# 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(48, 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(50, 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(51, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/SING__IFF__EMPTY__REST', aHLu_FALSITY)).
fof(54, axiom,![X5]:(s(t_bool,f)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/pred_set/SING__IFF__EMPTY__REST', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(64, axiom,(p(s(t_bool,f))<=>![X5]:p(s(t_bool,X5))),file('i/f/pred_set/SING__IFF__EMPTY__REST', ah4s_bools_Fu_u_DEF)).
fof(65, 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(68, axiom,![X1]:s(t_bool,h4s_predu_u_sets_sing(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))=s(t_bool,f),file('i/f/pred_set/SING__IFF__EMPTY__REST', ah4s_predu_u_sets_SINGu_u_EMPTY)).
fof(69, axiom,![X1]:![X6]:p(s(t_bool,h4s_predu_u_sets_sing(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_SING0)).
# SZS output end CNFRefutation
