# 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(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MOD__ONE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MOD__ONE', aHLu_FALSITY)).
fof(4, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/arithmetic/MOD__ONE', aHLu_BOOLu_CASES)).
fof(11, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)<=>p(s(t_bool,X2))),file('i/f/arithmetic/MOD__ONE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X5]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/MOD__ONE', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(13, axiom,![X5]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5))))=>![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,X5))),s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,h4s_arithmetics_mod(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,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,X5)))))),file('i/f/arithmetic/MOD__ONE', ah4s_arithmetics_DIVISION)).
fof(14, axiom,![X5]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5)))))),file('i/f/arithmetic/MOD__ONE', ah4s_primu_u_recs_LESSu_u_SUCu_u_REFL)).
fof(15, axiom,![X5]:![X6]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5))))))<=>(s(t_h4s_nums_num,X6)=s(t_h4s_nums_num,X5)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X5)))))),file('i/f/arithmetic/MOD__ONE', ah4s_primu_u_recs_LESSu_u_THM)).
# SZS output end CNFRefutation
