# 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(2, axiom,p(s(t_bool,t)),file('i/f/intto/neg__ZERO__eq__ZERO__thm', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/intto/neg__ZERO__eq__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/neg__ZERO__eq__ZERO__thm', aHLu_BOOLu_CASES)).
fof(13, axiom,![X2]:![X4]:![X3]:![X8]:?[X9]:((p(s(t_bool,X9))<=>s(X2,X3)=s(X2,X4))&s(t_h4s_totos_cpn,happ(s(t_fun(X2,t_h4s_totos_cpn),happ(s(t_fun(X2,t_fun(X2,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(X2,t_fun(X2,t_bool)),X8))),s(X2,X3))),s(X2,X4)))=s(t_h4s_totos_cpn,h4s_bools_cond(s(t_bool,X9),s(t_h4s_totos_cpn,h4s_totos_equal),s(t_h4s_totos_cpn,h4s_bools_cond(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X8),s(X2,X3))),s(X2,X4))),s(t_h4s_totos_cpn,h4s_totos_less),s(t_h4s_totos_cpn,h4s_totos_greater)))))),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_totos_TOu_u_ofu_u_LinearOrder0)).
fof(14, 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/neg__ZERO__eq__ZERO__thm', ah4s_inttos_intOrd0)).
fof(16, axiom,![X14]:![X15]:(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,X14))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X15))))))<=>(~(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0))|~(s(t_h4s_nums_num,X15)=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(17, axiom,![X14]:![X15]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14)))=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,X15)))))<=>(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X15)=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(18, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_arithmetics_ALTu_u_ZERO)).
fof(20, axiom,![X2]:![X6]:![X7]:s(X2,h4s_bools_cond(s(t_bool,t),s(X2,X7),s(X2,X6)))=s(X2,X7),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(21, axiom,![X2]:![X6]:![X7]:s(X2,h4s_bools_cond(s(t_bool,f),s(X2,X7),s(X2,X6)))=s(X2,X6),file('i/f/intto/neg__ZERO__eq__ZERO__thm', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
# SZS output end CNFRefutation
