# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X2))))=>((s(t_h4s_lists_list(X1),h4s_lists_nil)=s(t_h4s_lists_list(X1),h4s_containers_bagu_u_tou_u_list(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))&(s(t_h4s_lists_list(X1),h4s_containers_bagu_u_tou_u_list(s(t_fun(X1,t_h4s_nums_num),X2)))=s(t_h4s_lists_list(X1),h4s_lists_nil)<=>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/container/BAG__TO__LIST__EQ__NIL', ch4s_containers_BAGu_u_TOu_u_LISTu_u_EQu_u_NIL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/container/BAG__TO__LIST__EQ__NIL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/container/BAG__TO__LIST__EQ__NIL', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/container/BAG__TO__LIST__EQ__NIL', aHLu_BOOLu_CASES)).
fof(6, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/container/BAG__TO__LIST__EQ__NIL', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(14, axiom,![X3]:(s(t_bool,t)=s(t_bool,X3)<=>p(s(t_bool,X3))),file('i/f/container/BAG__TO__LIST__EQ__NIL', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(16, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/container/BAG__TO__LIST__EQ__NIL', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(20, axiom,![X1]:![X6]:![X2]:~(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X6),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/container/BAG__TO__LIST__EQ__NIL', ah4s_bags_BAGu_u_INSERTu_u_NOTu_u_EMPTY)).
fof(21, axiom,![X1]:p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))),file('i/f/container/BAG__TO__LIST__EQ__NIL', ah4s_bags_FINITEu_u_BAGu_u_THMu_c0)).
fof(22, axiom,![X1]:![X13]:(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X13))))=>?[X14]:((p(s(t_bool,X14))<=>s(t_fun(X1,t_h4s_nums_num),X13)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag))&s(t_h4s_lists_list(X1),h4s_containers_bagu_u_tou_u_list(s(t_fun(X1,t_h4s_nums_num),X13)))=s(t_h4s_lists_list(X1),h4s_bools_cond(s(t_bool,X14),s(t_h4s_lists_list(X1),h4s_lists_nil),s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,h4s_bags_bagu_u_choice(s(t_fun(X1,t_h4s_nums_num),X13))),s(t_h4s_lists_list(X1),h4s_containers_bagu_u_tou_u_list(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_rest(s(t_fun(X1,t_h4s_nums_num),X13))))))))))),file('i/f/container/BAG__TO__LIST__EQ__NIL', ah4s_containers_BAGu_u_TOu_u_LISTu_u_THM)).
fof(23, axiom,![X1]:![X12]:![X2]:s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X12),s(t_fun(X1,t_h4s_nums_num),X2)))))=s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X2))),file('i/f/container/BAG__TO__LIST__EQ__NIL', ah4s_bags_FINITEu_u_BAGu_u_THMu_c1)).
fof(24, axiom,![X1]:![X15]:![X16]:~(s(t_h4s_lists_list(X1),h4s_lists_nil)=s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X16),s(t_h4s_lists_list(X1),X15)))),file('i/f/container/BAG__TO__LIST__EQ__NIL', ah4s_lists_NOTu_u_NILu_u_CONS)).
fof(26, axiom,![X1]:![X4]:![X5]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X5),s(X1,X4)))=s(X1,X5),file('i/f/container/BAG__TO__LIST__EQ__NIL', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(27, axiom,![X1]:![X4]:![X5]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X5),s(X1,X4)))=s(X1,X4),file('i/f/container/BAG__TO__LIST__EQ__NIL', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
# SZS output end CNFRefutation
