# 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(13, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t0)<=>p(s(t_bool,X4))),file('i/f/llist/LFINITE__INDUCTION', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(15, axiom,![X1]:![X21]:![X2]:(?[X10]:(s(X1,X10)=s(X1,X21)&p(s(t_bool,happ(s(t_fun(X1,t_bool),X2),s(X1,X10)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X2),s(X1,X21))))),file('i/f/llist/LFINITE__INDUCTION', ah4s_bools_UNWINDu_u_THM2)).
fof(52, axiom,![X1]:![X33]:((p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X33),s(t_h4s_llists_llist(X1),h4s_llists_lnil))))&![X3]:![X4]:((p(s(t_bool,h4s_llists_lfinite(s(t_h4s_llists_llist(X1),X4))))&p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X33),s(t_h4s_llists_llist(X1),X4)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X33),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),X33),s(t_h4s_llists_llist(X1),X5)))))),file('i/f/llist/LFINITE__INDUCTION', ah4s_llists_LFINITEu_u_strongind)).
fof(75, 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)).
fof(79, axiom,(~(p(s(t_bool,t0)))<=>p(s(t_bool,f))),file('i/f/llist/LFINITE__INDUCTION', ah4s_bools_NOTu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
