -join_commutative(c21) | join_commut(c21,A,B) = join_commut(c21,B,A). [resolve(1271,a,1283,b)]. 64.41/64.49 Derived: -join_commutative(c21) | empty_carrier(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | -below(c21,A,B) | -below(c21,B,A) | B = A. [resolve(1271,a,1284,a)]. 64.41/64.49 Derived: -join_commutative(c21) | empty_carrier(c21) | relation(the_L_join(c21)). [resolve(1271,a,1285,a)]. 64.41/64.49 Derived: -join_commutative(c21) | empty_carrier(c21) | v1_partfun1(the_L_join(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(1271,a,1287,a)]. 64.41/64.49 Derived: -join_commutative(c21) | empty_carrier(c21) | v1_binop_1(the_L_join(c21),the_carrier(c21)). [resolve(1271,a,1288,a)]. 64.41/64.49 1290 -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | empty_carrier(A) | element(join(A,C,B),the_carrier(A)) # label(dt_k1_lattices) # label(axiom). [clausify(421)]. 64.41/64.49 Derived: -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | empty_carrier(c21) | element(join(c21,B,A),the_carrier(c21)). [resolve(1290,a,1271,a)]. 64.41/64.49 1291 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,B,C) != C | below(A,B,C) # label(d3_lattices) # label(axiom). [clausify(461)]. 64.41/64.49 Derived: empty_carrier(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | join(c21,A,B) != B | below(c21,A,B). [resolve(1291,b,1271,a)]. 64.41/64.49 1292 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,B,C) = C | -below(A,B,C) # label(d3_lattices) # label(axiom). [clausify(461)]. 64.41/64.49 Derived: empty_carrier(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | join(c21,A,B) = B | -below(c21,A,B). [resolve(1292,b,1271,a)]. 64.41/64.49 1293 empty_carrier(A) | -join_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_semilatt_str(A) | element(join_commut(A,B,C),the_carrier(A)) # label(dt_k3_lattices) # label(axiom). [clausify(583)]. 64.41/64.49 Derived: empty_carrier(c21) | -join_commutative(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | element(join_commut(c21,A,B),the_carrier(c21)). [resolve(1293,e,1271,a)]. 64.41/64.49 1294 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(664)]. 64.41/64.49 Derived: -latt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(1294,b,1272,a)]. 64.41/64.49 Derived: -latt_str(A) | relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(1294,b,1273,a)]. 64.41/64.49 Derived: -latt_str(A) | function(the_L_join(A)). [resolve(1294,b,1274,a)]. 64.41/64.49 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -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). [resolve(1294,b,1275,b)]. 64.41/64.49 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(1294,b,1276,c)]. 64.41/64.49 Derived: -latt_str(A) | -join_associative(A) | empty_carrier(A) | relation(the_L_join(A)). [resolve(1294,b,1277,b)]. 64.41/64.49 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(1294,b,1278,b)]. 64.41/64.49 Derived: -latt_str(A) | -join_associative(A) | empty_carrier(A) | v2_binop_1(the_L_join(A),the_carrier(A)). [resolve(1294,b,1279,b)]. 64.41/64.49 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -join_commutative(A) | join_commut(A,B,C) = join_commut(A,C,B). [resolve(1294,b,1283,b)]. 64.41/64.49 Derived: -latt_str(A) | -join_commutative(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | -below(A,C,B) | C = B. [resolve(1294,b,1284,a)]. 71.46/71.54 Derived: -latt_str(A) | -join_commutative(A) | empty_carrier(A) | relation(the_L_join(A)). [resolve(1294,b,1285,a)]. 71.46/71.54 Derived: -latt_str(A) | -join_commutative(A) | empty_carrier(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(1294,b,1287,a)]. 71.46/71.54 Derived: -latt_str(A) | -join_commutative(A) | empty_carrier(A) | v1_binop_1(the_L_join(A),the_carrier(A)). [resolve(1294,b,1288,a)]. 71.46/71.54 Derived: -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | empty_carrier(A) | element(join(A,C,B),the_carrier(A)). [resolve(1294,b,1290,a)]. 71.46/71.54 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,B,C) != C | below(A,B,C). [resolve(1294,b,1291,b)]. 71.46/71.54 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,B,C) = C | -below(A,B,C). [resolve(1294,b,1292,b)]. 71.46/71.54 Derived: -latt_str(A) | empty_carrier(A) | -join_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(join_commut(A,B,C),the_carrier(A)). [resolve(1294,b,1293,e)]. 71.46/71.54 1295 -rel_str(A) | -rel_str(B) | subrelstr(B,A) | -subset(the_carrier(B),the_carrier(A)) | -subset(the_InternalRel(B),the_InternalRel(A)) # label(d13_yellow_0) # label(axiom). [clausify(48)]. 71.46/71.54 1296 -rel_str(A) | -rel_str(B) | -subrelstr(B,A) | subset(the_carrier(B),the_carrier(A)) # label(d13_yellow_0) # label(axiom). [clausify(48)]. 71.46/71.54 1297 -rel_str(A) | -rel_str(B) | -subrelstr(B,A) | subset(the_InternalRel(B),the_InternalRel(A)) # label(d13_yellow_0) # label(axiom). [clausify(48)]. 71.46/71.54 1298 -rel_str(A) | -subrelstr(B,A) | rel_str(B) # label(dt_m1_yellow_0) # label(axiom). [clausify(72)]. 71.46/71.54 1299 -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 | F != D | -related(B,E,F) | related(A,C,D) # label(t60_yellow_0) # label(lemma). [clausify(260)]. 71.46/71.54 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 | F != C | -related(E,D,F) | related(A,B,C) | -rel_str(A) | -rel_str(E) | -subset(the_carrier(E),the_carrier(A)) | -subset(the_InternalRel(E),the_InternalRel(A)). [resolve(1299,b,1295,c)]. 71.46/71.54 1300 -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)) | E != C | F != D | -related(A,C,D) | -in(E,the_carrier(B)) | -in(F,the_carrier(B)) | related(B,E,F) # label(t61_yellow_0) # label(lemma). [clausify(278)]. 71.46/71.54 Derived: -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)) | E != C | F != D | -related(A,C,D) | -in(E,the_carrier(B)) | -in(F,the_carrier(B)) | related(B,E,F) | -rel_str(A) | -rel_str(B) | -subset(the_carrier(B),the_carrier(A)) | -subset(the_InternalRel(B),the_InternalRel(A)). [resolve(1300,b,1295,c)]. 71.46/71.54 1301 -one_sorted_str(A) | -net_str(B,A) | -net_str(C,A) | -subnetstr(C,A,B) | subrelstr(C,B) # label(d8_yellow_6) # label(axiom). [clausify(338)]. 71.46/71.54 Derived: -one_sorted_str(A) | -net_str(B,A) | -net_str(C,A) | -subnetstr(C,A,B) | -rel_str(B) | -rel_str(C) | subset(the_InternalRel(C),the_InternalRel(B)). [resolve(1301,e,1297,c)]. 71.46/71.54 Derived: -one_sorted_str(A) | -net_str(B,A) | -net_str(C,A) | -subnetstr(C,A,B) | -rel_str(B) | -full_subrelstr(C,B) | -element(D,the_carrier(B)) | -element(E,the_carrier(B)) | -element(F,the_carrier(C)) | -element(V6,the_carrier(C)) | F != D | V6 != E | -related(B,D,E) | -in(F,the_carrier(C)) | -in(V6,the_carrier(C)) | related(C,F,V6). [resolve(1301,e,1300,b)]. 71.46/71.54 1302 -one_sorted_str(A) | -net_str(B,A) | -net_str(C,A) | subnetstr(C,A,B) | -subrelstr(C,B) | the_mapping(A,C) != relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C)) # label(d8_yellow_6) # label(axiom). [clausify(338)]. 71.46/71.54 Derived: -one_sorted_str(A) | -net_str(B,A) | -net_str(C,A) | subnetstr(C,A,B) | the_mapping(A,C) != relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C)) | -rel_str(B) | -rel_str(C) | -subset(the_carrier(C),the_carrier(B)) | -subset(the_InternalRel(C),the_InternalRel(B)). [resolve(1302,e,1295,c)]. 72.51/72.61 Derived: -one_sorted_str(A) | -net_str(B,A) | -net_str(C,A) | subnetstr(C,A,B) | the_mapping(A,C) != relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C)) | -one_sorted_str(D) | -net_str(B,D) | -net_str(C,D) | -subnetstr(C,D,B). [resolve(1302,e,1301,e)]. 72.51/72.61 1303 -one_sorted_str(A) | -net_str(B,A) | -subnetstr(C,A,B) | -subrelstr(C,B) | -full_subrelstr(C,B) | full_subnetstr(C,A,B) # label(d9_yellow_6) # label(axiom). [clausify(373)]. 72.51/72.61 Derived: -one_sorted_str(A) | -net_str(B,A) | -subnetstr(C,A,B) | -full_subrelstr(C,B) | full_subnetstr(C,A,B) | -rel_str(B) | -rel_str(C) | -subset(the_carrier(C),the_carrier(B)) | -subset(the_InternalRel(C),the_InternalRel(B)). [resolve(1303,d,1295,c)]. 72.51/72.61 Derived: -one_sorted_str(A) | -net_str(B,A) | -subnetstr(C,A,B) | -full_subrelstr(C,B) | full_subnetstr(C,A,B) | -one_sorted_str(D) | -net_str(B,D) | -net_str(C,D) | -subnetstr(C,D,B). [resolve(1303,d,1301,e)]. 72.51/72.61 1304 -one_sorted_str(A) | -net_str(B,A) | -subnetstr(C,A,B) | subrelstr(C,B) | -full_subnetstr(C,A,B) # label(d9_yellow_6) # label(axiom). [clausify(373)]. 72.51/72.61 Derived: -one_sorted_str(A) | -net_str(B,A) | -subnetstr(C,A,B) | -full_subnetstr(C,A,B) | -rel_str(B) | -rel_str(C) | subset(the_InternalRel(C),the_InternalRel(B)). [resolve(1304,d,1297,c)]. 72.51/72.61 Derived: -one_sorted_str(A) | -net_str(B,A) | -subnetstr(C,A,B) | -full_subnetstr(C,A,B) | -rel_str(B) | rel_str(C). [resolve(1304,d,1298,b)]. 72.51/72.61 Derived: -one_sorted_str(A) | -net_str(B,A) | -subnetstr(C,A,B) | -full_subnetstr(C,A,B) | -rel_str(B) | -full_subrelstr(C,B) | -element(D,the_carrier(B)) | -element(E,the_carrier(B)) | -element(F,the_carrier(C)) | -element(V6,the_carrier(C)) | F != D | V6 != E | -related(B,D,E) | -in(F,the_carrier(C)) | -in(V6,the_carrier(C)) | related(C,F,V6). [resolve(1304,d,1300,b)]. 72.51/72.61 Derived: -one_sorted_str(A) | -net_str(B,A) | -subnetstr(C,A,B) | -full_subnetstr(C,A,B) | -one_sorted_str(D) | -net_str(B,D) | -net_str(C,D) | subnetstr(C,D,B) | the_mapping(D,C) != relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(D),the_mapping(D,B),the_carrier(C)). [resolve(1304,d,1302,e)]. 72.51/72.61 Derived: -one_sorted_str(A) | -net_str(B,A) | -subnetstr(C,A,B) | -full_subnetstr(C,A,B) | -one_sorted_str(D) | -net_str(B,D) | -subnetstr(C,D,B) | -full_subrelstr(C,B) | full_subnetstr(C,D,B). [resolve(1304,d,1303,d)]. 72.51/72.61 1305 -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(615)]. 72.51/72.61 Derived: -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) != the_InternalRel(B) | full_subrelstr(B,A) | -rel_str(A) | -rel_str(B) | -subset(the_carrier(B),the_carrier(A)) | -subset(the_InternalRel(B),the_InternalRel(A)). [resolve(1305,b,1295,c)]. 72.51/72.61 Derived: -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) != the_InternalRel(B) | full_subrelstr(B,A) | -one_sorted_str(C) | -net_str(A,C) | -net_str(B,C) | -subnetstr(B,C,A). [resolve(1305,b,1301,e)]. 72.51/72.61 Derived: -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) != the_InternalRel(B) | full_subrelstr(B,A) | -one_sorted_str(C) | -net_str(A,C) | -subnetstr(B,C,A) | -full_subnetstr(B,C,A). [resolve(1305,b,1304,d)]. 72.51/72.61 1306 -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(615)]. 72.51/72.61 Derived: -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) = the_InternalRel(B) | -full_subrelstr(B,A) | -rel_str(A) | -rel_str(B) | -subset(the_carrier(B),the_carrier(A)) | -subset(the_InternalRel(B),the_InternalRel(A)). [resolve(1306,b,1295,c)]. 72.51/72.61 Derived: -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) = the_InternalRel(B) | -full_subrelstr(B,A) | -one_sorted_str(C) | -net_str(A,C) | -net_str(B,C) | -subnetstr(B,C,A). [resolve(1306,b,1301,e)]. 83.82/83.94 Derived: -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) = the_InternalRel(B) | -full_subrelstr(B,A) | -one_sorted_str(C) | -net_str(A,C) | -subnetstr(B,C,A) | -full_subnetstr(B,C,A). [resolve(1306,b,1304,d)]. 83.82/83.94 1307 -rel_str(A) | subrelstr(f386(A),A) # label(existence_m1_yellow_0) # label(axiom). [clausify(639)]. 83.82/83.94 Derived: -rel_str(A) | -rel_str(A) | -rel_str(f386(A)) | subset(the_carrier(f386(A)),the_carrier(A)). [resolve(1307,b,1296,c)]. 83.82/83.94 Derived: -rel_str(A) | -rel_str(A) | -rel_str(f386(A)) | subset(the_InternalRel(f386(A)),the_InternalRel(A)). [resolve(1307,b,1297,c)]. 83.82/83.94 Derived: -rel_str(A) | -rel_str(A) | rel_str(f386(A)). [resolve(1307,b,1298,b)]. 83.82/83.94 Derived: -rel_str(A) | -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -element(D,the_carrier(f386(A))) | -element(E,the_carrier(f386(A))) | D != B | E != C | -related(f386(A),D,E) | related(A,B,C). [resolve(1307,b,1299,b)]. 83.82/83.94 Derived: -rel_str(A) | -rel_str(A) | -full_subrelstr(f386(A),A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -element(D,the_carrier(f386(A))) | -element(E,the_carrier(f386(A))) | D != B | E != C | -related(A,B,C) | -in(D,the_carrier(f386(A))) | -in(E,the_carrier(f386(A))) | related(f386(A),D,E). [resolve(1307,b,1300,b)]. 83.82/83.94 Derived: -rel_str(A) | -one_sorted_str(B) | -net_str(A,B) | -net_str(f386(A),B) | subnetstr(f386(A),B,A) | the_mapping(B,f386(A)) != relation_dom_restr_as_relation_of(the_carrier(A),the_carrier(B),the_mapping(B,A),the_carrier(f386(A))). [resolve(1307,b,1302,e)]. 83.82/83.94 Derived: -rel_str(A) | -one_sorted_str(B) | -net_str(A,B) | -subnetstr(f386(A),B,A) | -full_subrelstr(f386(A),A) | full_subnetstr(f386(A),B,A). [resolve(1307,b,1303,d)]. 83.82/83.94 Derived: -rel_str(A) | -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(f386(A))) != the_InternalRel(f386(A)) | full_subrelstr(f386(A),A). [resolve(1307,b,1305,b)]. 83.82/83.94 Derived: -rel_str(A) | -rel_str(A) | relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(f386(A))) = the_InternalRel(f386(A)) | -full_subrelstr(f386(A),A). [resolve(1307,b,1306,b)]. 83.82/83.94 1308 -rel_str(A) | -with_infima_relstr(A) | -empty_carrier(A) # label(cc2_lattice3) # label(axiom). [clausify(182)]. 83.82/83.94 1309 -lattice(A) | -latt_str(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(51)]. 83.82/83.94 1310 with_infima_relstr(c6) # label(rc1_yellow_0) # label(axiom). [clausify(85)]. 83.82/83.94 1311 empty_carrier(A) | -latt_str(A) | -lower_bounded_semilattstr(A) | -lattice(A) | with_infima_relstr(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(137)]. 83.82/83.94 Derived: -rel_str(c6) | -empty_carrier(c6). [resolve(1308,b,1310,a)]. 83.82/83.94 1312 with_infima_relstr(c18) # label(rc2_yellow_0) # label(axiom). [clausify(275)]. 83.82/83.94 Derived: -rel_str(c18) | -empty_carrier(c18). [resolve(1312,a,1308,b)]. 83.82/83.94 1313 -latt_str(A) | -complete_latt_str(A) | -lattice(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(527)]. 83.82/83.94 1314 -rel_str(A) | empty_carrier(A) | -complete_relstr(A) | with_infima_relstr(A) # label(cc1_yellow_0) # label(axiom). [clausify(562)]. 83.82/83.94 1315 with_infima_relstr(c44) # label(rc2_lattice3) # label(axiom). [clausify(715)]. 83.82/83.94 Derived: -rel_str(c44) | -empty_carrier(c44). [resolve(1315,a,1308,b)]. 83.82/83.94 1316 with_infima_relstr(boole_POSet(A)) # label(fc8_yellow_1) # label(axiom). [clausify(719)]. 83.82/83.94 1317 -lattice(c4) | -latt_str(c4) | empty_carrier(c4) | with_infima_relstr(poset_of_lattice(c4)). [resolve(947,a,944,c)]. 83.82/83.94 Derived: -lattice(c4) | -latt_str(c4) | empty_carrier(c4) | -rel_str(poset_of_lattice(c4)) | -empty_carrier(poset_of_lattice(c4)). [resolve(1317,d,1308,b)]. 83.82/83.94 1318 -latt_str(A) | empty_carrier(A) | -bounded_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)). [resolve(948,d,944,c)]. 89.03/89.12 Derived: -latt_str(A) | empty_carrier(A) | -bounded_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -empty_carrier(poset_of_lattice(A)). [resolve(1318,g,1308,b)]. 89.03/89.12 1319 -lattice(c11) | -latt_str(c11) | empty_carrier(c11) | with_infima_relstr(poset_of_lattice(c11)). [resolve(949,a,944,c)]. 89.03/89.12 Derived: -lattice(c11) | -latt_str(c11) | empty_carrier(c11) | -rel_str(poset_of_lattice(c11)) | -empty_carrier(poset_of_lattice(c11)). [resolve(1319,d,1308,b)]. 89.03/89.12 1320 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_infima_relstr(poset_of_lattice(A)). [resolve(951,e,944,c)]. 89.03/89.12 Derived: -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -rel_str(poset_of_lattice(A)) | -empty_carrier(poset_of_lattice(A)). [resolve(1320,h,1308,b)]. 89.03/89.12 1321 -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | with_infima_relstr(poset_of_lattice(boole_lattice(A))). [resolve(952,a,944,c)]. 89.03/89.12 Derived: -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -rel_str(poset_of_lattice(boole_lattice(A))) | -empty_carrier(poset_of_lattice(boole_lattice(A))). [resolve(1321,d,1308,b)]. 89.03/89.12 1322 -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | with_infima_relstr(poset_of_lattice(c45)). [resolve(955,a,944,c)]. 89.03/89.12 Derived: -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | -rel_str(poset_of_lattice(c45)) | -empty_carrier(poset_of_lattice(c45)). [resolve(1322,d,1308,b)]. 89.03/89.12 1323 -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | with_infima_relstr(poset_of_lattice(c2)). [resolve(1016,c,1008,a)]. 89.03/89.12 Derived: -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | -rel_str(poset_of_lattice(c2)) | -empty_carrier(poset_of_lattice(c2)). [resolve(1323,f,1308,b)]. 89.03/89.12 1324 -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | with_infima_relstr(poset_of_lattice(c2)) | -latt_str(c2) | -bounded_lattstr(c2) | -distributive_lattstr(c2) | empty_carrier(c2). [resolve(1026,i,1020,a)]. 89.03/89.12 1325 -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | with_infima_relstr(poset_of_lattice(boole_lattice(A))) | -latt_str(boole_lattice(A)) | -bounded_lattstr(boole_lattice(A)) | -distributive_lattstr(boole_lattice(A)) | empty_carrier(boole_lattice(A)). [resolve(1026,i,1021,a)]. 89.03/89.12 1326 -latt_str(c45) | empty_carrier(c45) | -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | with_infima_relstr(poset_of_lattice(c45)) | -latt_str(c45) | -bounded_lattstr(c45) | -distributive_lattstr(c45) | empty_carrier(c45). [resolve(1026,i,1023,a)]. 89.03/89.12 1327 -rel_str(A) | -with_suprema_relstr(A) | -empty_carrier(A) # label(cc1_lattice3) # label(axiom). [clausify(501)]. 89.03/89.12 1328 -lattice(A) | -latt_str(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(51)]. 89.03/89.12 1329 with_suprema_relstr(c6) # label(rc1_yellow_0) # label(axiom). [clausify(85)]. 89.03/89.12 1330 empty_carrier(A) | -latt_str(A) | -lower_bounded_semilattstr(A) | -lattice(A) | with_suprema_relstr(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(137)]. 89.03/89.12 1331 with_suprema_relstr(c18) # label(rc2_yellow_0) # label(axiom). [clausify(275)]. 89.03/89.12 Derived: -rel_str(poset_of_lattice(A)) | -empty_carrier(poset_of_lattice(A)) | -lattice(A) | -latt_str(A) | empty_carrier(A). [resolve(1327,b,1328,d)]. 89.03/89.12 1332 -latt_str(A) | -complete_latt_str(A) | -lattice(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(527)]. 89.03/89.12 1333 -rel_str(A) | empty_carrier(A) | -complete_relstr(A) | with_suprema_relstr(A) # label(cc1_yellow_0) # label(axiom). [clausify(562)]. 89.03/89.12 1334 with_suprema_relstr(c44) # label(rc2_lattice3) # label(axiom). [clausify(715)]. 89.03/89.12 1335 with_suprema_relstr(boole_POSet(A)) # label(fc8_yellow_1) # label(axiom). [clausify(719)]. 95.96/96.10 1336 -lattice(c4) | -latt_str(c4) | empty_carrier(c4) | with_suprema_relstr(poset_of_lattice(c4)). [resolve(947,a,945,c)]. 95.96/96.10 1337 -latt_str(A) | empty_carrier(A) | -bounded_lattstr(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)). [resolve(948,d,945,c)]. 95.96/96.10 1338 -lattice(c11) | -latt_str(c11) | empty_carrier(c11) | with_suprema_relstr(poset_of_lattice(c11)). [resolve(949,a,945,c)]. 95.96/96.10 1339 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | with_suprema_relstr(poset_of_lattice(A)). [resolve(951,e,945,c)]. 95.96/96.10 1340 -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | with_suprema_relstr(poset_of_lattice(boole_lattice(A))). [resolve(952,a,945,c)]. 95.96/96.10 1341 -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | with_suprema_relstr(poset_of_lattice(c45)). [resolve(955,a,945,c)]. 95.96/96.10 1342 -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | with_suprema_relstr(poset_of_lattice(c2)). [resolve(1017,c,1008,a)]. 95.96/96.10 1343 -latt_str(c2) | empty_carrier(c2) | -lattice(c2) | -latt_str(c2) | empty_carrier(c2) | with_suprema_relstr(poset_of_lattice(c2)) | -latt_str(c2) | -bounded_lattstr(c2) | -distributive_lattstr(c2) | empty_carrier(c2). [resolve(1027,i,1020,a)]. 95.96/96.10 1344 -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -latt_str(boole_lattice(A)) | empty_carrier(boole_lattice(A)) | with_suprema_relstr(poset_of_lattice(boole_lattice(A))) | -latt_str(boole_lattice(A)) | -bounded_lattstr(boole_lattice(A)) | -distributive_lattstr(boole_lattice(A)) | empty_carrier(boole_lattice(A)). [resolve(1027,i,1021,a)]. 95.96/96.10 1345 -latt_str(c45) | empty_carrier(c45) | -lattice(c45) | -latt_str(c45) | empty_carrier(c45) | with_suprema_relstr(poset_of_lattice(c45)) | -latt_str(c45) | -bounded_lattstr(c45) | -distributive_lattstr(c45) | empty_carrier(c45). [resolve(1027,i,1023,a)]. 95.96/96.10 1346 -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(183)]. 95.96/96.10 1347 -lattice(A) | -latt_str(A) | empty_carrier(A) | strict_rel_str(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(51)]. 95.96/96.10 1348 empty_carrier(A) | -latt_str(A) | -lattice(A) | strict_rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(58)]. 95.96/96.10 1349 strict_rel_str(c6) # label(rc1_yellow_0) # label(axiom). [clausify(85)]. 95.96/96.10 1350 empty_carrier(A) | -latt_str(A) | -lower_bounded_semilattstr(A) | -lattice(A) | strict_rel_str(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(137)]. 95.96/96.10 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(1346,b,1347,d)]. 95.96/96.10 Derived: -rel_str(c6) | rel_str_of(the_carrier(c6),the_InternalRel(c6)) = c6. [resolve(1346,b,1349,a)]. 95.96/96.10 1351 strict_rel_str(boole_POSet(A)) # label(fc7_yellow_1) # label(axiom). [clausify(200)]. 95.96/96.10 Derived: -rel_str(boole_POSet(A)) | rel_str_of(the_carrier(boole_POSet(A)),the_InternalRel(boole_POSet(A))) = boole_POSet(A). [resolve(1351,a,1346,b)]. 95.96/96.10 1352 strict_rel_str(boole_POSet(A)) # label(dt_k3_yellow_1) # label(axiom). [clausify(243)]. 95.96/96.10 1353 strict_rel_str(c15) # label(rc2_orders_2) # label(axiom). [clausify(254)]. 95.96/96.10 Derived: -rel_str(c15) | rel_str_of(the_carrier(c15),the_InternalRel(c15)) = c15. [resolve(1353,a,1346,b)]. 95.96/96.10 1354 strict_rel_str(c17) # label(rc1_orders_2) # label(axiom). [clausify(270)]. 95.96/96.10 Derived: -rel_str(c17) | rel_str_of(the_carrier(c17),the_InternalRel(c17)) = c17. [resolve(1354,a,1346,b)]. 95.96/96.10 1355 strict_rel_str(incl_POSet(A)) # label(dt_k2_yellow_1) # label(axiom). [clausify(317)]. 95.96/96.10 Derived: -rel_str(incl_POSet(A)) | rel_str_of(the_carrier(incl_POSet(A)),the_InternalRel(incl_POSet(A))) = incl_POSet(A). [resolve(1355,a,1346,b)]. 95.96/96.10 1356 empty_carrier(A) | -latt_str(A) | -lattice(A) | sAlarm clock 119.97/120.05 Prover9 interrupted 119.97/120.05 EOF