# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:~(p(s(t_bool,h4s_wordss_wordu_u_le(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))),file('i/f/words/WORD__LESS__0__word__T_c1', ch4s_wordss_WORDu_u_LESSu_u_0u_u_wordu_u_Tu_c1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/words/WORD__LESS__0__word__T_c1', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/words/WORD__LESS__0__word__T_c1', aHLu_FALSITY)).
fof(5, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)<=>p(s(t_bool,X2))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X5]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5)))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(18, axiom,![X2]:(s(t_bool,f)=s(t_bool,X2)<=>~(p(s(t_bool,X2)))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(20, axiom,![X5]:![X7]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X5)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X7))))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_arithmetics_NOTu_u_LESS)).
fof(49, axiom,![X3]:![X19]:![X20]:(p(s(t_bool,h4s_wordss_wordu_u_le(s(t_h4s_fcps_cart(t_bool,X3),X20),s(t_h4s_fcps_cart(t_bool,X3),X19))))<=>((s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X3),X20)))=s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X3),X19)))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X3),X20))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X3),X19)))))))|(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X3),X20))))&~(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X3),X19)))))))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_wordss_WORDu_u_LE)).
fof(55, axiom,![X3]:p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X3),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,X3),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_wordss_wordu_u_msbu_u_wordu_u_T)).
fof(57, axiom,![X3]:~(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X3),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_wordss_WORDu_u_0u_u_POS)).
fof(59, axiom,![X5]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_numerals_numeralu_u_distribu_c27)).
fof(61, axiom,![X5]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_numerals_numeralu_u_distribu_c17)).
fof(75, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/words/WORD__LESS__0__word__T_c1', aHLu_BOOLu_CASES)).
fof(79, axiom,![X5]:![X7]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X5)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X5))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_arithmetics_LESSu_u_EQ)).
fof(81, axiom,![X5]:![X7]:(~(s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,X5))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X5))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,X7)))))),file('i/f/words/WORD__LESS__0__word__T_c1', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
# SZS output end CNFRefutation
