# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:~(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_polys_poly(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_cons(s(t_h4s_realaxs_real,X1),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_cons(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_lists_list(t_h4s_realaxs_real),h4s_lists_nil)))))))=s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_polys_poly(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)))),file('i/f/poly/POLY__PRIME__EQ__0', ch4s_polys_POLYu_u_PRIMEu_u_EQu_u_0)).
fof(10, axiom,![X6]:![X7]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_ADDu_u_SYM)).
fof(11, axiom,![X11]:![X6]:![X7]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X11)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,X11))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_ADDu_u_ASSOC)).
fof(12, axiom,![X7]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_polys_poly(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil))),s(t_h4s_realaxs_real,X7)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_polys_polyu_u_defu_c0)).
fof(13, axiom,![X7]:![X4]:![X12]:s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_polys_poly(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_cons(s(t_h4s_realaxs_real,X12),s(t_h4s_lists_list(t_h4s_realaxs_real),X4))))),s(t_h4s_realaxs_real,X7)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_polys_poly(s(t_h4s_lists_list(t_h4s_realaxs_real),X4))),s(t_h4s_realaxs_real,X7))))))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_polys_polyu_u_defu_c1)).
fof(14, axiom,![X7]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X7)))=s(t_h4s_realaxs_real,X7),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_ADDu_u_LID)).
fof(16, axiom,![X7]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_realaxs_real,X7),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_ADDu_u_RID)).
fof(19, axiom,![X7]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X7)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_MULu_u_LZERO)).
fof(20, axiom,![X7]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_MULu_u_RZERO)).
fof(21, axiom,![X6]:![X7]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7)))))<=>s(t_h4s_realaxs_real,X7)=s(t_h4s_realaxs_real,X6)),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(29, axiom,![X11]:![X6]:![X7]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,X11)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X11))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X11))))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_ADDu_u_RDISTRIB)).
fof(33, axiom,![X7]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,X7),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_MULu_u_RID)).
fof(35, axiom,![X18]:![X19]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X19))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X18)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_OFu_u_NUMu_u_LE)).
fof(36, axiom,![X18]:![X19]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X19))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X18)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_reals_REALu_u_OFu_u_NUMu_u_MUL)).
fof(37, axiom,![X18]:![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X19)))))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19))))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_numerals_numeralu_u_distribu_c5)).
fof(38, axiom,![X18]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_numerals_numeralu_u_distribu_c17)).
fof(39, axiom,![X18]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_numerals_numeralu_u_equ_c1)).
fof(40, axiom,![X18]:![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19))))),s(t_h4s_nums_num,X19))))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_numerals_numeralu_u_multu_c2)).
fof(41, axiom,![X18]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X18)))))=s(t_h4s_nums_num,X18),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_numerals_numeralu_u_addu_c0)).
fof(42, axiom,s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_numerals_iDUBu_u_removalu_c2)).
fof(43, axiom,![X18]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_numerals_numeralu_u_multu_c0)).
fof(44, axiom,p(s(t_bool,t)),file('i/f/poly/POLY__PRIME__EQ__0', aHLu_TRUTH)).
fof(45, axiom,~(p(s(t_bool,f))),file('i/f/poly/POLY__PRIME__EQ__0', aHLu_FALSITY)).
fof(46, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/poly/POLY__PRIME__EQ__0', aHLu_BOOLu_CASES)).
fof(54, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(56, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(62, axiom,![X18]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X18)))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(63, axiom,![X18]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,h4s_nums_0))))<=>s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_arithmetics_LEu_c0)).
fof(64, axiom,![X18]:![X19]:(s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,X18)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19)))))),file('i/f/poly/POLY__PRIME__EQ__0', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
