ITP001 Axioms: ITP053+5.ax
%------------------------------------------------------------------------------
% File : ITP053+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : sorting+2.ax [Gau20]
% : HL4053+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 159 ( 0 unt; 0 def)
% Number of atoms : 1067 ( 104 equ)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 911 ( 3 ~; 2 |; 96 &)
% ( 54 <=>; 756 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 10 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 88 ( 88 usr; 14 con; 0-5 aty)
% Number of variables : 689 ( 681 !; 8 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,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))
<=> p(ap(ap(c_2Esorting_2EPERM(A_27a),V1l2),V0l1)) ) ) ) ) ).
fof(conj_thm_2Esorting_2EPERM__CONG,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,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),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),V0l1))) ) ) ) ).
fof(conj_thm_2Esorting_2ECONS__PERM,axiom,
! [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,axiom,
! [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(lameq_f1101,axiom,
! [A_27a,V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V3x] : ap(f1101(A_27a,V0P,V1Q),V3x) = ap(ap(c_2Emin_2E_3D(bool),ap(V0P,V3x)),ap(c_2Ebool_2E_7E,ap(V1Q,V3x))) ) ) ).
fof(conj_thm_2Esorting_2EPERM__SPLIT__IF,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,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(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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,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))
=> ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27a),V1l2) ) ) ) ) ).
fof(conj_thm_2Esorting_2EPERM__MEM__EQ,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)
=> ( 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,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))
=> ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1) = ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2) ) ) ) ) ).
fof(conj_thm_2Esorting_2ESORTED__IND,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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(lameq_f1102,axiom,
! [A_27a,V2ord] :
( mem(V2ord,arr(A_27a,arr(A_27a,bool)))
=> ! [V3h] :
( mem(V3h,A_27a)
=> ! [V7y] : ap(f1102(A_27a,V2ord,V3h),V7y) = ap(ap(V2ord,V7y),V3h) ) ) ).
fof(lameq_f1103,axiom,
! [A_27a,V2ord] :
( mem(V2ord,arr(A_27a,arr(A_27a,bool)))
=> ! [V3h] :
( mem(V3h,A_27a)
=> ! [V10y] : ap(f1103(A_27a,V2ord,V3h),V10y) = ap(ap(V2ord,V10y),V3h) ) ) ).
fof(conj_thm_2Esorting_2EQSORT__IND,axiom,
! [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(lameq_f1104,axiom,
! [A_27a,V4l1] :
( mem(V4l1,ty_2Elist_2Elist(A_27a))
=> ! [V3h] :
( mem(V3h,A_27a)
=> ! [V2ord] :
( mem(V2ord,arr(A_27a,arr(A_27a,bool)))
=> ! [V5l2] : ap(f1104(A_27a,V4l1,V3h,V2ord),V5l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Esorting_2EQSORT(A_27a),V2ord),V4l1)),ap(ap(c_2Elist_2ECONS(A_27a),V3h),c_2Elist_2ENIL(A_27a)))),ap(ap(c_2Esorting_2EQSORT(A_27a),V2ord),V5l2)) ) ) ) ).
fof(lameq_f1105,axiom,
! [A_27a,V3h] :
( mem(V3h,A_27a)
=> ! [V2ord] :
( mem(V2ord,arr(A_27a,arr(A_27a,bool)))
=> ! [V4l1] : ap(f1105(A_27a,V3h,V2ord),V4l1) = f1104(A_27a,V4l1,V3h,V2ord) ) ) ).
fof(lameq_f1106,axiom,
! [A_27a,V2ord] :
( mem(V2ord,arr(A_27a,arr(A_27a,bool)))
=> ! [V3h] :
( mem(V3h,A_27a)
=> ! [V6y] : ap(f1106(A_27a,V2ord,V3h),V6y) = ap(ap(V2ord,V6y),V3h) ) ) ).
fof(conj_thm_2Esorting_2EQSORT__DEF,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,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))
<=> p(ap(ap(c_2Esorting_2EPERM__SINGLE__SWAP(A_27a),V1l2),V0l1)) ) ) ) ) ).
fof(conj_thm_2Esorting_2EPERM__SINGLE__SWAP__I,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,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))
=> ( 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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,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))
=> ( 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,axiom,
! [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,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),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,axiom,
! [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,axiom,
! [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,axiom,
! [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(lameq_f1107,axiom,
! [V3k] :
( mem(V3k,ty_2Enum_2Enum)
=> ! [V4m] :
( mem(V4m,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V5x] : ap(f1107(V3k,V4m,V2f),V5x) = ap(V2f,ap(ap(c_2Earithmetic_2E_2B,V5x),ap(ap(c_2Earithmetic_2E_2A,V3k),V4m))) ) ) ) ).
fof(conj_thm_2Esorting_2ESUM__IMAGE__count__MULT,axiom,
! [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(lameq_f1108,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V3m] : ap(f1108(V0f,V1a),V3m) = ap(ap(c_2Epred__set_2ESUM__IMAGE(ty_2Enum_2Enum),ap(V0f,V3m)),ap(c_2Epred__set_2Ecount,V1a)) ) ) ).
fof(lameq_f1109,axiom,
! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V4m] : ap(f1109(V0f,V1a),V4m) = ap(ap(V0f,ap(ap(c_2Earithmetic_2EDIV,V4m),V1a)),ap(ap(c_2Earithmetic_2EMOD,V4m),V1a)) ) ) ).
fof(conj_thm_2Esorting_2Esum__of__sums,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,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))
=> ! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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(lameq_f1110,axiom,
! [A_27a,V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2hd] :
( mem(V2hd,A_27a)
=> ! [V3x] : ap(f1110(A_27a,V0R,V2hd),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0R,V3x),V2hd)),ap(c_2Ebool_2E_7E,ap(ap(V0R,V2hd),V3x))) ) ) ).
fof(lameq_f1111,axiom,
! [A_27a,V2hd] :
( mem(V2hd,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V4x] : ap(f1111(A_27a,V2hd,V0R),V4x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0R,V4x),V2hd)),ap(ap(V0R,V2hd),V4x)) ) ) ).
fof(lameq_f1112,axiom,
! [A_27a,V2hd] :
( mem(V2hd,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V5x] : ap(f1112(A_27a,V2hd,V0R),V5x) = ap(c_2Ebool_2E_7E,ap(ap(V0R,V5x),V2hd)) ) ) ).
fof(conj_thm_2Esorting_2EPART3__FILTER,axiom,
! [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,axiom,
! [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(lameq_f1113,axiom,
! [A_27a,V4lo] :
( mem(V4lo,ty_2Elist_2Elist(A_27a))
=> ! [V2hd] :
( mem(V2hd,A_27a)
=> ! [V5eq] :
( mem(V5eq,ty_2Elist_2Elist(A_27a))
=> ! [V3R] :
( mem(V3R,arr(A_27a,arr(A_27a,bool)))
=> ! [V6hi] : ap(f1113(A_27a,V4lo,V2hd,V5eq,V3R),V6hi) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Esorting_2EQSORT3(A_27a),V3R),V4lo)),ap(ap(c_2Elist_2ECONS(A_27a),V2hd),V5eq))),ap(ap(c_2Esorting_2EQSORT3(A_27a),V3R),V6hi)) ) ) ) ) ).
fof(lameq_f1114,axiom,
! [A_27a,V4lo] :
( mem(V4lo,ty_2Elist_2Elist(A_27a))
=> ! [V2hd] :
( mem(V2hd,A_27a)
=> ! [V3R] :
( mem(V3R,arr(A_27a,arr(A_27a,bool)))
=> ! [V5eq] : ap(f1114(A_27a,V4lo,V2hd,V3R),V5eq) = f1113(A_27a,V4lo,V2hd,V5eq,V3R) ) ) ) ).
fof(lameq_f1115,axiom,
! [A_27a,V3R] :
( mem(V3R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2hd] :
( mem(V2hd,A_27a)
=> ! [V4lo] : ap(f1115(A_27a,V3R,V2hd),V4lo) = ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),f1114(A_27a,V4lo,V2hd,V3R)) ) ) ).
fof(conj_thm_2Esorting_2EQSORT3__DEF,axiom,
! [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,axiom,
! [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(lameq_f1116,axiom,
! [A_27a,V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3x] : ap(f1116(A_27a,V0R,V2h),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0R,V3x),V2h)),ap(c_2Ebool_2E_7E,ap(ap(V0R,V2h),V3x))) ) ) ).
fof(lameq_f1117,axiom,
! [A_27a,V2h] :
( mem(V2h,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V4x] : ap(f1117(A_27a,V2h,V0R),V4x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0R,V4x),V2h)),ap(ap(V0R,V2h),V4x)) ) ) ).
fof(lameq_f1118,axiom,
! [A_27a,V2h] :
( mem(V2h,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V5x] : ap(f1118(A_27a,V2h,V0R),V5x) = ap(c_2Ebool_2E_7E,ap(ap(V0R,V5x),V2h)) ) ) ).
fof(conj_thm_2Esorting_2EPERM3__FILTER,axiom,
! [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,axiom,
! [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(lameq_f1119,axiom,
! [A_27a,V0hd] :
( mem(V0hd,A_27a)
=> ! [V2R] :
( mem(V2R,arr(A_27a,arr(A_27a,bool)))
=> ! [V3x] : ap(f1119(A_27a,V0hd,V2R),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V2R,V3x),V0hd)),ap(ap(V2R,V0hd),V3x)) ) ) ).
fof(conj_thm_2Esorting_2ESORTED__EQ__PART,axiom,
! [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,axiom,
! [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(lameq_f1120,axiom,
! [A_27a,V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2e] :
( mem(V2e,A_27a)
=> ! [V3x] : ap(f1120(A_27a,V0R,V2e),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0R,V3x),V2e)),ap(c_2Ebool_2E_7E,ap(ap(V0R,V2e),V3x))) ) ) ).
fof(lameq_f1121,axiom,
! [A_27a,V2e] :
( mem(V2e,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V4x] : ap(f1121(A_27a,V2e,V0R),V4x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0R,V4x),V2e)),ap(ap(V0R,V2e),V4x)) ) ) ).
fof(lameq_f1122,axiom,
! [A_27a,V2e] :
( mem(V2e,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V5x] : ap(f1122(A_27a,V2e,V0R),V5x) = ap(c_2Ebool_2E_7E,ap(ap(V0R,V5x),V2e)) ) ) ).
fof(conj_thm_2Esorting_2EQSORT3__SPLIT,axiom,
! [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,axiom,
! [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,axiom,
! [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,axiom,
! [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))) ) ) ) ) ).
fof(conj_thm_2Esorting_2Esorted__count__list,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> p(ap(ap(c_2Esorting_2ESORTED(ty_2Enum_2Enum),c_2Earithmetic_2E_3C_3D),ap(c_2Erich__list_2ECOUNT__LIST,V0n))) ) ).
fof(conj_thm_2Esorting_2Esorted__map,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1f] :
( mem(V1f,arr(A_27b,A_27a))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27b))
=> ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R))
=> ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),ap(ap(c_2Elist_2EMAP(A_27b,A_27a),V1f),V2l)))
<=> p(ap(ap(c_2Esorting_2ESORTED(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f)),V2l)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Esorting_2Esorted__perm__count__list,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0y] :
( mem(V0y,A_27a)
=> ! [V1f] :
( mem(V1f,arr(A_27b,ty_2Enum_2Enum))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27b))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Esorting_2ESORTED(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,ty_2Enum_2Enum),c_2Earithmetic_2E_3C_3D),V1f)),V2l))
& p(ap(ap(c_2Esorting_2EPERM(ty_2Enum_2Enum),ap(ap(c_2Elist_2EMAP(A_27b,ty_2Enum_2Enum),V1f),V2l)),ap(c_2Erich__list_2ECOUNT__LIST,V3n))) )
=> ap(ap(c_2Elist_2EMAP(A_27b,ty_2Enum_2Enum),V1f),V2l) = ap(c_2Erich__list_2ECOUNT__LIST,V3n) ) ) ) ) ) ) ) ).
fof(conj_thm_2Esorting_2ESORTED__weaken,axiom,
! [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))
=> ( ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V0R),V2ls))
& ! [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)))
& p(ap(ap(V0R,V3x),V4y)) )
=> p(ap(ap(V1R_27,V3x),V4y)) ) ) ) )
=> p(ap(ap(c_2Esorting_2ESORTED(A_27a),V1R_27),V2ls)) ) ) ) ) ) ).
fof(conj_thm_2Esorting_2Eless__sorted__eq,axiom,
! [V0L] :
( mem(V0L,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Esorting_2ESORTED(ty_2Enum_2Enum),c_2Eprim__rec_2E_3C),ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V1x),V0L)))
<=> ( p(ap(ap(c_2Esorting_2ESORTED(ty_2Enum_2Enum),c_2Eprim__rec_2E_3C),V0L))
& ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V2y),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),V0L)))
=> p(ap(ap(c_2Eprim__rec_2E_3C,V1x),V2y)) ) ) ) ) ) ) ).
fof(conj_thm_2Esorting_2ESORTED__GENLIST__PLUS,axiom,
! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> p(ap(ap(c_2Esorting_2ESORTED(ty_2Enum_2Enum),c_2Eprim__rec_2E_3C),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V1k)),V0n))) ) ) ).
fof(conj_thm_2Esorting_2ESORTED__ALL__DISTINCT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( ( p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R))
& 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))
=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1ls)) ) ) ) ) ) ).
fof(conj_thm_2Esorting_2Esorted__filter,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1R] :
( mem(V1R,arr(A_27a,arr(A_27a,bool)))
=> ! [V2ls] :
( mem(V2ls,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Erelation_2Etransitive(A_27a),V1R))
=> ( p(ap(ap(c_2Esorting_2ESORTED(A_27a),V1R),V2ls))
=> p(ap(ap(c_2Esorting_2ESORTED(A_27a),V1R),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V2ls))) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------