# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(X1),X4))),s(t_fun(X1,t_bool),X3))))&p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(X1),X4))),s(t_fun(X1,t_bool),X2)))))=>p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(X1),X4))),s(t_fun(X1,t_bool),h4s_topologys_reu_u_intersect(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))))),file('i/f/topology/TOPOLOGY_c2', ch4s_topologys_TOPOLOGYu_c2)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/topology/TOPOLOGY_c2', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/topology/TOPOLOGY_c2', aHLu_FALSITY)).
fof(49, axiom,![X1]:![X19]:![X20]:(![X3]:(s(X1,X3)=s(X1,X19)=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X3)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X19))))),file('i/f/topology/TOPOLOGY_c2', ah4s_bools_UNWINDu_u_FORALLu_u_THM2)).
fof(65, axiom,![X1]:![X4]:(p(s(t_bool,happ(s(t_fun(t_fun(t_fun(X1,t_bool),t_bool),t_bool),h4s_topologys_istopology),s(t_fun(t_fun(X1,t_bool),t_bool),X4))))<=>(p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))&(p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_univ))))&(![X29]:![X30]:((p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X4),s(t_fun(X1,t_bool),X29))))&p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X4),s(t_fun(X1,t_bool),X30)))))=>p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X4),s(t_fun(X1,t_bool),h4s_topologys_reu_u_intersect(s(t_fun(X1,t_bool),X29),s(t_fun(X1,t_bool),X30)))))))&![X18]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(t_fun(X1,t_bool),t_bool),X18),s(t_fun(t_fun(X1,t_bool),t_bool),X4))))=>p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_bigunion(s(t_fun(t_fun(X1,t_bool),t_bool),X18))))))))))),file('i/f/topology/TOPOLOGY_c2', ah4s_topologys_istopology0)).
fof(73, axiom,![X1]:![X29]:s(t_h4s_topologys_topology(X1),h4s_topologys_topology0(s(t_fun(t_fun(X1,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(X1),X29)))))=s(t_h4s_topologys_topology(X1),X29),file('i/f/topology/TOPOLOGY_c2', ah4s_topologys_topologyu_u_tybiju_c0)).
fof(74, axiom,![X1]:![X15]:(p(s(t_bool,happ(s(t_fun(t_fun(t_fun(X1,t_bool),t_bool),t_bool),h4s_topologys_istopology),s(t_fun(t_fun(X1,t_bool),t_bool),X15))))<=>s(t_fun(t_fun(X1,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(X1),h4s_topologys_topology0(s(t_fun(t_fun(X1,t_bool),t_bool),X15)))))=s(t_fun(t_fun(X1,t_bool),t_bool),X15)),file('i/f/topology/TOPOLOGY_c2', ah4s_topologys_topologyu_u_tybiju_c1)).
fof(78, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/topology/TOPOLOGY_c2', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
