# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(X2,h4s_combins_update(s(X1,X5),s(X2,X3),s(t_fun(X1,X2),X4),s(X1,X5)))=s(X2,X3),file('i/f/combin/UPDATE__APPLY_c0', ch4s_combins_UPDATEu_u_APPLYu_c0)).
fof(15, axiom,![X2]:![X1]:![X15]:![X5]:![X3]:![X16]:?[X17]:((p(s(t_bool,X17))<=>s(X1,X5)=s(X1,X16))&s(X2,h4s_combins_update(s(X1,X5),s(X2,X15),s(t_fun(X1,X2),X3),s(X1,X16)))=s(X2,h4s_bools_cond(s(t_bool,X17),s(X2,X15),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X16)))))),file('i/f/combin/UPDATE__APPLY_c0', ah4s_combins_UPDATEu_u_def)).
fof(43, axiom,![X1]:![X11]:![X12]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X12),s(X1,X11)))=s(X1,X12),file('i/f/combin/UPDATE__APPLY_c0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(44, axiom,![X1]:![X20]:![X13]:![X21]:![X3]:![X19]:![X18]:((s(t_bool,X18)=s(t_bool,X19)&((p(s(t_bool,X19))=>s(X1,X3)=s(X1,X21))&(~(p(s(t_bool,X19)))=>s(X1,X13)=s(X1,X20))))=>s(X1,h4s_bools_cond(s(t_bool,X18),s(X1,X3),s(X1,X13)))=s(X1,h4s_bools_cond(s(t_bool,X19),s(X1,X21),s(X1,X20)))),file('i/f/combin/UPDATE__APPLY_c0', ah4s_bools_boolu_u_caseu_u_CONG)).
fof(46, axiom,![X1]:![X11]:![X12]:s(X1,h4s_bools_cond(s(t_bool,f0),s(X1,X12),s(X1,X11)))=s(X1,X11),file('i/f/combin/UPDATE__APPLY_c0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(51, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/combin/UPDATE__APPLY_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
# SZS output end CNFRefutation
