# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(s(t_h4s_llists_llist(X1),X3)=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X4),s(t_h4s_llists_llist(X1),X2)))<=>(s(t_h4s_options_option(X1),h4s_llists_lhd(s(t_h4s_llists_llist(X1),X3)))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4)))&s(t_h4s_options_option(t_h4s_llists_llist(X1)),h4s_llists_ltl(s(t_h4s_llists_llist(X1),X3)))=s(t_h4s_options_option(t_h4s_llists_llist(X1)),h4s_options_some(s(t_h4s_llists_llist(X1),X2))))),file('i/f/llist/LHDTL__EQ__SOME', ch4s_llists_LHDTLu_u_EQu_u_SOME)).
fof(13, axiom,![X1]:![X8]:![X7]:(s(t_h4s_options_option(X1),h4s_options_some(s(X1,X7)))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X8)))<=>s(X1,X7)=s(X1,X8)),file('i/f/llist/LHDTL__EQ__SOME', ah4s_options_SOMEu_u_11)).
fof(15, axiom,![X1]:![X7]:~(s(t_h4s_options_option(X1),h4s_options_none)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X7)))),file('i/f/llist/LHDTL__EQ__SOME', ah4s_options_NOTu_u_NONEu_u_SOME)).
fof(16, axiom,![X11]:![X2]:![X4]:s(t_h4s_options_option(X11),h4s_llists_lhd(s(t_h4s_llists_llist(X11),h4s_llists_lcons(s(X11,X4),s(t_h4s_llists_llist(X11),X2)))))=s(t_h4s_options_option(X11),h4s_options_some(s(X11,X4))),file('i/f/llist/LHDTL__EQ__SOME', ah4s_llists_LHDu_u_THMu_c1)).
fof(17, axiom,![X11]:![X2]:![X4]:s(t_h4s_options_option(t_h4s_llists_llist(X11)),h4s_llists_ltl(s(t_h4s_llists_llist(X11),h4s_llists_lcons(s(X11,X4),s(t_h4s_llists_llist(X11),X2)))))=s(t_h4s_options_option(t_h4s_llists_llist(X11)),h4s_options_some(s(t_h4s_llists_llist(X11),X2))),file('i/f/llist/LHDTL__EQ__SOME', ah4s_llists_LTLu_u_THMu_c1)).
fof(18, axiom,![X1]:![X12]:(s(t_h4s_llists_llist(X1),X12)=s(t_h4s_llists_llist(X1),h4s_llists_lnil)|?[X4]:?[X2]:s(t_h4s_llists_llist(X1),X12)=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X4),s(t_h4s_llists_llist(X1),X2)))),file('i/f/llist/LHDTL__EQ__SOME', ah4s_llists_llistu_u_CASES)).
fof(20, axiom,![X1]:s(t_h4s_options_option(t_h4s_llists_llist(X1)),h4s_llists_ltl(s(t_h4s_llists_llist(X1),h4s_llists_lnil)))=s(t_h4s_options_option(t_h4s_llists_llist(X1)),h4s_options_none),file('i/f/llist/LHDTL__EQ__SOME', ah4s_llists_LTLu_u_THMu_c0)).
# SZS output end CNFRefutation
