# 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,X3),s(t_h4s_nums_num,X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/bag/BAG__INN__EMPTY__BAG', ch4s_bags_BAGu_u_INNu_u_EMPTYu_u_BAG)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__INN__EMPTY__BAG', aHLu_FALSITY)).
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__EMPTY__BAG', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(18, axiom,![X14]:![X15]:![X16]:((p(s(t_bool,X16))<=>s(t_bool,X15)=s(t_bool,X14))<=>((p(s(t_bool,X16))|(p(s(t_bool,X15))|p(s(t_bool,X14))))&((p(s(t_bool,X16))|(~(p(s(t_bool,X14)))|~(p(s(t_bool,X15)))))&((p(s(t_bool,X15))|(~(p(s(t_bool,X14)))|~(p(s(t_bool,X16)))))&(p(s(t_bool,X14))|(~(p(s(t_bool,X15)))|~(p(s(t_bool,X16))))))))),file('i/f/bag/BAG__INN__EMPTY__BAG', ah4s_sats_dcu_u_eq)).
fof(22, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))),file('i/f/bag/BAG__INN__EMPTY__BAG', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(25, axiom,![X1]:s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)=s(t_fun(X1,t_h4s_nums_num),h4s_combins_k(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__INN__EMPTY__BAG', ah4s_bags_EMPTYu_u_BAG0)).
fof(27, axiom,![X2]:![X17]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X2),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,X2))),file('i/f/bag/BAG__INN__EMPTY__BAG', ah4s_arithmetics_GREATERu_u_EQ)).
fof(29, axiom,![X2]:![X17]:(~(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X2))<=>(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,X2))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X17)))))),file('i/f/bag/BAG__INN__EMPTY__BAG', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(30, axiom,![X2]:![X17]:(~(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2)))))<=>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,X2))))),file('i/f/bag/BAG__INN__EMPTY__BAG', ah4s_arithmetics_NOTu_u_GREATERu_u_EQ)).
fof(33, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__INN__EMPTY__BAG', aHLu_TRUTH)).
fof(38, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/bag/BAG__INN__EMPTY__BAG', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(39, axiom,![X1]:![X2]:![X3]:![X18]:s(t_bool,h4s_bags_bagu_u_inn(s(X1,X3),s(t_h4s_nums_num,X2),s(t_fun(X1,t_h4s_nums_num),X18)))=s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X18),s(X1,X3))),s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__INN__EMPTY__BAG', ah4s_bags_BAGu_u_INN0)).
fof(41, axiom,![X23]:![X1]:![X6]:![X5]:s(X1,happ(s(t_fun(X23,X1),h4s_combins_k(s(X1,X5))),s(X23,X6)))=s(X1,X5),file('i/f/bag/BAG__INN__EMPTY__BAG', ah4s_combins_Ku_u_THM)).
fof(42, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/bag/BAG__INN__EMPTY__BAG', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
