# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/pred_set/BIGINTER__INTER', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/BIGINTER__INTER', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/pred_set/BIGINTER__INTER', aHLu_BOOLu_CASES)).
fof(19, axiom,![X7]:![X10]:![X9]:s(t_fun(X7,t_bool),h4s_predu_u_sets_biginter(s(t_fun(t_fun(X7,t_bool),t_bool),h4s_predu_u_sets_insert(s(t_fun(X7,t_bool),X10),s(t_fun(t_fun(X7,t_bool),t_bool),X9)))))=s(t_fun(X7,t_bool),h4s_predu_u_sets_inter(s(t_fun(X7,t_bool),X10),s(t_fun(X7,t_bool),h4s_predu_u_sets_biginter(s(t_fun(t_fun(X7,t_bool),t_bool),X9))))),file('i/f/pred_set/BIGINTER__INTER', ah4s_predu_u_sets_BIGINTERu_u_INSERT)).
fof(20, axiom,![X7]:s(t_fun(X7,t_bool),h4s_predu_u_sets_biginter(s(t_fun(t_fun(X7,t_bool),t_bool),h4s_predu_u_sets_empty)))=s(t_fun(X7,t_bool),h4s_predu_u_sets_univ),file('i/f/pred_set/BIGINTER__INTER', ah4s_predu_u_sets_BIGINTERu_u_EMPTY)).
fof(26, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/pred_set/BIGINTER__INTER', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(34, axiom,![X7]:![X1]:![X8]:s(t_fun(X7,t_bool),h4s_predu_u_sets_inter(s(t_fun(X7,t_bool),X8),s(t_fun(X7,t_bool),X1)))=s(t_fun(X7,t_bool),h4s_predu_u_sets_inter(s(t_fun(X7,t_bool),X1),s(t_fun(X7,t_bool),X8))),file('i/f/pred_set/BIGINTER__INTER', ah4s_predu_u_sets_INTERu_u_COMM)).
fof(42, axiom,![X7]:![X1]:![X8]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X7,t_bool),X8),s(t_fun(X7,t_bool),X1))))<=>s(t_fun(X7,t_bool),h4s_predu_u_sets_inter(s(t_fun(X7,t_bool),X8),s(t_fun(X7,t_bool),X1)))=s(t_fun(X7,t_bool),X8)),file('i/f/pred_set/BIGINTER__INTER', ah4s_predu_u_sets_SUBSETu_u_INTERu_u_ABSORPTION)).
fof(49, axiom,![X7]:![X6]:p(s(t_bool,h4s_bools_in(s(X7,X6),s(t_fun(X7,t_bool),h4s_predu_u_sets_univ)))),file('i/f/pred_set/BIGINTER__INTER', ah4s_predu_u_sets_INu_u_UNIV)).
fof(54, axiom,![X7]:![X1]:![X8]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X7,t_bool),X8),s(t_fun(X7,t_bool),X1))))<=>![X6]:(p(s(t_bool,h4s_bools_in(s(X7,X6),s(t_fun(X7,t_bool),X8))))=>p(s(t_bool,h4s_bools_in(s(X7,X6),s(t_fun(X7,t_bool),X1)))))),file('i/f/pred_set/BIGINTER__INTER', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(133, conjecture,![X7]:![X27]:![X10]:s(t_fun(X7,t_bool),h4s_predu_u_sets_biginter(s(t_fun(t_fun(X7,t_bool),t_bool),h4s_predu_u_sets_insert(s(t_fun(X7,t_bool),X10),s(t_fun(t_fun(X7,t_bool),t_bool),h4s_predu_u_sets_insert(s(t_fun(X7,t_bool),X27),s(t_fun(t_fun(X7,t_bool),t_bool),h4s_predu_u_sets_empty)))))))=s(t_fun(X7,t_bool),h4s_predu_u_sets_inter(s(t_fun(X7,t_bool),X10),s(t_fun(X7,t_bool),X27))),file('i/f/pred_set/BIGINTER__INTER', ch4s_predu_u_sets_BIGINTERu_u_INTER)).
# SZS output end CNFRefutation
