# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(~(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))=>p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),X2))),s(t_fun(X1,t_bool),X2))))),file('i/f/pred_set/REST__PSUBSET', ch4s_predu_u_sets_RESTu_u_PSUBSET)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/REST__PSUBSET', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/REST__PSUBSET', aHLu_FALSITY)).
fof(13, axiom,![X5]:(s(t_bool,t)=s(t_bool,X5)<=>p(s(t_bool,X5))),file('i/f/pred_set/REST__PSUBSET', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(15, axiom,![X5]:(s(t_bool,X5)=s(t_bool,f)<=>~(p(s(t_bool,X5)))),file('i/f/pred_set/REST__PSUBSET', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(17, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/pred_set/REST__PSUBSET', aHLu_BOOLu_CASES)).
fof(19, axiom,![X1]:![X5]:![X2]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X5))))<=>(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X5))))&~(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),X5)))),file('i/f/pred_set/REST__PSUBSET', ah4s_predu_u_sets_PSUBSETu_u_DEF)).
fof(21, axiom,![X1]:![X9]:![X6]:![X2]:(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X2),s(X1,X9))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X2))))&~(s(X1,X6)=s(X1,X9)))),file('i/f/pred_set/REST__PSUBSET', ah4s_predu_u_sets_INu_u_DELETE)).
fof(22, axiom,![X1]:![X2]:(~(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))=>p(s(t_bool,h4s_bools_in(s(X1,h4s_predu_u_sets_choice(s(t_fun(X1,t_bool),X2))),s(t_fun(X1,t_bool),X2))))),file('i/f/pred_set/REST__PSUBSET', ah4s_predu_u_sets_CHOICEu_u_DEF)).
fof(23, 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/REST__PSUBSET', ah4s_predu_u_sets_RESTu_u_DEF)).
fof(24, axiom,![X1]:![X2]:p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),X2))),s(t_fun(X1,t_bool),X2)))),file('i/f/pred_set/REST__PSUBSET', ah4s_predu_u_sets_RESTu_u_SUBSET)).
# SZS output end CNFRefutation
