# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__IN__BAG__OF__SET', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/bag/BAG__IN__BAG__OF__SET', aHLu_BOOLu_CASES)).
fof(7, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(18, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(19, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X8),s(X9,X7)))=s(X9,X8),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(20, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(21, axiom,![X1]:((p(s(t_bool,X1))=>p(s(t_bool,f)))<=>s(t_bool,X1)=s(t_bool,f)),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(26, axiom,![X18]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,X18),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(27, axiom,![X19]:![X18]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_arithmetics_ADDu_u_SYM)).
fof(29, axiom,![X20]:![X19]:![X18]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X20)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(30, axiom,![X19]:![X18]:(~(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,X19))))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_arithmetics_NOTu_u_GREATERu_u_EQ)).
fof(31, axiom,![X19]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X19))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(32, axiom,![X19]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_numerals_numeralu_u_distribu_c17)).
fof(33, axiom,![X19]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_numerals_numeralu_u_distribu_c27)).
fof(34, axiom,![X19]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X19))))<=>s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_numerals_numeralu_u_distribu_c30)).
fof(35, axiom,![X19]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_numerals_numeralu_u_equ_c1)).
fof(36, axiom,![X19]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_numerals_numeralu_u_lteu_c1)).
fof(37, axiom,![X9]:![X19]:![X21]:![X13]:s(t_bool,h4s_bags_bagu_u_inn(s(X9,X21),s(t_h4s_nums_num,X19),s(t_fun(X9,t_h4s_nums_num),X13)))=s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,happ(s(t_fun(X9,t_h4s_nums_num),X13),s(X9,X21))),s(t_h4s_nums_num,X19))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_bags_BAGu_u_INN0)).
fof(38, axiom,![X9]:![X21]:![X13]:s(t_bool,h4s_bags_bagu_u_in(s(X9,X21),s(t_fun(X9,t_h4s_nums_num),X13)))=s(t_bool,h4s_bags_bagu_u_inn(s(X9,X21),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_fun(X9,t_h4s_nums_num),X13))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_bags_BAGu_u_IN0)).
fof(39, axiom,![X9]:![X17]:![X6]:s(t_h4s_nums_num,happ(s(t_fun(X9,t_h4s_nums_num),h4s_bags_bagu_u_ofu_u_set(s(t_fun(X9,t_bool),X17))),s(X9,X6)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X17))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__IN__BAG__OF__SET', ah4s_bags_BAGu_u_OFu_u_SET0)).
fof(40, conjecture,![X9]:![X20]:![X17]:s(t_bool,h4s_bags_bagu_u_in(s(X9,X20),s(t_fun(X9,t_h4s_nums_num),h4s_bags_bagu_u_ofu_u_set(s(t_fun(X9,t_bool),X17)))))=s(t_bool,h4s_bools_in(s(X9,X20),s(t_fun(X9,t_bool),X17))),file('i/f/bag/BAG__IN__BAG__OF__SET', ch4s_bags_BAGu_u_INu_u_BAGu_u_OFu_u_SET)).
# SZS output end CNFRefutation
