# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X2),s(t_h4s_nums_num,h4s_nums_0),s(t_fun(X1,t_h4s_nums_num),X3)))),file('i/f/bag/BAG__INN__0', ch4s_bags_BAGu_u_INNu_u_0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__INN__0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__INN__0', aHLu_FALSITY)).
fof(8, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/bag/BAG__INN__0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X4]:((p(s(t_bool,X4))=>p(s(t_bool,f)))<=>s(t_bool,X4)=s(t_bool,f)),file('i/f/bag/BAG__INN__0', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(10, axiom,![X6]:![X7]:![X8]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X6)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X6))))),file('i/f/bag/BAG__INN__0', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(11, axiom,![X7]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X7)))),file('i/f/bag/BAG__INN__0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(12, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/bag/BAG__INN__0', aHLu_BOOLu_CASES)).
fof(13, axiom,![X1]:![X7]:![X2]:![X3]:s(t_bool,h4s_bags_bagu_u_inn(s(X1,X2),s(t_h4s_nums_num,X7),s(t_fun(X1,t_h4s_nums_num),X3)))=s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X3),s(X1,X2))),s(t_h4s_nums_num,X7))),file('i/f/bag/BAG__INN__0', ah4s_bags_BAGu_u_INN0)).
fof(15, axiom,![X6]:![X7]:![X8]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X6)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X6))),file('i/f/bag/BAG__INN__0', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(16, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X7),file('i/f/bag/BAG__INN__0', ah4s_numerals_numeralu_u_distribu_c1)).
fof(17, axiom,![X7]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/bag/BAG__INN__0', ah4s_numerals_numeralu_u_distribu_c27)).
fof(18, axiom,![X7]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/bag/BAG__INN__0', ah4s_numerals_numeralu_u_lteu_c1)).
fof(19, axiom,![X7]:![X8]:(~(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X7))))),file('i/f/bag/BAG__INN__0', ah4s_arithmetics_NOTu_u_GREATERu_u_EQ)).
fof(20, axiom,![X7]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))=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,X7))),file('i/f/bag/BAG__INN__0', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
# SZS output end CNFRefutation
