# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:?[X7]:((p(s(t_bool,X7))<=>s(X2,X6)=s(X2,X4))&s(X1,happ(s(t_fun(X2,X1),happ(s(t_fun(t_fun(X2,X1),t_fun(X2,X1)),h4s_combins_update(s(X2,X6),s(X1,X5))),s(t_fun(X2,X1),X3))),s(X2,X4)))=s(X1,h4s_bools_cond(s(t_bool,X7),s(X1,X5),s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X4)))))),file('i/f/update/APPLY__UPDATE__THM', ch4s_updates_APPLYu_u_UPDATEu_u_THM)).
fof(41, axiom,![X1]:![X2]:![X5]:![X6]:![X11]:![X27]:?[X7]:((p(s(t_bool,X7))<=>s(X2,X6)=s(X2,X27))&s(X1,happ(s(t_fun(X2,X1),happ(s(t_fun(t_fun(X2,X1),t_fun(X2,X1)),h4s_combins_update(s(X2,X6),s(X1,X5))),s(t_fun(X2,X1),X11))),s(X2,X27)))=s(X1,h4s_bools_cond(s(t_bool,X7),s(X1,X5),s(X1,happ(s(t_fun(X2,X1),X11),s(X2,X27)))))),file('i/f/update/APPLY__UPDATE__THM', ah4s_combins_UPDATEu_u_def)).
fof(60, axiom,p(s(t_bool,t)),file('i/f/update/APPLY__UPDATE__THM', aHLu_TRUTH)).
fof(61, axiom,~(p(s(t_bool,f0))),file('i/f/update/APPLY__UPDATE__THM', aHLu_FALSITY)).
fof(62, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)|s(t_bool,X12)=s(t_bool,f0)),file('i/f/update/APPLY__UPDATE__THM', aHLu_BOOLu_CASES)).
fof(77, axiom,(p(s(t_bool,f0))<=>![X12]:p(s(t_bool,X12))),file('i/f/update/APPLY__UPDATE__THM', ah4s_bools_Fu_u_DEF)).
fof(81, axiom,![X12]:(s(t_bool,X12)=s(t_bool,f0)<=>~(p(s(t_bool,X12)))),file('i/f/update/APPLY__UPDATE__THM', ah4s_bools_EQu_u_CLAUSESu_c3)).
# SZS output end CNFRefutation
