# 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),X2),s(t_h4s_extreals_extreal,X3))))=>?[X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X1),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,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X2))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X1))))))),file('i/f/extreal/sup__le__sup__imp', ch4s_extreals_supu_u_leu_u_supu_u_imp)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/extreal/sup__le__sup__imp', aHLu_FALSITY)).
fof(22, axiom,![X16]:![X4]:![X3]:((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,X4),s(t_h4s_extreals_extreal,X16)))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X16))))),file('i/f/extreal/sup__le__sup__imp', ah4s_extreals_leu_u_trans)).
fof(23, axiom,![X3]:![X2]:(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,X3),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X2))))))),file('i/f/extreal/sup__le__sup__imp', ah4s_extreals_leu_u_supu_u_imp)).
fof(24, axiom,![X3]:![X2]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X2))),s(t_h4s_extreals_extreal,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,X4),s(t_h4s_extreals_extreal,X3)))))),file('i/f/extreal/sup__le__sup__imp', ah4s_extreals_supu_u_le)).
fof(27, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/extreal/sup__le__sup__imp', aHLu_BOOLu_CASES)).
fof(29, axiom,p(s(t_bool,t)),file('i/f/extreal/sup__le__sup__imp', aHLu_TRUTH)).
fof(31, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/extreal/sup__le__sup__imp', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
