# 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,f))),file('i/f/pred_set/REST__PSUBSET', aHLu_FALSITY)).
fof(11, 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(35, 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(44, axiom,![X1]:![X2]:(~(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))=>s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,h4s_predu_u_sets_choice(s(t_fun(X1,t_bool),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),X2)),file('i/f/pred_set/REST__PSUBSET', ah4s_predu_u_sets_CHOICEu_u_INSERTu_u_REST)).
fof(45, axiom,![X1]:![X2]:~(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),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),X2))))))),file('i/f/pred_set/REST__PSUBSET', ah4s_predu_u_sets_CHOICEu_u_NOTu_u_INu_u_REST)).
fof(46, 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)).
fof(67, 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(68, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/pred_set/REST__PSUBSET', ah4s_bools_NOTu_u_CLAUSESu_c2)).
fof(73, axiom,![X1]:![X5]:![X2]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X5))))<=>![X6]:(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X2))))=>p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X5)))))),file('i/f/pred_set/REST__PSUBSET', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(76, axiom,![X1]:![X6]:![X5]:![X2]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X6),s(t_fun(X1,t_bool),X2))),s(t_fun(X1,t_bool),X5))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X6),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)))))),file('i/f/pred_set/REST__PSUBSET', ah4s_predu_u_sets_INSERTu_u_SUBSET)).
# SZS output end CNFRefutation
