# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),X4))),s(t_fun(X1,t_bool),X3))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X3))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3)))))),file('i/f/pred_set/INSERT__SUBSET', ch4s_predu_u_sets_INSERTu_u_SUBSET)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/pred_set/INSERT__SUBSET', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/INSERT__SUBSET', aHLu_FALSITY)).
fof(6, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)<=>p(s(t_bool,X3))),file('i/f/pred_set/INSERT__SUBSET', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X1]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3))))<=>![X2]:(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X4))))=>p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X3)))))),file('i/f/pred_set/INSERT__SUBSET', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(8, axiom,![X1]:![X7]:![X2]:![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X7),s(t_fun(X1,t_bool),X4))))))<=>(s(X1,X2)=s(X1,X7)|p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X4)))))),file('i/f/pred_set/INSERT__SUBSET', ah4s_predu_u_sets_INu_u_INSERT)).
fof(9, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)|s(t_bool,X3)=s(t_bool,f)),file('i/f/pred_set/INSERT__SUBSET', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
