# 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_neg(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_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_totos_cpn,h4s_totos_equal),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ch4s_inttos_negu_u_ZEROu_u_equ_u_ZEROu_u_thm)).
fof(20, axiom,s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_totos_cpn,h4s_totos_equal),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_totos_numeralOrdu_c0)).
fof(34, axiom,![X24]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_numerals_numeralu_u_ltu_c2)).
fof(43, axiom,![X24]:![X25]: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,X25))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X24)))))=s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord),s(t_h4s_nums_num,X25))),s(t_h4s_nums_num,X24))),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_inttos_posu_u_posu_u_thm)).
fof(44, axiom,![X24]:![X25]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X24)))=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,X25)))))<=>(s(t_h4s_nums_num,X24)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(45, axiom,![X24]:![X25]:(p(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_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X24))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X25))))))<=>(~(s(t_h4s_nums_num,X24)=s(t_h4s_nums_num,h4s_nums_0))|~(s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c2)).
fof(47, axiom,![X24]:![X25]: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,X24))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X25)))))=s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,X25))),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(54, axiom,![X24]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X24)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X24)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_numerals_numeralu_u_distribu_c17)).
fof(77, axiom,![X11]:(s(t_bool,f)=s(t_bool,X11)<=>~(p(s(t_bool,X11)))),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
