# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/MOD__ONE', ch4s_arithmetics_MODu_u_ONE)).
fof(31, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/MOD__ONE', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(33, axiom,![X4]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4)))))),file('i/f/arithmetic/MOD__ONE', ah4s_primu_u_recs_LESSu_u_0)).
fof(35, axiom,![X4]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/MOD__ONE', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(42, axiom,![X4]:![X15]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4))))))<=>(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,X4)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X4)))))),file('i/f/arithmetic/MOD__ONE', ah4s_primu_u_recs_LESSu_u_THM)).
fof(54, axiom,![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X4))))=>![X1]:(s(t_h4s_nums_num,X1)=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,X1),s(t_h4s_nums_num,X4))),s(t_h4s_nums_num,X4))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X4)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X4))),s(t_h4s_nums_num,X4)))))),file('i/f/arithmetic/MOD__ONE', ah4s_arithmetics_DIVISION)).
fof(72, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/arithmetic/MOD__ONE', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
