# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),h4s_lists_front(s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X3))),s(t_h4s_lists_list(X1),X2)))))))=s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),X2))),file('i/f/list/FRONT__CONS__EQ__NIL_c2', ch4s_lists_FRONTu_u_CONSu_u_EQu_u_NILu_c2)).
fof(4, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/list/FRONT__CONS__EQ__NIL_c2', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(43, axiom,![X1]:![X22]:(p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),X22))))<=>s(t_h4s_lists_list(X1),X22)=s(t_h4s_lists_list(X1),h4s_lists_nil)),file('i/f/list/FRONT__CONS__EQ__NIL_c2', ah4s_lists_NULLu_u_EQ)).
fof(46, axiom,![X1]:![X22]:(p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),X22))))<=>s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X22)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/list/FRONT__CONS__EQ__NIL_c2', ah4s_lists_NULLu_u_LENGTH)).
fof(48, axiom,![X1]:s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),h4s_lists_nil)))=s(t_bool,t),file('i/f/list/FRONT__CONS__EQ__NIL_c2', ah4s_lists_NULLu_u_DEFu_c0)).
fof(60, axiom,![X8]:(s(t_bool,f)=s(t_bool,X8)<=>~(p(s(t_bool,X8)))),file('i/f/list/FRONT__CONS__EQ__NIL_c2', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(73, axiom,![X1]:![X2]:![X3]:s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),h4s_lists_front(s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X3))),s(t_h4s_lists_list(X1),X2)))))))=s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X2))),file('i/f/list/FRONT__CONS__EQ__NIL_c2', ah4s_lists_LENGTHu_u_FRONTu_u_CONS)).
fof(74, axiom,![X1]:![X2]:![X3]:(s(t_h4s_lists_list(X1),h4s_lists_front(s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X3))),s(t_h4s_lists_list(X1),X2)))))=s(t_h4s_lists_list(X1),h4s_lists_nil)<=>s(t_h4s_lists_list(X1),X2)=s(t_h4s_lists_list(X1),h4s_lists_nil)),file('i/f/list/FRONT__CONS__EQ__NIL_c2', ah4s_lists_FRONTu_u_CONSu_u_EQu_u_NILu_c0)).
fof(77, axiom,p(s(t_bool,t)),file('i/f/list/FRONT__CONS__EQ__NIL_c2', aHLu_TRUTH)).
# SZS output end CNFRefutation
