# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,X1))))))<=>![X3]:((s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,h4s_nums_0)))))&(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3)))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X3))))))),file('i/f/arithmetic/PRE__ELIM__THM', ch4s_arithmetics_PREu_u_ELIMu_u_THM)).
fof(35, axiom,![X3]:(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/PRE__ELIM__THM', ah4s_arithmetics_numu_u_CASES)).
fof(36, axiom,![X1]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/PRE__ELIM__THM', ah4s_nums_NOTu_u_SUC)).
fof(50, axiom,![X3]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3)))))=s(t_h4s_nums_num,X3),file('i/f/arithmetic/PRE__ELIM__THM', ah4s_primu_u_recs_PRE0u_c1)).
fof(56, axiom,s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/PRE__ELIM__THM', ah4s_primu_u_recs_PRE0u_c0)).
# SZS output end CNFRefutation
