# 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))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2d(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)))),file('i/f/arithmetic/SUB__MOD', ch4s_arithmetics_SUBu_u_MOD)).
fof(17, axiom,![X8]:![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))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/SUB__MOD', ah4s_arithmetics_ADDu_u_MODULUSu_c1)).
fof(18, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/SUB__MOD', ah4s_arithmetics_ADDu_u_SYM)).
fof(19, axiom,![X12]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,X13),file('i/f/arithmetic/SUB__MOD', ah4s_arithmetics_ADDu_u_SUB)).
fof(20, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))<=>?[X11]:s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X11)))),file('i/f/arithmetic/SUB__MOD', ah4s_arithmetics_LESSu_u_EQu_u_EXISTS)).
fof(33, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUB__MOD', aHLu_TRUTH)).
fof(35, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/SUB__MOD', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
