# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_bools_in(s(t_fun(X2,X1),X3),s(t_fun(t_fun(X2,X1),t_bool),h4s_utilu_u_probs_dfunset(s(t_fun(X2,t_bool),X5),s(t_fun(X2,t_fun(X1,t_bool)),X4))))))<=>![X6]:(p(s(t_bool,h4s_bools_in(s(X2,X6),s(t_fun(X2,t_bool),X5))))=>p(s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X6))),s(t_fun(X1,t_bool),happ(s(t_fun(X2,t_fun(X1,t_bool)),X4),s(X2,X6)))))))),file('i/f/util_prob/IN__DFUNSET', ch4s_utilu_u_probs_INu_u_DFUNSET)).
fof(3, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/util_prob/IN__DFUNSET', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,![X2]:![X6]:![X20]:s(t_bool,h4s_bools_in(s(X2,X6),s(t_fun(X2,t_bool),X20)))=s(t_bool,happ(s(t_fun(X2,t_bool),X20),s(X2,X6))),file('i/f/util_prob/IN__DFUNSET', ah4s_bools_INu_u_DEF)).
fof(36, axiom,![X2]:![X25]:![X3]:(![X6]:(s(X2,X6)=s(X2,X25)=>p(s(t_bool,happ(s(t_fun(X2,t_bool),X3),s(X2,X6)))))<=>p(s(t_bool,happ(s(t_fun(X2,t_bool),X3),s(X2,X25))))),file('i/f/util_prob/IN__DFUNSET', ah4s_bools_UNWINDu_u_FORALLu_u_THM2)).
fof(47, axiom,![X1]:![X2]:![X4]:![X5]:![X6]:(p(s(t_bool,happ(s(t_fun(t_fun(X2,X1),t_bool),h4s_utilu_u_probs_dfunset(s(t_fun(X2,t_bool),X5),s(t_fun(X2,t_fun(X1,t_bool)),X4))),s(t_fun(X2,X1),X6))))<=>![X20]:(p(s(t_bool,h4s_bools_in(s(X2,X20),s(t_fun(X2,t_bool),X5))))=>p(s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X6),s(X2,X20))),s(t_fun(X1,t_bool),happ(s(t_fun(X2,t_fun(X1,t_bool)),X4),s(X2,X20)))))))),file('i/f/util_prob/IN__DFUNSET', ah4s_utilu_u_probs_DFUNSETu_u_def)).
# SZS output end CNFRefutation
