# 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_mod(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,X5)))))))),file('i/f/arithmetic/MOD__P', ch4s_arithmetics_MODu_u_P)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MOD__P', aHLu_TRUTH)).
fof(8, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/arithmetic/MOD__P', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X5]:![X11]:![X4]:(?[X1]:(s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X11))),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,X11)))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,X5)),file('i/f/arithmetic/MOD__P', ah4s_arithmetics_MODu_u_UNIQUE)).
fof(11, axiom,![X11]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11))))=>![X4]:(s(t_h4s_nums_num,X4)=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,X4),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X11)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X11)))))),file('i/f/arithmetic/MOD__P', ah4s_arithmetics_DIVISION)).
# SZS output end CNFRefutation
