# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:![X8]:![X9]:((s(t_h4s_sums_sum(X1,X2),X9)=s(t_h4s_sums_sum(X1,X2),X8)&(![X10]:(s(t_h4s_sums_sum(X1,X2),X8)=s(t_h4s_sums_sum(X1,X2),h4s_sums_inl(s(X1,X10)))=>s(X3,happ(s(t_fun(X1,X3),X7),s(X1,X10)))=s(X3,happ(s(t_fun(X1,X3),X6),s(X1,X10))))&![X11]:(s(t_h4s_sums_sum(X1,X2),X8)=s(t_h4s_sums_sum(X1,X2),h4s_sums_inr(s(X2,X11)))=>s(X3,happ(s(t_fun(X2,X3),X5),s(X2,X11)))=s(X3,happ(s(t_fun(X2,X3),X4),s(X2,X11))))))=>s(X3,h4s_sums_sumu_u_case(s(t_h4s_sums_sum(X1,X2),X9),s(t_fun(X1,X3),X7),s(t_fun(X2,X3),X5)))=s(X3,h4s_sums_sumu_u_case(s(t_h4s_sums_sum(X1,X2),X8),s(t_fun(X1,X3),X6),s(t_fun(X2,X3),X4)))),file('i/f/sum/sum__case__cong', ch4s_sums_sumu_u_caseu_u_cong)).
fof(6, axiom,![X1]:![X2]:![X16]:(?[X10]:s(t_h4s_sums_sum(X1,X2),X16)=s(t_h4s_sums_sum(X1,X2),h4s_sums_inl(s(X1,X10)))|?[X11]:s(t_h4s_sums_sum(X1,X2),X16)=s(t_h4s_sums_sum(X1,X2),h4s_sums_inr(s(X2,X11)))),file('i/f/sum/sum__case__cong', ah4s_sums_sumu_u_CASES)).
fof(7, axiom,![X2]:![X3]:![X1]:![X10]:![X5]:![X7]:s(X3,h4s_sums_sumu_u_case(s(t_h4s_sums_sum(X1,X2),h4s_sums_inl(s(X1,X10))),s(t_fun(X1,X3),X7),s(t_fun(X2,X3),X5)))=s(X3,happ(s(t_fun(X1,X3),X7),s(X1,X10))),file('i/f/sum/sum__case__cong', ah4s_sums_sumu_u_caseu_u_defu_c0)).
fof(8, axiom,![X1]:![X3]:![X2]:![X11]:![X5]:![X7]:s(X3,h4s_sums_sumu_u_case(s(t_h4s_sums_sum(X1,X2),h4s_sums_inr(s(X2,X11))),s(t_fun(X1,X3),X7),s(t_fun(X2,X3),X5)))=s(X3,happ(s(t_fun(X2,X3),X5),s(X2,X11))),file('i/f/sum/sum__case__cong', ah4s_sums_sumu_u_caseu_u_defu_c1)).
# SZS output end CNFRefutation
