# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:(~(s(X2,X5)=s(X2,X4))=>~(s(t_fun(X1,X2),h4s_combins_update(s(X1,X6),s(X2,X5),s(t_fun(X1,X2),X3)))=s(t_fun(X1,X2),h4s_combins_update(s(X1,X6),s(X2,X4),s(t_fun(X1,X2),X3))))),file('i/f/combin/SAME__KEY__UPDATE__DIFFER', ch4s_combins_SAMEu_u_KEYu_u_UPDATEu_u_DIFFER)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/combin/SAME__KEY__UPDATE__DIFFER', aHLu_FALSITY)).
fof(4, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f0)),file('i/f/combin/SAME__KEY__UPDATE__DIFFER', aHLu_BOOLu_CASES)).
fof(10, axiom,![X13]:![X12]:![X5]:![X6]:![X11]:![X14]:?[X15]:((p(s(t_bool,X15))<=>s(X12,X6)=s(X12,X14))&s(X13,happ(s(t_fun(X12,X13),h4s_combins_update(s(X12,X6),s(X13,X5),s(t_fun(X12,X13),X11))),s(X12,X14)))=s(X13,h4s_bools_cond(s(t_bool,X15),s(X13,X5),s(X13,happ(s(t_fun(X12,X13),X11),s(X12,X14)))))),file('i/f/combin/SAME__KEY__UPDATE__DIFFER', ah4s_combins_UPDATEu_u_def)).
fof(11, axiom,![X12]:![X16]:![X17]:s(X12,h4s_bools_cond(s(t_bool,t),s(X12,X17),s(X12,X16)))=s(X12,X17),file('i/f/combin/SAME__KEY__UPDATE__DIFFER', ah4s_bools_CONDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
