# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X6),s(t_fun(X2,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X2,X3),X5),s(t_fun(X3,t_bool),X4)))))=s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X3),h4s_combins_o(s(t_fun(X2,X3),X5),s(t_fun(X1,X2),X6))),s(t_fun(X3,t_bool),X4))),file('i/f/util_prob/PREIMAGE__COMP', ch4s_utilu_u_probs_PREIMAGEu_u_COMP)).
fof(2, axiom,![X1]:![X2]:![X7]:![X4]:![X6]:s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X6),s(t_fun(X2,t_bool),X4)))))=s(t_bool,h4s_bools_in(s(X2,happ(s(t_fun(X1,X2),X6),s(X1,X7))),s(t_fun(X2,t_bool),X4))),file('i/f/util_prob/PREIMAGE__COMP', ah4s_utilu_u_probs_INu_u_PREIMAGE)).
fof(3, axiom,![X2]:![X1]:![X3]:![X7]:![X5]:![X6]:s(X2,happ(s(t_fun(X3,X2),h4s_combins_o(s(t_fun(X1,X2),X6),s(t_fun(X3,X1),X5))),s(X3,X7)))=s(X2,happ(s(t_fun(X1,X2),X6),s(X1,happ(s(t_fun(X3,X1),X5),s(X3,X7))))),file('i/f/util_prob/PREIMAGE__COMP', ah4s_combins_ou_u_THM)).
fof(4, axiom,![X1]:![X8]:![X4]:(s(t_fun(X1,t_bool),X4)=s(t_fun(X1,t_bool),X8)<=>![X7]:s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X4)))=s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X8)))),file('i/f/util_prob/PREIMAGE__COMP', ah4s_predu_u_sets_EXTENSION)).
# SZS output end CNFRefutation
