include('Axioms/sum_num+2.ax').
fof(mem_c_2Esorting_2EPART,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2EPART(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))))) ) )).
fof(mem_c_2Esorting_2EPART3,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2EPART3(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))))) ) )).
fof(mem_c_2Esorting_2EPARTITION,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2EPARTITION(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))) ) )).
fof(mem_c_2Esorting_2EPERM,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2EPERM(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool))) ) )).
fof(mem_c_2Esorting_2EPERM__SINGLE__SWAP,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool))) ) )).
fof(mem_c_2Esorting_2EQSORT,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2EQSORT(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) )).
fof(mem_c_2Esorting_2EQSORT3,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2EQSORT3(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) )).
fof(mem_c_2Esorting_2ESORTED,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2ESORTED(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),bool))) ) )).
fof(mem_c_2Esorting_2ESORTS,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2ESORTS(A_27a),arr(arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),arr(arr(A_27a,arr(A_27a,bool)),bool))) ) )).
fof(mem_c_2Esorting_2ESTABLE,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Esorting_2ESTABLE(A_27a),arr(arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),arr(arr(A_27a,arr(A_27a,bool)),bool))) ) )).
fof(ax_thm_2Esorting_2EPERM__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0L1] : ( mem(V0L1,ty_2Elist_2Elist(A_27a)) => ! [V1L2] : ( mem(V1L2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0L1),V1L2)) <=> ! [V2x] : ( mem(V2x,A_27a) => ( ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V2x)),V0L1) = ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V2x)),V1L2) ) ) ) ) ) ) )).
fof(conj_thm_2Esorting_2EPERM__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0L] : ( mem(V0L,ty_2Elist_2Elist(A_27a)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V0L),V0L)) )))).
fof(conj_thm_2Esorting_2EPERM__INTRO,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Elist_2Elist(A_27a)) => ! [V1y] : ( mem(V1y,ty_2Elist_2Elist(A_27a)) => ( ( V0x = V1y ) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V0x),V1y)) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__transitive,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(c_2Erelation_2Etransitive(ty_2Elist_2Elist(A_27a)),c_2Esorting_2EPERM(A_27a)))))).
fof(conj_thm_2Esorting_2EPERM__TRANS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Elist_2Elist(A_27a)) => ! [V1y] : ( mem(V1y,ty_2Elist_2Elist(A_27a)) => ! [V2z] : ( mem(V2z,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0x),V1y)) & p(ap(ap(c_2Esorting_2EPERM(A_27a),V1y),V2z)) ) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V0x),V2z)) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SYM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l2),V0l1)) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__CONG,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0L1] : ( mem(V0L1,ty_2Elist_2Elist(A_27a)) => ! [V1L2] : ( mem(V1L2,ty_2Elist_2Elist(A_27a)) => ! [V2L3] : ( mem(V2L3,ty_2Elist_2Elist(A_27a)) => ! [V3L4] : ( mem(V3L4,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0L1),V2L3)) & p(ap(ap(c_2Esorting_2EPERM(A_27a),V1L2),V3L4)) ) => p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0L1),V1L2)),ap(ap(c_2Elist_2EAPPEND(A_27a),V2L3),V3L4))) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__MONO,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V0l1)),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V1l2))) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__CONS__IFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ! [V2l1] : ( mem(V2l1,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V2l1)),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l2))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V2l1),V1l2)) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__NIL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0L] : ( mem(V0L,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0L),c_2Elist_2ENIL(A_27a))) <=> ( V0L = c_2Elist_2ENIL(A_27a) ) ) & ( p(ap(ap(c_2Esorting_2EPERM(A_27a),c_2Elist_2ENIL(A_27a)),V0L)) <=> ( V0L = c_2Elist_2ENIL(A_27a) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SING,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0L] : ( mem(V0L,ty_2Elist_2Elist(A_27a)) => ! [V1x] : ( mem(V1x,A_27a) => ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0L),ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)))) <=> ( V0L = ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)) ) ) & ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a))),V0L)) <=> ( V0L = ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__CONS__EQ__APPEND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0t] : ( mem(V0t,ty_2Elist_2Elist(A_27a)) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ! [V2h] : ( mem(V2h,A_27a) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V0t)),V1L)) <=> ? [V3M] : ( mem(V3M,ty_2Elist_2Elist(A_27a)) & ? [V4N] : ( mem(V4N,ty_2Elist_2Elist(A_27a)) & ( ( V1L = ap(ap(c_2Elist_2EAPPEND(A_27a),V3M),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V4N)) ) & p(ap(ap(c_2Esorting_2EPERM(A_27a),V0t),ap(ap(c_2Elist_2EAPPEND(A_27a),V3M),V4N))) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__APPEND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),V0l1))) ) )))).
fof(conj_thm_2Esorting_2ECONS__PERM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ! [V2M] : ( mem(V2M,ty_2Elist_2Elist(A_27a)) => ! [V3N] : ( mem(V3N,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V1L),ap(ap(c_2Elist_2EAPPEND(A_27a),V2M),V3N))) => p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1L)),ap(ap(c_2Elist_2EAPPEND(A_27a),V2M),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V3N)))) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EAPPEND__PERM__SYM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0A] : ( mem(V0A,ty_2Elist_2Elist(A_27a)) => ! [V1B] : ( mem(V1B,ty_2Elist_2Elist(A_27a)) => ! [V2C] : ( mem(V2C,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0A),V1B)),V2C)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1B),V0A)),V2C)) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SPLIT__IF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ! [V2l] : ( mem(V2l,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Elist_2EEVERY(A_27a),f1101(A_27a,V0P,V1Q)),V2l)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V2l),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V2l)),ap(ap(c_2Elist_2EFILTER(A_27a),V1Q),V2l)))) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SPLIT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)),ap(ap(c_2Elist_2EFILTER(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V1l)))) ) )))).
fof(conj_thm_2Esorting_2EFILTER__EQ__REP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0x)),V1l) = ap(ap(c_2Erich__list_2EREPLICATE(A_27a),ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0x)),V1l))),V0x) ) ) )))).
fof(conj_thm_2Esorting_2EFILTER__EQ__LENGTHS__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0x)),V1l1)) = ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0x)),V2l2)) ) => ( ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0x)),V1l1) = ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0x)),V2l2) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__alt,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0L1] : ( mem(V0L1,ty_2Elist_2Elist(A_27a)) => ! [V1L2] : ( mem(V1L2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0L1),V1L2)) <=> ! [V2x] : ( mem(V2x,A_27a) => ( ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V2x)),V0L1)) = ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V2x)),V1L2)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__IND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool))) => ( ( p(ap(ap(V0P,c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a))) & ( ( ! [V1x] : ( mem(V1x,A_27a) => ! [V2l1] : ( mem(V2l1,ty_2Elist_2Elist(A_27a)) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(V0P,V2l1),V3l2)) => p(ap(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V1x),V2l1)),ap(ap(c_2Elist_2ECONS(A_27a),V1x),V3l2))) ) ) ) ) ) & ( ( ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ! [V6l1] : ( mem(V6l1,ty_2Elist_2Elist(A_27a)) => ! [V7l2] : ( mem(V7l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(V0P,V6l1),V7l2)) => p(ap(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V4x),ap(ap(c_2Elist_2ECONS(A_27a),V5y),V6l1))),ap(ap(c_2Elist_2ECONS(A_27a),V5y),ap(ap(c_2Elist_2ECONS(A_27a),V4x),V7l2)))) ) ) ) ) ) ) & ! [V8l1] : ( mem(V8l1,ty_2Elist_2Elist(A_27a)) => ! [V9l2] : ( mem(V9l2,ty_2Elist_2Elist(A_27a)) => ! [V10l3] : ( mem(V10l3,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(V0P,V8l1),V9l2)) & p(ap(ap(V0P,V9l2),V10l3)) ) => p(ap(ap(V0P,V8l1),V10l3)) ) ) ) ) ) ) ) => ! [V11l1] : ( mem(V11l1,ty_2Elist_2Elist(A_27a)) => ! [V12l2] : ( mem(V12l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V11l1),V12l2)) => p(ap(ap(V0P,V11l1),V12l2)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SWAP__AT__FRONT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2l1] : ( mem(V2l1,ty_2Elist_2Elist(A_27a)) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),ap(ap(c_2Elist_2ECONS(A_27a),V1y),V2l1))),ap(ap(c_2Elist_2ECONS(A_27a),V1y),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V3l2)))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V2l1),V3l2)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SWAP__L__AT__FRONT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ! [V2x] : ( mem(V2x,ty_2Elist_2Elist(A_27a)) => ! [V3y] : ( mem(V3y,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2x),V3y)),V0l1)),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V3y),V2x)),V1l2))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__STRONG__IND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool))) => ( ( p(ap(ap(V0P,c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a))) & ( ( ! [V1x] : ( mem(V1x,A_27a) => ! [V2l1] : ( mem(V2l1,ty_2Elist_2Elist(A_27a)) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V2l1),V3l2)) & p(ap(ap(V0P,V2l1),V3l2)) ) => p(ap(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V1x),V2l1)),ap(ap(c_2Elist_2ECONS(A_27a),V1x),V3l2))) ) ) ) ) ) & ( ( ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ! [V6l1] : ( mem(V6l1,ty_2Elist_2Elist(A_27a)) => ! [V7l2] : ( mem(V7l2,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V6l1),V7l2)) & p(ap(ap(V0P,V6l1),V7l2)) ) => p(ap(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V4x),ap(ap(c_2Elist_2ECONS(A_27a),V5y),V6l1))),ap(ap(c_2Elist_2ECONS(A_27a),V5y),ap(ap(c_2Elist_2ECONS(A_27a),V4x),V7l2)))) ) ) ) ) ) ) & ! [V8l1] : ( mem(V8l1,ty_2Elist_2Elist(A_27a)) => ! [V9l2] : ( mem(V9l2,ty_2Elist_2Elist(A_27a)) => ! [V10l3] : ( mem(V10l3,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V8l1),V9l2)) & ( p(ap(ap(V0P,V8l1),V9l2)) & ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V9l2),V10l3)) & p(ap(ap(V0P,V9l2),V10l3)) ) ) ) => p(ap(ap(V0P,V8l1),V10l3)) ) ) ) ) ) ) ) => ! [V11l1] : ( mem(V11l1,ty_2Elist_2Elist(A_27a)) => ! [V12l2] : ( mem(V12l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V11l1),V12l2)) => p(ap(ap(V0P,V11l1),V12l2)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__LENGTH,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) => ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27a),V1l2) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__MEM__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__LIST__TO__SET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) => ( ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1) = ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2) ) ) ) )))).
fof(conj_thm_2Esorting_2ESORTED__IND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),bool))) => ( ( ( ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => p(ap(ap(V0P,V1R),c_2Elist_2ENIL(A_27a))) ) ) & ( ( ! [V2R] : ( mem(V2R,arr(A_27a,arr(A_27a,bool))) => ! [V3x] : ( mem(V3x,A_27a) => p(ap(ap(V0P,V2R),ap(ap(c_2Elist_2ECONS(A_27a),V3x),c_2Elist_2ENIL(A_27a)))) ) ) ) & ! [V4R] : ( mem(V4R,arr(A_27a,arr(A_27a,bool))) => ! [V5x] : ( mem(V5x,A_27a) => ! [V6y] : ( mem(V6y,A_27a) => ! [V7rst] : ( mem(V7rst,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(V0P,V4R),ap(ap(c_2Elist_2ECONS(A_27a),V6y),V7rst))) => p(ap(ap(V0P,V4R),ap(ap(c_2Elist_2ECONS(A_27a),V5x),ap(ap(c_2Elist_2ECONS(A_27a),V6y),V7rst)))) ) ) ) ) ) ) ) => ! [V8v] : ( mem(V8v,arr(A_27a,arr(A_27a,bool))) => ! [V9v1] : ( mem(V9v1,ty_2Elist_2Elist(A_27a)) => p(ap(ap(V0P,V8v),V9v1)) ) ) ) )))).
fof(conj_thm_2Esorting_2ESORTED__DEF,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),c_2Elist_2ENIL(A_27a))) <=> $true ) ) ) & ( ( ! [V1x] : ( mem(V1x,A_27a) => ! [V2R] : ( mem(V2R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V2R),ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)))) <=> $true ) ) ) ) & ! [V3y] : ( mem(V3y,A_27a) => ! [V4x] : ( mem(V4x,A_27a) => ! [V5rst] : ( mem(V5rst,ty_2Elist_2Elist(A_27a)) => ! [V6R] : ( mem(V6R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V6R),ap(ap(c_2Elist_2ECONS(A_27a),V4x),ap(ap(c_2Elist_2ECONS(A_27a),V3y),V5rst)))) <=> ( p(ap(ap(V6R,V4x),V3y)) & p(ap(ap(c_2Esorting_2ESORTED(A_27a),V6R),ap(ap(c_2Elist_2ECONS(A_27a),V3y),V5rst))) ) ) ) ) ) ) ) )))).
fof(ax_thm_2Esorting_2ESORTS__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0f] : ( mem(V0f,arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(ap(c_2Esorting_2ESORTS(A_27a),V0f),V1R)) <=> ! [V2l] : ( mem(V2l,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V2l),ap(ap(V0f,V1R),V2l))) & p(ap(ap(c_2Esorting_2ESORTED(A_27a),V1R),ap(ap(V0f,V1R),V2l))) ) ) ) ) ) ) )).
fof(conj_thm_2Esorting_2ESORTED__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) => ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V1L))) <=> ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V1L)) & ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1L))) => p(ap(ap(V0R,V2x),V3y)) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2ESORTED__APPEND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1L1] : ( mem(V1L1,ty_2Elist_2Elist(A_27a)) => ! [V2L2] : ( mem(V2L2,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V1L1)) & ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V2L2)) & ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1L1))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2L2))) ) => p(ap(ap(V0R,V3x),V4y)) ) ) ) ) ) ) => p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),ap(ap(c_2Elist_2EAPPEND(A_27a),V1L1),V2L2))) ) ) ) )))).
fof(ax_thm_2Esorting_2EPART__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ( ( ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( ap(ap(ap(ap(c_2Esorting_2EPART(A_27a),V0P),c_2Elist_2ENIL(A_27a)),V1l1),V2l2) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V1l1),V2l2) ) ) ) ) ) & ! [V3P] : ( mem(V3P,arr(A_27a,bool)) => ! [V4h] : ( mem(V4h,A_27a) => ! [V5rst] : ( mem(V5rst,ty_2Elist_2Elist(A_27a)) => ! [V6l1] : ( mem(V6l1,ty_2Elist_2Elist(A_27a)) => ! [V7l2] : ( mem(V7l2,ty_2Elist_2Elist(A_27a)) => ( ap(ap(ap(ap(c_2Esorting_2EPART(A_27a),V3P),ap(ap(c_2Elist_2ECONS(A_27a),V4h),V5rst)),V6l1),V7l2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),ap(V3P,V4h)),ap(ap(ap(ap(c_2Esorting_2EPART(A_27a),V3P),V5rst),ap(ap(c_2Elist_2ECONS(A_27a),V4h),V6l1)),V7l2)),ap(ap(ap(ap(c_2Esorting_2EPART(A_27a),V3P),V5rst),V6l1),ap(ap(c_2Elist_2ECONS(A_27a),V4h),V7l2))) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Esorting_2EPART__LENGTH,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ! [V2l1] : ( mem(V2l1,ty_2Elist_2Elist(A_27a)) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ! [V4p] : ( mem(V4p,ty_2Elist_2Elist(A_27a)) => ! [V5q] : ( mem(V5q,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V4p),V5q) = ap(ap(ap(ap(c_2Esorting_2EPART(A_27a),V0P),V1L),V2l1),V3l2) ) => ( ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),V1L)),ap(c_2Elist_2ELENGTH(A_27a),V2l1))),ap(c_2Elist_2ELENGTH(A_27a),V3l2)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),V4p)),ap(c_2Elist_2ELENGTH(A_27a),V5q)) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPART__LENGTH__LEM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ! [V2l1] : ( mem(V2l1,ty_2Elist_2Elist(A_27a)) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ! [V4p] : ( mem(V4p,ty_2Elist_2Elist(A_27a)) => ! [V5q] : ( mem(V5q,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V4p),V5q) = ap(ap(ap(ap(c_2Esorting_2EPART(A_27a),V0P),V1L),V2l1),V3l2) ) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V4p)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),V1L)),ap(c_2Elist_2ELENGTH(A_27a),V2l1))),ap(c_2Elist_2ELENGTH(A_27a),V3l2)))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V5q)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),V1L)),ap(c_2Elist_2ELENGTH(A_27a),V2l1))),ap(c_2Elist_2ELENGTH(A_27a),V3l2)))) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPARTs__HAVE__PROP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ! [V2A] : ( mem(V2A,ty_2Elist_2Elist(A_27a)) => ! [V3B] : ( mem(V3B,ty_2Elist_2Elist(A_27a)) => ! [V4l1] : ( mem(V4l1,ty_2Elist_2Elist(A_27a)) => ! [V5l2] : ( mem(V5l2,ty_2Elist_2Elist(A_27a)) => ( ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V2A),V3B) = ap(ap(ap(ap(c_2Esorting_2EPART(A_27a),V0P),V1L),V4l1),V5l2) ) & ( ( ! [V6x] : ( mem(V6x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V4l1))) => p(ap(V0P,V6x)) ) ) ) & ! [V7x] : ( mem(V7x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V7x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V5l2))) => ( ~~ p(ap(V0P,V7x)) ) ) ) ) ) => ( ( ! [V8z] : ( mem(V8z,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V8z),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2A))) => p(ap(V0P,V8z)) ) ) ) & ! [V9z] : ( mem(V9z,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V9z),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3B))) => ( ~~ p(ap(V0P,V9z)) ) ) ) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPART__MEM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ! [V2a1] : ( mem(V2a1,ty_2Elist_2Elist(A_27a)) => ! [V3a2] : ( mem(V3a2,ty_2Elist_2Elist(A_27a)) => ! [V4l1] : ( mem(V4l1,ty_2Elist_2Elist(A_27a)) => ! [V5l2] : ( mem(V5l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V2a1),V3a2) = ap(ap(ap(ap(c_2Esorting_2EPART(A_27a),V0P),V1L),V4l1),V5l2) ) => ! [V6x] : ( mem(V6x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1L),ap(ap(c_2Elist_2EAPPEND(A_27a),V4l1),V5l2))))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2a1),V3a2)))) ) ) ) ) ) ) ) ) )))).
fof(ax_thm_2Esorting_2EPARTITION__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Esorting_2EPARTITION(A_27a),V0P),V1l) = ap(ap(ap(ap(c_2Esorting_2EPART(A_27a),V0P),V1l),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a)) ) ) ) ) )).
fof(conj_thm_2Esorting_2EQSORT__IND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),bool))) => ( ( ( ! [V1ord] : ( mem(V1ord,arr(A_27a,arr(A_27a,bool))) => p(ap(ap(V0P,V1ord),c_2Elist_2ENIL(A_27a))) ) ) & ! [V2ord] : ( mem(V2ord,arr(A_27a,arr(A_27a,bool))) => ! [V3h] : ( mem(V3h,A_27a) => ! [V4t] : ( mem(V4t,ty_2Elist_2Elist(A_27a)) => ( ( ( ! [V5l1] : ( mem(V5l1,ty_2Elist_2Elist(A_27a)) => ! [V6l2] : ( mem(V6l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V5l1),V6l2) = ap(ap(c_2Esorting_2EPARTITION(A_27a),f1102(A_27a,V2ord,V3h)),V4t) ) => p(ap(ap(V0P,V2ord),V6l2)) ) ) ) ) & ! [V8l1] : ( mem(V8l1,ty_2Elist_2Elist(A_27a)) => ! [V9l2] : ( mem(V9l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V8l1),V9l2) = ap(ap(c_2Esorting_2EPARTITION(A_27a),f1103(A_27a,V2ord,V3h)),V4t) ) => p(ap(ap(V0P,V2ord),V8l1)) ) ) ) ) => p(ap(ap(V0P,V2ord),ap(ap(c_2Elist_2ECONS(A_27a),V3h),V4t))) ) ) ) ) ) => ! [V11v] : ( mem(V11v,arr(A_27a,arr(A_27a,bool))) => ! [V12v1] : ( mem(V12v1,ty_2Elist_2Elist(A_27a)) => p(ap(ap(V0P,V11v),V12v1)) ) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT__DEF,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0ord] : ( mem(V0ord,arr(A_27a,arr(A_27a,bool))) => ( ap(ap(c_2Esorting_2EQSORT(A_27a),V0ord),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) ) ) ) & ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(A_27a)) => ! [V2ord] : ( mem(V2ord,arr(A_27a,arr(A_27a,bool))) => ! [V3h] : ( mem(V3h,A_27a) => ( ap(ap(c_2Esorting_2EQSORT(A_27a),V2ord),ap(ap(c_2Elist_2ECONS(A_27a),V3h),V1t)) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),f1105(A_27a,V3h,V2ord))),ap(ap(c_2Esorting_2EPARTITION(A_27a),f1106(A_27a,V2ord,V3h)),V1t)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT__MEM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Esorting_2EQSORT(A_27a),V0R),V1L)))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1L))) ) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT__PERM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V1L),ap(ap(c_2Esorting_2EQSORT(A_27a),V0R),V1L))) ) )))).
fof(conj_thm_2Esorting_2EQSORT__SORTED,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Etotal(A_27a),V0R)) ) => p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),ap(ap(c_2Esorting_2EQSORT(A_27a),V0R),V1L))) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT__SORTS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Etotal(A_27a),V0R)) ) => p(ap(ap(c_2Esorting_2ESORTS(A_27a),c_2Esorting_2EQSORT(A_27a)),V0R)) ) )))).
fof(conj_thm_2Esorting_2EPERM__APPEND__IFF,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),V1l1)),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),V2l2))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1),V2l2)) ) ) ) ) ) & ! [V3l] : ( mem(V3l,ty_2Elist_2Elist(A_27a)) => ! [V4l1] : ( mem(V4l1,ty_2Elist_2Elist(A_27a)) => ! [V5l2] : ( mem(V5l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V4l1),V3l)),ap(ap(c_2Elist_2EAPPEND(A_27a),V5l2),V3l))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V4l1),V5l2)) ) ) ) ) )))).
fof(ax_thm_2Esorting_2EPERM__SINGLE__SWAP__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),V0l1),V1l2)) <=> ? [V2x1] : ( mem(V2x1,ty_2Elist_2Elist(A_27a)) & ? [V3x2] : ( mem(V3x2,ty_2Elist_2Elist(A_27a)) & ? [V4x3] : ( mem(V4x3,ty_2Elist_2Elist(A_27a)) & ( ( V0l1 = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2x1),V3x2)),V4x3) ) & ( V1l2 = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2x1),V4x3)),V3x2) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Esorting_2EPERM__SINGLE__SWAP__SYM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),V0l1),V1l2)) <=> p(ap(ap(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),V1l2),V0l1)) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SINGLE__SWAP__I,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x1] : ( mem(V0x1,ty_2Elist_2Elist(A_27a)) => ! [V1x2] : ( mem(V1x2,ty_2Elist_2Elist(A_27a)) => ! [V2x3] : ( mem(V2x3,ty_2Elist_2Elist(A_27a)) => p(ap(ap(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0x1),V1x2)),V2x3)),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0x1),V2x3)),V1x2))) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SINGLE__SWAP__APPEND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x2] : ( mem(V0x2,ty_2Elist_2Elist(A_27a)) => ! [V1x3] : ( mem(V1x3,ty_2Elist_2Elist(A_27a)) => p(ap(ap(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0x2),V1x3)),ap(ap(c_2Elist_2EAPPEND(A_27a),V1x3),V0x2))) ) )))).
fof(conj_thm_2Esorting_2EPERM__SINGLE__SWAP__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => p(ap(ap(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),V0l),V0l)) )))).
fof(conj_thm_2Esorting_2EPERM__SINGLE__SWAP__CONS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0M] : ( mem(V0M,ty_2Elist_2Elist(A_27a)) => ! [V1N] : ( mem(V1N,ty_2Elist_2Elist(A_27a)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),V0M),V1N)) => p(ap(ap(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V0M)),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V1N))) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SINGLE__SWAP__TC__CONS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1M] : ( mem(V1M,ty_2Elist_2Elist(A_27a)) => ! [V2N] : ( mem(V2N,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(ap(c_2Erelation_2ETC(ty_2Elist_2Elist(A_27a)),c_2Esorting_2EPERM__SINGLE__SWAP(A_27a)),V1M),V2N)) => p(ap(ap(ap(c_2Erelation_2ETC(ty_2Elist_2Elist(A_27a)),c_2Esorting_2EPERM__SINGLE__SWAP(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1M)),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V2N))) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__TC,lemma,( ! [A_27a]: ( ne(A_27a) => ( c_2Esorting_2EPERM(A_27a) = ap(c_2Erelation_2ETC(ty_2Elist_2Elist(A_27a)),c_2Esorting_2EPERM__SINGLE__SWAP(A_27a)) )))).
fof(conj_thm_2Esorting_2EPERM__RTC,lemma,( ! [A_27a]: ( ne(A_27a) => ( c_2Esorting_2EPERM(A_27a) = ap(c_2Erelation_2ERTC(ty_2Elist_2Elist(A_27a)),c_2Esorting_2EPERM__SINGLE__SWAP(A_27a)) )))).
fof(conj_thm_2Esorting_2EPERM__EQC,lemma,( ! [A_27a]: ( ne(A_27a) => ( c_2Esorting_2EPERM(A_27a) = ap(c_2Erelation_2EEQC(ty_2Elist_2Elist(A_27a)),c_2Esorting_2EPERM__SINGLE__SWAP(A_27a)) )))).
fof(conj_thm_2Esorting_2EPERM__lifts__transitive__relations,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(ty_2Elist_2Elist(A_27a),A_27b)) => ! [V1Q] : ( mem(V1Q,arr(A_27b,arr(A_27b,bool))) => ( ( ( ! [V2x1] : ( mem(V2x1,ty_2Elist_2Elist(A_27a)) => ! [V3x2] : ( mem(V3x2,ty_2Elist_2Elist(A_27a)) => ! [V4x3] : ( mem(V4x3,ty_2Elist_2Elist(A_27a)) => p(ap(ap(V1Q,ap(V0f,ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2x1),V3x2)),V4x3))),ap(V0f,ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2x1),V4x3)),V3x2)))) ) ) ) ) & p(ap(c_2Erelation_2Etransitive(A_27b),V1Q)) ) => ! [V5x] : ( mem(V5x,ty_2Elist_2Elist(A_27a)) => ! [V6y] : ( mem(V6y,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V5x),V6y)) => p(ap(ap(V1Q,ap(V0f,V5x)),ap(V0f,V6y))) ) ) ) ) ) ))))).
fof(conj_thm_2Esorting_2EPERM__lifts__equalities,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(ty_2Elist_2Elist(A_27a),A_27b)) => ( ( ! [V1x1] : ( mem(V1x1,ty_2Elist_2Elist(A_27a)) => ! [V2x2] : ( mem(V2x2,ty_2Elist_2Elist(A_27a)) => ! [V3x3] : ( mem(V3x3,ty_2Elist_2Elist(A_27a)) => ( ap(V0f,ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1x1),V2x2)),V3x3)) = ap(V0f,ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1x1),V3x3)),V2x2)) ) ) ) ) ) => ! [V4x] : ( mem(V4x,ty_2Elist_2Elist(A_27a)) => ! [V5y] : ( mem(V5y,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V4x),V5y)) => ( ap(V0f,V4x) = ap(V0f,V5y) ) ) ) ) ) ))))).
fof(conj_thm_2Esorting_2EPERM__lifts__invariants,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) => ( ( ! [V1x1] : ( mem(V1x1,ty_2Elist_2Elist(A_27a)) => ! [V2x2] : ( mem(V2x2,ty_2Elist_2Elist(A_27a)) => ! [V3x3] : ( mem(V3x3,ty_2Elist_2Elist(A_27a)) => ( p(ap(V0P,ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1x1),V2x2)),V3x3))) => p(ap(V0P,ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1x1),V3x3)),V2x2))) ) ) ) ) ) => ! [V4x] : ( mem(V4x,ty_2Elist_2Elist(A_27a)) => ! [V5y] : ( mem(V5y,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(V0P,V4x)) & p(ap(ap(c_2Esorting_2EPERM(A_27a),V4x),V5y)) ) => p(ap(V0P,V5y)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__lifts__monotonicities,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b))) => ( ( ! [V1x1] : ( mem(V1x1,ty_2Elist_2Elist(A_27a)) => ! [V2x2] : ( mem(V2x2,ty_2Elist_2Elist(A_27a)) => ! [V3x3] : ( mem(V3x3,ty_2Elist_2Elist(A_27a)) => ? [V4x1_27] : ( mem(V4x1_27,ty_2Elist_2Elist(A_27b)) & ? [V5x2_27] : ( mem(V5x2_27,ty_2Elist_2Elist(A_27b)) & ? [V6x3_27] : ( mem(V6x3_27,ty_2Elist_2Elist(A_27b)) & ( ( ap(V0f,ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1x1),V2x2)),V3x3)) = ap(ap(c_2Elist_2EAPPEND(A_27b),ap(ap(c_2Elist_2EAPPEND(A_27b),V4x1_27),V5x2_27)),V6x3_27) ) & ( ap(V0f,ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1x1),V3x3)),V2x2)) = ap(ap(c_2Elist_2EAPPEND(A_27b),ap(ap(c_2Elist_2EAPPEND(A_27b),V4x1_27),V6x3_27)),V5x2_27) ) ) ) ) ) ) ) ) ) => ! [V7x] : ( mem(V7x,ty_2Elist_2Elist(A_27a)) => ! [V8y] : ( mem(V8y,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V7x),V8y)) => p(ap(ap(c_2Esorting_2EPERM(A_27b),ap(V0f,V7x)),ap(V0f,V8y))) ) ) ) ) ))))).
fof(conj_thm_2Esorting_2EPERM__EQUIVALENCE,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(c_2Erelation_2Eequivalence(ty_2Elist_2Elist(A_27a)),c_2Esorting_2EPERM(A_27a)))))).
fof(conj_thm_2Esorting_2EPERM__EQUIVALENCE__ALT__DEF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Elist_2Elist(A_27a)) => ! [V1y] : ( mem(V1y,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0x),V1y)) <=> ( ap(c_2Esorting_2EPERM(A_27a),V0x) = ap(c_2Esorting_2EPERM(A_27a),V1y) ) ) ) )))).
fof(conj_thm_2Esorting_2EALL__DISTINCT__PERM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) => ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l1)) <=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1l2)) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__ALL__DISTINCT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l1)) & ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1l2)) & ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))) ) ) ) ) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) ) ) )))).
fof(conj_thm_2Esorting_2EALL__DISTINCT__PERM__LIST__TO__SET__TO__LIST,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0ls] : ( mem(V0ls,ty_2Elist_2Elist(A_27a)) => ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0ls)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V0ls),ap(c_2Elist_2ESET__TO__LIST(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls)))) ) )))).
fof(conj_thm_2Esorting_2EPERM__MAP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1),V2l2)) => p(ap(ap(c_2Esorting_2EPERM(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l1)),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l2))) ) ) ) ))))).
fof(conj_thm_2Esorting_2EPERM__SUM,lemma,(! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(ty_2Enum_2Enum)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(ty_2Enum_2Enum)) => ( p(ap(ap(c_2Esorting_2EPERM(ty_2Enum_2Enum),V0l1),V1l2)) => ( ap(c_2Elist_2ESUM,V0l1) = ap(c_2Elist_2ESUM,V1l2) ) ) ) ))).
fof(conj_thm_2Esorting_2EPERM__FILTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1),V2l2)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l1)),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V2l2))) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__REVERSE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0ls] : ( mem(V0ls,ty_2Elist_2Elist(A_27a)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V0ls),ap(c_2Elist_2EREVERSE(A_27a),V0ls))) )))).
fof(conj_thm_2Esorting_2EPERM__REVERSE__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0l1)),V1l2)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) ) & ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),ap(c_2Elist_2EREVERSE(A_27a),V1l2))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) ) ) ) )))).
fof(conj_thm_2Esorting_2EFOLDR__PERM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0f] : ( mem(V0f,arr(A_27a,arr(A_27a,A_27a))) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ! [V3e] : ( mem(V3e,A_27a) => ( ( p(ap(c_2Ecombin_2EASSOC(A_27a),V0f)) & p(ap(c_2Ecombin_2ECOMM(A_27a,A_27a),V0f)) ) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1),V2l2)) => ( ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27a),V0f),V3e),V1l1) = ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27a),V0f),V3e),V2l2) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__SET__TO__LIST__count__COUNT__LIST,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Esorting_2EPERM(ty_2Enum_2Enum),ap(c_2Elist_2ESET__TO__LIST(ty_2Enum_2Enum),ap(c_2Epred__set_2Ecount,V0n))),ap(c_2Erich__list_2ECOUNT__LIST,V0n))) ))).
fof(conj_thm_2Esorting_2ESUM__IMAGE__count__SUM__GENLIST,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Epred__set_2ESUM__IMAGE(ty_2Enum_2Enum),V0f),ap(c_2Epred__set_2Ecount,V1n)) = ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),V0f),V1n)) ) ) ))).
fof(conj_thm_2Esorting_2ESUM__IMAGE__count__MULT,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1g] : ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) => ! [V2f] : ( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) => ! [V3k] : ( mem(V3k,ty_2Enum_2Enum) => ( ( ! [V4m] : ( mem(V4m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V4m),V0n)) => ( ap(V1g,V4m) = ap(ap(c_2Epred__set_2ESUM__IMAGE(ty_2Enum_2Enum),f1107(V3k,V4m,V2f)),ap(c_2Epred__set_2Ecount,V3k)) ) ) ) ) => ( ap(ap(c_2Epred__set_2ESUM__IMAGE(ty_2Enum_2Enum),V2f),ap(c_2Epred__set_2Ecount,ap(ap(c_2Earithmetic_2E_2A,V3k),V0n))) = ap(ap(c_2Epred__set_2ESUM__IMAGE(ty_2Enum_2Enum),V1g),ap(c_2Epred__set_2Ecount,V0n)) ) ) ) ) ) ))).
fof(conj_thm_2Esorting_2Esum__of__sums,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) => ! [V1a] : ( mem(V1a,ty_2Enum_2Enum) => ! [V2b] : ( mem(V2b,ty_2Enum_2Enum) => ( ap(ap(c_2Epred__set_2ESUM__IMAGE(ty_2Enum_2Enum),f1108(V0f,V1a)),ap(c_2Epred__set_2Ecount,V2b)) = ap(ap(c_2Epred__set_2ESUM__IMAGE(ty_2Enum_2Enum),f1109(V0f,V1a)),ap(c_2Epred__set_2Ecount,ap(ap(c_2Earithmetic_2E_2A,V1a),V2b))) ) ) ) ))).
fof(conj_thm_2Esorting_2ESORTED__NIL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),c_2Elist_2ENIL(A_27a))) )))).
fof(conj_thm_2Esorting_2ESORTED__SING,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)))) ) )))).
fof(conj_thm_2Esorting_2ESORTED__TL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2xs] : ( mem(V2xs,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1x),V2xs))) => p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V2xs)) ) ) ) )))).
fof(conj_thm_2Esorting_2ESORTED__EL__SUC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1ls] : ( mem(V1ls,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V1ls)) <=> ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V2n)),ap(c_2Elist_2ELENGTH(A_27a),V1ls))) => p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V2n),V1ls)),ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Enum_2ESUC,V2n)),V1ls))) ) ) ) ) )))).
fof(conj_thm_2Esorting_2ESORTED__EL__LESS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) => ! [V1ls] : ( mem(V1ls,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V1ls)) <=> ! [V2m] : ( mem(V2m,ty_2Enum_2Enum) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V3n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Elist_2ELENGTH(A_27a),V1ls))) ) => p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V2m),V1ls)),ap(ap(c_2Elist_2EEL(A_27a),V3n),V1ls))) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2ESORTED__APPEND__IFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1L1] : ( mem(V1L1,ty_2Elist_2Elist(A_27a)) => ! [V2L2] : ( mem(V2L2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),ap(ap(c_2Elist_2EAPPEND(A_27a),V1L1),V2L2))) <=> ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V1L1)) & ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V2L2)) & ( ( V1L1 = c_2Elist_2ENIL(A_27a) ) | ( ( V2L2 = c_2Elist_2ENIL(A_27a) ) | p(ap(ap(V0R,ap(c_2Elist_2ELAST(A_27a),V1L1)),ap(c_2Elist_2EHD(A_27a),V2L2))) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EMEM__PERM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l2)) => ! [V2a] : ( mem(V2a,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))) ) ) ) ) )))).
fof(conj_thm_2Esorting_2ESORTED__PERM__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) ) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V1l1)) & ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V2l2)) & p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1),V2l2)) ) ) => ( V1l1 = V2l2 ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT__eq__if__PERM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Etotal(A_27a),V0R)) & ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) ) ) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Esorting_2EQSORT(A_27a),V0R),V1l1) = ap(ap(c_2Esorting_2EQSORT(A_27a),V0R),V2l2) ) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1),V2l2)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2ESORTED__FILTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1ls] : ( mem(V1ls,ty_2Elist_2Elist(A_27a)) => ! [V2P] : ( mem(V2P,arr(A_27a,bool)) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V1ls)) ) => p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),ap(ap(c_2Elist_2EFILTER(A_27a),V2P),V1ls))) ) ) ) )))).
fof(conj_thm_2Esorting_2EALL__DISTINCT__SORTED__WEAKEN,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1R_27] : ( mem(V1R_27,arr(A_27a,arr(A_27a,bool))) => ! [V2ls] : ( mem(V2ls,ty_2Elist_2Elist(A_27a)) => ( ( ( ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2ls))) & ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2ls))) & ( ~~ ( V3x = V4y ) ) ) ) => ( p(ap(ap(V0R,V3x),V4y)) <=> p(ap(ap(V1R_27,V3x),V4y)) ) ) ) ) ) & ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V2ls)) & p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V2ls)) ) ) => p(ap(ap(c_2Esorting_2ESORTED(A_27a),V1R_27),V2ls)) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__APPEND__C,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l1_27] : ( mem(V1l1_27,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ! [V3l2_27] : ( mem(V3l2_27,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V0l1) = ap(c_2Esorting_2EPERM(A_27a),V1l1_27) ) => ( ( ap(c_2Esorting_2EPERM(A_27a),V2l2) = ap(c_2Esorting_2EPERM(A_27a),V3l2_27) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V2l2)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1_27),V3l2_27)) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__CONS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l1_27] : ( mem(V2l1_27,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V1l1) = ap(c_2Esorting_2EPERM(A_27a),V2l1_27) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l1)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V2l1_27)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__APPEND__CONS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V2l2))) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l1)),V2l2)) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__SWAP__AT__FRONT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2l] : ( mem(V2l,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),ap(ap(c_2Elist_2ECONS(A_27a),V1y),V2l))) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1y),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V2l))) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__CONS__11__SWAP__AT__FRONT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0y] : ( mem(V0y,A_27a) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V1l1) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3l2)) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0y),V1l1)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),ap(ap(c_2Elist_2ECONS(A_27a),V0y),V3l2))) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__CONS__11__APPEND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0y] : ( mem(V0y,A_27a) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ! [V3l3] : ( mem(V3l3,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V1l1) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2l2),V3l3)) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0y),V1l1)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2l2),ap(ap(c_2Elist_2ECONS(A_27a),V0y),V3l3))) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__CONS__APPEND__1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V1l1) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3l2)) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V0l)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),ap(ap(c_2Elist_2EAPPEND(A_27a),V3l2),V0l))) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__CONS__APPEND__2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V1l1) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3l2)) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),V1l1)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),V3l2))) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__APPEND__APPEND__1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ! [V2l3] : ( mem(V2l3,ty_2Elist_2Elist(A_27a)) => ! [V3l4] : ( mem(V3l4,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V0l1) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),V2l3)) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V3l4)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),ap(ap(c_2Elist_2EAPPEND(A_27a),V2l3),V3l4))) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__APPEND__APPEND__2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ! [V2l3] : ( mem(V2l3,ty_2Elist_2Elist(A_27a)) => ! [V3l4] : ( mem(V3l4,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V0l1) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),V2l3)) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V3l4),V0l1)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),ap(ap(c_2Elist_2EAPPEND(A_27a),V3l4),V2l3))) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__APPEND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),V0l1)) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__CONS__IFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V1l1) = ap(c_2Esorting_2EPERM(A_27a),V2l2) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l1)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V2l2)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__APPEND__IFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V1l1) = ap(c_2Esorting_2EPERM(A_27a),V2l2) ) => ( ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),V1l1)) = ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),V2l2)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__CONG,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l1_27] : ( mem(V1l1_27,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ! [V3l2_27] : ( mem(V3l2_27,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Esorting_2EPERM(A_27a),V0l1) = ap(c_2Esorting_2EPERM(A_27a),V1l1_27) ) => ( ( ap(c_2Esorting_2EPERM(A_27a),V2l2) = ap(c_2Esorting_2EPERM(A_27a),V3l2_27) ) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V2l2)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1_27),V3l2_27)) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__CONG__2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l1_27] : ( mem(V1l1_27,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ! [V3l2_27] : ( mem(V3l2_27,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V1l1_27)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V2l2),V3l2_27)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V2l2)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1_27),V3l2_27)) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__CONG__APPEND__IFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l1_27] : ( mem(V2l1_27,ty_2Elist_2Elist(A_27a)) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ! [V4l2_27] : ( mem(V4l2_27,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),V2l1_27))) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V3l2),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),V4l2_27))) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1),V3l2)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V2l1_27),V4l2_27)) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__CONG__APPEND__IFF2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l1_27] : ( mem(V1l1_27,ty_2Elist_2Elist(A_27a)) => ! [V2l1_27_27] : ( mem(V2l1_27_27,ty_2Elist_2Elist(A_27a)) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ! [V4l2_27] : ( mem(V4l2_27,ty_2Elist_2Elist(A_27a)) => ! [V5l2_27_27] : ( mem(V5l2_27_27,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1_27),V2l1_27_27))) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V3l2),ap(ap(c_2Elist_2EAPPEND(A_27a),V4l2_27),V5l2_27_27))) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l1_27),V4l2_27)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l1),V3l2)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V2l1_27_27),V5l2_27_27)) ) ) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__FUN__SPLIT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l1_27] : ( mem(V2l1_27,ty_2Elist_2Elist(A_27a)) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V3l2))) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V2l1_27),V1l1)) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l),ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1_27),V3l2))) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__REWR,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1r] : ( mem(V1r,ty_2Elist_2Elist(A_27a)) => ! [V2l1] : ( mem(V2l1,ty_2Elist_2Elist(A_27a)) => ! [V3l2] : ( mem(V3l2,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l),V1r)) => ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),V2l1)),V3l2)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1r),V2l1)),V3l2)) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__TO__APPEND__SIMPS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => ! [V2r1] : ( mem(V2r1,ty_2Elist_2Elist(A_27a)) => ! [V3r2] : ( mem(V3r2,ty_2Elist_2Elist(A_27a)) => ! [V4xs] : ( mem(V4xs,ty_2Elist_2Elist(A_27a)) => ! [V5ys] : ( mem(V5ys,ty_2Elist_2Elist(A_27a)) => ! [V6zs] : ( mem(V6zs,ty_2Elist_2Elist(A_27a)) => ! [V7r] : ( mem(V7r,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l)),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V2r1)),V3r2))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l),ap(ap(c_2Elist_2EAPPEND(A_27a),V2r1),V3r2))) ) & ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l)),ap(ap(c_2Elist_2EAPPEND(A_27a),V2r1),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V3r2)))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l),ap(ap(c_2Elist_2EAPPEND(A_27a),V2r1),V3r2))) ) & ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V4xs),V5ys)),V6zs)),V7r)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V4xs),ap(ap(c_2Elist_2EAPPEND(A_27a),V5ys),V6zs))),V7r)) ) & ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V5ys)),V6zs)),V7r)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),ap(ap(c_2Elist_2EAPPEND(A_27a),V5ys),V6zs))),V7r)) ) & ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),c_2Elist_2ENIL(A_27a)),V1l)),V7r)) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l),V7r)) ) & ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V4xs),V1l)),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V4xs),V2r1)),V3r2))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l),ap(ap(c_2Elist_2EAPPEND(A_27a),V2r1),V3r2))) ) & ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V4xs),V1l)),ap(ap(c_2Elist_2EAPPEND(A_27a),V2r1),ap(ap(c_2Elist_2EAPPEND(A_27a),V4xs),V3r2)))) <=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l),ap(ap(c_2Elist_2EAPPEND(A_27a),V2r1),V3r2))) ) & ( ( p(ap(ap(c_2Esorting_2EPERM(A_27b),c_2Elist_2ENIL(A_27b)),ap(ap(c_2Elist_2EAPPEND(A_27b),c_2Elist_2ENIL(A_27b)),c_2Elist_2ENIL(A_27b)))) <=> $true ) & ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V4xs),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V4xs),c_2Elist_2ENIL(A_27a))),c_2Elist_2ENIL(A_27a)))) <=> $true ) & ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V4xs),ap(ap(c_2Elist_2EAPPEND(A_27a),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2EAPPEND(A_27a),V4xs),c_2Elist_2ENIL(A_27a))))) <=> $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))))).
fof(ax_thm_2Esorting_2ESTABLE__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0sort] : ( mem(V0sort,arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) => ! [V1r] : ( mem(V1r,arr(A_27a,arr(A_27a,bool))) => ( p(ap(ap(c_2Esorting_2ESTABLE(A_27a),V0sort),V1r)) <=> ( p(ap(ap(c_2Esorting_2ESORTS(A_27a),V0sort),V1r)) & ! [V2p] : ( mem(V2p,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ( ( p(ap(V2p,V3x)) & p(ap(V2p,V4y)) ) => p(ap(ap(V1r,V3x),V4y)) ) ) ) ) => ! [V5l] : ( mem(V5l,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Elist_2EFILTER(A_27a),V2p),V5l) = ap(ap(c_2Elist_2EFILTER(A_27a),V2p),ap(ap(V0sort,V1r),V5l)) ) ) ) ) ) ) ) ) ) )).
fof(ax_thm_2Esorting_2EPART3__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ( ( ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1h] : ( mem(V1h,A_27a) => ( ap(ap(ap(c_2Esorting_2EPART3(A_27a),V0R),V1h),c_2Elist_2ENIL(A_27a)) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a))) ) ) ) ) & ! [V2R] : ( mem(V2R,arr(A_27a,arr(A_27a,bool))) => ! [V3h] : ( mem(V3h,A_27a) => ! [V4hd] : ( mem(V4hd,A_27a) => ! [V5tl] : ( mem(V5tl,ty_2Elist_2Elist(A_27a)) => ( ap(ap(ap(c_2Esorting_2EPART3(A_27a),V2R),V3h),ap(ap(c_2Elist_2ECONS(A_27a),V4hd),V5tl)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V2R,V3h),V4hd)),ap(ap(V2R,V4hd),V3h))),ap(ap(ap(c_2Epair_2E_23_23(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a))),ap(ap(c_2Epair_2E_23_23(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ECONS(A_27a),V4hd)),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a)))),ap(ap(ap(c_2Esorting_2EPART3(A_27a),V2R),V3h),V5tl))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))),ap(ap(V2R,V4hd),V3h)),ap(ap(ap(c_2Epair_2E_23_23(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),ap(c_2Elist_2ECONS(A_27a),V4hd)),ap(ap(c_2Epair_2E_23_23(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a))),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a)))),ap(ap(ap(c_2Esorting_2EPART3(A_27a),V2R),V3h),V5tl))),ap(ap(ap(c_2Epair_2E_23_23(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a))),ap(ap(c_2Epair_2E_23_23(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a))),ap(c_2Elist_2ECONS(A_27a),V4hd))),ap(ap(ap(c_2Esorting_2EPART3(A_27a),V2R),V3h),V5tl)))) ) ) ) ) ) ) ) )).
fof(conj_thm_2Esorting_2EPART3__FILTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1tl] : ( mem(V1tl,ty_2Elist_2Elist(A_27a)) => ! [V2hd] : ( mem(V2hd,A_27a) => ( ap(ap(ap(c_2Esorting_2EPART3(A_27a),V0R),V2hd),V1tl) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),ap(ap(c_2Elist_2EFILTER(A_27a),f1110(A_27a,V0R,V2hd)),V1tl)),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ap(ap(c_2Elist_2EFILTER(A_27a),f1111(A_27a,V2hd,V0R)),V1tl)),ap(ap(c_2Elist_2EFILTER(A_27a),f1112(A_27a,V2hd,V0R)),V1tl))) ) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT3__IND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),bool))) => ( ( ( ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => p(ap(ap(V0P,V1R),c_2Elist_2ENIL(A_27a))) ) ) & ! [V2R] : ( mem(V2R,arr(A_27a,arr(A_27a,bool))) => ! [V3hd] : ( mem(V3hd,A_27a) => ! [V4tl] : ( mem(V4tl,ty_2Elist_2Elist(A_27a)) => ( ( ( ! [V5lo] : ( mem(V5lo,ty_2Elist_2Elist(A_27a)) => ! [V6eq] : ( mem(V6eq,ty_2Elist_2Elist(A_27a)) => ! [V7hi] : ( mem(V7hi,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),V5lo),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V6eq),V7hi)) = ap(ap(ap(c_2Esorting_2EPART3(A_27a),V2R),V3hd),V4tl) ) => p(ap(ap(V0P,V2R),V7hi)) ) ) ) ) ) & ! [V8lo] : ( mem(V8lo,ty_2Elist_2Elist(A_27a)) => ! [V9eq] : ( mem(V9eq,ty_2Elist_2Elist(A_27a)) => ! [V10hi] : ( mem(V10hi,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),V8lo),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V9eq),V10hi)) = ap(ap(ap(c_2Esorting_2EPART3(A_27a),V2R),V3hd),V4tl) ) => p(ap(ap(V0P,V2R),V8lo)) ) ) ) ) ) => p(ap(ap(V0P,V2R),ap(ap(c_2Elist_2ECONS(A_27a),V3hd),V4tl))) ) ) ) ) ) => ! [V11v] : ( mem(V11v,arr(A_27a,arr(A_27a,bool))) => ! [V12v1] : ( mem(V12v1,ty_2Elist_2Elist(A_27a)) => p(ap(ap(V0P,V11v),V12v1)) ) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT3__DEF,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ap(ap(c_2Esorting_2EQSORT3(A_27a),V0R),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) ) ) ) & ! [V1tl] : ( mem(V1tl,ty_2Elist_2Elist(A_27a)) => ! [V2hd] : ( mem(V2hd,A_27a) => ! [V3R] : ( mem(V3R,arr(A_27a,arr(A_27a,bool))) => ( ap(ap(c_2Esorting_2EQSORT3(A_27a),V3R),ap(ap(c_2Elist_2ECONS(A_27a),V2hd),V1tl)) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),ty_2Elist_2Elist(A_27a)),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(A_27a),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)),f1115(A_27a,V3R,V2hd))),ap(ap(ap(c_2Esorting_2EPART3(A_27a),V3R),V2hd),V1tl)) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM3,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Elist_2Elist(A_27a)) => ! [V1a] : ( mem(V1a,ty_2Elist_2Elist(A_27a)) => ! [V2a_27] : ( mem(V2a_27,ty_2Elist_2Elist(A_27a)) => ! [V3b] : ( mem(V3b,ty_2Elist_2Elist(A_27a)) => ! [V4b_27] : ( mem(V4b_27,ty_2Elist_2Elist(A_27a)) => ! [V5c] : ( mem(V5c,ty_2Elist_2Elist(A_27a)) => ! [V6c_27] : ( mem(V6c_27,ty_2Elist_2Elist(A_27a)) => ( ( ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V1a),V2a_27)) & ( p(ap(ap(c_2Esorting_2EPERM(A_27a),V3b),V4b_27)) & p(ap(ap(c_2Esorting_2EPERM(A_27a),V5c),V6c_27)) ) ) & p(ap(ap(c_2Esorting_2EPERM(A_27a),V0x),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1a),V3b)),V5c))) ) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V0x),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2a_27),V4b_27)),V6c_27))) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EPERM3__FILTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => ! [V2h] : ( mem(V2h,A_27a) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),f1116(A_27a,V0R,V2h)),V1l)),ap(ap(c_2Elist_2EFILTER(A_27a),f1117(A_27a,V2h,V0R)),V1l))),ap(ap(c_2Elist_2EFILTER(A_27a),f1118(A_27a,V2h,V0R)),V1l)))) ) ) )))).
fof(conj_thm_2Esorting_2EPERM__QSORT3,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => p(ap(ap(c_2Esorting_2EPERM(A_27a),V0l),ap(ap(c_2Esorting_2EQSORT3(A_27a),V1R),V0l))) ) )))).
fof(conj_thm_2Esorting_2ESORTED__EQ__PART,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0hd] : ( mem(V0hd,A_27a) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => ! [V2R] : ( mem(V2R,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Erelation_2Etransitive(A_27a),V2R)) => p(ap(ap(c_2Esorting_2ESORTED(A_27a),V2R),ap(ap(c_2Elist_2EFILTER(A_27a),f1119(A_27a,V0hd,V2R)),V1l))) ) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT3__SORTS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Etotal(A_27a),V0R)) ) => p(ap(ap(c_2Esorting_2ESORTS(A_27a),c_2Esorting_2EQSORT3(A_27a)),V0R)) ) )))).
fof(conj_thm_2Esorting_2EQSORT3__SPLIT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Etotal(A_27a),V0R)) ) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => ! [V2e] : ( mem(V2e,A_27a) => ( ap(ap(c_2Esorting_2EQSORT3(A_27a),V0R),V1l) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Esorting_2EQSORT3(A_27a),V0R),ap(ap(c_2Elist_2EFILTER(A_27a),f1120(A_27a,V0R,V2e)),V1l))),ap(ap(c_2Elist_2EFILTER(A_27a),f1121(A_27a,V2e,V0R)),V1l))),ap(ap(c_2Esorting_2EQSORT3(A_27a),V0R),ap(ap(c_2Elist_2EFILTER(A_27a),f1122(A_27a,V2e,V0R)),V1l))) ) ) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT3__STABLE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Etotal(A_27a),V0R)) ) => p(ap(ap(c_2Esorting_2ESTABLE(A_27a),c_2Esorting_2EQSORT3(A_27a)),V0R)) ) )))).
fof(conj_thm_2Esorting_2EQSORT3__MEM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Esorting_2EQSORT3(A_27a),V0R),V1L)))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1L))) ) ) ) )))).
fof(conj_thm_2Esorting_2EQSORT3__SORTED,conjecture,( ! [A_27a]: ( ne(A_27a) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1L] : ( mem(V1L,ty_2Elist_2Elist(A_27a)) => ( ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Etotal(A_27a),V0R)) ) => p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),ap(ap(c_2Esorting_2EQSORT3(A_27a),V0R),V1L))) ) ) )))).
