# 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,X2))))=>p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__MOD', ch4s_arithmetics_MODEQu_u_MOD)).
fof(34, axiom,![X2]:![X20]:![X21]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X20))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MODEQ__MOD', ah4s_arithmetics_MODEQu_u_NONZEROu_u_MODEQUALITY)).
fof(40, axiom,![X7]:![X1]:![X2]:s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X7)))=s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X1))),file('i/f/arithmetic/MODEQ__MOD', ah4s_arithmetics_MODEQu_u_SYM)).
fof(43, axiom,![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>![X29]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X29),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X29),s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/MODEQ__MOD', ah4s_arithmetics_MODu_u_MOD)).
# SZS output end CNFRefutation
