# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(10, axiom,![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/arithmetic/MOD__TIMES2', ah4s_arithmetics_MULTu_u_COMM)).
fof(12, axiom,![X9]:![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10))))),file('i/f/arithmetic/MOD__TIMES2', ah4s_arithmetics_LEFTu_u_ADDu_u_DISTRIB)).
fof(13, axiom,![X9]:![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X9))),file('i/f/arithmetic/MOD__TIMES2', ah4s_arithmetics_MULTu_u_ASSOC)).
fof(14, axiom,![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10))))=>![X12]:(s(t_h4s_nums_num,X12)=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,X12),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X10)))))),file('i/f/arithmetic/MOD__TIMES2', ah4s_arithmetics_DIVISION)).
fof(15, axiom,![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10))))=>![X13]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X10)))),file('i/f/arithmetic/MOD__TIMES2', ah4s_arithmetics_MODu_u_TIMES)).
fof(16, conjecture,![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10))))=>![X15]:![X12]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10))))),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,X10)))),file('i/f/arithmetic/MOD__TIMES2', ch4s_arithmetics_MODu_u_TIMES2)).
# SZS output end CNFRefutation
