# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),h4s_llists_lnil))))&![X3]:![X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),X4))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X4))))))))=>![X5]:(p(s(t_bool,h4s_llists_lfinite(s(t_h4s_llists_llist(X1),X5))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),X5)))))),file('i/f/llist/LFINITE__INDUCTION', ch4s_llists_LFINITEu_u_INDUCTION)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/llist/LFINITE__INDUCTION', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/llist/LFINITE__INDUCTION', aHLu_FALSITY)).
fof(5, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/llist/LFINITE__INDUCTION', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X1]:![X10]:(p(s(t_bool,h4s_llists_lfinite(s(t_h4s_llists_llist(X1),X10))))<=>![X13]:(![X14]:((s(t_h4s_llists_llist(X1),X14)=s(t_h4s_llists_llist(X1),h4s_llists_lnil)|?[X3]:?[X4]:(s(t_h4s_llists_llist(X1),X14)=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X4)))&p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X13),s(t_h4s_llists_llist(X1),X4))))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X13),s(t_h4s_llists_llist(X1),X14)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X13),s(t_h4s_llists_llist(X1),X10)))))),file('i/f/llist/LFINITE__INDUCTION', ah4s_llists_LFINITEu_u_def)).
fof(13, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t0)|s(t_bool,X4)=s(t_bool,f)),file('i/f/llist/LFINITE__INDUCTION', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
