# 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(10, axiom,![X1]:![X2]:![X12]:![X14]:?[X6]:(p(s(t_bool,h4s_primu_u_recs_simpu_u_recu_u_rel(s(t_fun(t_h4s_nums_num,X1),X6),s(X1,X2),s(t_fun(X1,X1),X14),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))))))&s(X1,h4s_primu_u_recs_simpu_u_rec(s(X1,X2),s(t_fun(X1,X1),X14),s(t_h4s_nums_num,X12)))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X6),s(t_h4s_nums_num,X12)))),file('i/f/prim_rec/SIMP__REC__THM_c0', ah4s_primu_u_recs_SIMPu_u_REC0)).
fof(11, axiom,![X1]:![X2]:![X12]:![X15]:![X3]:(p(s(t_bool,h4s_primu_u_recs_simpu_u_recu_u_rel(s(t_fun(t_h4s_nums_num,X1),X15),s(X1,X2),s(t_fun(X1,X1),X3),s(t_h4s_nums_num,X12))))<=>(s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X15),s(t_h4s_nums_num,h4s_nums_0)))=s(X1,X2)&![X13]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X12))))=>s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X15),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))))=s(X1,happ(s(t_fun(X1,X1),X3),s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X15),s(t_h4s_nums_num,X13)))))))),file('i/f/prim_rec/SIMP__REC__THM_c0', ah4s_primu_u_recs_SIMPu_u_RECu_u_REL0)).
# SZS output end CNFRefutation
