# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_utilu_u_probs_pair(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ),s(t_fun(X2,t_bool),h4s_predu_u_sets_univ)))=s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_predu_u_sets_univ),file('i/f/util_prob/PAIR__UNIV', ch4s_utilu_u_probs_PAIRu_u_UNIV)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/util_prob/PAIR__UNIV', aHLu_TRUTH)).
fof(6, axiom,![X3]:(s(t_bool,t)=s(t_bool,X3)<=>p(s(t_bool,X3))),file('i/f/util_prob/PAIR__UNIV', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(8, axiom,![X1]:![X3]:![X5]:(s(t_fun(X1,t_bool),X5)=s(t_fun(X1,t_bool),X3)<=>![X4]:s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X5)))=s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X3)))),file('i/f/util_prob/PAIR__UNIV', ah4s_predu_u_sets_EXTENSION)).
fof(9, axiom,![X1]:![X4]:p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)))),file('i/f/util_prob/PAIR__UNIV', ah4s_predu_u_sets_INu_u_UNIV)).
fof(11, axiom,![X1]:![X2]:![X4]:![X10]:![X11]:(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X2),X4),s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_utilu_u_probs_pair(s(t_fun(X1,t_bool),X11),s(t_fun(X2,t_bool),X10))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,X2),X4))),s(t_fun(X1,t_bool),X11))))&p(s(t_bool,h4s_bools_in(s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),X4))),s(t_fun(X2,t_bool),X10)))))),file('i/f/util_prob/PAIR__UNIV', ah4s_utilu_u_probs_INu_u_PAIR)).
fof(12, axiom,~(p(s(t_bool,f))),file('i/f/util_prob/PAIR__UNIV', aHLu_FALSITY)).
fof(13, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/util_prob/PAIR__UNIV', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
