# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,X1),X3),s(t_h4s_fcps_cart(t_bool,X1),X2)))=s(t_h4s_fcps_cart(t_bool,X1),X3)<=>s(t_h4s_fcps_cart(t_bool,X1),X2)=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/words/WORD__ADD__INV__0__EQ', ch4s_wordss_WORDu_u_ADDu_u_INVu_u_0u_u_EQ)).
fof(7, axiom,![X10]:![X11]:((p(s(t_bool,X11))=>p(s(t_bool,X10)))=>((p(s(t_bool,X10))=>p(s(t_bool,X11)))=>s(t_bool,X11)=s(t_bool,X10))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,![X1]:![X2]:![X3]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,X1),X3),s(t_h4s_fcps_cart(t_bool,X1),X2)))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X3))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X2))))))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_wordss_wordu_u_addu_u_def)).
fof(29, axiom,![X1]:![X2]:?[X18]:(s(t_h4s_fcps_cart(t_bool,X1),X2)=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X18)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_wordss_rangedu_u_wordu_u_nchotomy)).
fof(30, axiom,![X1]:![X18]:![X19]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X19))),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X18)))))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_wordss_wordu_u_addu_u_n2w)).
fof(33, axiom,![X1]:![X2]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,X1),X2),s(t_h4s_fcps_cart(t_bool,X1),X2)))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_wordss_WORDu_u_SUBu_u_REFL)).
fof(37, axiom,![X18]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_numerals_numeralu_u_distribu_c27)).
fof(38, axiom,![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,X19),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(39, 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/words/WORD__ADD__INV__0__EQ', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(40, axiom,![X18]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X18),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_numerals_numeralu_u_distribu_c1)).
fof(41, axiom,![X16]:![X18]:![X19]:(s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X16)))<=>(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X16)))=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,h4s_nums_0))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X16))))))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_arithmetics_SUBu_u_LEFTu_u_EQ)).
fof(44, 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/words/WORD__ADD__INV__0__EQ', ah4s_numerals_numeralu_u_distribu_c17)).
fof(52, axiom,![X18]:![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_arithmetics_ADDu_u_SYM)).
fof(58, axiom,![X1]:![X5]:![X2]:![X3]:(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,X1),X3),s(t_h4s_fcps_cart(t_bool,X1),X2)))=s(t_h4s_fcps_cart(t_bool,X1),X5)<=>s(t_h4s_fcps_cart(t_bool,X1),X3)=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,X1),X5),s(t_h4s_fcps_cart(t_bool,X1),X2)))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_wordss_WORDu_u_ADDu_u_EQu_u_SUB)).
fof(63, axiom,~(p(s(t_bool,f))),file('i/f/words/WORD__ADD__INV__0__EQ', aHLu_FALSITY)).
fof(69, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/words/WORD__ADD__INV__0__EQ', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
