# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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))))=>![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/DIV__LESS__EQ', ch4s_arithmetics_DIVu_u_LESSu_u_EQ)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/DIV__LESS__EQ', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/DIV__LESS__EQ', aHLu_FALSITY)).
fof(5, axiom,![X1]:![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1))))=>~(s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,X1))),file('i/f/arithmetic/DIV__LESS__EQ', ah4s_primu_u_recs_LESSu_u_NOTu_u_EQ)).
fof(6, axiom,![X1]:![X4]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/DIV__LESS__EQ', ah4s_arithmetics_LESSu_u_EQu_u_ADD)).
fof(7, axiom,![X5]:![X1]:![X4]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X5)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X5))),file('i/f/arithmetic/DIV__LESS__EQ', ah4s_arithmetics_ADDu_u_ASSOC)).
fof(8, axiom,![X4]:(s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/DIV__LESS__EQ', ah4s_arithmetics_numu_u_CASES)).
fof(9, axiom,![X1]:![X4]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/DIV__LESS__EQ', ah4s_arithmetics_MULTu_u_CLAUSESu_c5)).
fof(10, 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))))=>![X2]:(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,h4s_arithmetics_div(s(t_h4s_nums_num,X2),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,X2),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,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/DIV__LESS__EQ', ah4s_arithmetics_DIVISION)).
fof(11, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/DIV__LESS__EQ', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
