# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:(~(s(X2,X6)=s(X2,X5))=>s(X1,h4s_combins_update(s(X2,X6),s(X1,X3),s(t_fun(X2,X1),X4),s(X2,X5)))=s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X5)))),file('i/f/combin/UPDATE__APPLY_c1', ch4s_combins_UPDATEu_u_APPLYu_c1)).
fof(22, axiom,![X7]:![X8]:![X5]:![X6]:![X3]:![X19]:?[X18]:((p(s(t_bool,X18))<=>s(X8,X6)=s(X8,X19))&s(X7,h4s_combins_update(s(X8,X6),s(X7,X5),s(t_fun(X8,X7),X3),s(X8,X19)))=s(X7,h4s_bools_cond(s(t_bool,X18),s(X7,X5),s(X7,happ(s(t_fun(X8,X7),X3),s(X8,X19)))))),file('i/f/combin/UPDATE__APPLY_c1', ah4s_combins_UPDATEu_u_def)).
fof(24, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/combin/UPDATE__APPLY_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(41, axiom,![X8]:![X9]:![X10]:s(X8,h4s_bools_cond(s(t_bool,f0),s(X8,X10),s(X8,X9)))=s(X8,X9),file('i/f/combin/UPDATE__APPLY_c1', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(42, axiom,![X8]:![X9]:![X10]:s(X8,h4s_bools_cond(s(t_bool,t),s(X8,X10),s(X8,X9)))=s(X8,X10),file('i/f/combin/UPDATE__APPLY_c1', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(47, axiom,![X9]:![X10]:![X5]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X5),s(t_bool,X10),s(t_bool,X9))))<=>((p(s(t_bool,X5))&p(s(t_bool,X10)))|(~(p(s(t_bool,X5)))&p(s(t_bool,X9))))),file('i/f/combin/UPDATE__APPLY_c1', ah4s_bools_CONDu_u_EXPANDu_u_OR)).
# SZS output end CNFRefutation
