# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_every(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2))))))<=>(p(s(t_bool,h4s_bags_bagu_u_every(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_h4s_nums_num),X3))))&p(s(t_bool,h4s_bags_bagu_u_every(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_h4s_nums_num),X2)))))),file('i/f/bag/BAG__EVERY__UNION', ch4s_bags_BAGu_u_EVERYu_u_UNION)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__EVERY__UNION', aHLu_FALSITY)).
fof(22, axiom,![X1]:![X19]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_every(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_h4s_nums_num),X19))))<=>![X20]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X20),s(t_fun(X1,t_h4s_nums_num),X19))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,X20)))))),file('i/f/bag/BAG__EVERY__UNION', ah4s_bags_BAGu_u_EVERY0)).
fof(24, axiom,![X1]:![X20]:![X2]:![X3]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X20),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2))))))<=>(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X20),s(t_fun(X1,t_h4s_nums_num),X3))))|p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X20),s(t_fun(X1,t_h4s_nums_num),X2)))))),file('i/f/bag/BAG__EVERY__UNION', ah4s_bags_BAGu_u_INu_u_BAGu_u_UNION)).
fof(25, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/bag/BAG__EVERY__UNION', aHLu_BOOLu_CASES)).
fof(26, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__EVERY__UNION', aHLu_TRUTH)).
fof(28, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/bag/BAG__EVERY__UNION', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
