# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(~(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)))))<=>p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,X1),X2),s(t_h4s_fcps_cart(t_bool,X1),X3))))),file('i/f/words/WORD__NOT__LOWER', ch4s_wordss_WORDu_u_NOTu_u_LOWER)).
fof(19, axiom,![X13]:![X14]:(s(t_bool,X14)=s(t_bool,X13)<=>((p(s(t_bool,X14))&p(s(t_bool,X13)))|(~(p(s(t_bool,X14)))&~(p(s(t_bool,X13)))))),file('i/f/words/WORD__NOT__LOWER', ah4s_bools_EQu_u_EXPAND)).
fof(33, axiom,![X12]:![X15]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X12)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X15))))),file('i/f/words/WORD__NOT__LOWER', ah4s_arithmetics_NOTu_u_LESS)).
fof(43, 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__NOT__LOWER', ah4s_wordss_WORDu_u_LS)).
fof(51, 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__NOT__LOWER', ah4s_wordss_WORDu_u_LO)).
# SZS output end CNFRefutation
