# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))=>(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X2)<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/X__MOD__Y__EQ__X', ch4s_arithmetics_Xu_u_MODu_u_Yu_u_EQu_u_X)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/X__MOD__Y__EQ__X', aHLu_FALSITY)).
fof(6, axiom,![X3]:![X5]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X3))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,X5)),file('i/f/arithmetic/X__MOD__Y__EQ__X', ah4s_arithmetics_LESSu_u_MOD)).
fof(18, axiom,![X3]:![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X3))))),file('i/f/arithmetic/X__MOD__Y__EQ__X', ah4s_arithmetics_MODu_u_LESS)).
fof(46, axiom,![X12]:(s(t_bool,X12)=s(t_bool,f)<=>~(p(s(t_bool,X12)))),file('i/f/arithmetic/X__MOD__Y__EQ__X', ah4s_bools_EQu_u_CLAUSESu_c3)).
# SZS output end CNFRefutation
