# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2))))=>p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),X2))))))),file('i/f/pred_set/FINITE__REST', ch4s_predu_u_sets_FINITEu_u_REST)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/FINITE__REST', aHLu_FALSITY)).
fof(4, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/pred_set/FINITE__REST', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X3]:(s(t_bool,X3)=s(t_bool,f)<=>~(p(s(t_bool,X3)))),file('i/f/pred_set/FINITE__REST', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(22, axiom,![X9]:![X10]:![X11]:((p(s(t_bool,X11))<=>s(t_bool,X10)=s(t_bool,X9))<=>((p(s(t_bool,X11))|(p(s(t_bool,X10))|p(s(t_bool,X9))))&((p(s(t_bool,X11))|(~(p(s(t_bool,X9)))|~(p(s(t_bool,X10)))))&((p(s(t_bool,X10))|(~(p(s(t_bool,X9)))|~(p(s(t_bool,X11)))))&(p(s(t_bool,X9))|(~(p(s(t_bool,X10)))|~(p(s(t_bool,X11))))))))),file('i/f/pred_set/FINITE__REST', ah4s_sats_dcu_u_eq)).
fof(37, axiom,(p(s(t_bool,f))<=>![X3]:p(s(t_bool,X3))),file('i/f/pred_set/FINITE__REST', ah4s_bools_Fu_u_DEF)).
fof(53, axiom,![X1]:![X4]:![X2]:s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X2),s(X1,X4)))))=s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2))),file('i/f/pred_set/FINITE__REST', ah4s_predu_u_sets_FINITEu_u_DELETE)).
fof(55, axiom,![X1]:![X2]:s(t_fun(X1,t_bool),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),X2)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X2),s(X1,h4s_predu_u_sets_choice(s(t_fun(X1,t_bool),X2))))),file('i/f/pred_set/FINITE__REST', ah4s_predu_u_sets_RESTu_u_DEF)).
fof(73, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/pred_set/FINITE__REST', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
