# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3))))=>(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1)))))))),file('i/f/arithmetic/MODEQ__PLUS__CONG', ch4s_arithmetics_MODEQu_u_PLUSu_u_CONG)).
fof(2, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/arithmetic/MODEQ__PLUS__CONG', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(26, 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))))=>![X26]:![X27]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X26),s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X27),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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X26),s(t_h4s_nums_num,X27))),s(t_h4s_nums_num,X5)))),file('i/f/arithmetic/MODEQ__PLUS__CONG', ah4s_arithmetics_MODu_u_PLUS)).
fof(27, axiom,![X5]:(~(s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_0))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5))))),file('i/f/arithmetic/MODEQ__PLUS__CONG', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(28, axiom,![X5]:![X24]:![X25]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5))))=>(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X24))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X5))))),file('i/f/arithmetic/MODEQ__PLUS__CONG', ah4s_arithmetics_MODEQu_u_NONZEROu_u_MODEQUALITY)).
fof(29, axiom,![X5]:![X24]:![X25]:(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X24))))<=>((s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,X24))|(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X5)))))),file('i/f/arithmetic/MODEQ__PLUS__CONG', ah4s_arithmetics_MODEQu_u_THM)).
# SZS output end CNFRefutation
