fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Elbtree_2Ebf__flatten_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X0_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Ellist_2Ellist(A_27a)),c_2Elbtree_2Ebf__flatten_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X0_2E0))))).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))))).
fof(arityeq3_2Ec_2Elbtree_2ENd_2E3_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,X0_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),X2_2E0))) = s(tyop_2Elbtree_2Elbtree(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Elbtree_2Elbtree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Elbtree_2Elbtree(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Emin_2Efun(tyop_2Elbtree_2Elbtree(A_27a),tyop_2Elbtree_2Elbtree(A_27a)))),c_2Elbtree_2ENd_2E0),s(A_27a,X0_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),X1_2E0))),s(tyop_2Elbtree_2Elbtree(A_27a),X2_2E0))))).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Elbtree_2Elbtree_28A_27a_29,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),X1_2E0))))).
fof(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELCONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))))).
fof(lbtreeTheory_2Ebf__flatten__def,axiom,![A_27a]: ((s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ENIL_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)) & (![V0ts_2E0]: (s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ELf_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V0ts_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V0ts_2E0)))) & ![V1a_2E0, V2t1_2E0, V3t2_2E0, V4ts_2E0]: (s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),c_2Elbtree_2ENd_2E3(s(A_27a,V1a_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0))),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V4ts_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1a_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Elbtree_2Ebf__flatten_2E1(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),V4ts_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),V2t1_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elbtree_2Elbtree(A_27a),V3t2_2E0),s(tyop_2Elist_2Elist(tyop_2Elbtree_2Elbtree(A_27a)),c_2Elist_2ENIL_2E0))))))))))))))).
