# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/extreal/sup__lt', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/extreal/sup__lt', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/extreal/sup__lt', aHLu_BOOLu_CASES)).
fof(6, axiom,![X6]:![X7]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X7),s(t_h4s_extreals_extreal,X6))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X7))))))),file('i/f/extreal/sup__lt', ah4s_extreals_leu_u_supu_u_imp)).
fof(7, axiom,![X6]:![X7]:(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),X7))),s(t_h4s_extreals_extreal,X6))))<=>![X8]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X7),s(t_h4s_extreals_extreal,X8))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X8),s(t_h4s_extreals_extreal,X6)))))),file('i/f/extreal/sup__lt', ah4s_extreals_supu_u_le)).
fof(10, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/extreal/sup__lt', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(56, axiom,![X9]:![X8]:![X6]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,X8))))&p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X8),s(t_h4s_extreals_extreal,X9)))))=>p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,X9))))),file('i/f/extreal/sup__lt', ah4s_extreals_letu_u_trans)).
fof(73, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/extreal/sup__lt', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(91, axiom,![X8]:![X6]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,X8))))&p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X8),s(t_h4s_extreals_extreal,X6)))))<=>s(t_h4s_extreals_extreal,X6)=s(t_h4s_extreals_extreal,X8)),file('i/f/extreal/sup__lt', ah4s_extreals_leu_u_antisym)).
fof(119, axiom,![X8]:![X6]:(p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,X8))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,X8))))),file('i/f/extreal/sup__lt', ah4s_extreals_ltu_u_impu_u_le)).
fof(120, axiom,![X8]:![X6]:(p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,X8))))<=>~(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X8),s(t_h4s_extreals_extreal,X6)))))),file('i/f/extreal/sup__lt', ah4s_extreals_extrealu_u_ltu_u_def)).
fof(133, conjecture,![X8]:![X23]:(?[X6]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X23),s(t_h4s_extreals_extreal,X6))))&p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X8),s(t_h4s_extreals_extreal,X6)))))<=>p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X8),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X23))))))),file('i/f/extreal/sup__lt', ch4s_extreals_supu_u_lt)).
# SZS output end CNFRefutation
