# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_fun(X2,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X2,X1),X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)))=s(t_fun(X2,t_bool),h4s_predu_u_sets_univ),file('i/f/util_prob/PREIMAGE__UNIV', ch4s_utilu_u_probs_PREIMAGEu_u_UNIV)).
fof(5, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/util_prob/PREIMAGE__UNIV', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(7, axiom,![X2]:![X4]:![X6]:(s(t_fun(X2,t_bool),X6)=s(t_fun(X2,t_bool),X4)<=>![X5]:s(t_bool,h4s_bools_in(s(X2,X5),s(t_fun(X2,t_bool),X6)))=s(t_bool,h4s_bools_in(s(X2,X5),s(t_fun(X2,t_bool),X4)))),file('i/f/util_prob/PREIMAGE__UNIV', ah4s_predu_u_sets_EXTENSION)).
fof(8, axiom,![X2]:![X5]:p(s(t_bool,h4s_bools_in(s(X2,X5),s(t_fun(X2,t_bool),h4s_predu_u_sets_univ)))),file('i/f/util_prob/PREIMAGE__UNIV', ah4s_predu_u_sets_INu_u_UNIV)).
fof(10, axiom,![X2]:![X1]:![X5]:![X6]:![X3]:s(t_bool,h4s_bools_in(s(X2,X5),s(t_fun(X2,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X2,X1),X3),s(t_fun(X1,t_bool),X6)))))=s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X5))),s(t_fun(X1,t_bool),X6))),file('i/f/util_prob/PREIMAGE__UNIV', ah4s_utilu_u_probs_INu_u_PREIMAGE)).
# SZS output end CNFRefutation
