# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_relations_wf(s(t_fun(X1,t_fun(X1,t_bool)),X4))))=>((p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_fun(t_fun(X1,t_h4s_nums_num),t_bool)),h4s_relations_tc(s(t_fun(t_fun(X1,t_h4s_nums_num),t_fun(t_fun(X1,t_h4s_nums_num),t_bool)),h4s_bags_mlt1(s(t_fun(X1,t_fun(X1,t_bool)),X4))))),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),X3),s(t_fun(X1,t_h4s_nums_num),X2))))))<=>(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3))))&(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X2))))&~(s(t_fun(X1,t_h4s_nums_num),X2)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))))&(p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_fun(t_fun(X1,t_h4s_nums_num),t_bool)),h4s_relations_tc(s(t_fun(t_fun(X1,t_h4s_nums_num),t_fun(t_fun(X1,t_h4s_nums_num),t_bool)),h4s_bags_mlt1(s(t_fun(X1,t_fun(X1,t_bool)),X4))))),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),X3))))))<=>(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3))))&(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X2))))&~(s(t_fun(X1,t_h4s_nums_num),X2)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))))),file('i/f/bag/mlt__UNION__CANCEL__EQN', ch4s_bags_mltu_u_UNIONu_u_CANCELu_u_EQN)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/bag/mlt__UNION__CANCEL__EQN', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(21, axiom,![X1]:![X19]:s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X19),s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))=s(t_fun(X1,t_h4s_nums_num),X19),file('i/f/bag/mlt__UNION__CANCEL__EQN', ah4s_bags_BAGu_u_UNIONu_u_EMPTYu_c0)).
fof(23, axiom,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X2))))&(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3))))&~(s(t_fun(X1,t_h4s_nums_num),X2)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))=>p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_fun(t_fun(X1,t_h4s_nums_num),t_bool)),h4s_relations_tc(s(t_fun(t_fun(X1,t_h4s_nums_num),t_fun(t_fun(X1,t_h4s_nums_num),t_bool)),h4s_bags_mlt1(s(t_fun(X1,t_fun(X1,t_bool)),X4))))),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),X3),s(t_fun(X1,t_h4s_nums_num),X2))))))),file('i/f/bag/mlt__UNION__CANCEL__EQN', ah4s_bags_TCu_u_mlt1u_u_UNION2u_u_I)).
fof(24, axiom,![X1]:![X2]:![X3]: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)))=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))),file('i/f/bag/mlt__UNION__CANCEL__EQN', ah4s_bags_COMMu_u_BAGu_u_UNION)).
fof(25, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_bags_finiteu_u_bag(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_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3))))&p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X2)))))),file('i/f/bag/mlt__UNION__CANCEL__EQN', ah4s_bags_FINITEu_u_BAGu_u_UNION)).
fof(26, axiom,![X1]:![X4]:(p(s(t_bool,h4s_relations_wf(s(t_fun(X1,t_fun(X1,t_bool)),X4))))=>p(s(t_bool,h4s_relations_wf(s(t_fun(t_fun(X1,t_h4s_nums_num),t_fun(t_fun(X1,t_h4s_nums_num),t_bool)),h4s_bags_mlt1(s(t_fun(X1,t_fun(X1,t_bool)),X4))))))),file('i/f/bag/mlt__UNION__CANCEL__EQN', ah4s_bags_WFu_u_mlt1)).
fof(27, axiom,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_fun(t_fun(X1,t_h4s_nums_num),t_bool)),h4s_relations_tc(s(t_fun(t_fun(X1,t_h4s_nums_num),t_fun(t_fun(X1,t_h4s_nums_num),t_bool)),h4s_bags_mlt1(s(t_fun(X1,t_fun(X1,t_bool)),X4))))),s(t_fun(X1,t_h4s_nums_num),X3))),s(t_fun(X1,t_h4s_nums_num),X2))))=>(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3))))&p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X2)))))),file('i/f/bag/mlt__UNION__CANCEL__EQN', ah4s_bags_TCu_u_mlt1u_u_FINITEu_u_BAG)).
fof(29, axiom,![X1]:![X9]:![X8]:![X4]:(p(s(t_bool,h4s_relations_wf(s(t_fun(X1,t_fun(X1,t_bool)),X4))))=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X4),s(X1,X8))),s(X1,X9))))=>~(s(X1,X8)=s(X1,X9)))),file('i/f/bag/mlt__UNION__CANCEL__EQN', ah4s_relations_WFu_u_NOTu_u_REFL)).
fof(30, axiom,![X1]:![X4]:s(t_bool,h4s_relations_wf(s(t_fun(X1,t_fun(X1,t_bool)),h4s_relations_tc(s(t_fun(X1,t_fun(X1,t_bool)),X4)))))=s(t_bool,h4s_relations_wf(s(t_fun(X1,t_fun(X1,t_bool)),X4))),file('i/f/bag/mlt__UNION__CANCEL__EQN', ah4s_relations_WFu_u_TCu_u_EQN)).
# SZS output end CNFRefutation
