# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(X1,h4s_primu_u_recs_simpu_u_rec(s(X1,X2),s(t_fun(X1,X1),X3),s(t_h4s_nums_num,h4s_nums_0)))=s(X1,X2),file('i/f/prim_rec/SIMP__REC__THM_c0', ch4s_primu_u_recs_SIMPu_u_RECu_u_THMu_c0)).
fof(20, axiom,![X1]:![X2]:![X16]:![X17]:?[X18]:(p(s(t_bool,h4s_primu_u_recs_simpu_u_recu_u_rel(s(t_fun(t_h4s_nums_num,X1),X18),s(X1,X2),s(t_fun(X1,X1),X17),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16))))))&s(X1,h4s_primu_u_recs_simpu_u_rec(s(X1,X2),s(t_fun(X1,X1),X17),s(t_h4s_nums_num,X16)))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X18),s(t_h4s_nums_num,X16)))),file('i/f/prim_rec/SIMP__REC__THM_c0', ah4s_primu_u_recs_SIMPu_u_REC0)).
fof(46, axiom,![X1]:![X2]:![X16]:![X25]:![X3]:(p(s(t_bool,h4s_primu_u_recs_simpu_u_recu_u_rel(s(t_fun(t_h4s_nums_num,X1),X25),s(X1,X2),s(t_fun(X1,X1),X3),s(t_h4s_nums_num,X16))))<=>(s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X25),s(t_h4s_nums_num,h4s_nums_0)))=s(X1,X2)&![X20]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X16))))=>s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X25),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X20)))))=s(X1,happ(s(t_fun(X1,X1),X3),s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X25),s(t_h4s_nums_num,X20)))))))),file('i/f/prim_rec/SIMP__REC__THM_c0', ah4s_primu_u_recs_SIMPu_u_RECu_u_REL0)).
# SZS output end CNFRefutation
