# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))=>p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__TRANS', ch4s_arithmetics_MODEQu_u_TRANS)).
fof(12, axiom,![X12]:![X13]:((p(s(t_bool,X13))=>p(s(t_bool,X12)))=>((p(s(t_bool,X12))=>p(s(t_bool,X13)))=>s(t_bool,X13)=s(t_bool,X12))),file('i/f/arithmetic/MODEQ__TRANS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(30, axiom,![X4]:![X21]:![X22]:(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X21))))<=>((s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X22)=s(t_h4s_nums_num,X21))|(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X4))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X4)))))),file('i/f/arithmetic/MODEQ__TRANS', ah4s_arithmetics_MODEQu_u_THM)).
fof(34, axiom,![X3]:![X4]:p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X3)))),file('i/f/arithmetic/MODEQ__TRANS', ah4s_arithmetics_MODEQu_u_REFL)).
fof(35, axiom,![X2]:![X3]:![X4]:s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))),file('i/f/arithmetic/MODEQ__TRANS', ah4s_arithmetics_MODEQu_u_SYM)).
fof(42, axiom,![X4]:(~(s(t_h4s_nums_num,X4)=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,X4))))),file('i/f/arithmetic/MODEQ__TRANS', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
# SZS output end CNFRefutation
