# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))<=>![X4]:![X5]:((s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X5)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,X4))))))),file('i/f/arithmetic/DIV__P__UNIV', ch4s_arithmetics_DIVu_u_Pu_u_UNIV)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/DIV__P__UNIV', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/DIV__P__UNIV', aHLu_FALSITY)).
fof(8, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/arithmetic/DIV__P__UNIV', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X4]:![X1]:![X11]:(?[X5]:(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X5)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1)))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X4)),file('i/f/arithmetic/DIV__P__UNIV', ah4s_arithmetics_DIVu_u_UNIQUE)).
fof(11, axiom,![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))=>![X11]:(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/DIV__P__UNIV', ah4s_arithmetics_DIVISION)).
fof(12, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/arithmetic/DIV__P__UNIV', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
