# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_fixedpoints_monotone(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2))))=>![X3]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_bool),X3))))=>p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_fixedpoints_lfp(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2))),s(t_fun(X1,t_bool),X3)))))),file('i/f/fixedPoint/lfp__induction', ch4s_fixedPoints_lfpu_u_induction)).
fof(55, axiom,![X1]:![X2]:(p(s(t_bool,h4s_fixedpoints_monotone(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2))))=>(p(s(t_bool,h4s_fixedpoints_closed(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2),s(t_fun(X1,t_bool),h4s_fixedpoints_lfp(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2))))))&![X3]:(p(s(t_bool,h4s_fixedpoints_closed(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2),s(t_fun(X1,t_bool),X3))))=>p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_fixedpoints_lfp(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2))),s(t_fun(X1,t_bool),X3))))))),file('i/f/fixedPoint/lfp__induction', ah4s_fixedPoints_lfpu_u_leastu_u_closed)).
fof(77, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_fixedpoints_closed(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2),s(t_fun(X1,t_bool),X3)))=s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X2),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_bool),X3))),file('i/f/fixedPoint/lfp__induction', ah4s_fixedPoints_closedu_u_def)).
# SZS output end CNFRefutation
