# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/MODEQ__REFL', ch4s_arithmetics_MODEQu_u_REFL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MODEQ__REFL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MODEQ__REFL', aHLu_FALSITY)).
fof(9, axiom,![X2]:(~(s(t_h4s_nums_num,X2)=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,X2))))),file('i/f/arithmetic/MODEQ__REFL', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(11, axiom,![X2]:![X6]:![X7]:(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X6))))<=>((s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,X6))|(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/MODEQ__REFL', ah4s_arithmetics_MODEQu_u_THM)).
fof(12, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/MODEQ__REFL', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
