0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.02/0.24 % Computer : n151.star.cs.uiowa.edu 0.02/0.24 % Model : x86_64 x86_64 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.24 % Memory : 32218.625MB 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.24 % CPULimit : 300 0.02/0.24 % DateTime : Fri Jul 13 15:56:59 CDT 2018 0.02/0.24 % CPUTime : 0.06/0.53 ============================== Prover9 =============================== 0.06/0.53 Prover9 (32) version 2009-11A, November 2009. 0.06/0.53 Process 16120 was started by sandbox2 on n151.star.cs.uiowa.edu, 0.06/0.53 Fri Jul 13 15:56:59 2018 0.06/0.53 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16087_n151.star.cs.uiowa.edu". 0.06/0.53 ============================== end of head =========================== 0.06/0.53 0.06/0.53 ============================== INPUT ================================= 0.06/0.53 0.06/0.53 % Reading from file /tmp/Prover9_16087_n151.star.cs.uiowa.edu 0.06/0.53 0.06/0.53 set(prolog_style_variables). 0.06/0.53 set(auto2). 0.06/0.53 % set(auto2) -> set(auto). 0.06/0.53 % set(auto) -> set(auto_inference). 0.06/0.53 % set(auto) -> set(auto_setup). 0.06/0.53 % set(auto_setup) -> set(predicate_elim). 0.06/0.53 % set(auto_setup) -> assign(eq_defs, unfold). 0.06/0.53 % set(auto) -> set(auto_limits). 0.06/0.53 % set(auto_limits) -> assign(max_weight, "100.000"). 0.06/0.53 % set(auto_limits) -> assign(sos_limit, 20000). 0.06/0.53 % set(auto) -> set(auto_denials). 0.06/0.53 % set(auto) -> set(auto_process). 0.06/0.53 % set(auto2) -> assign(new_constants, 1). 0.06/0.53 % set(auto2) -> assign(fold_denial_max, 3). 0.06/0.53 % set(auto2) -> assign(max_weight, "200.000"). 0.06/0.53 % set(auto2) -> assign(max_hours, 1). 0.06/0.53 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.06/0.53 % set(auto2) -> assign(max_seconds, 0). 0.06/0.53 % set(auto2) -> assign(max_minutes, 5). 0.06/0.53 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.06/0.53 % set(auto2) -> set(sort_initial_sos). 0.06/0.53 % set(auto2) -> assign(sos_limit, -1). 0.06/0.53 % set(auto2) -> assign(lrs_ticks, 3000). 0.06/0.53 % set(auto2) -> assign(max_megs, 400). 0.06/0.53 % set(auto2) -> assign(stats, some). 0.06/0.53 % set(auto2) -> clear(echo_input). 0.06/0.53 % set(auto2) -> set(quiet). 0.06/0.53 % set(auto2) -> clear(print_initial_clauses). 0.06/0.53 % set(auto2) -> clear(print_given). 0.06/0.53 assign(lrs_ticks,-1). 0.06/0.53 assign(sos_limit,10000). 0.06/0.53 assign(order,kbo). 0.06/0.53 set(lex_order_vars). 0.06/0.53 clear(print_given). 0.06/0.53 0.06/0.53 % formulas(sos). % not echoed (45 formulas) 0.06/0.53 0.06/0.53 ============================== end of input ========================== 0.06/0.53 0.06/0.53 % From the command line: assign(max_seconds, 300). 0.06/0.53 0.06/0.53 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.06/0.53 0.06/0.53 % Formulas that are not ordinary clauses: 0.06/0.53 1 (all A (top_str(A) -> one_sorted_str(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 2 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (transitive_relstr(B) & net_str(B,A) & directed_relstr(B) & -empty_carrier(B) -> (all C (is_eventually_in(A,B,C) -> is_often_in(A,B,C))))))) # label(t28_yellow_6) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 3 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 4 (all A (-empty_carrier(A) & top_str(A) & topological_space(A) -> (all B (transitive_relstr(B) & directed_relstr(B) & net_str(B,A) & -empty_carrier(B) -> (all C (element(C,powerset(the_carrier(A))) -> ((all D (element(D,the_carrier(A)) -> ((all E (point_neighbourhood(E,A,D) -> is_eventually_in(A,B,E))) <-> in(D,C)))) <-> C = lim_points_of_net(A,B)))))))) # label(d18_yellow_6) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 5 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 6 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 7 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 8 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 9 (all A all B (-empty_carrier(A) & topological_space(A) & element(B,the_carrier(A)) & top_str(A) -> (exists C point_neighbourhood(C,A,B)))) # label(existence_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 10 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 11 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 12 (all A (one_sorted_str(A) & -empty_carrier(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 13 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 14 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 15 (exists A top_str(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 16 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 17 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 18 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 19 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 20 (all A all B (-empty_carrier(A) & topological_space(A) & net_str(B,A) & directed_relstr(B) & transitive_relstr(B) & -empty_carrier(B) & top_str(A) -> element(lim_points_of_net(A,B),powerset(the_carrier(A))))) # label(dt_k11_yellow_6) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 21 (all A (-empty(A) -> (exists B (-empty(B) & finite(B) & element(B,powerset(A)))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 22 (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]. 0.06/0.53 23 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 24 (all A (cup_closed(powerset(A)) & diff_closed(powerset(A)) & preboolean(powerset(A)) & -empty(powerset(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 25 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 26 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 27 (all A (one_sorted_str(A) -> (exists B net_str(B,A)))) # label(existence_l1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 28 (all A all B all C -(in(A,B) & empty(C) & element(B,powerset(C)))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 29 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 30 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 31 (all A all B -(empty(A) & B != A & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 32 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 33 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 34 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 35 (all A all B (topological_space(A) & top_str(A) & element(B,the_carrier(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]. 0.06/0.53 36 (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]. 0.06/0.53 37 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 38 (all A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 39 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 40 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 41 (all A (-empty_carrier(A) & topological_space(A) & top_str(A) -> (all B (-empty_carrier(B) & net_str(B,A) -> (all C (element(C,the_carrier(A)) -> (is_a_cluster_point_of_netstr(A,B,C) <-> (all D (point_neighbourhood(D,A,C) -> is_often_in(A,B,D)))))))))) # label(d9_waybel_9) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 42 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 43 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 0.06/0.53 44 -(all A (-empty_carrier(A) & top_str(A) & topological_space(A) -> (all B (-empty_carrier(B) & transitive_relstr(B) & net_str(B,A) & directed_relstr(B) -> (all C (element(C,the_carrier(A)) -> (in(C,lim_points_of_net(A,B)) -> is_a_cluster_point_of_netstr(A,B,C)))))))) # label(t29_waybel_9) # label(negated_conjecture) # label(non_clause). [assumption]. 0.06/0.53 0.06/0.53 ============================== end of process non-clausal formulas === 0.06/0.53 0.06/0.53 ============================== PROCESS INITIAL CLAUSES =============== 0.06/0.53 0.06/0.53 ============================== PREDICATE ELIMINATION ================= 0.06/0.53 45 -one_sorted_str(A) | net_str(f7(A),A) # label(existence_l1_waybel_0) # label(axiom). [clausify(27)]. 0.06/0.53 46 one_sorted_str(c1) # label(existence_l1_struct_0) # label(axiom). [clausify(6)]. 0.06/0.53 47 one_sorted_str(c6) # label(rc3_struct_0) # label(axiom). [clausify(29)]. 0.06/0.53 48 -top_str(A) | one_sorted_str(A) # label(dt_l1_pre_topc) # label(axiom). [clausify(1)]. 0.06/0.53 49 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(17)]. 0.06/0.53 Derived: net_str(f7(c1),c1). [resolve(45,a,46,a)]. 0.06/0.53 Derived: net_str(f7(c6),c6). [resolve(45,a,47,a)]. 0.06/0.53 Derived: net_str(f7(A),A) | -top_str(A). [resolve(45,a,48,b)]. 0.06/0.53 Derived: net_str(f7(A),A) | -rel_str(A). [resolve(45,a,49,b)]. 0.06/0.53 50 -one_sorted_str(A) | empty_carrier(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(12)]. 0.06/0.53 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(50,a,46,a)]. 0.06/0.53 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(50,a,47,a)]. 0.06/0.53 Derived: empty_carrier(A) | -empty(the_carrier(A)) | -top_str(A). [resolve(50,a,48,b)]. 0.06/0.53 Derived: empty_carrier(A) | -empty(the_carrier(A)) | -rel_str(A). [resolve(50,a,49,b)]. 0.06/0.53 51 empty_carrier(A) | -one_sorted_str(A) | -empty(f6(A)) # label(rc5_struct_0) # label(axiom). [clausify(22)]. 0.06/0.53 Derived: empty_carrier(c1) | -empty(f6(c1)). [resolve(51,b,46,a)]. 0.06/0.53 Derived: empty_carrier(c6) | -empty(f6(c6)). [resolve(51,b,47,a)]. 0.06/0.53 Derived: empty_carrier(A) | -empty(f6(A)) | -top_str(A). [resolve(51,b,48,b)]. 0.06/0.53 Derived: empty_carrier(A) | -empty(f6(A)) | -rel_str(A). [resolve(51,b,49,b)]. 0.06/0.53 52 -one_sorted_str(A) | -net_str(B,A) | rel_str(B) # label(dt_l1_waybel_0) # label(axiom). [clausify(36)]. 0.06/0.53 Derived: -net_str(A,c1) | rel_str(A). [resolve(52,a,46,a)]. 0.06/0.53 Derived: -net_str(A,c6) | rel_str(A). [resolve(52,a,47,a)]. 0.06/0.53 Derived: -net_str(A,B) | rel_str(A) | -top_str(B). [resolve(52,a,48,b)]. 0.06/0.53 Derived: -net_str(A,B) | rel_str(A) | -rel_str(B). [resolve(52,a,49,b)]. 0.06/0.53 53 empty_carrier(A) | -one_sorted_str(A) | element(f6(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(22)]. 0.06/0.53 Derived: empty_carrier(c1) | element(f6(c1),powerset(the_carrier(c1))). [resolve(53,b,46,a)]. 0.06/0.53 Derived: empty_carrier(c6) | element(f6(c6),powerset(the_carrier(c6))). [resolve(53,b,47,a)]. 0.06/0.53 Derived: empty_carrier(A) | element(f6(A),powerset(the_carrier(A))) | -top_str(A). [resolve(53,b,48,b)]. 0.06/0.53 Derived: empty_carrier(A) | element(f6(A),powerset(the_carrier(A))) | -rel_str(A). [resolve(53,b,49,b)]. 0.06/0.53 54 -one_sorted_str(A) | empty_carrier(A) | -transitive_relstr(B) | -net_str(B,A) | -directed_relstr(B) | empty_carrier(B) | -is_eventually_in(A,B,C) | is_often_in(A,B,C) # label(t28_yellow_6) # label(axiom). [clausify(2)]. 0.06/0.53 Derived: empty_carrier(c1) | -transitive_relstr(A) | -net_str(A,c1) | -directed_relstr(A) | empty_carrier(A) | -is_eventually_in(c1,A,B) | is_often_in(c1,A,B). [resolve(54,a,46,a)]. 0.06/0.53 Derived: empty_carrier(c6) | -transitive_relstr(A) | -net_str(A,c6) | -directed_relstr(A) | empty_carrier(A) | -is_eventually_in(c6,A,B) | is_often_in(c6,A,B). [resolve(54,a,47,a)]. 0.06/0.53 Derived: empty_carrier(A) | -transitive_relstr(B) | -net_str(B,A) | -directed_relstr(B) | empty_carrier(B) | -is_eventually_in(A,B,C) | is_often_in(A,B,C) | -top_str(A). [resolve(54,a,48,b)]. 0.06/0.53 Derived: empty_carrier(A) | -transitive_relstr(B) | -net_str(B,A) | -directed_relstr(B) | empty_carrier(B) | -is_eventually_in(A,B,C) | is_often_in(A,B,C) | -rel_str(A). [resolve(54,a,49,b)]. 0.06/0.53 55 empty_carrier(A) | -topological_space(A) | -element(B,the_carrier(A)) | -top_str(A) | point_neighbourhood(f4(A,B),A,B) # label(existence_m1_connsp_2) # label(axiom). [clausify(9)]. 0.06/0.53 56 top_str(c3) # label(existence_l1_pre_topc) # label(axiom). [clausify(15)]. 0.06/0.53 57 top_str(c8) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | -element(A,the_carrier(c3)) | point_neighbourhood(f4(c3,A),c3,A). [resolve(55,d,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | -element(A,the_carrier(c8)) | point_neighbourhood(f4(c8,A),c8,A). [resolve(55,d,57,a)]. 0.06/0.53 58 -topological_space(A) | -top_str(A) | -element(B,the_carrier(A)) | empty_carrier(A) | -point_neighbourhood(C,A,B) | element(C,powerset(the_carrier(A))) # label(dt_m1_connsp_2) # label(axiom). [clausify(35)]. 0.06/0.53 Derived: -topological_space(c3) | -element(A,the_carrier(c3)) | empty_carrier(c3) | -point_neighbourhood(B,c3,A) | element(B,powerset(the_carrier(c3))). [resolve(58,b,56,a)]. 0.06/0.53 Derived: -topological_space(c8) | -element(A,the_carrier(c8)) | empty_carrier(c8) | -point_neighbourhood(B,c8,A) | element(B,powerset(the_carrier(c8))). [resolve(58,b,57,a)]. 0.06/0.53 59 empty_carrier(A) | -topological_space(A) | -net_str(B,A) | -directed_relstr(B) | -transitive_relstr(B) | empty_carrier(B) | -top_str(A) | element(lim_points_of_net(A,B),powerset(the_carrier(A))) # label(dt_k11_yellow_6) # label(axiom). [clausify(20)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | -net_str(A,c3) | -directed_relstr(A) | -transitive_relstr(A) | empty_carrier(A) | element(lim_points_of_net(c3,A),powerset(the_carrier(c3))). [resolve(59,g,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | -net_str(A,c8) | -directed_relstr(A) | -transitive_relstr(A) | empty_carrier(A) | element(lim_points_of_net(c8,A),powerset(the_carrier(c8))). [resolve(59,g,57,a)]. 0.06/0.53 60 empty_carrier(A) | -topological_space(A) | -top_str(A) | empty_carrier(B) | -net_str(B,A) | -element(C,the_carrier(A)) | is_a_cluster_point_of_netstr(A,B,C) | point_neighbourhood(f10(A,B,C),A,C) # label(d9_waybel_9) # label(axiom). [clausify(41)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | empty_carrier(A) | -net_str(A,c3) | -element(B,the_carrier(c3)) | is_a_cluster_point_of_netstr(c3,A,B) | point_neighbourhood(f10(c3,A,B),c3,B). [resolve(60,c,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | empty_carrier(A) | -net_str(A,c8) | -element(B,the_carrier(c8)) | is_a_cluster_point_of_netstr(c8,A,B) | point_neighbourhood(f10(c8,A,B),c8,B). [resolve(60,c,57,a)]. 0.06/0.53 61 empty_carrier(A) | -topological_space(A) | -top_str(A) | empty_carrier(B) | -net_str(B,A) | -element(C,the_carrier(A)) | is_a_cluster_point_of_netstr(A,B,C) | -is_often_in(A,B,f10(A,B,C)) # label(d9_waybel_9) # label(axiom). [clausify(41)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | empty_carrier(A) | -net_str(A,c3) | -element(B,the_carrier(c3)) | is_a_cluster_point_of_netstr(c3,A,B) | -is_often_in(c3,A,f10(c3,A,B)). [resolve(61,c,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | empty_carrier(A) | -net_str(A,c8) | -element(B,the_carrier(c8)) | is_a_cluster_point_of_netstr(c8,A,B) | -is_often_in(c8,A,f10(c8,A,B)). [resolve(61,c,57,a)]. 0.06/0.53 62 empty_carrier(A) | -topological_space(A) | -top_str(A) | empty_carrier(B) | -net_str(B,A) | -element(C,the_carrier(A)) | -is_a_cluster_point_of_netstr(A,B,C) | -point_neighbourhood(D,A,C) | is_often_in(A,B,D) # label(d9_waybel_9) # label(axiom). [clausify(41)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | empty_carrier(A) | -net_str(A,c3) | -element(B,the_carrier(c3)) | -is_a_cluster_point_of_netstr(c3,A,B) | -point_neighbourhood(C,c3,B) | is_often_in(c3,A,C). [resolve(62,c,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | empty_carrier(A) | -net_str(A,c8) | -element(B,the_carrier(c8)) | -is_a_cluster_point_of_netstr(c8,A,B) | -point_neighbourhood(C,c8,B) | is_often_in(c8,A,C). [resolve(62,c,57,a)]. 0.06/0.53 63 empty_carrier(A) | -top_str(A) | -topological_space(A) | -transitive_relstr(B) | -directed_relstr(B) | -net_str(B,A) | empty_carrier(B) | -element(C,powerset(the_carrier(A))) | element(f1(A,B,C),the_carrier(A)) | lim_points_of_net(A,B) = C # label(d18_yellow_6) # label(axiom). [clausify(4)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | element(f1(c3,A,B),the_carrier(c3)) | lim_points_of_net(c3,A) = B. [resolve(63,b,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | element(f1(c8,A,B),the_carrier(c8)) | lim_points_of_net(c8,A) = B. [resolve(63,b,57,a)]. 0.06/0.53 64 empty_carrier(A) | -top_str(A) | -topological_space(A) | -transitive_relstr(B) | -directed_relstr(B) | -net_str(B,A) | empty_carrier(B) | -element(C,powerset(the_carrier(A))) | -is_eventually_in(A,B,f2(A,B,C)) | -in(f1(A,B,C),C) | lim_points_of_net(A,B) = C # label(d18_yellow_6) # label(axiom). [clausify(4)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -is_eventually_in(c3,A,f2(c3,A,B)) | -in(f1(c3,A,B),B) | lim_points_of_net(c3,A) = B. [resolve(64,b,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -is_eventually_in(c8,A,f2(c8,A,B)) | -in(f1(c8,A,B),B) | lim_points_of_net(c8,A) = B. [resolve(64,b,57,a)]. 0.06/0.53 65 empty_carrier(A) | -top_str(A) | -topological_space(A) | -transitive_relstr(B) | -directed_relstr(B) | -net_str(B,A) | empty_carrier(B) | -element(C,powerset(the_carrier(A))) | -element(D,the_carrier(A)) | point_neighbourhood(f3(A,B,C,D),A,D) | in(D,C) | lim_points_of_net(A,B) != C # label(d18_yellow_6) # label(axiom). [clausify(4)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -element(C,the_carrier(c3)) | point_neighbourhood(f3(c3,A,B,C),c3,C) | in(C,B) | lim_points_of_net(c3,A) != B. [resolve(65,b,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -element(C,the_carrier(c8)) | point_neighbourhood(f3(c8,A,B,C),c8,C) | in(C,B) | lim_points_of_net(c8,A) != B. [resolve(65,b,57,a)]. 0.06/0.53 66 empty_carrier(A) | -top_str(A) | -topological_space(A) | -transitive_relstr(B) | -directed_relstr(B) | -net_str(B,A) | empty_carrier(B) | -element(C,powerset(the_carrier(A))) | -element(D,the_carrier(A)) | -is_eventually_in(A,B,f3(A,B,C,D)) | in(D,C) | lim_points_of_net(A,B) != C # label(d18_yellow_6) # label(axiom). [clausify(4)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -element(C,the_carrier(c3)) | -is_eventually_in(c3,A,f3(c3,A,B,C)) | in(C,B) | lim_points_of_net(c3,A) != B. [resolve(66,b,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -element(C,the_carrier(c8)) | -is_eventually_in(c8,A,f3(c8,A,B,C)) | in(C,B) | lim_points_of_net(c8,A) != B. [resolve(66,b,57,a)]. 0.06/0.53 67 empty_carrier(A) | -top_str(A) | -topological_space(A) | -transitive_relstr(B) | -directed_relstr(B) | -net_str(B,A) | empty_carrier(B) | -element(C,powerset(the_carrier(A))) | -element(D,the_carrier(A)) | -point_neighbourhood(E,A,D) | is_eventually_in(A,B,E) | -in(D,C) | lim_points_of_net(A,B) != C # label(d18_yellow_6) # label(axiom). [clausify(4)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -element(C,the_carrier(c3)) | -point_neighbourhood(D,c3,C) | is_eventually_in(c3,A,D) | -in(C,B) | lim_points_of_net(c3,A) != B. [resolve(67,b,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -element(C,the_carrier(c8)) | -point_neighbourhood(D,c8,C) | is_eventually_in(c8,A,D) | -in(C,B) | lim_points_of_net(c8,A) != B. [resolve(67,b,57,a)]. 0.06/0.53 68 empty_carrier(A) | -top_str(A) | -topological_space(A) | -transitive_relstr(B) | -directed_relstr(B) | -net_str(B,A) | empty_carrier(B) | -element(C,powerset(the_carrier(A))) | point_neighbourhood(f2(A,B,C),A,f1(A,B,C)) | -in(f1(A,B,C),C) | lim_points_of_net(A,B) = C # label(d18_yellow_6) # label(axiom). [clausify(4)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | point_neighbourhood(f2(c3,A,B),c3,f1(c3,A,B)) | -in(f1(c3,A,B),B) | lim_points_of_net(c3,A) = B. [resolve(68,b,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | point_neighbourhood(f2(c8,A,B),c8,f1(c8,A,B)) | -in(f1(c8,A,B),B) | lim_points_of_net(c8,A) = B. [resolve(68,b,57,a)]. 0.06/0.53 69 empty_carrier(A) | -top_str(A) | -topological_space(A) | -transitive_relstr(B) | -directed_relstr(B) | -net_str(B,A) | empty_carrier(B) | -element(C,powerset(the_carrier(A))) | -point_neighbourhood(D,A,f1(A,B,C)) | is_eventually_in(A,B,D) | in(f1(A,B,C),C) | lim_points_of_net(A,B) = C # label(d18_yellow_6) # label(axiom). [clausify(4)]. 0.06/0.53 Derived: empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -point_neighbourhood(C,c3,f1(c3,A,B)) | is_eventually_in(c3,A,C) | in(f1(c3,A,B),B) | lim_points_of_net(c3,A) = B. [resolve(69,b,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -point_neighbourhood(C,c8,f1(c8,A,B)) | is_eventually_in(c8,A,C) | in(f1(c8,A,B),B) | lim_points_of_net(c8,A) = B. [resolve(69,b,57,a)]. 0.06/0.53 70 net_str(f7(A),A) | -top_str(A). [resolve(45,a,48,b)]. 0.06/0.53 Derived: net_str(f7(c3),c3). [resolve(70,b,56,a)]. 0.06/0.53 Derived: net_str(f7(c8),c8). [resolve(70,b,57,a)]. 0.06/0.53 71 empty_carrier(A) | -empty(the_carrier(A)) | -top_str(A). [resolve(50,a,48,b)]. 0.06/0.53 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(71,c,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -empty(the_carrier(c8)). [resolve(71,c,57,a)]. 0.06/0.53 72 empty_carrier(A) | -empty(f6(A)) | -top_str(A). [resolve(51,b,48,b)]. 0.06/0.53 Derived: empty_carrier(c3) | -empty(f6(c3)). [resolve(72,c,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -empty(f6(c8)). [resolve(72,c,57,a)]. 0.06/0.53 73 -net_str(A,B) | rel_str(A) | -top_str(B). [resolve(52,a,48,b)]. 0.06/0.53 Derived: -net_str(A,c3) | rel_str(A). [resolve(73,c,56,a)]. 0.06/0.53 Derived: -net_str(A,c8) | rel_str(A). [resolve(73,c,57,a)]. 0.06/0.53 74 empty_carrier(A) | element(f6(A),powerset(the_carrier(A))) | -top_str(A). [resolve(53,b,48,b)]. 0.06/0.53 Derived: empty_carrier(c3) | element(f6(c3),powerset(the_carrier(c3))). [resolve(74,c,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | element(f6(c8),powerset(the_carrier(c8))). [resolve(74,c,57,a)]. 0.06/0.53 75 empty_carrier(A) | -transitive_relstr(B) | -net_str(B,A) | -directed_relstr(B) | empty_carrier(B) | -is_eventually_in(A,B,C) | is_often_in(A,B,C) | -top_str(A). [resolve(54,a,48,b)]. 0.06/0.53 Derived: empty_carrier(c3) | -transitive_relstr(A) | -net_str(A,c3) | -directed_relstr(A) | empty_carrier(A) | -is_eventually_in(c3,A,B) | is_often_in(c3,A,B). [resolve(75,h,56,a)]. 0.06/0.53 Derived: empty_carrier(c8) | -transitive_relstr(A) | -net_str(A,c8) | -directed_relstr(A) | empty_carrier(A) | -is_eventually_in(c8,A,B) | is_often_in(c8,A,B). [resolve(75,h,57,a)]. 0.06/0.54 76 empty_carrier(c1) | -transitive_relstr(A) | -net_str(A,c1) | -directed_relstr(A) | empty_carrier(A) | -is_eventually_in(c1,A,B) | is_often_in(c1,A,B). [resolve(54,a,46,a)]. 0.06/0.54 77 transitive_relstr(c9) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.06/0.54 Derived: empty_carrier(c1) | -net_str(c9,c1) | -directed_relstr(c9) | empty_carrier(c9) | -is_eventually_in(c1,c9,A) | is_often_in(c1,c9,A). [resolve(76,b,77,a)]. 0.06/0.54 78 empty_carrier(c6) | -transitive_relstr(A) | -net_str(A,c6) | -directed_relstr(A) | empty_carrier(A) | -is_eventually_in(c6,A,B) | is_often_in(c6,A,B). [resolve(54,a,47,a)]. 0.06/0.54 Derived: empty_carrier(c6) | -net_str(c9,c6) | -directed_relstr(c9) | empty_carrier(c9) | -is_eventually_in(c6,c9,A) | is_often_in(c6,c9,A). [resolve(78,b,77,a)]. 0.06/0.54 79 empty_carrier(A) | -transitive_relstr(B) | -net_str(B,A) | -directed_relstr(B) | empty_carrier(B) | -is_eventually_in(A,B,C) | is_often_in(A,B,C) | -rel_str(A). [resolve(54,a,49,b)]. 0.06/0.54 Derived: empty_carrier(A) | -net_str(c9,A) | -directed_relstr(c9) | empty_carrier(c9) | -is_eventually_in(A,c9,B) | is_often_in(A,c9,B) | -rel_str(A). [resolve(79,b,77,a)]. 0.06/0.54 80 empty_carrier(c3) | -topological_space(c3) | -net_str(A,c3) | -directed_relstr(A) | -transitive_relstr(A) | empty_carrier(A) | element(lim_points_of_net(c3,A),powerset(the_carrier(c3))). [resolve(59,g,56,a)]. 0.06/0.54 Derived: empty_carrier(c3) | -topological_space(c3) | -net_str(c9,c3) | -directed_relstr(c9) | empty_carrier(c9) | element(lim_points_of_net(c3,c9),powerset(the_carrier(c3))). [resolve(80,e,77,a)]. 0.06/0.54 81 empty_carrier(c8) | -topological_space(c8) | -net_str(A,c8) | -directed_relstr(A) | -transitive_relstr(A) | empty_carrier(A) | element(lim_points_of_net(c8,A),powerset(the_carrier(c8))). [resolve(59,g,57,a)]. 0.06/0.54 Derived: empty_carrier(c8) | -topological_space(c8) | -net_str(c9,c8) | -directed_relstr(c9) | empty_carrier(c9) | element(lim_points_of_net(c8,c9),powerset(the_carrier(c8))). [resolve(81,e,77,a)]. 0.06/0.54 82 empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | element(f1(c3,A,B),the_carrier(c3)) | lim_points_of_net(c3,A) = B. [resolve(63,b,56,a)]. 0.06/0.54 Derived: empty_carrier(c3) | -topological_space(c3) | -directed_relstr(c9) | -net_str(c9,c3) | empty_carrier(c9) | -element(A,powerset(the_carrier(c3))) | element(f1(c3,c9,A),the_carrier(c3)) | lim_points_of_net(c3,c9) = A. [resolve(82,c,77,a)]. 0.06/0.54 83 empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | element(f1(c8,A,B),the_carrier(c8)) | lim_points_of_net(c8,A) = B. [resolve(63,b,57,a)]. 0.06/0.54 Derived: empty_carrier(c8) | -topological_space(c8) | -directed_relstr(c9) | -net_str(c9,c8) | empty_carrier(c9) | -element(A,powerset(the_carrier(c8))) | element(f1(c8,c9,A),the_carrier(c8)) | lim_points_of_net(c8,c9) = A. [resolve(83,c,77,a)]. 0.06/0.54 84 empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -is_eventually_in(c3,A,f2(c3,A,B)) | -in(f1(c3,A,B),B) | lim_points_of_net(c3,A) = B. [resolve(64,b,56,a)]. 0.06/0.54 Derived: empty_carrier(c3) | -topological_space(c3) | -directed_relstr(c9) | -net_str(c9,c3) | empty_carrier(c9) | -element(A,powerset(the_carrier(c3))) | -is_eventually_in(c3,c9,f2(c3,c9,A)) | -in(f1(c3,c9,A),A) | lim_points_of_net(c3,c9) = A. [resolve(84,c,77,a)]. 0.06/0.54 85 empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -is_eventually_in(c8,A,f2(c8,A,B)) | -in(f1(c8,A,B),B) | lim_points_of_net(c8,A) = B. [resolve(64,b,57,a)]. 0.06/0.54 Derived: empty_carrier(c8) | -topological_space(c8) | -directed_relstr(c9) | -net_str(c9,c8) | empty_carrier(c9) | -element(A,powerset(the_carrier(c8))) | -is_eventually_in(c8,c9,f2(c8,c9,A)) | -in(f1(c8,c9,A),A) | lim_points_of_net(c8,c9) = A. [resolve(85,c,77,a)]. 0.06/0.54 86 empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -element(C,the_carrier(c3)) | point_neighbourhood(f3(c3,A,B,C),c3,C) | in(C,B) | lim_points_of_net(c3,A) != B. [resolve(65,b,56,a)]. 0.06/0.54 Derived: empty_carrier(c3) | -topological_space(c3) | -directed_relstr(c9) | -net_str(c9,c3) | empty_carrier(c9) | -element(A,powerset(the_carrier(c3))) | -element(B,the_carrier(c3)) | point_neighbourhood(f3(c3,c9,A,B),c3,B) | in(B,A) | lim_points_of_net(c3,c9) != A. [resolve(86,c,77,a)]. 0.06/0.54 87 empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -element(C,the_carrier(c8)) | point_neighbourhood(f3(c8,A,B,C),c8,C) | in(C,B) | lim_points_of_net(c8,A) != B. [resolve(65,b,57,a)]. 0.06/0.54 Derived: empty_carrier(c8) | -topological_space(c8) | -directed_relstr(c9) | -net_str(c9,c8) | empty_carrier(c9) | -element(A,powerset(the_carrier(c8))) | -element(B,the_carrier(c8)) | point_neighbourhood(f3(c8,c9,A,B),c8,B) | in(B,A) | lim_points_of_net(c8,c9) != A. [resolve(87,c,77,a)]. 0.06/0.54 88 empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -element(C,the_carrier(c3)) | -is_eventually_in(c3,A,f3(c3,A,B,C)) | in(C,B) | lim_points_of_net(c3,A) != B. [resolve(66,b,56,a)]. 0.06/0.54 Derived: empty_carrier(c3) | -topological_space(c3) | -directed_relstr(c9) | -net_str(c9,c3) | empty_carrier(c9) | -element(A,powerset(the_carrier(c3))) | -element(B,the_carrier(c3)) | -is_eventually_in(c3,c9,f3(c3,c9,A,B)) | in(B,A) | lim_points_of_net(c3,c9) != A. [resolve(88,c,77,a)]. 0.06/0.54 89 empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -element(C,the_carrier(c8)) | -is_eventually_in(c8,A,f3(c8,A,B,C)) | in(C,B) | lim_points_of_net(c8,A) != B. [resolve(66,b,57,a)]. 0.06/0.54 Derived: empty_carrier(c8) | -topological_space(c8) | -directed_relstr(c9) | -net_str(c9,c8) | empty_carrier(c9) | -element(A,powerset(the_carrier(c8))) | -element(B,the_carrier(c8)) | -is_eventually_in(c8,c9,f3(c8,c9,A,B)) | in(B,A) | lim_points_of_net(c8,c9) != A. [resolve(89,c,77,a)]. 0.06/0.54 90 empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -element(C,the_carrier(c3)) | -point_neighbourhood(D,c3,C) | is_eventually_in(c3,A,D) | -in(C,B) | lim_points_of_net(c3,A) != B. [resolve(67,b,56,a)]. 0.06/0.54 Derived: empty_carrier(c3) | -topological_space(c3) | -directed_relstr(c9) | -net_str(c9,c3) | empty_carrier(c9) | -element(A,powerset(the_carrier(c3))) | -element(B,the_carrier(c3)) | -point_neighbourhood(C,c3,B) | is_eventually_in(c3,c9,C) | -in(B,A) | lim_points_of_net(c3,c9) != A. [resolve(90,c,77,a)]. 0.06/0.54 91 empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -element(C,the_carrier(c8)) | -point_neighbourhood(D,c8,C) | is_eventually_in(c8,A,D) | -in(C,B) | lim_points_of_net(c8,A) != B. [resolve(67,b,57,a)]. 0.06/0.54 Derived: empty_carrier(c8) | -topological_space(c8) | -directed_relstr(c9) | -net_str(c9,c8) | empty_carrier(c9) | -element(A,powerset(the_carrier(c8))) | -element(B,the_carrier(c8)) | -point_neighbourhood(C,c8,B) | is_eventually_in(c8,c9,C) | -in(B,A) | lim_points_of_net(c8,c9) != A. [resolve(91,c,77,a)]. 0.06/0.54 92 empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | point_neighbourhood(f2(c3,A,B),c3,f1(c3,A,B)) | -in(f1(c3,A,B),B) | lim_points_of_net(c3,A) = B. [resolve(68,b,56,a)]. 0.06/0.54 Derived: empty_carrier(c3) | -topological_space(c3) | -directed_relstr(c9) | -net_str(c9,c3) | empty_carrier(c9) | -element(A,powerset(the_carrier(c3))) | point_neighbourhood(f2(c3,c9,A),c3,f1(c3,c9,A)) | -in(f1(c3,c9,A),A) | lim_points_of_net(c3,c9) = A. [resolve(92,c,77,a)]. 0.28/0.54 93 empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | point_neighbourhood(f2(c8,A,B),c8,f1(c8,A,B)) | -in(f1(c8,A,B),B) | lim_points_of_net(c8,A) = B. [resolve(68,b,57,a)]. 0.28/0.54 Derived: empty_carrier(c8) | -topological_space(c8) | -directed_relstr(c9) | -net_str(c9,c8) | empty_carrier(c9) | -element(A,powerset(the_carrier(c8))) | point_neighbourhood(f2(c8,c9,A),c8,f1(c8,c9,A)) | -in(f1(c8,c9,A),A) | lim_points_of_net(c8,c9) = A. [resolve(93,c,77,a)]. 0.28/0.54 94 empty_carrier(c3) | -topological_space(c3) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c3) | empty_carrier(A) | -element(B,powerset(the_carrier(c3))) | -point_neighbourhood(C,c3,f1(c3,A,B)) | is_eventually_in(c3,A,C) | in(f1(c3,A,B),B) | lim_points_of_net(c3,A) = B. [resolve(69,b,56,a)]. 0.28/0.54 Derived: empty_carrier(c3) | -topological_space(c3) | -directed_relstr(c9) | -net_str(c9,c3) | empty_carrier(c9) | -element(A,powerset(the_carrier(c3))) | -point_neighbourhood(B,c3,f1(c3,c9,A)) | is_eventually_in(c3,c9,B) | in(f1(c3,c9,A),A) | lim_points_of_net(c3,c9) = A. [resolve(94,c,77,a)]. 0.28/0.54 95 empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -point_neighbourhood(C,c8,f1(c8,A,B)) | is_eventually_in(c8,A,C) | in(f1(c8,A,B),B) | lim_points_of_net(c8,A) = B. [resolve(69,b,57,a)]. 0.28/0.54 Derived: empty_carrier(c8) | -topological_space(c8) | -directed_relstr(c9) | -net_str(c9,c8) | empty_carrier(c9) | -element(A,powerset(the_carrier(c8))) | -point_neighbourhood(B,c8,f1(c8,c9,A)) | is_eventually_in(c8,c9,B) | in(f1(c8,c9,A),A) | lim_points_of_net(c8,c9) = A. [resolve(95,c,77,a)]. 0.28/0.54 96 empty_carrier(c3) | -transitive_relstr(A) | -net_str(A,c3) | -directed_relstr(A) | empty_carrier(A) | -is_eventually_in(c3,A,B) | is_often_in(c3,A,B). [resolve(75,h,56,a)]. 0.28/0.54 Derived: empty_carrier(c3) | -net_str(c9,c3) | -directed_relstr(c9) | empty_carrier(c9) | -is_eventually_in(c3,c9,A) | is_often_in(c3,c9,A). [resolve(96,b,77,a)]. 0.28/0.54 97 empty_carrier(c8) | -transitive_relstr(A) | -net_str(A,c8) | -directed_relstr(A) | empty_carrier(A) | -is_eventually_in(c8,A,B) | is_often_in(c8,A,B). [resolve(75,h,57,a)]. 0.28/0.54 Derived: empty_carrier(c8) | -net_str(c9,c8) | -directed_relstr(c9) | empty_carrier(c9) | -is_eventually_in(c8,c9,A) | is_often_in(c8,c9,A). [resolve(97,b,77,a)]. 0.28/0.54 98 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(42)]. 0.28/0.54 99 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(11)]. 0.28/0.54 100 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(42)]. 0.28/0.54 Derived: element(A,powerset(A)). [resolve(98,b,99,a)]. 0.28/0.54 101 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(8)]. 0.28/0.54 102 cup_closed(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(24)]. 0.28/0.54 103 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(23)]. 0.28/0.54 Derived: -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(101,a,102,a)]. 0.28/0.54 104 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(23)]. 0.28/0.54 105 preboolean(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(24)]. 0.28/0.54 Derived: diff_closed(powerset(A)). [resolve(104,a,105,a)]. 0.28/0.54 106 -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(101,a,102,a)]. 0.28/0.54 0.28/0.54 ============================== end predicate elimination ============= 0.28/0.54 0.28/0.54 Auto_denials: (non-Horn, no changes). 0.28/0.54 0.28/0.54 Term ordering decisions: 0.28/0.54 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. lim_points_of_net=1. f4=1. the_carrier=1. powerset=1. f5=1. f6=1. f7=1. f8=1. f9=1. f1=1. f2=1. f10=1. f3=1. 0.28/0.54 0.28/0.54 ============================== end of process initial clauses ======== 0.28/0.54 0.28/0.54 ============================== CLAUSES FOR SEARCH ==================== 0.28/0.54 0.28/0.54 ============================== end of clauses for search ============= 0.40/0.72 0.40/0.72 ============================== SEARCH ================================ 0.40/0.72 0.40/0.72 % Starting search at 0.02 seconds. 0.40/0.72 0.40/0.72 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 220 (0.00 of 0.11 sec). 0.40/0.72 0.40/0.72 ============================== PROOF ================================= 0.40/0.72 % SZS status Theorem 0.40/0.72 % SZS output start Refutation 0.40/0.72 0.40/0.72 % Proof 1 at 0.19 (+ 0.01) seconds. 0.40/0.72 % Length of proof is 41. 0.40/0.72 % Level of proof is 7. 0.40/0.72 % Maximum clause weight is 25.000. 0.40/0.72 % Given clauses 864. 0.40/0.72 0.40/0.72 1 (all A (top_str(A) -> one_sorted_str(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 0.40/0.72 2 (all A (one_sorted_str(A) & -empty_carrier(A) -> (all B (transitive_relstr(B) & net_str(B,A) & directed_relstr(B) & -empty_carrier(B) -> (all C (is_eventually_in(A,B,C) -> is_often_in(A,B,C))))))) # label(t28_yellow_6) # label(axiom) # label(non_clause). [assumption]. 0.40/0.72 4 (all A (-empty_carrier(A) & top_str(A) & topological_space(A) -> (all B (transitive_relstr(B) & directed_relstr(B) & net_str(B,A) & -empty_carrier(B) -> (all C (element(C,powerset(the_carrier(A))) -> ((all D (element(D,the_carrier(A)) -> ((all E (point_neighbourhood(E,A,D) -> is_eventually_in(A,B,E))) <-> in(D,C)))) <-> C = lim_points_of_net(A,B)))))))) # label(d18_yellow_6) # label(axiom) # label(non_clause). [assumption]. 0.40/0.72 20 (all A all B (-empty_carrier(A) & topological_space(A) & net_str(B,A) & directed_relstr(B) & transitive_relstr(B) & -empty_carrier(B) & top_str(A) -> element(lim_points_of_net(A,B),powerset(the_carrier(A))))) # label(dt_k11_yellow_6) # label(axiom) # label(non_clause). [assumption]. 0.40/0.72 41 (all A (-empty_carrier(A) & topological_space(A) & top_str(A) -> (all B (-empty_carrier(B) & net_str(B,A) -> (all C (element(C,the_carrier(A)) -> (is_a_cluster_point_of_netstr(A,B,C) <-> (all D (point_neighbourhood(D,A,C) -> is_often_in(A,B,D)))))))))) # label(d9_waybel_9) # label(axiom) # label(non_clause). [assumption]. 0.40/0.72 44 -(all A (-empty_carrier(A) & top_str(A) & topological_space(A) -> (all B (-empty_carrier(B) & transitive_relstr(B) & net_str(B,A) & directed_relstr(B) -> (all C (element(C,the_carrier(A)) -> (in(C,lim_points_of_net(A,B)) -> is_a_cluster_point_of_netstr(A,B,C)))))))) # label(t29_waybel_9) # label(negated_conjecture) # label(non_clause). [assumption]. 0.40/0.72 48 -top_str(A) | one_sorted_str(A) # label(dt_l1_pre_topc) # label(axiom). [clausify(1)]. 0.40/0.72 54 -one_sorted_str(A) | empty_carrier(A) | -transitive_relstr(B) | -net_str(B,A) | -directed_relstr(B) | empty_carrier(B) | -is_eventually_in(A,B,C) | is_often_in(A,B,C) # label(t28_yellow_6) # label(axiom). [clausify(2)]. 0.40/0.72 57 top_str(c8) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 59 empty_carrier(A) | -topological_space(A) | -net_str(B,A) | -directed_relstr(B) | -transitive_relstr(B) | empty_carrier(B) | -top_str(A) | element(lim_points_of_net(A,B),powerset(the_carrier(A))) # label(dt_k11_yellow_6) # label(axiom). [clausify(20)]. 0.40/0.72 60 empty_carrier(A) | -topological_space(A) | -top_str(A) | empty_carrier(B) | -net_str(B,A) | -element(C,the_carrier(A)) | is_a_cluster_point_of_netstr(A,B,C) | point_neighbourhood(f10(A,B,C),A,C) # label(d9_waybel_9) # label(axiom). [clausify(41)]. 0.40/0.72 61 empty_carrier(A) | -topological_space(A) | -top_str(A) | empty_carrier(B) | -net_str(B,A) | -element(C,the_carrier(A)) | is_a_cluster_point_of_netstr(A,B,C) | -is_often_in(A,B,f10(A,B,C)) # label(d9_waybel_9) # label(axiom). [clausify(41)]. 0.40/0.72 67 empty_carrier(A) | -top_str(A) | -topological_space(A) | -transitive_relstr(B) | -directed_relstr(B) | -net_str(B,A) | empty_carrier(B) | -element(C,powerset(the_carrier(A))) | -element(D,the_carrier(A)) | -point_neighbourhood(E,A,D) | is_eventually_in(A,B,E) | -in(D,C) | lim_points_of_net(A,B) != C # label(d18_yellow_6) # label(axiom). [clausify(4)]. 0.40/0.72 75 empty_carrier(A) | -transitive_relstr(B) | -net_str(B,A) | -directed_relstr(B) | empty_carrier(B) | -is_eventually_in(A,B,C) | is_often_in(A,B,C) | -top_str(A). [resolve(54,a,48,b)]. 0.40/0.72 77 transitive_relstr(c9) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 81 empty_carrier(c8) | -topological_space(c8) | -net_str(A,c8) | -directed_relstr(A) | -transitive_relstr(A) | empty_carrier(A) | element(lim_points_of_net(c8,A),powerset(the_carrier(c8))). [resolve(59,g,57,a)]. 0.40/0.72 91 empty_carrier(c8) | -topological_space(c8) | -transitive_relstr(A) | -directed_relstr(A) | -net_str(A,c8) | empty_carrier(A) | -element(B,powerset(the_carrier(c8))) | -element(C,the_carrier(c8)) | -point_neighbourhood(D,c8,C) | is_eventually_in(c8,A,D) | -in(C,B) | lim_points_of_net(c8,A) != B. [resolve(67,b,57,a)]. 0.40/0.72 97 empty_carrier(c8) | -transitive_relstr(A) | -net_str(A,c8) | -directed_relstr(A) | empty_carrier(A) | -is_eventually_in(c8,A,B) | is_often_in(c8,A,B). [resolve(75,h,57,a)]. 0.40/0.72 111 topological_space(c8) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 112 directed_relstr(c9) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 113 net_str(c9,c8) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 115 element(c10,the_carrier(c8)) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 118 in(c10,lim_points_of_net(c8,c9)) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 124 -empty_carrier(c8) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 125 -empty_carrier(c9) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 127 -is_a_cluster_point_of_netstr(c8,c9,c10) # label(t29_waybel_9) # label(negated_conjecture). [clausify(44)]. 0.40/0.72 165 empty_carrier(c8) | -topological_space(c8) | empty_carrier(A) | -net_str(A,c8) | -element(B,the_carrier(c8)) | is_a_cluster_point_of_netstr(c8,A,B) | point_neighbourhood(f10(c8,A,B),c8,B). [resolve(60,c,57,a)]. 0.40/0.72 166 empty_carrier(A) | -net_str(A,c8) | -element(B,the_carrier(c8)) | is_a_cluster_point_of_netstr(c8,A,B) | point_neighbourhood(f10(c8,A,B),c8,B). [copy(165),unit_del(a,124),unit_del(b,111)]. 0.40/0.72 168 empty_carrier(c8) | -topological_space(c8) | empty_carrier(A) | -net_str(A,c8) | -element(B,the_carrier(c8)) | is_a_cluster_point_of_netstr(c8,A,B) | -is_often_in(c8,A,f10(c8,A,B)). [resolve(61,c,57,a)]. 0.40/0.72 169 empty_carrier(A) | -net_str(A,c8) | -element(B,the_carrier(c8)) | is_a_cluster_point_of_netstr(c8,A,B) | -is_often_in(c8,A,f10(c8,A,B)). [copy(168),unit_del(a,124),unit_del(b,111)]. 0.40/0.72 194 empty_carrier(c8) | -topological_space(c8) | -net_str(c9,c8) | -directed_relstr(c9) | empty_carrier(c9) | element(lim_points_of_net(c8,c9),powerset(the_carrier(c8))). [resolve(81,e,77,a)]. 0.40/0.72 195 element(lim_points_of_net(c8,c9),powerset(the_carrier(c8))). [copy(194),unit_del(a,124),unit_del(b,111),unit_del(c,113),unit_del(d,112),unit_del(e,125)]. 0.40/0.72 214 empty_carrier(c8) | -topological_space(c8) | -directed_relstr(c9) | -net_str(c9,c8) | empty_carrier(c9) | -element(A,powerset(the_carrier(c8))) | -element(B,the_carrier(c8)) | -point_neighbourhood(C,c8,B) | is_eventually_in(c8,c9,C) | -in(B,A) | lim_points_of_net(c8,c9) != A. [resolve(91,c,77,a)]. 0.40/0.72 215 -element(A,powerset(the_carrier(c8))) | -element(B,the_carrier(c8)) | -point_neighbourhood(C,c8,B) | is_eventually_in(c8,c9,C) | -in(B,A) | lim_points_of_net(c8,c9) != A. [copy(214),unit_del(a,124),unit_del(b,111),unit_del(c,112),unit_del(d,113),unit_del(e,125)]. 0.40/0.72 226 empty_carrier(c8) | -net_str(c9,c8) | -directed_relstr(c9) | empty_carrier(c9) | -is_eventually_in(c8,c9,A) | is_often_in(c8,c9,A). [resolve(97,b,77,a)]. 0.40/0.72 227 -is_eventually_in(c8,c9,A) | is_often_in(c8,c9,A). [copy(226),unit_del(a,124),unit_del(b,113),unit_del(c,112),unit_del(d,125)]. 0.40/0.72 276 -element(A,the_carrier(c8)) | is_a_cluster_point_of_netstr(c8,c9,A) | point_neighbourhood(f10(c8,c9,A),c8,A). [resolve(166,b,113,a),unit_del(a,125)]. 0.40/0.72 277 -is_often_in(c8,c9,f10(c8,c9,c10)). [ur(169,a,125,a,b,113,a,c,115,a,d,127,a)]. 0.40/0.72 614 point_neighbourhood(f10(c8,c9,c10),c8,c10). [resolve(276,a,115,a),unit_del(a,127)]. 0.40/0.72 633 -is_eventually_in(c8,c9,f10(c8,c9,c10)). [ur(227,b,277,a)]. 0.40/0.72 2986 $F. [ur(215,b,115,a,c,614,a,d,633,a,e,118,a,f,xx),unit_del(a,195)]. 0.40/0.72 0.40/0.72 % SZS output end Refutation 0.40/0.72 ============================== end of proof ========================== 0.40/0.72 0.40/0.72 ============================== STATISTICS ============================ 0.40/0.72 0.40/0.72 Given=864. Generated=4139. Kept=2847. proofs=1. 0.40/0.72 Usable=859. Sos=1964. Demods=4. Limbo=0, Disabled=179. Hints=0. 0.40/0.72 Megabytes=2.80. 0.40/0.72 User_CPU=0.19, System_CPU=0.01, Wall_clock=0. 0.40/0.72 0.40/0.72 ============================== end of statistics ===================== 0.40/0.72 0.40/0.72 ============================== end of search ========================= 0.40/0.72 0.40/0.72 THEOREM PROVED 0.40/0.72 % SZS status Theorem 0.40/0.72 0.40/0.72 Exiting with 1 proof. 0.40/0.72 0.40/0.72 Process 16120 exit (max_proofs) Fri Jul 13 15:56:59 2018 0.40/0.72 Prover9 interrupted 0.40/0.73 EOF