# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,X1),X3),s(t_h4s_fcps_cart(t_bool,X1),X2))))<=>(p(s(t_bool,h4s_wordss_wordu_u_lo(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))),file('i/f/words/WORD__LOWER__OR__EQ', ch4s_wordss_WORDu_u_LOWERu_u_ORu_u_EQ)).
fof(23, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,X1),X3),s(t_h4s_fcps_cart(t_bool,X1),X2)))=s(t_bool,h4s_primu_u_recs_u_3c(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__LOWER__OR__EQ', ah4s_wordss_WORDu_u_LO)).
fof(24, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,X1),X3),s(t_h4s_fcps_cart(t_bool,X1),X2)))=s(t_bool,h4s_arithmetics_u_3cu_3d(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__LOWER__OR__EQ', ah4s_wordss_WORDu_u_LS)).
fof(25, axiom,![X16]:![X17]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17))))),file('i/f/words/WORD__LOWER__OR__EQ', ah4s_arithmetics_NOTu_u_LESS)).
fof(26, axiom,![X16]:![X17]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))|s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X16))),file('i/f/words/WORD__LOWER__OR__EQ', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(30, axiom,![X16]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X16))))),file('i/f/words/WORD__LOWER__OR__EQ', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(31, axiom,![X1]:![X18]:![X19]:(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X19)))=s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X18)))<=>s(t_h4s_fcps_cart(t_bool,X1),X19)=s(t_h4s_fcps_cart(t_bool,X1),X18)),file('i/f/words/WORD__LOWER__OR__EQ', ah4s_wordss_w2nu_u_11)).
fof(37, axiom,![X16]:![X17]:(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X16)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X17)))))),file('i/f/words/WORD__LOWER__OR__EQ', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
