# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/lebesgue/max__fn__seq__mono', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/lebesgue/max__fn__seq__mono', aHLu_FALSITY)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/lebesgue/max__fn__seq__mono', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/lebesgue/max__fn__seq__mono', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X8),s(X9,X7)))=s(X9,X8),file('i/f/lebesgue/max__fn__seq__mono', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(11, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/lebesgue/max__fn__seq__mono', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(12, axiom,![X6]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,X6)))),file('i/f/lebesgue/max__fn__seq__mono', ah4s_extreals_leu_u_refl)).
fof(13, axiom,![X10]:![X6]:s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_max(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,X10)))=s(t_h4s_extreals_extreal,h4s_bools_cond(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X6),s(t_h4s_extreals_extreal,X10))),s(t_h4s_extreals_extreal,X10),s(t_h4s_extreals_extreal,X6))),file('i/f/lebesgue/max__fn__seq__mono', ah4s_extreals_extrealu_u_maxu_u_def)).
fof(14, axiom,![X9]:![X6]:![X11]:![X5]:s(t_h4s_extreals_extreal,h4s_lebesgues_maxu_u_fnu_u_seq(s(t_fun(t_h4s_nums_num,t_fun(X9,t_h4s_extreals_extreal)),X5),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))),s(X9,X6)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_max(s(t_h4s_extreals_extreal,h4s_lebesgues_maxu_u_fnu_u_seq(s(t_fun(t_h4s_nums_num,t_fun(X9,t_h4s_extreals_extreal)),X5),s(t_h4s_nums_num,X11),s(X9,X6))),s(t_h4s_extreals_extreal,happ(s(t_fun(X9,t_h4s_extreals_extreal),happ(s(t_fun(t_h4s_nums_num,t_fun(X9,t_h4s_extreals_extreal)),X5),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))))),s(X9,X6))))),file('i/f/lebesgue/max__fn__seq__mono', ah4s_lebesgues_maxu_u_fnu_u_sequ_u_defu_c1)).
fof(15, conjecture,![X9]:![X6]:![X11]:![X5]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_lebesgues_maxu_u_fnu_u_seq(s(t_fun(t_h4s_nums_num,t_fun(X9,t_h4s_extreals_extreal)),X5),s(t_h4s_nums_num,X11),s(X9,X6))),s(t_h4s_extreals_extreal,h4s_lebesgues_maxu_u_fnu_u_seq(s(t_fun(t_h4s_nums_num,t_fun(X9,t_h4s_extreals_extreal)),X5),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))),s(X9,X6)))))),file('i/f/lebesgue/max__fn__seq__mono', ch4s_lebesgues_maxu_u_fnu_u_sequ_u_mono)).
# SZS output end CNFRefutation
