# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__IN__DIFF__I', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__IN__DIFF__I', 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__DIFF__I', aHLu_BOOLu_CASES)).
fof(12, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(15, 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__DIFF__I', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(18, axiom,![X16]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_arithmetics_ADDu_u_SYM)).
fof(20, axiom,![X18]:![X16]:![X17]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X18)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X18))))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(21, axiom,![X16]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X16)))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(22, axiom,![X16]:![X17]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_arithmetics_GREATERu_u_EQ)).
fof(23, axiom,![X18]:![X16]:![X17]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X18)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X18))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(24, axiom,![X16]:![X17]:(~(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X16))))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_arithmetics_NOTu_u_GREATERu_u_EQ)).
fof(25, axiom,![X16]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16)))=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,X16))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(26, axiom,![X18]:![X16]:![X17]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,X18))))<=>(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X18))))))|p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X18)))))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_arithmetics_SUBu_u_RIGHTu_u_GREATERu_u_EQ)).
fof(27, axiom,![X16]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X16),file('i/f/bag/BAG__IN__DIFF__I', ah4s_numerals_numeralu_u_distribu_c1)).
fof(28, axiom,![X16]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X16)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/bag/BAG__IN__DIFF__I', ah4s_numerals_numeralu_u_distribu_c17)).
fof(29, axiom,![X16]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_numerals_numeralu_u_distribu_c27)).
fof(30, axiom,![X16]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X16))))<=>s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/bag/BAG__IN__DIFF__I', ah4s_numerals_numeralu_u_distribu_c30)).
fof(32, axiom,![X16]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/bag/BAG__IN__DIFF__I', ah4s_numerals_numeralu_u_lteu_c1)).
fof(33, axiom,![X7]:![X16]:![X19]:![X20]:s(t_bool,h4s_bags_bagu_u_inn(s(X7,X19),s(t_h4s_nums_num,X16),s(t_fun(X7,t_h4s_nums_num),X20)))=s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),X20),s(X7,X19))),s(t_h4s_nums_num,X16))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_bags_BAGu_u_INN0)).
fof(34, axiom,![X7]:![X19]:![X20]:s(t_bool,h4s_bags_bagu_u_in(s(X7,X19),s(t_fun(X7,t_h4s_nums_num),X20)))=s(t_bool,h4s_bags_bagu_u_inn(s(X7,X19),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(X7,t_h4s_nums_num),X20))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_bags_BAGu_u_IN0)).
fof(35, axiom,![X7]:![X21]:![X22]:![X6]:s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(X7,t_h4s_nums_num),X22),s(t_fun(X7,t_h4s_nums_num),X21))),s(X7,X6)))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),X22),s(X7,X6))),s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),X21),s(X7,X6))))),file('i/f/bag/BAG__IN__DIFF__I', ah4s_bags_BAGu_u_DIFF0)).
fof(36, conjecture,![X7]:![X19]:![X21]:![X22]:((p(s(t_bool,h4s_bags_bagu_u_in(s(X7,X19),s(t_fun(X7,t_h4s_nums_num),X22))))&~(p(s(t_bool,h4s_bags_bagu_u_in(s(X7,X19),s(t_fun(X7,t_h4s_nums_num),X21))))))=>p(s(t_bool,h4s_bags_bagu_u_in(s(X7,X19),s(t_fun(X7,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(X7,t_h4s_nums_num),X22),s(t_fun(X7,t_h4s_nums_num),X21))))))),file('i/f/bag/BAG__IN__DIFF__I', ch4s_bags_BAGu_u_INu_u_DIFFu_u_I)).
# SZS output end CNFRefutation
