# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:((s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,X6)&((s(t_h4s_nums_num,X6)=s(t_h4s_nums_num,h4s_nums_0)=>s(X1,X3)=s(X1,X2))&![X8]:(s(t_h4s_nums_num,X6)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))=>s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X5),s(t_h4s_nums_num,X8)))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X4),s(t_h4s_nums_num,X8))))))=>s(X1,h4s_arithmetics_numu_u_case(s(t_h4s_nums_num,X7),s(X1,X3),s(t_fun(t_h4s_nums_num,X1),X5)))=s(X1,h4s_arithmetics_numu_u_case(s(t_h4s_nums_num,X6),s(X1,X2),s(t_fun(t_h4s_nums_num,X1),X4)))),file('i/f/arithmetic/num__case__cong', ch4s_arithmetics_numu_u_caseu_u_cong)).
fof(6, axiom,![X1]:![X3]:![X5]:s(X1,h4s_arithmetics_numu_u_case(s(t_h4s_nums_num,h4s_nums_0),s(X1,X3),s(t_fun(t_h4s_nums_num,X1),X5)))=s(X1,X3),file('i/f/arithmetic/num__case__cong', ah4s_arithmetics_numu_u_caseu_u_defu_c0)).
fof(7, axiom,![X1]:![X3]:![X8]:![X5]:s(X1,h4s_arithmetics_numu_u_case(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8))),s(X1,X3),s(t_fun(t_h4s_nums_num,X1),X5)))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X5),s(t_h4s_nums_num,X8))),file('i/f/arithmetic/num__case__cong', ah4s_arithmetics_numu_u_caseu_u_defu_c1)).
fof(8, axiom,![X14]:(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0)|?[X8]:s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))),file('i/f/arithmetic/num__case__cong', ah4s_arithmetics_numu_u_CASES)).
# SZS output end CNFRefutation
