# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_inf(s(t_fun(t_h4s_extreals_extreal,t_bool),X2)))=s(t_h4s_extreals_extreal,X1)<=>(![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X2),s(t_h4s_extreals_extreal,X3))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X3)))))&![X3]:(![X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X2),s(t_h4s_extreals_extreal,X4))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X4)))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X1))))))),file('i/f/extreal/inf__eq', ch4s_extreals_infu_u_eq)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/extreal/inf__eq', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(19, axiom,![X3]:![X1]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),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,X1)))))<=>s(t_h4s_extreals_extreal,X1)=s(t_h4s_extreals_extreal,X3)),file('i/f/extreal/inf__eq', ah4s_extreals_leu_u_antisym)).
fof(24, axiom,![X1]:![X2]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_inf(s(t_fun(t_h4s_extreals_extreal,t_bool),X2))))))<=>![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X2),s(t_h4s_extreals_extreal,X3))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X3)))))),file('i/f/extreal/inf__eq', ah4s_extreals_leu_u_inf)).
fof(25, axiom,![X1]:![X2]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_inf(s(t_fun(t_h4s_extreals_extreal,t_bool),X2))),s(t_h4s_extreals_extreal,X1))))<=>![X3]:(![X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X2),s(t_h4s_extreals_extreal,X4))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X4)))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X1)))))),file('i/f/extreal/inf__eq', ah4s_extreals_infu_u_le)).
# SZS output end CNFRefutation
