# 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)))))&~(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),X2),s(t_h4s_fcps_cart(t_bool,X1),X3))))),file('i/f/words/WORD__LOWER__CASES__IMP', ch4s_wordss_WORDu_u_LOWERu_u_CASESu_u_IMP)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/words/WORD__LOWER__CASES__IMP', aHLu_FALSITY)).
fof(23, axiom,![X4]:((p(s(t_bool,X4))=>p(s(t_bool,f)))<=>s(t_bool,X4)=s(t_bool,f)),file('i/f/words/WORD__LOWER__CASES__IMP', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(44, axiom,![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__LOWER__CASES__IMP', ah4s_wordss_WORDu_u_NOTu_u_LOWER)).
fof(47, axiom,![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__CASES__IMP', ah4s_wordss_WORDu_u_LOWERu_u_ORu_u_EQ)).
fof(54, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/words/WORD__LOWER__CASES__IMP', aHLu_BOOLu_CASES)).
fof(55, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/words/WORD__LOWER__CASES__IMP', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
