# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_integers_int,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_inttos_intord),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))=s(t_h4s_totos_cpn,h4s_totos_equal),file('i/f/intto/ZERO__eq__neg__ZERO__thm', ch4s_inttos_ZEROu_u_equ_u_negu_u_ZEROu_u_thm)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/intto/ZERO__eq__neg__ZERO__thm', aHLu_FALSITY)).
fof(4, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/intto/ZERO__eq__neg__ZERO__thm', aHLu_BOOLu_CASES)).
fof(12, axiom,![X7]:![X10]:![X11]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X11),s(X7,X10)))=s(X7,X11),file('i/f/intto/ZERO__eq__neg__ZERO__thm', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(13, axiom,![X7]:![X10]:![X11]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X11),s(X7,X10)))=s(X7,X10),file('i/f/intto/ZERO__eq__neg__ZERO__thm', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(14, axiom,![X7]:![X8]:![X6]:![X16]:?[X17]:((p(s(t_bool,X17))<=>s(X7,X6)=s(X7,X8))&s(t_h4s_totos_cpn,happ(s(t_fun(X7,t_h4s_totos_cpn),happ(s(t_fun(X7,t_fun(X7,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(X7,t_fun(X7,t_bool)),X16))),s(X7,X6))),s(X7,X8)))=s(t_h4s_totos_cpn,h4s_bools_cond(s(t_bool,X17),s(t_h4s_totos_cpn,h4s_totos_equal),s(t_h4s_totos_cpn,h4s_bools_cond(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X16),s(X7,X6))),s(X7,X8))),s(t_h4s_totos_cpn,h4s_totos_less),s(t_h4s_totos_cpn,h4s_totos_greater)))))),file('i/f/intto/ZERO__eq__neg__ZERO__thm', ah4s_totos_TOu_u_ofu_u_LinearOrder0)).
fof(15, axiom,s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_inttos_intord)=s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt))),file('i/f/intto/ZERO__eq__neg__ZERO__thm', ah4s_inttos_intOrd0)).
fof(16, axiom,![X18]:![X19]:s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X18))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X19)))))))=s(t_bool,f),file('i/f/intto/ZERO__eq__neg__ZERO__thm', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c3)).
fof(17, axiom,![X18]:![X19]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X18)))=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X19)))))<=>(s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/intto/ZERO__eq__neg__ZERO__thm', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(18, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/intto/ZERO__eq__neg__ZERO__thm', ah4s_arithmetics_ALTu_u_ZERO)).
# SZS output end CNFRefutation
