# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_sing(s(t_fun(X1,t_bool),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_rest(s(t_fun(X1,t_bool),X2)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))),file('i/f/pred_set/SING__IFF__EMPTY__REST', ch4s_predu_u_sets_SINGu_u_IFFu_u_EMPTYu_u_REST)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/SING__IFF__EMPTY__REST', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/SING__IFF__EMPTY__REST', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/pred_set/SING__IFF__EMPTY__REST', aHLu_BOOLu_CASES)).
fof(13, axiom,![X3]:(s(t_bool,X3)=s(t_bool,f)<=>~(p(s(t_bool,X3)))),file('i/f/pred_set/SING__IFF__EMPTY__REST', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(14, axiom,![X1]:![X6]:~(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/SING__IFF__EMPTY__REST', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(15, 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/SING__IFF__EMPTY__REST', ah4s_predu_u_sets_CHOICEu_u_INSERTu_u_REST)).
fof(16, axiom,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_sing(s(t_fun(X1,t_bool),X2))))<=>?[X6]:s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))),file('i/f/pred_set/SING__IFF__EMPTY__REST', ah4s_predu_u_sets_SINGu_u_DEF)).
fof(19, axiom,![X1]:![X6]:s(t_fun(X1,t_bool),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),file('i/f/pred_set/SING__IFF__EMPTY__REST', ah4s_predu_u_sets_RESTu_u_SING)).
fof(21, axiom,![X1]:![X7]:![X6]:![X2]:(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X7),s(t_fun(X1,t_bool),X2))))))<=>(s(X1,X6)=s(X1,X7)|p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X2)))))),file('i/f/pred_set/SING__IFF__EMPTY__REST', ah4s_predu_u_sets_INu_u_INSERT)).
# SZS output end CNFRefutation
