# 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(2, axiom,p(s(t_bool,t)),file('i/f/words/WORD__LOWER__OR__EQ', aHLu_TRUTH)).
fof(6, axiom,![X1]:![X6]:![X7]:(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X7)))=s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X6)))<=>s(t_h4s_fcps_cart(t_bool,X1),X7)=s(t_h4s_fcps_cart(t_bool,X1),X6)),file('i/f/words/WORD__LOWER__OR__EQ', ah4s_wordss_w2nu_u_11)).
fof(7, 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(8, 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(9, axiom,~(p(s(t_bool,f))),file('i/f/words/WORD__LOWER__OR__EQ', aHLu_FALSITY)).
fof(10, axiom,![X8]:![X9]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))|s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,X8))),file('i/f/words/WORD__LOWER__OR__EQ', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(11, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/words/WORD__LOWER__OR__EQ', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
