# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2))))=>![X4]:p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X2))))))),file('i/f/bag/SUB__BAG__UNION_c1', ch4s_bags_SUBu_u_BAGu_u_UNIONu_c1)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bag/SUB__BAG__UNION_c1', aHLu_FALSITY)).
fof(3, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2))))=>![X4]:p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_h4s_nums_num),X4))))))),file('i/f/bag/SUB__BAG__UNION_c1', ah4s_bags_SUBu_u_BAGu_u_UNIONu_c0)).
fof(11, axiom,![X5]:((p(s(t_bool,X5))=>p(s(t_bool,f)))<=>s(t_bool,X5)=s(t_bool,f)),file('i/f/bag/SUB__BAG__UNION_c1', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(13, axiom,![X1]:![X18]:![X2]:![X3]:((p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2))))&p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_h4s_nums_num),X18)))))=>p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X18))))),file('i/f/bag/SUB__BAG__UNION_c1', ah4s_bags_SUBu_u_BAGu_u_TRANS)).
fof(15, axiom,![X1]:![X4]:p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X4)))),file('i/f/bag/SUB__BAG__UNION_c1', ah4s_bags_SUBu_u_BAGu_u_REFL)).
fof(53, axiom,![X1]:![X18]:![X2]:![X3]:s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_h4s_nums_num),X3))),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X18),s(t_fun(X1,t_h4s_nums_num),X3)))))=s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_h4s_nums_num),X18))),file('i/f/bag/SUB__BAG__UNION_c1', ah4s_bags_SUBu_u_BAGu_u_UNIONu_u_eliminateu_c3)).
fof(54, axiom,![X1]:![X30]:![X4]:(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X30)))=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)<=>p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X30))))),file('i/f/bag/SUB__BAG__UNION_c1', ah4s_bags_BAGu_u_DIFFu_u_EQu_u_EMPTY)).
fof(59, axiom,![X1]:![X30]:![X4]:(s(t_fun(X1,t_h4s_nums_num),X4)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X30),s(t_fun(X1,t_h4s_nums_num),X4)))<=>s(t_fun(X1,t_h4s_nums_num),X30)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)),file('i/f/bag/SUB__BAG__UNION_c1', ah4s_bags_BAGu_u_UNIONu_u_EQu_u_RCANCEL1)).
fof(63, axiom,![X1]:![X30]:![X4]:s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X30))),s(t_fun(X1,t_h4s_nums_num),X30)))=s(t_fun(X1,t_h4s_nums_num),X4),file('i/f/bag/SUB__BAG__UNION_c1', ah4s_bags_BAGu_u_UNIONu_u_DIFFu_u_eliminateu_c0)).
fof(75, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/bag/SUB__BAG__UNION_c1', aHLu_BOOLu_CASES)).
fof(76, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/bag/SUB__BAG__UNION_c1', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
