# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,X2))),s(t_h4s_extreals_extreal,X3))))<=>s(t_h4s_extreals_extreal,X3)=s(t_h4s_extreals_extreal,X2))=>![X2]:s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_inf(s(t_fun(t_h4s_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,X2)))))=s(t_h4s_extreals_extreal,X2)),file('i/f/extreal/inf__const', ch4s_extreals_infu_u_const)).
fof(5, axiom,![X2]:![X5]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_inf(s(t_fun(t_h4s_extreals_extreal,t_bool),X5))))))<=>![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X5),s(t_h4s_extreals_extreal,X3))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X3)))))),file('i/f/extreal/inf__const', ah4s_extreals_leu_u_inf)).
fof(6, axiom,![X2]:![X5]:(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_inf(s(t_fun(t_h4s_extreals_extreal,t_bool),X5)))=s(t_h4s_extreals_extreal,X2)<=>(![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X5),s(t_h4s_extreals_extreal,X3))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X3)))))&![X3]:(![X6]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X5),s(t_h4s_extreals_extreal,X6))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X6)))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))))))),file('i/f/extreal/inf__const', ah4s_extreals_infu_u_eq)).
fof(12, axiom,![X4]:![X12]:(~(?[X2]:p(s(t_bool,happ(s(t_fun(X4,t_bool),X12),s(X4,X2)))))<=>![X2]:~(p(s(t_bool,happ(s(t_fun(X4,t_bool),X12),s(X4,X2)))))),file('i/f/extreal/inf__const', ah4s_bools_NOTu_u_EXISTSu_u_THM)).
fof(35, axiom,![X3]:![X2]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X3))))&p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2)))))<=>s(t_h4s_extreals_extreal,X2)=s(t_h4s_extreals_extreal,X3)),file('i/f/extreal/inf__const', ah4s_extreals_leu_u_antisym)).
# SZS output end CNFRefutation
