%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU386+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:46 AM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU386+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:57:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(is_eventually_in_type, type, (
% 0.19/0.42 is_eventually_in: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_B_17_type, type, (
% 0.19/0.42 tptp_fun_B_17: $i)).
% 0.19/0.42 tff(tptp_fun_A_16_type, type, (
% 0.19/0.42 tptp_fun_A_16: $i)).
% 0.19/0.42 tff(point_neighbourhood_type, type, (
% 0.19/0.42 point_neighbourhood: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_C_18_type, type, (
% 0.19/0.42 tptp_fun_C_18: $i)).
% 0.19/0.42 tff(in_type, type, (
% 0.19/0.42 in: ( $i * $i ) > $o)).
% 0.19/0.42 tff(lim_points_of_net_type, type, (
% 0.19/0.42 lim_points_of_net: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_E_0_type, type, (
% 0.19/0.42 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(element_type, type, (
% 0.19/0.42 element: ( $i * $i ) > $o)).
% 0.19/0.42 tff(the_carrier_type, type, (
% 0.19/0.42 the_carrier: $i > $i)).
% 0.19/0.42 tff(tptp_fun_D_1_type, type, (
% 0.19/0.42 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_E_2_type, type, (
% 0.19/0.42 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(powerset_type, type, (
% 0.19/0.42 powerset: $i > $i)).
% 0.19/0.42 tff(net_str_type, type, (
% 0.19/0.42 net_str: ( $i * $i ) > $o)).
% 0.19/0.42 tff(directed_relstr_type, type, (
% 0.19/0.42 directed_relstr: $i > $o)).
% 0.19/0.42 tff(transitive_relstr_type, type, (
% 0.19/0.42 transitive_relstr: $i > $o)).
% 0.19/0.42 tff(empty_carrier_type, type, (
% 0.19/0.42 empty_carrier: $i > $o)).
% 0.19/0.42 tff(top_str_type, type, (
% 0.19/0.42 top_str: $i > $o)).
% 0.19/0.42 tff(is_a_cluster_point_of_netstr_type, type, (
% 0.19/0.42 is_a_cluster_point_of_netstr: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(topological_space_type, type, (
% 0.19/0.42 topological_space: $i > $o)).
% 0.19/0.42 tff(tptp_fun_D_3_type, type, (
% 0.19/0.42 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(is_often_in_type, type, (
% 0.19/0.42 is_often_in: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(one_sorted_str_type, type, (
% 0.19/0.42 one_sorted_str: $i > $o)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 ((((~empty_carrier(A!16)) & topological_space(A!16) & top_str(A!16)) & ((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))))) <=> ((~empty_carrier(A!16)) & topological_space(A!16) & top_str(A!16) & (~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 ((((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16)) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17)))))) <=> ((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 ((~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))) <=> (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 ((((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16)) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17)))))) <=> (((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16)) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 ((((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16)) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17)))))) <=> ((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 ((((~empty_carrier(A!16)) & topological_space(A!16) & top_str(A!16)) & (((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16)) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))))) <=> (((~empty_carrier(A!16)) & topological_space(A!16) & top_str(A!16)) & ((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17)))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 ((((~empty_carrier(A!16)) & topological_space(A!16) & top_str(A!16)) & (((~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16)) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))))) <=> ((~empty_carrier(A!16)) & topological_space(A!16) & top_str(A!16) & (~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[6, 1])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 ((~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : (is_a_cluster_point_of_netstr(A, B, C) | (~element(C, the_carrier(A))) | (~in(C, lim_points_of_net(A, B))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : (is_a_cluster_point_of_netstr(A, B, C) | (~element(C, the_carrier(A))) | (~in(C, lim_points_of_net(A, B)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 ((~![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, lim_points_of_net(A, B)) => is_a_cluster_point_of_netstr(A, B, C)))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : (is_a_cluster_point_of_netstr(A, B, C) | (~element(C, the_carrier(A))) | (~in(C, lim_points_of_net(A, B)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(10,axiom,(~![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, lim_points_of_net(A, B)) => is_a_cluster_point_of_netstr(A, B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t29_waybel_9')).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : (is_a_cluster_point_of_netstr(A, B, C) | (~element(C, the_carrier(A))) | (~in(C, lim_points_of_net(A, B))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : (is_a_cluster_point_of_netstr(A, B, C) | (~element(C, the_carrier(A))) | (~in(C, lim_points_of_net(A, B))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : (is_a_cluster_point_of_netstr(A, B, C) | (~element(C, the_carrier(A))) | (~in(C, lim_points_of_net(A, B))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : (is_a_cluster_point_of_netstr(A, B, C) | (~element(C, the_carrier(A))) | (~in(C, lim_points_of_net(A, B))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 ((~empty_carrier(A!16)) & topological_space(A!16) & top_str(A!16) & (~empty_carrier(B!17)) & transitive_relstr(B!17) & directed_relstr(B!17) & net_str(B!17, A!16) & (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (top_str(A!16)),
% 0.19/0.42 inference(and_elim,[status(thm)],[15])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (topological_space(A!16)),
% 0.19/0.42 inference(and_elim,[status(thm)],[15])).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 (~empty_carrier(A!16)),
% 0.19/0.42 inference(and_elim,[status(thm)],[15])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 (^[A: $i] : rewrite((empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (^[A: $i] : refl((empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (^[A: $i] : rewrite((empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[24, 22])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A)) <=> (~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)) <=> (~(empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))))), ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) <=> (~(~(empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))))))), rewrite((~(~(empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))))) <=> (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)))), ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) <=> (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))) <=> ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))), (![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))), (((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))) <=> ((empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))), rewrite(((empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))) <=> (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))), (((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))) <=> (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))))), (![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))) <=> ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))) <=> ((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))))), rewrite(((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (^[A: $i] : rewrite(((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) <=> ((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B))), (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) <=> (((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B)) & net_str(B, A)))), rewrite((((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B)) & net_str(B, A)) <=> ((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))), (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) <=> ((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E))))) <=> ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))))), ((element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E)))))) <=> (element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))))))), rewrite((element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))))) <=> ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))), ((element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E)))))) <=> ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))))), (![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E)))))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))))))), ((((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E))))))) <=> (((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))))), rewrite((((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))) <=> ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))))))), ((((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E))))))) <=> ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))))))))), (![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E))))))) <=> ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E)))))))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))))))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E)))))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E)))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.44 tff(33,axiom,(![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = lim_points_of_net(A, B)) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (point_neighbourhood(E, A, D) => is_eventually_in(A, B, E))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d18_yellow_6')).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = lim_points_of_net(A, B)) <=> ![D: $i] : ((~element(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.44 tff(36,plain,(
% 0.19/0.44 ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A))))))))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[35])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E))) & (in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A)))))))) & ((C = lim_points_of_net(A, B)) | (element(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[38, 25])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[39, 20])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))) | (empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B)))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))) | empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B)))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 ((empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((C = lim_points_of_net(A!16, B)) | (~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E))))))))))))) <=> (empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B)))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))) | (empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((C = lim_points_of_net(A!16, B)) | (~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))) | (empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))) | (empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((C = lim_points_of_net(A!16, B)) | (~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))) | empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B)))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[43, 41])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))) | (empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((C = lim_points_of_net(A!16, B)) | (~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = lim_points_of_net(A, B))) | ![D: $i] : ((~element(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A, D)) | is_eventually_in(A, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A), A, D)) | is_eventually_in(A, B, tptp_fun_E_0(D, B, A))))))))))) | (~((C = lim_points_of_net(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A), A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, tptp_fun_E_2(C, B, A)))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~point_neighbourhood(E, A, tptp_fun_D_1(C, B, A))) | is_eventually_in(A, B, E)))))))))))))) | empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[46, 40, 18, 17, 16])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (net_str(B!17, A!16)),
% 0.19/0.45 inference(and_elim,[status(thm)],[15])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (directed_relstr(B!17)),
% 0.19/0.45 inference(and_elim,[status(thm)],[15])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (transitive_relstr(B!17)),
% 0.19/0.45 inference(and_elim,[status(thm)],[15])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (~empty_carrier(B!17)),
% 0.19/0.45 inference(and_elim,[status(thm)],[15])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))) | (empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))))))))) <=> ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))) | empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) <=> (empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (^[C: $i] : rewrite(((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17))))))) <=> ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 (![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17))))))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 ((empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))))))) <=> (empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 ((empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))))))) <=> (empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[56, 53])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))) | (empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17))))))))) <=> ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))) | (empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[57])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))) | (empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17))))))))) <=> ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))) | empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[58, 52])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))) | (empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~(C = lim_points_of_net(A!16, B))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B, A!16), A!16, D)) | is_eventually_in(A!16, B, tptp_fun_E_0(D, B, A!16))))))))))) | (~((~((~element(tptp_fun_D_1(C, B, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B, A!16), A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, tptp_fun_E_2(C, B, A!16)))))) | (~(in(tptp_fun_D_1(C, B, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B, A!16))) | is_eventually_in(A!16, B, E)))))) | (C = lim_points_of_net(A!16, B))))))))) | empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[61, 51, 50, 49, 48, 47])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (^[A: $i, B: $i] : refl((empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A))) <=> (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A))) <=> ![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)) <=> (~(empty_carrier(B) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) <=> (~(~(empty_carrier(B) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A))))))), rewrite((~(~(empty_carrier(B) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A))))) <=> (empty_carrier(B) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) <=> (empty_carrier(B) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A)))) <=> ((empty_carrier(B) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A)))))), rewrite(((empty_carrier(B) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A)))) <=> (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A)))) <=> (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) & (~empty_carrier(B))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) & (~empty_carrier(B))) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B))))), ((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B))) & transitive_relstr(B)))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B))) & transitive_relstr(B)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B))), ((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B)))), (((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) & directed_relstr(B)) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B))), (((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) & directed_relstr(B)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B)))), ((((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B)) & net_str(B, A)))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B)) & net_str(B, A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))), ((((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)))), (((((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => element(lim_points_of_net(A, B), powerset(the_carrier(A)))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)) => element(lim_points_of_net(A, B), powerset(the_carrier(A)))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)) => element(lim_points_of_net(A, B), powerset(the_carrier(A)))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A))))), (((((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => element(lim_points_of_net(A, B), powerset(the_carrier(A)))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => element(lim_points_of_net(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.47 tff(70,axiom,(![A: $i, B: $i] : ((((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & (~empty_carrier(B))) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => element(lim_points_of_net(A, B), powerset(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k11_yellow_6')).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.47 tff(73,plain,(
% 0.19/0.47 ![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & (~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | element(lim_points_of_net(A, B), powerset(the_carrier(A))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[72])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 (![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 (((~![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))) | (empty_carrier(A!16) | empty_carrier(B!17) | (~topological_space(A!16)) | (~top_str(A!16)) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)))) <=> ((~![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))) | empty_carrier(A!16) | empty_carrier(B!17) | (~topological_space(A!16)) | (~top_str(A!16)) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 ((empty_carrier(B!17) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | empty_carrier(A!16) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~topological_space(A!16)) | (~top_str(A!16))) <=> (empty_carrier(A!16) | empty_carrier(B!17) | (~topological_space(A!16)) | (~top_str(A!16)) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 (((~![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))) | (empty_carrier(B!17) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | empty_carrier(A!16) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~topological_space(A!16)) | (~top_str(A!16)))) <=> ((~![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))) | (empty_carrier(A!16) | empty_carrier(B!17) | (~topological_space(A!16)) | (~top_str(A!16)) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 (((~![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))) | (empty_carrier(B!17) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | empty_carrier(A!16) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~topological_space(A!16)) | (~top_str(A!16)))) <=> ((~![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))) | empty_carrier(A!16) | empty_carrier(B!17) | (~topological_space(A!16)) | (~top_str(A!16)) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))) | (empty_carrier(B!17) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | empty_carrier(A!16) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | (~topological_space(A!16)) | (~top_str(A!16)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (empty_carrier(B) | element(lim_points_of_net(A, B), powerset(the_carrier(A))) | empty_carrier(A) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | (~topological_space(A)) | (~top_str(A)))) | empty_carrier(A!16) | empty_carrier(B!17) | (~topological_space(A!16)) | (~top_str(A!16)) | element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16))) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[81, 75, 18, 17, 16, 51, 50, 49, 48])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) | ((~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) | (~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (((~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), lim_points_of_net(A!16, B!17))) | (~((~point_neighbourhood(tptp_fun_E_2(lim_points_of_net(A!16, B!17), B!17, A!16), A!16, tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(lim_points_of_net(A!16, B!17), B!17, A!16)))))) | (~(in(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), lim_points_of_net(A!16, B!17)) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (lim_points_of_net(A!16, B!17) = lim_points_of_net(A!16, B!17)))) | (~((~(lim_points_of_net(A!16, B!17) = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))))))) <=> ((~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) | ((~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), lim_points_of_net(A!16, B!17))) | (~((~point_neighbourhood(tptp_fun_E_2(lim_points_of_net(A!16, B!17), B!17, A!16), A!16, tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(lim_points_of_net(A!16, B!17), B!17, A!16)))))) | (~(in(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), lim_points_of_net(A!16, B!17)) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (lim_points_of_net(A!16, B!17) = lim_points_of_net(A!16, B!17)))) | (~((~(lim_points_of_net(A!16, B!17) = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) | ((~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) | ((~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), lim_points_of_net(A!16, B!17))) | (~((~point_neighbourhood(tptp_fun_E_2(lim_points_of_net(A!16, B!17), B!17, A!16), A!16, tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(lim_points_of_net(A!16, B!17), B!17, A!16)))))) | (~(in(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), lim_points_of_net(A!16, B!17)) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (lim_points_of_net(A!16, B!17) = lim_points_of_net(A!16, B!17)))) | (~((~(lim_points_of_net(A!16, B!17) = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) | (~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) | ((~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), lim_points_of_net(A!16, B!17))) | (~((~point_neighbourhood(tptp_fun_E_2(lim_points_of_net(A!16, B!17), B!17, A!16), A!16, tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(lim_points_of_net(A!16, B!17), B!17, A!16)))))) | (~(in(tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16), lim_points_of_net(A!16, B!17)) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(lim_points_of_net(A!16, B!17), B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (lim_points_of_net(A!16, B!17) = lim_points_of_net(A!16, B!17)))) | (~((~(lim_points_of_net(A!16, B!17) = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!16)))) | (~((~((~((~element(tptp_fun_D_1(C, B!17, A!16), the_carrier(A!16))) | (~((~in(tptp_fun_D_1(C, B!17, A!16), C)) | (~((~point_neighbourhood(tptp_fun_E_2(C, B!17, A!16), A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, tptp_fun_E_2(C, B!17, A!16)))))) | (~(in(tptp_fun_D_1(C, B!17, A!16), C) | ![E: $i] : ((~point_neighbourhood(E, A!16, tptp_fun_D_1(C, B!17, A!16))) | is_eventually_in(A!16, B!17, E)))))) | (C = lim_points_of_net(A!16, B!17)))) | (~((~(C = lim_points_of_net(A!16, B!17))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, C)) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, C) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16))))))))))))))) | (~element(lim_points_of_net(A!16, B!17), powerset(the_carrier(A!16)))) | ![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 (![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[88, 82, 62])).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~element(C!18, the_carrier(A!16))) | (~in(C!18, lim_points_of_net(A!16, B!17))))),
% 0.19/0.48 inference(and_elim,[status(thm)],[15])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (element(C!18, the_carrier(A!16))),
% 0.19/0.48 inference(or_elim,[status(thm)],[90])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 (((~![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))) | ((~element(C!18, the_carrier(A!16))) | (~((~((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E)))) | (~(in(C!18, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(C!18, B!17, A!16)))))))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))) | (~element(C!18, the_carrier(A!16))) | (~((~((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E)))) | (~(in(C!18, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(C!18, B!17, A!16)))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 ((~![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))) | ((~element(C!18, the_carrier(A!16))) | (~((~((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E)))) | (~(in(C!18, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(C!18, B!17, A!16)))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 ((~![D: $i] : ((~element(D, the_carrier(A!16))) | (~((~((~in(D, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, D)) | is_eventually_in(A!16, B!17, E)))) | (~(in(D, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(D, B!17, A!16), A!16, D)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(D, B!17, A!16)))))))))) | (~element(C!18, the_carrier(A!16))) | (~((~((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E)))) | (~(in(C!18, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(C!18, B!17, A!16))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.48 tff(95,plain,
% 0.19/0.48 (~((~((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E)))) | (~(in(C!18, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(C!18, B!17, A!16)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[94, 91, 89])).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (((~((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E)))) | (~(in(C!18, lim_points_of_net(A!16, B!17)) | (~((~point_neighbourhood(tptp_fun_E_0(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_E_0(C!18, B!17, A!16))))))) | ((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 ((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (in(C!18, lim_points_of_net(A!16, B!17))),
% 0.19/0.48 inference(or_elim,[status(thm)],[90])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 ((~((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E)))) | (~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 ((~((~in(C!18, lim_points_of_net(A!16, B!17))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E)))) | ![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (^[A: $i] : refl((empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 (^[A: $i] : rewrite((empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A)) <=> (~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(B)) & net_str(B, A)) <=> (~(empty_carrier(B) | (~net_str(B, A))))), ((~((~empty_carrier(B)) & net_str(B, A))) <=> (~(~(empty_carrier(B) | (~net_str(B, A))))))), rewrite((~(~(empty_carrier(B) | (~net_str(B, A))))) <=> (empty_carrier(B) | (~net_str(B, A)))), ((~((~empty_carrier(B)) & net_str(B, A))) <=> (empty_carrier(B) | (~net_str(B, A))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~element(C, the_carrier(A))) | (((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))) & (is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))) <=> ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))), (![C: $i] : ((~element(C, the_carrier(A))) | (((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))) & (is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))), (((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))) & (is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))) <=> ((empty_carrier(B) | (~net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))), rewrite(((empty_carrier(B) | (~net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))) <=> (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))), (((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))) & (is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))) <=> (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))))), (![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))) & (is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))) <=> ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))) & (is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))) <=> ((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))))), rewrite(((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))) & (is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))) & (is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A))))))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D))) <=> (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))), ((element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D)))) <=> (element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))))), rewrite((element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) <=> ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))), ((element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D)))) <=> ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))))), (![C: $i] : (element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D)))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))))), ((((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D))))) <=> (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))))), rewrite((((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))) <=> ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))))), ((((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D))))) <=> ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))))))), (![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D))))) <=> ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D)))))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 (![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.49 tff(112,axiom,(![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (((~empty_carrier(B)) & net_str(B, A)) => ![C: $i] : (element(C, the_carrier(A)) => (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : (point_neighbourhood(D, A, C) => is_often_in(A, B, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_waybel_9')).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (is_a_cluster_point_of_netstr(A, B, C) <=> ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.19/0.49 tff(115,plain,(
% 0.19/0.49 ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & net_str(B, A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D))) & (is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[114])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))) | (empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A!16), A!16, C)) | is_often_in(A!16, B, tptp_fun_D_3(C, B, A!16)))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))) | empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A!16), A!16, C)) | is_often_in(A!16, B, tptp_fun_D_3(C, B, A!16)))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))) | (empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A!16), A!16, C)) | is_often_in(A!16, B, tptp_fun_D_3(C, B, A!16)))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~((~is_a_cluster_point_of_netstr(A, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A, C)) | is_often_in(A, B, D)))) | (~(is_a_cluster_point_of_netstr(A, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A), A, C)) | is_often_in(A, B, tptp_fun_D_3(C, B, A)))))))))))) | empty_carrier(A!16) | (~top_str(A!16)) | (~topological_space(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A!16), A!16, C)) | is_often_in(A!16, B, tptp_fun_D_3(C, B, A!16))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 (![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A!16), A!16, C)) | is_often_in(A!16, B, tptp_fun_D_3(C, B, A!16))))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[120, 117, 18, 17, 16])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 (((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A!16), A!16, C)) | is_often_in(A!16, B, tptp_fun_D_3(C, B, A!16))))))))))) | (empty_carrier(B!17) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B!17, A!16), A!16, C)) | is_often_in(A!16, B!17, tptp_fun_D_3(C, B!17, A!16))))))))))) <=> ((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A!16), A!16, C)) | is_often_in(A!16, B, tptp_fun_D_3(C, B, A!16))))))))))) | empty_carrier(B!17) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B!17, A!16), A!16, C)) | is_often_in(A!16, B!17, tptp_fun_D_3(C, B!17, A!16))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 ((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A!16), A!16, C)) | is_often_in(A!16, B, tptp_fun_D_3(C, B, A!16))))))))))) | (empty_carrier(B!17) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B!17, A!16), A!16, C)) | is_often_in(A!16, B!17, tptp_fun_D_3(C, B!17, A!16))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 ((~![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B, A!16), A!16, C)) | is_often_in(A!16, B, tptp_fun_D_3(C, B, A!16))))))))))) | empty_carrier(B!17) | (~net_str(B!17, A!16)) | ![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B!17, A!16), A!16, C)) | is_often_in(A!16, B!17, tptp_fun_D_3(C, B!17, A!16)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.49 tff(125,plain,
% 0.19/0.49 (![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B!17, A!16), A!16, C)) | is_often_in(A!16, B!17, tptp_fun_D_3(C, B!17, A!16)))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[124, 51, 48, 121])).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 (((~![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B!17, A!16), A!16, C)) | is_often_in(A!16, B!17, tptp_fun_D_3(C, B!17, A!16)))))))))) | ((~element(C!18, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C!18)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C!18)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B!17, A!16), A!16, C)) | is_often_in(A!16, B!17, tptp_fun_D_3(C, B!17, A!16)))))))))) | (~element(C!18, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C!18)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C!18)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 ((~![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B!17, A!16), A!16, C)) | is_often_in(A!16, B!17, tptp_fun_D_3(C, B!17, A!16)))))))))) | ((~element(C!18, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C!18)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C!18)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 ((~![C: $i] : ((~element(C, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C) | (~((~point_neighbourhood(tptp_fun_D_3(C, B!17, A!16), A!16, C)) | is_often_in(A!16, B!17, tptp_fun_D_3(C, B!17, A!16)))))))))) | (~element(C!18, the_carrier(A!16))) | (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C!18)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C!18)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 (~((~((~is_a_cluster_point_of_netstr(A!16, B!17, C!18)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C!18)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[128, 91, 125])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (((~((~is_a_cluster_point_of_netstr(A!16, B!17, C!18)) | ![D: $i] : ((~point_neighbourhood(D, A!16, C!18)) | is_often_in(A!16, B!17, D)))) | (~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))))))) | (is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (~is_a_cluster_point_of_netstr(A!16, B!17, C!18)),
% 0.19/0.49 inference(or_elim,[status(thm)],[90])).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 ((~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))))) | is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 ((~(is_a_cluster_point_of_netstr(A!16, B!17, C!18) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))))) | (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.49 tff(135,plain,
% 0.19/0.49 (~((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[134, 131])).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 (((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))) | (~is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 (~is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (^[A: $i] : refl((one_sorted_str(A) | (~top_str(A))) <=> (one_sorted_str(A) | (~top_str(A))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 (^[A: $i] : rewrite((top_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~top_str(A))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 (![A: $i] : (top_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[141])).
% 0.19/0.49 tff(143,axiom,(![A: $i] : (top_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 0.19/0.49 tff(144,plain,
% 0.19/0.49 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.49 tff(145,plain,
% 0.19/0.49 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.19/0.49 tff(146,plain,(
% 0.19/0.49 ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[145])).
% 0.19/0.49 tff(147,plain,
% 0.19/0.49 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.19/0.49 tff(148,plain,
% 0.19/0.49 (((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!16) | (~top_str(A!16)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!16) | (~top_str(A!16)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(149,plain,
% 0.19/0.49 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!16) | (~top_str(A!16)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(150,plain,
% 0.19/0.49 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!16) | (~top_str(A!16))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.49 tff(151,plain,
% 0.19/0.49 (one_sorted_str(A!16)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[150, 147, 16])).
% 0.19/0.49 tff(152,plain,
% 0.19/0.49 (^[A: $i] : rewrite((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(153,plain,
% 0.19/0.49 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[152])).
% 0.19/0.49 tff(154,plain,
% 0.19/0.49 (^[A: $i] : refl((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 (^[A: $i] : rewrite((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[157, 155])).
% 0.19/0.49 tff(159,plain,
% 0.19/0.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)) <=> (~(empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))))), ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) <=> (~(~(empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))))))), rewrite((~(~(empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))))) <=> (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)))), ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) <=> (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))))), (((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))) <=> ((empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))), rewrite(((empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))) <=> (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))), (((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))) <=> (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))))), (![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))) <=> ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))) <=> ((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))))), rewrite(((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B)))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[159])).
% 0.19/0.49 tff(161,plain,
% 0.19/0.49 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(162,plain,
% 0.19/0.49 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) <=> ((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B))), (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) <=> (((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B)) & net_str(B, A)))), rewrite((((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B)) & net_str(B, A)) <=> ((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))), (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) <=> ((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)))), quant_intro(proof_bind(^[C: $i] : rewrite((is_eventually_in(A, B, C) => is_often_in(A, B, C)) <=> ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))), (![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C)) <=> ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))), ((((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C))) <=> (((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)) => ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))), rewrite((((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A)) => ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))) <=> ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))), ((((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C))) <=> ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))))), (![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C))) <=> ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C)))) <=> (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))))), rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C)))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(163,plain,
% 0.19/0.50 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[162])).
% 0.19/0.50 tff(164,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (((((~empty_carrier(B)) & transitive_relstr(B)) & directed_relstr(B)) & net_str(B, A)) => ![C: $i] : (is_eventually_in(A, B, C) => is_often_in(A, B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_yellow_6')).
% 0.19/0.50 tff(165,plain,
% 0.19/0.50 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.50 tff(166,plain,
% 0.19/0.50 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.19/0.50 tff(167,plain,(
% 0.19/0.50 ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~((~empty_carrier(B)) & transitive_relstr(B) & directed_relstr(B) & net_str(B, A))) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[166])).
% 0.19/0.50 tff(168,plain,
% 0.19/0.50 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.19/0.50 tff(169,plain,
% 0.19/0.50 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C)) | (~transitive_relstr(B)) | (~directed_relstr(B))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[168, 158])).
% 0.19/0.50 tff(170,plain,
% 0.19/0.50 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[169, 153])).
% 0.19/0.50 tff(171,plain,
% 0.19/0.50 (((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))) | (empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16))))) <=> ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))) | empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(172,plain,
% 0.19/0.50 ((empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)))) <=> (empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(173,plain,
% 0.19/0.50 (((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))) | (empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C))))) <=> ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))) | (empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[172])).
% 0.19/0.50 tff(174,plain,
% 0.19/0.50 (((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))) | (empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C))))) <=> ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))) | empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[173, 171])).
% 0.19/0.50 tff(175,plain,
% 0.19/0.50 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))) | (empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A!16)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(176,plain,
% 0.19/0.50 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : (empty_carrier(B) | (~net_str(B, A)) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A, B, C)) | is_often_in(A, B, C))))) | empty_carrier(A!16) | (~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.50 tff(177,plain,
% 0.19/0.50 ((~one_sorted_str(A!16)) | ![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[176, 170, 18])).
% 0.19/0.50 tff(178,plain,
% 0.19/0.50 (![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[177, 151])).
% 0.19/0.50 tff(179,plain,
% 0.19/0.50 (((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))) | (empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C)))) <=> ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))) | empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(180,plain,
% 0.19/0.50 ((empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C)) | (~net_str(B!17, A!16))) <=> (empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(181,plain,
% 0.19/0.50 (((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))) | (empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C)) | (~net_str(B!17, A!16)))) <=> ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))) | (empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[180])).
% 0.19/0.50 tff(182,plain,
% 0.19/0.50 (((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))) | (empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C)) | (~net_str(B!17, A!16)))) <=> ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))) | empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[181, 179])).
% 0.19/0.50 tff(183,plain,
% 0.19/0.50 ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))) | (empty_carrier(B!17) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C)) | (~net_str(B!17, A!16)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(184,plain,
% 0.19/0.50 ((~![B: $i] : (empty_carrier(B) | (~transitive_relstr(B)) | (~directed_relstr(B)) | ![C: $i] : ((~is_eventually_in(A!16, B, C)) | is_often_in(A!16, B, C)) | (~net_str(B, A!16)))) | empty_carrier(B!17) | (~net_str(B!17, A!16)) | (~transitive_relstr(B!17)) | (~directed_relstr(B!17)) | ![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.50 tff(185,plain,
% 0.19/0.50 (![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[184, 51, 50, 49, 48, 178])).
% 0.19/0.50 tff(186,plain,
% 0.19/0.50 (((~![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C))) | ((~is_eventually_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))) <=> ((~![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C))) | (~is_eventually_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(187,plain,
% 0.19/0.50 ((~![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C))) | ((~is_eventually_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(188,plain,
% 0.19/0.50 ((~![C: $i] : ((~is_eventually_in(A!16, B!17, C)) | is_often_in(A!16, B!17, C))) | (~is_eventually_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.50 tff(189,plain,
% 0.19/0.50 (~is_eventually_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[188, 185, 137])).
% 0.19/0.50 tff(190,plain,
% 0.19/0.50 (((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_often_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))) | point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(191,plain,
% 0.19/0.50 (point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[190, 135])).
% 0.19/0.50 tff(192,plain,
% 0.19/0.50 (((~![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E))) | ((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))) <=> ((~![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E))) | (~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(193,plain,
% 0.19/0.50 ((~![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E))) | ((~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(194,plain,
% 0.19/0.50 ((~![E: $i] : ((~point_neighbourhood(E, A!16, C!18)) | is_eventually_in(A!16, B!17, E))) | (~point_neighbourhood(tptp_fun_D_3(C!18, B!17, A!16), A!16, C!18)) | is_eventually_in(A!16, B!17, tptp_fun_D_3(C!18, B!17, A!16))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.50 tff(195,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[194, 191, 189, 101])).
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------