ITP001 Axioms: ITP066+5.ax
%------------------------------------------------------------------------------
% File : ITP066+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 : lbtree+2.ax [Gau20]
% : HL4066+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 134 ( 4 unt; 0 def)
% Number of atoms : 802 ( 137 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 669 ( 1 ~; 12 |; 126 &)
% ( 20 <=>; 510 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 10 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 124 ( 124 usr; 13 con; 0-8 aty)
% Number of variables : 655 ( 603 !; 52 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(ne_ty_2Elbtree_2Elbtree,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Elbtree_2Elbtree(A0)) ) ).
fof(mem_c_2Elbtree_2ELf,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2ELf(A_27a),ty_2Elbtree_2Elbtree(A_27a)) ) ).
fof(mem_c_2Elbtree_2ELfrep,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elbtree_2ELfrep(A_27a,A_27b),arr(A_27a,ty_2Eoption_2Eoption(A_27b))) ) ) ).
fof(mem_c_2Elbtree_2ENd,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2ENd(A_27a),arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Elbtree_2Elbtree(A_27a),ty_2Elbtree_2Elbtree(A_27a))))) ) ).
fof(mem_c_2Elbtree_2ENdrep,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2ENdrep(A_27a),arr(A_27a,arr(arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)),arr(arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)),arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))))) ) ).
fof(mem_c_2Elbtree_2Ebf__flatten,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2Ebf__flatten(A_27a),arr(ty_2Elist_2Elist(ty_2Elbtree_2Elbtree(A_27a)),ty_2Ellist_2Ellist(A_27a))) ) ).
fof(mem_c_2Elbtree_2Edepth,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2Edepth(A_27a),arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool)))) ) ).
fof(mem_c_2Elbtree_2Efinite,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2Efinite(A_27a),arr(ty_2Elbtree_2Elbtree(A_27a),bool)) ) ).
fof(mem_c_2Elbtree_2Eis__lbtree,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2Eis__lbtree(A_27a),arr(arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)),bool)) ) ).
fof(mem_c_2Elbtree_2Eis__mmindex,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2Eis__mmindex(A_27a),arr(arr(A_27a,ty_2Eoption_2Eoption(ty_2Enum_2Enum)),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))))) ) ).
fof(mem_c_2Elbtree_2Elbtree__abs,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2Elbtree__abs(A_27a),arr(arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)),ty_2Elbtree_2Elbtree(A_27a))) ) ).
fof(mem_c_2Elbtree_2Elbtree__case,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elbtree_2Elbtree__case(A_27a,A_27b),arr(A_27a,arr(arr(A_27b,arr(ty_2Elbtree_2Elbtree(A_27b),arr(ty_2Elbtree_2Elbtree(A_27b),A_27a))),arr(ty_2Elbtree_2Elbtree(A_27b),A_27a)))) ) ) ).
fof(mem_c_2Elbtree_2Elbtree__rep,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2Elbtree__rep(A_27a),arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))) ) ).
fof(mem_c_2Elbtree_2Emap,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elbtree_2Emap(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Elbtree_2Elbtree(A_27a),ty_2Elbtree_2Elbtree(A_27b)))) ) ) ).
fof(mem_c_2Elbtree_2Emem,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2Emem(A_27a),arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool))) ) ).
fof(mem_c_2Elbtree_2Emindepth,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elbtree_2Emindepth(A_27a),arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),ty_2Eoption_2Eoption(ty_2Enum_2Enum)))) ) ).
fof(mem_c_2Elbtree_2Eoptmin,axiom,
mem(c_2Elbtree_2Eoptmin,arr(ty_2Eoption_2Eoption(ty_2Enum_2Enum),arr(ty_2Eoption_2Eoption(ty_2Enum_2Enum),ty_2Eoption_2Eoption(ty_2Enum_2Enum)))) ).
fof(mem_c_2Elbtree_2Epath__follow,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elbtree_2Epath__follow(A_27a,A_27b),arr(arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27b)))),arr(A_27b,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a))))) ) ) ).
fof(ax_thm_2Elbtree_2ELfrep__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Elbtree_2ELfrep(A_27a,A_27b) = k(A_27a,c_2Eoption_2ENONE(A_27b)) ) ) ).
fof(lameq_f1952,axiom,
! [A_27a,V4v] :
( mem(V4v,bool)
=> ! [V1t1] :
( mem(V1t1,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ! [V2t2] :
( mem(V2t2,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ! [V5xs] : ap(f1952(A_27a,V4v,V1t1,V2t2),V5xs) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V4v),ap(V1t1,V5xs)),ap(V2t2,V5xs)) ) ) ) ).
fof(lameq_f1953,axiom,
! [A_27a,V1t1] :
( mem(V1t1,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ! [V2t2] :
( mem(V2t2,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ! [V4v] : ap(f1953(A_27a,V1t1,V2t2),V4v) = f1952(A_27a,V4v,V1t1,V2t2) ) ) ).
fof(lameq_f1954,axiom,
! [A_27a,V0a] :
( mem(V0a,A_27a)
=> ! [V1t1] :
( mem(V1t1,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ! [V2t2] :
( mem(V2t2,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ! [V3l] : ap(f1954(A_27a,V0a,V1t1,V2t2),V3l) = ap(ap(ap(c_2Elist_2Elist__CASE(bool,ty_2Eoption_2Eoption(A_27a)),V3l),ap(c_2Eoption_2ESOME(A_27a),V0a)),f1953(A_27a,V1t1,V2t2)) ) ) ) ).
fof(ax_thm_2Elbtree_2ENdrep__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,A_27a)
=> ! [V1t1] :
( mem(V1t1,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ! [V2t2] :
( mem(V2t2,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ap(ap(ap(c_2Elbtree_2ENdrep(A_27a),V0a),V1t1),V2t2) = f1954(A_27a,V0a,V1t1,V2t2) ) ) ) ) ).
fof(ax_thm_2Elbtree_2Eis__lbtree__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ( p(ap(c_2Elbtree_2Eis__lbtree(A_27a),V0t))
<=> ? [V1P] :
( mem(V1P,arr(arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)),bool))
& ! [V2t] :
( mem(V2t,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ( p(ap(V1P,V2t))
=> ( V2t = c_2Elbtree_2ELfrep(ty_2Elist_2Elist(bool),A_27a)
| ? [V3a] :
( mem(V3a,A_27a)
& ? [V4t1] :
( mem(V4t1,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
& ? [V5t2] :
( mem(V5t2,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
& p(ap(V1P,V4t1))
& p(ap(V1P,V5t2))
& V2t = ap(ap(ap(c_2Elbtree_2ENdrep(A_27a),V3a),V4t1),V5t2) ) ) ) ) ) )
& p(ap(V1P,V0t)) ) ) ) ) ).
fof(ax_thm_2Elbtree_2Elbtree__TY__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ? [V0rep] :
( mem(V0rep,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a))))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)),ty_2Elbtree_2Elbtree(A_27a)),c_2Elbtree_2Eis__lbtree(A_27a)),V0rep)) ) ) ).
fof(ax_thm_2Elbtree_2Elbtree__absrep,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0a] :
( mem(V0a,ty_2Elbtree_2Elbtree(A_27a))
=> ap(c_2Elbtree_2Elbtree__abs(A_27a),ap(c_2Elbtree_2Elbtree__rep(A_27a),V0a)) = V0a )
& ! [V1r] :
( mem(V1r,arr(ty_2Elist_2Elist(bool),ty_2Eoption_2Eoption(A_27a)))
=> ( p(ap(c_2Elbtree_2Eis__lbtree(A_27a),V1r))
<=> ap(c_2Elbtree_2Elbtree__rep(A_27a),ap(c_2Elbtree_2Elbtree__abs(A_27a),V1r)) = V1r ) ) ) ) ).
fof(lameq_f1955,axiom,
! [A_27a,A_27b,V2g] :
( mem(V2g,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27b)))))
=> ! [V9y] :
( mem(V9y,A_27b)
=> ! [V4h] :
( mem(V4h,bool)
=> ! [V5t] :
( mem(V5t,ty_2Elist_2Elist(bool))
=> ! [V10z] : ap(f1955(A_27a,A_27b,V2g,V9y,V4h,V5t),V10z) = ap(ap(ap(c_2Elbtree_2Epath__follow(A_27a,A_27b),V2g),ap(ap(ap(c_2Ebool_2ECOND(A_27b),V4h),V9y),V10z)),V5t) ) ) ) ) ).
fof(lameq_f1956,axiom,
! [A_27a,A_27b,V2g] :
( mem(V2g,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27b)))))
=> ! [V4h] :
( mem(V4h,bool)
=> ! [V5t] :
( mem(V5t,ty_2Elist_2Elist(bool))
=> ! [V9y] : ap(f1956(A_27a,A_27b,V2g,V4h,V5t),V9y) = f1955(A_27a,A_27b,V2g,V9y,V4h,V5t) ) ) ) ).
fof(lameq_f1957,axiom,
! [A_27a,A_27b,V5t] :
( mem(V5t,ty_2Elist_2Elist(bool))
=> ! [V4h] :
( mem(V4h,bool)
=> ! [V2g] :
( mem(V2g,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27b)))))
=> ! [V8v2] : ap(f1957(A_27a,A_27b,V5t,V4h,V2g),V8v2) = ap(ap(c_2Epair_2Epair__CASE(ty_2Eoption_2Eoption(A_27a),A_27b,A_27b),V8v2),f1956(A_27a,A_27b,V2g,V4h,V5t)) ) ) ) ).
fof(lameq_f1958,axiom,
! [A_27b,A_27a,V2g] :
( mem(V2g,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27b)))))
=> ! [V4h] :
( mem(V4h,bool)
=> ! [V5t] :
( mem(V5t,ty_2Elist_2Elist(bool))
=> ! [V6v] : ap(f1958(A_27b,A_27a,V2g,V4h,V5t),V6v) = ap(ap(c_2Epair_2Epair__CASE(ty_2Eoption_2Eoption(A_27a),A_27a,ty_2Epair_2Eprod(A_27b,A_27b)),V6v),k(A_27a,f1957(A_27a,A_27b,V5t,V4h,V2g))) ) ) ) ).
fof(ax_thm_2Elbtree_2Epath__follow__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0g] :
( mem(V0g,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27b)))))
=> ! [V1x] :
( mem(V1x,A_27b)
=> ap(ap(ap(c_2Elbtree_2Epath__follow(A_27a,A_27b),V0g),V1x),c_2Elist_2ENIL(bool)) = ap(ap(c_2Eoption_2EOPTION__MAP(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27b)),A_27a),c_2Epair_2EFST(A_27a,ty_2Epair_2Eprod(A_27b,A_27b))),ap(V0g,V1x)) ) )
& ! [V2g] :
( mem(V2g,arr(A_27b,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27b)))))
=> ! [V3x] :
( mem(V3x,A_27b)
=> ! [V4h] :
( mem(V4h,bool)
=> ! [V5t] :
( mem(V5t,ty_2Elist_2Elist(bool))
=> ap(ap(ap(c_2Elbtree_2Epath__follow(A_27a,A_27b),V2g),V3x),ap(ap(c_2Elist_2ECONS(bool),V4h),V5t)) = ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(A_27b,A_27b)),ty_2Eoption_2Eoption(A_27a)),ap(V2g,V3x)),c_2Eoption_2ENONE(A_27a)),f1958(A_27b,A_27a,V2g,V4h,V5t)) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elbtree_2ELf__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Elbtree_2ELf(A_27a) = ap(c_2Elbtree_2Elbtree__abs(A_27a),c_2Elbtree_2ELfrep(ty_2Elist_2Elist(bool),A_27a)) ) ).
fof(ax_thm_2Elbtree_2ENd__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,A_27a)
=> ! [V1t1] :
( mem(V1t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V2t2] :
( mem(V2t2,ty_2Elbtree_2Elbtree(A_27a))
=> ap(ap(ap(c_2Elbtree_2ENd(A_27a),V0a),V1t1),V2t2) = ap(c_2Elbtree_2Elbtree__abs(A_27a),ap(ap(ap(c_2Elbtree_2ENdrep(A_27a),V0a),ap(c_2Elbtree_2Elbtree__rep(A_27a),V1t1)),ap(c_2Elbtree_2Elbtree__rep(A_27a),V2t2))) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Elbtree__cases,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Elbtree_2Elbtree(A_27a))
=> ( V0t = c_2Elbtree_2ELf(A_27a)
| ? [V1a] :
( mem(V1a,A_27a)
& ? [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
& V0t = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1a),V2t1),V3t2) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2ELf__NOT__Nd,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,A_27a)
=> ! [V1t1] :
( mem(V1t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V2t2] :
( mem(V2t2,ty_2Elbtree_2Elbtree(A_27a))
=> c_2Elbtree_2ELf(A_27a) != ap(ap(ap(c_2Elbtree_2ENd(A_27a),V0a),V1t1),V2t2) ) ) ) ) ).
fof(conj_thm_2Elbtree_2ENd__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a1] :
( mem(V0a1,A_27a)
=> ! [V1t1] :
( mem(V1t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V2u1] :
( mem(V2u1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3a2] :
( mem(V3a2,A_27a)
=> ! [V4t2] :
( mem(V4t2,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V5u2] :
( mem(V5u2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ap(ap(ap(c_2Elbtree_2ENd(A_27a),V0a1),V1t1),V2u1) = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V3a2),V4t2),V5u2)
<=> ( V0a1 = V3a2
& V1t1 = V4t2
& V2u1 = V5u2 ) ) ) ) ) ) ) ) ) ).
fof(lameq_f1959,axiom,
! [A_27b,A_27a,V4b] :
( mem(V4b,A_27b)
=> ! [V6y] :
( mem(V6y,A_27a)
=> ! [V1g] :
( mem(V1g,arr(A_27a,ty_2Elbtree_2Elbtree(A_27b)))
=> ! [V7z] : ap(f1959(A_27b,A_27a,V4b,V6y,V1g),V7z) = ap(ap(ap(c_2Elbtree_2ENd(A_27b),V4b),ap(V1g,V6y)),ap(V1g,V7z)) ) ) ) ).
fof(lameq_f1960,axiom,
! [A_27b,A_27a,V4b] :
( mem(V4b,A_27b)
=> ! [V1g] :
( mem(V1g,arr(A_27a,ty_2Elbtree_2Elbtree(A_27b)))
=> ! [V6y] : ap(f1960(A_27b,A_27a,V4b,V1g),V6y) = f1959(A_27b,A_27a,V4b,V6y,V1g) ) ) ).
fof(lameq_f1961,axiom,
! [A_27b,A_27a,V1g] :
( mem(V1g,arr(A_27a,ty_2Elbtree_2Elbtree(A_27b)))
=> ! [V4b] :
( mem(V4b,A_27b)
=> ! [V5v2] : ap(f1961(A_27b,A_27a,V1g,V4b),V5v2) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elbtree_2Elbtree(A_27b),A_27a,A_27a),V5v2),f1960(A_27b,A_27a,V4b,V1g)) ) ) ).
fof(lameq_f1962,axiom,
! [A_27a,A_27b,V1g] :
( mem(V1g,arr(A_27a,ty_2Elbtree_2Elbtree(A_27b)))
=> ! [V4b] : ap(f1962(A_27a,A_27b,V1g),V4b) = f1961(A_27b,A_27a,V1g,V4b) ) ).
fof(lameq_f1963,axiom,
! [A_27a,A_27b,V1g] :
( mem(V1g,arr(A_27a,ty_2Elbtree_2Elbtree(A_27b)))
=> ! [V3v] : ap(f1963(A_27a,A_27b,V1g),V3v) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elbtree_2Elbtree(A_27b),A_27b,ty_2Epair_2Eprod(A_27a,A_27a)),V3v),f1962(A_27a,A_27b,V1g)) ) ).
fof(lameq_f1964,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,ty_2Epair_2Eprod(A_27a,A_27a)))))
=> ! [V1g] :
( mem(V1g,arr(A_27a,ty_2Elbtree_2Elbtree(A_27b)))
=> ! [V2x] : ap(f1964(A_27b,A_27a,V0f,V1g),V2x) = ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27b)),ap(V1g,V2x)),ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Epair_2Eprod(A_27b,ty_2Epair_2Eprod(A_27a,A_27a)),ty_2Elbtree_2Elbtree(A_27b)),ap(V0f,V2x)),c_2Elbtree_2ELf(A_27b)),f1963(A_27a,A_27b,V1g))) ) ) ).
fof(lameq_f1965,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,ty_2Epair_2Eprod(A_27a,A_27a)))))
=> ! [V1g] : ap(f1965(A_27b,A_27a,V0f),V1g) = ap(c_2Ebool_2E_21(A_27a),f1964(A_27b,A_27a,V0f,V1g)) ) ).
fof(conj_thm_2Elbtree_2Elbtree__ue__Axiom,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(ty_2Epair_2Eprod(A_27b,ty_2Epair_2Eprod(A_27a,A_27a)))))
=> p(ap(c_2Ebool_2E_3F_21(arr(A_27a,ty_2Elbtree_2Elbtree(A_27b))),f1965(A_27b,A_27a,V0f))) ) ) ) ).
fof(lameq_f1966,axiom,
! [A_27b,V3a] :
( mem(V3a,A_27b)
=> ! [V4t1] :
( mem(V4t1,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V5t2] : ap(f1966(A_27b,V3a,V4t1,V2t),V5t2) = ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27b)),V2t),ap(ap(ap(c_2Elbtree_2ENd(A_27b),V3a),V4t1),V5t2)) ) ) ) ).
fof(lameq_f1967,axiom,
! [A_27b,V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V3a] :
( mem(V3a,A_27b)
=> ! [V4t1] : ap(f1967(A_27b,V2t,V3a),V4t1) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27b)),f1966(A_27b,V3a,V4t1,V2t)) ) ) ).
fof(lameq_f1968,axiom,
! [A_27b,V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V3a] : ap(f1968(A_27b,V2t),V3a) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27b)),f1967(A_27b,V2t,V3a)) ) ).
fof(lameq_f1969,axiom,
! [A_27b,V7a] :
( mem(V7a,A_27b)
=> ! [V6t1] :
( mem(V6t1,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V8t2] : ap(f1969(A_27b,V7a,V6t1,V2t),V8t2) = ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27b)),V2t),ap(ap(ap(c_2Elbtree_2ENd(A_27b),V7a),V6t1),V8t2)) ) ) ) ).
fof(lameq_f1970,axiom,
! [A_27b,V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V6t1] :
( mem(V6t1,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V7a] : ap(f1970(A_27b,V2t,V6t1),V7a) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27b)),f1969(A_27b,V7a,V6t1,V2t)) ) ) ).
fof(lameq_f1971,axiom,
! [A_27b,V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V6t1] : ap(f1971(A_27b,V2t),V6t1) = ap(c_2Ebool_2E_3F(A_27b),f1970(A_27b,V2t,V6t1)) ) ).
fof(lameq_f1972,axiom,
! [A_27b,V9t2] :
( mem(V9t2,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V10a] :
( mem(V10a,A_27b)
=> ! [V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V11t1] : ap(f1972(A_27b,V9t2,V10a,V2t),V11t1) = ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27b)),V2t),ap(ap(ap(c_2Elbtree_2ENd(A_27b),V10a),V11t1),V9t2)) ) ) ) ).
fof(lameq_f1973,axiom,
! [A_27b,V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V9t2] :
( mem(V9t2,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V10a] : ap(f1973(A_27b,V2t,V9t2),V10a) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27b)),f1972(A_27b,V9t2,V10a,V2t)) ) ) ).
fof(lameq_f1974,axiom,
! [A_27b,V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V9t2] : ap(f1974(A_27b,V2t),V9t2) = ap(c_2Ebool_2E_3F(A_27b),f1973(A_27b,V2t,V9t2)) ) ).
fof(ax_thm_2Elbtree_2Elbtree__case__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1f] :
( mem(V1f,arr(A_27b,arr(ty_2Elbtree_2Elbtree(A_27b),arr(ty_2Elbtree_2Elbtree(A_27b),A_27a))))
=> ! [V2t] :
( mem(V2t,ty_2Elbtree_2Elbtree(A_27b))
=> ap(ap(ap(c_2Elbtree_2Elbtree__case(A_27a,A_27b),V0e),V1f),V2t) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27b)),V2t),c_2Elbtree_2ELf(A_27b))),V0e),ap(ap(ap(V1f,ap(c_2Emin_2E_40(A_27b),f1968(A_27b,V2t))),ap(c_2Emin_2E_40(ty_2Elbtree_2Elbtree(A_27b)),f1971(A_27b,V2t))),ap(c_2Emin_2E_40(ty_2Elbtree_2Elbtree(A_27b)),f1974(A_27b,V2t)))) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Elbtree__case__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1f] :
( mem(V1f,arr(A_27b,arr(ty_2Elbtree_2Elbtree(A_27b),arr(ty_2Elbtree_2Elbtree(A_27b),A_27a))))
=> ! [V2a] :
( mem(V2a,A_27b)
=> ! [V3t1] :
( mem(V3t1,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V4t2] :
( mem(V4t2,ty_2Elbtree_2Elbtree(A_27b))
=> ( ap(ap(ap(c_2Elbtree_2Elbtree__case(A_27a,A_27b),V0e),V1f),c_2Elbtree_2ELf(A_27b)) = V0e
& ap(ap(ap(c_2Elbtree_2Elbtree__case(A_27a,A_27b),V0e),V1f),ap(ap(ap(c_2Elbtree_2ENd(A_27b),V2a),V3t1),V4t2)) = ap(ap(ap(V1f,V2a),V3t1),V4t2) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Elbtree__bisimulation,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V1u] :
( mem(V1u,ty_2Elbtree_2Elbtree(A_27a))
=> ( V0t = V1u
<=> ? [V2R] :
( mem(V2R,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
& p(ap(ap(V2R,V0t),V1u))
& ! [V3t] :
( mem(V3t,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4u] :
( mem(V4u,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(V2R,V3t),V4u))
=> ( ( V3t = c_2Elbtree_2ELf(A_27a)
& V4u = c_2Elbtree_2ELf(A_27a) )
| ? [V5a] :
( mem(V5a,A_27a)
& ? [V6t1] :
( mem(V6t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V7u1] :
( mem(V7u1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V8t2] :
( mem(V8t2,ty_2Elbtree_2Elbtree(A_27a))
& ? [V9u2] :
( mem(V9u2,ty_2Elbtree_2Elbtree(A_27a))
& p(ap(ap(V2R,V6t1),V7u1))
& p(ap(ap(V2R,V8t2),V9u2))
& V3t = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V5a),V6t1),V8t2)
& V4u = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V5a),V7u1),V9u2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Elbtree__strong__bisimulation,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V1u] :
( mem(V1u,ty_2Elbtree_2Elbtree(A_27a))
=> ( V0t = V1u
<=> ? [V2R] :
( mem(V2R,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
& p(ap(ap(V2R,V0t),V1u))
& ! [V3t] :
( mem(V3t,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4u] :
( mem(V4u,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(V2R,V3t),V4u))
=> ( V3t = V4u
| ? [V5a] :
( mem(V5a,A_27a)
& ? [V6t1] :
( mem(V6t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V7u1] :
( mem(V7u1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V8t2] :
( mem(V8t2,ty_2Elbtree_2Elbtree(A_27a))
& ? [V9u2] :
( mem(V9u2,ty_2Elbtree_2Elbtree(A_27a))
& p(ap(ap(V2R,V6t1),V7u1))
& p(ap(ap(V2R,V8t2),V9u2))
& V3t = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V5a),V6t1),V8t2)
& V4u = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V5a),V7u1),V9u2) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f1975,axiom,
! [A_27a,V3a0] :
( mem(V3a0,A_27a)
=> ! [V5t1] :
( mem(V5t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4a1] :
( mem(V4a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V6t2] : ap(f1975(A_27a,V3a0,V5t1,V4a1),V6t2) = ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),V4a1),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V3a0),V5t1),V6t2)) ) ) ) ).
fof(lameq_f1976,axiom,
! [A_27a,V4a1] :
( mem(V4a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3a0] :
( mem(V3a0,A_27a)
=> ! [V5t1] : ap(f1976(A_27a,V4a1,V3a0),V5t1) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1975(A_27a,V3a0,V5t1,V4a1)) ) ) ).
fof(lameq_f1977,axiom,
! [A_27a,V7b] :
( mem(V7b,A_27a)
=> ! [V4a1] :
( mem(V4a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3a0] :
( mem(V3a0,A_27a)
=> ! [V2mem_27] :
( mem(V2mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ! [V8t1] :
( mem(V8t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V9t2] : ap(f1977(A_27a,V7b,V4a1,V3a0,V2mem_27,V8t1),V9t2) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),V4a1),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V7b),V8t1),V9t2))),ap(ap(V2mem_27,V3a0),V8t1)) ) ) ) ) ) ).
fof(lameq_f1978,axiom,
! [A_27a,V2mem_27] :
( mem(V2mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ! [V3a0] :
( mem(V3a0,A_27a)
=> ! [V4a1] :
( mem(V4a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V7b] :
( mem(V7b,A_27a)
=> ! [V8t1] : ap(f1978(A_27a,V2mem_27,V3a0,V4a1,V7b),V8t1) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1977(A_27a,V7b,V4a1,V3a0,V2mem_27,V8t1)) ) ) ) ) ).
fof(lameq_f1979,axiom,
! [A_27a,V4a1] :
( mem(V4a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3a0] :
( mem(V3a0,A_27a)
=> ! [V2mem_27] :
( mem(V2mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ! [V7b] : ap(f1979(A_27a,V4a1,V3a0,V2mem_27),V7b) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1978(A_27a,V2mem_27,V3a0,V4a1,V7b)) ) ) ) ).
fof(lameq_f1980,axiom,
! [A_27a,V10b] :
( mem(V10b,A_27a)
=> ! [V11t1] :
( mem(V11t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4a1] :
( mem(V4a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3a0] :
( mem(V3a0,A_27a)
=> ! [V2mem_27] :
( mem(V2mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ! [V12t2] : ap(f1980(A_27a,V10b,V11t1,V4a1,V3a0,V2mem_27),V12t2) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),V4a1),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V10b),V11t1),V12t2))),ap(ap(V2mem_27,V3a0),V12t2)) ) ) ) ) ) ).
fof(lameq_f1981,axiom,
! [A_27a,V2mem_27] :
( mem(V2mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ! [V3a0] :
( mem(V3a0,A_27a)
=> ! [V4a1] :
( mem(V4a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V10b] :
( mem(V10b,A_27a)
=> ! [V11t1] : ap(f1981(A_27a,V2mem_27,V3a0,V4a1,V10b),V11t1) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1980(A_27a,V10b,V11t1,V4a1,V3a0,V2mem_27)) ) ) ) ) ).
fof(lameq_f1982,axiom,
! [A_27a,V4a1] :
( mem(V4a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3a0] :
( mem(V3a0,A_27a)
=> ! [V2mem_27] :
( mem(V2mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ! [V10b] : ap(f1982(A_27a,V4a1,V3a0,V2mem_27),V10b) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1981(A_27a,V2mem_27,V3a0,V4a1,V10b)) ) ) ) ).
fof(lameq_f1983,axiom,
! [A_27a,V3a0] :
( mem(V3a0,A_27a)
=> ! [V2mem_27] :
( mem(V2mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ! [V4a1] : ap(f1983(A_27a,V3a0,V2mem_27),V4a1) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1976(A_27a,V4a1,V3a0))),ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(A_27a),f1979(A_27a,V4a1,V3a0,V2mem_27))),ap(c_2Ebool_2E_3F(A_27a),f1982(A_27a,V4a1,V3a0,V2mem_27))))),ap(ap(V2mem_27,V3a0),V4a1)) ) ) ).
fof(lameq_f1984,axiom,
! [A_27a,V2mem_27] :
( mem(V2mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ! [V3a0] : ap(f1984(A_27a,V2mem_27),V3a0) = ap(c_2Ebool_2E_21(ty_2Elbtree_2Elbtree(A_27a)),f1983(A_27a,V3a0,V2mem_27)) ) ).
fof(lameq_f1985,axiom,
! [A_27a,V1a1] :
( mem(V1a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V0a0] :
( mem(V0a0,A_27a)
=> ! [V2mem_27] : ap(f1985(A_27a,V1a1,V0a0),V2mem_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(A_27a),f1984(A_27a,V2mem_27))),ap(ap(V2mem_27,V0a0),V1a1)) ) ) ).
fof(lameq_f1986,axiom,
! [A_27a,V0a0] :
( mem(V0a0,A_27a)
=> ! [V1a1] : ap(f1986(A_27a,V0a0),V1a1) = ap(c_2Ebool_2E_21(arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool))),f1985(A_27a,V1a1,V0a0)) ) ).
fof(lameq_f1987,axiom,
! [A_27a,V0a0] : ap(f1987(A_27a),V0a0) = f1986(A_27a,V0a0) ).
fof(ax_thm_2Elbtree_2Emem__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Elbtree_2Emem(A_27a) = f1987(A_27a) ) ).
fof(conj_thm_2Elbtree_2Emem__rules,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0a] :
( mem(V0a,A_27a)
=> ! [V1t1] :
( mem(V1t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V2t2] :
( mem(V2t2,ty_2Elbtree_2Elbtree(A_27a))
=> p(ap(ap(c_2Elbtree_2Emem(A_27a),V0a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V0a),V1t1),V2t2))) ) ) )
& ! [V3a] :
( mem(V3a,A_27a)
=> ! [V4b] :
( mem(V4b,A_27a)
=> ! [V5t1] :
( mem(V5t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V6t2] :
( mem(V6t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V3a),V5t1))
=> p(ap(ap(c_2Elbtree_2Emem(A_27a),V3a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V4b),V5t1),V6t2))) ) ) ) ) )
& ! [V7a] :
( mem(V7a,A_27a)
=> ! [V8b] :
( mem(V8b,A_27a)
=> ! [V9t1] :
( mem(V9t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V10t2] :
( mem(V10t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V7a),V10t2))
=> p(ap(ap(c_2Elbtree_2Emem(A_27a),V7a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V8b),V9t1),V10t2))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emem__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0mem_27] :
( mem(V0mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ( ( ! [V1a] :
( mem(V1a,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> p(ap(ap(V0mem_27,V1a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1a),V2t1),V3t2))) ) ) )
& ! [V4a] :
( mem(V4a,A_27a)
=> ! [V5b] :
( mem(V5b,A_27a)
=> ! [V6t1] :
( mem(V6t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V7t2] :
( mem(V7t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(V0mem_27,V4a),V6t1))
=> p(ap(ap(V0mem_27,V4a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V5b),V6t1),V7t2))) ) ) ) ) )
& ! [V8a] :
( mem(V8a,A_27a)
=> ! [V9b] :
( mem(V9b,A_27a)
=> ! [V10t1] :
( mem(V10t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V11t2] :
( mem(V11t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(V0mem_27,V8a),V11t2))
=> p(ap(ap(V0mem_27,V8a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V9b),V10t1),V11t2))) ) ) ) ) ) )
=> ! [V12a0] :
( mem(V12a0,A_27a)
=> ! [V13a1] :
( mem(V13a1,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V12a0),V13a1))
=> p(ap(ap(V0mem_27,V12a0),V13a1)) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emem__strongind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0mem_27] :
( mem(V0mem_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),bool)))
=> ( ( ! [V1a] :
( mem(V1a,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> p(ap(ap(V0mem_27,V1a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1a),V2t1),V3t2))) ) ) )
& ! [V4a] :
( mem(V4a,A_27a)
=> ! [V5b] :
( mem(V5b,A_27a)
=> ! [V6t1] :
( mem(V6t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V7t2] :
( mem(V7t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V4a),V6t1))
& p(ap(ap(V0mem_27,V4a),V6t1)) )
=> p(ap(ap(V0mem_27,V4a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V5b),V6t1),V7t2))) ) ) ) ) )
& ! [V8a] :
( mem(V8a,A_27a)
=> ! [V9b] :
( mem(V9b,A_27a)
=> ! [V10t1] :
( mem(V10t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V11t2] :
( mem(V11t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V8a),V11t2))
& p(ap(ap(V0mem_27,V8a),V11t2)) )
=> p(ap(ap(V0mem_27,V8a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V9b),V10t1),V11t2))) ) ) ) ) ) )
=> ! [V12a0] :
( mem(V12a0,A_27a)
=> ! [V13a1] :
( mem(V13a1,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V12a0),V13a1))
=> p(ap(ap(V0mem_27,V12a0),V13a1)) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emem__cases,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a0] :
( mem(V0a0,A_27a)
=> ! [V1a1] :
( mem(V1a1,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V0a0),V1a1))
<=> ( ? [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
& V1a1 = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V0a0),V2t1),V3t2) ) )
| ? [V4b] :
( mem(V4b,A_27a)
& ? [V5t1] :
( mem(V5t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V6t2] :
( mem(V6t2,ty_2Elbtree_2Elbtree(A_27a))
& V1a1 = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V4b),V5t1),V6t2)
& p(ap(ap(c_2Elbtree_2Emem(A_27a),V0a0),V5t1)) ) ) )
| ? [V7b] :
( mem(V7b,A_27a)
& ? [V8t1] :
( mem(V8t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V9t2] :
( mem(V9t2,ty_2Elbtree_2Elbtree(A_27a))
& V1a1 = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V7b),V8t1),V9t2)
& p(ap(ap(c_2Elbtree_2Emem(A_27a),V0a0),V9t2)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emem__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,A_27a)
=> ! [V1b] :
( mem(V1b,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V0a),c_2Elbtree_2ELf(A_27a)))
<=> $false )
& ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V0a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1b),V2t1),V3t2)))
<=> ( V0a = V1b
| p(ap(ap(c_2Elbtree_2Emem(A_27a),V0a),V2t1))
| p(ap(ap(c_2Elbtree_2Emem(A_27a),V0a),V3t2)) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elbtree_2Emap__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ( ap(ap(c_2Elbtree_2Emap(A_27a,A_27b),V0f),c_2Elbtree_2ELf(A_27a)) = c_2Elbtree_2ELf(A_27b)
& ! [V1a] :
( mem(V1a,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> ap(ap(c_2Elbtree_2Emap(A_27a,A_27b),V0f),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1a),V2t1),V3t2)) = ap(ap(ap(c_2Elbtree_2ENd(A_27b),ap(V0f,V1a)),ap(ap(c_2Elbtree_2Emap(A_27a,A_27b),V0f),V2t1)),ap(ap(c_2Elbtree_2Emap(A_27a,A_27b),V0f),V3t2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emap__eq__Lf,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Elbtree_2Elbtree(A_27b))
=> ( ( ap(ap(c_2Elbtree_2Emap(A_27b,A_27a),V0f),V1t) = c_2Elbtree_2ELf(A_27a)
<=> V1t = c_2Elbtree_2ELf(A_27b) )
& ( c_2Elbtree_2ELf(A_27a) = ap(ap(c_2Elbtree_2Emap(A_27b,A_27a),V0f),V1t)
<=> V1t = c_2Elbtree_2ELf(A_27b) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emap__eq__Nd,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V2a] :
( mem(V2a,A_27a)
=> ! [V3t1] :
( mem(V3t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4t2] :
( mem(V4t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ap(ap(c_2Elbtree_2Emap(A_27b,A_27a),V0f),V1t) = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V2a),V3t1),V4t2)
<=> ? [V5a_27] :
( mem(V5a_27,A_27b)
& ? [V6t1_27] :
( mem(V6t1_27,ty_2Elbtree_2Elbtree(A_27b))
& ? [V7t2_27] :
( mem(V7t2_27,ty_2Elbtree_2Elbtree(A_27b))
& V1t = ap(ap(ap(c_2Elbtree_2ENd(A_27b),V5a_27),V6t1_27),V7t2_27)
& V2a = ap(V0f,V5a_27)
& V3t1 = ap(ap(c_2Elbtree_2Emap(A_27b,A_27a),V0f),V6t1_27)
& V4t2 = ap(ap(c_2Elbtree_2Emap(A_27b,A_27a),V0f),V7t2_27) ) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f1988,axiom,
! [A_27a,V3a] :
( mem(V3a,A_27a)
=> ! [V2a0] :
( mem(V2a0,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4t1] :
( mem(V4t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V1finite_27] :
( mem(V1finite_27,arr(ty_2Elbtree_2Elbtree(A_27a),bool))
=> ! [V5t2] : ap(f1988(A_27a,V3a,V2a0,V4t1,V1finite_27),V5t2) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),V2a0),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V3a),V4t1),V5t2))),ap(ap(c_2Ebool_2E_2F_5C,ap(V1finite_27,V4t1)),ap(V1finite_27,V5t2))) ) ) ) ) ).
fof(lameq_f1989,axiom,
! [A_27a,V1finite_27] :
( mem(V1finite_27,arr(ty_2Elbtree_2Elbtree(A_27a),bool))
=> ! [V2a0] :
( mem(V2a0,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3a] :
( mem(V3a,A_27a)
=> ! [V4t1] : ap(f1989(A_27a,V1finite_27,V2a0,V3a),V4t1) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1988(A_27a,V3a,V2a0,V4t1,V1finite_27)) ) ) ) ).
fof(lameq_f1990,axiom,
! [A_27a,V2a0] :
( mem(V2a0,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V1finite_27] :
( mem(V1finite_27,arr(ty_2Elbtree_2Elbtree(A_27a),bool))
=> ! [V3a] : ap(f1990(A_27a,V2a0,V1finite_27),V3a) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1989(A_27a,V1finite_27,V2a0,V3a)) ) ) ).
fof(lameq_f1991,axiom,
! [A_27a,V1finite_27] :
( mem(V1finite_27,arr(ty_2Elbtree_2Elbtree(A_27a),bool))
=> ! [V2a0] : ap(f1991(A_27a,V1finite_27),V2a0) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),V2a0),c_2Elbtree_2ELf(A_27a))),ap(c_2Ebool_2E_3F(A_27a),f1990(A_27a,V2a0,V1finite_27)))),ap(V1finite_27,V2a0)) ) ).
fof(lameq_f1992,axiom,
! [A_27a,V0a0] :
( mem(V0a0,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V1finite_27] : ap(f1992(A_27a,V0a0),V1finite_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Elbtree_2Elbtree(A_27a)),f1991(A_27a,V1finite_27))),ap(V1finite_27,V0a0)) ) ).
fof(lameq_f1993,axiom,
! [A_27a,V0a0] : ap(f1993(A_27a),V0a0) = ap(c_2Ebool_2E_21(arr(ty_2Elbtree_2Elbtree(A_27a),bool)),f1992(A_27a,V0a0)) ).
fof(ax_thm_2Elbtree_2Efinite__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Elbtree_2Efinite(A_27a) = f1993(A_27a) ) ).
fof(conj_thm_2Elbtree_2Efinite__rules,axiom,
! [A_27a] :
( ne(A_27a)
=> ( p(ap(c_2Elbtree_2Efinite(A_27a),c_2Elbtree_2ELf(A_27a)))
& ! [V0a] :
( mem(V0a,A_27a)
=> ! [V1t1] :
( mem(V1t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V2t2] :
( mem(V2t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ( p(ap(c_2Elbtree_2Efinite(A_27a),V1t1))
& p(ap(c_2Elbtree_2Efinite(A_27a),V2t2)) )
=> p(ap(c_2Elbtree_2Efinite(A_27a),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V0a),V1t1),V2t2))) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Efinite__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0finite_27] :
( mem(V0finite_27,arr(ty_2Elbtree_2Elbtree(A_27a),bool))
=> ( ( p(ap(V0finite_27,c_2Elbtree_2ELf(A_27a)))
& ! [V1a] :
( mem(V1a,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ( p(ap(V0finite_27,V2t1))
& p(ap(V0finite_27,V3t2)) )
=> p(ap(V0finite_27,ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1a),V2t1),V3t2))) ) ) ) ) )
=> ! [V4a0] :
( mem(V4a0,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(c_2Elbtree_2Efinite(A_27a),V4a0))
=> p(ap(V0finite_27,V4a0)) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Efinite__strongind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0finite_27] :
( mem(V0finite_27,arr(ty_2Elbtree_2Elbtree(A_27a),bool))
=> ( ( p(ap(V0finite_27,c_2Elbtree_2ELf(A_27a)))
& ! [V1a] :
( mem(V1a,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ( p(ap(c_2Elbtree_2Efinite(A_27a),V2t1))
& p(ap(V0finite_27,V2t1))
& p(ap(c_2Elbtree_2Efinite(A_27a),V3t2))
& p(ap(V0finite_27,V3t2)) )
=> p(ap(V0finite_27,ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1a),V2t1),V3t2))) ) ) ) ) )
=> ! [V4a0] :
( mem(V4a0,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(c_2Elbtree_2Efinite(A_27a),V4a0))
=> p(ap(V0finite_27,V4a0)) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Efinite__cases,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a0] :
( mem(V0a0,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(c_2Elbtree_2Efinite(A_27a),V0a0))
<=> ( V0a0 = c_2Elbtree_2ELf(A_27a)
| ? [V1a] :
( mem(V1a,A_27a)
& ? [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
& V0a0 = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1a),V2t1),V3t2)
& p(ap(c_2Elbtree_2Efinite(A_27a),V2t1))
& p(ap(c_2Elbtree_2Efinite(A_27a),V3t2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Efinite__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,A_27b)
=> ! [V1t1] :
( mem(V1t1,ty_2Elbtree_2Elbtree(A_27b))
=> ! [V2t2] :
( mem(V2t2,ty_2Elbtree_2Elbtree(A_27b))
=> ( ( p(ap(c_2Elbtree_2Efinite(A_27a),c_2Elbtree_2ELf(A_27a)))
<=> $true )
& ( p(ap(c_2Elbtree_2Efinite(A_27b),ap(ap(ap(c_2Elbtree_2ENd(A_27b),V0a),V1t1),V2t2)))
<=> ( p(ap(c_2Elbtree_2Efinite(A_27b),V1t1))
& p(ap(c_2Elbtree_2Efinite(A_27b),V2t2)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Efinite__map,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Elbtree_2Elbtree(A_27b))
=> ( p(ap(c_2Elbtree_2Efinite(A_27a),ap(ap(c_2Elbtree_2Emap(A_27b,A_27a),V0f),V1t)))
<=> p(ap(c_2Elbtree_2Efinite(A_27b),V1t)) ) ) ) ) ) ).
fof(ax_thm_2Elbtree_2Ebf__flatten__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ap(c_2Elbtree_2Ebf__flatten(A_27a),c_2Elist_2ENIL(ty_2Elbtree_2Elbtree(A_27a))) = c_2Ellist_2ELNIL(A_27a)
& ! [V0ts] :
( mem(V0ts,ty_2Elist_2Elist(ty_2Elbtree_2Elbtree(A_27a)))
=> ap(c_2Elbtree_2Ebf__flatten(A_27a),ap(ap(c_2Elist_2ECONS(ty_2Elbtree_2Elbtree(A_27a)),c_2Elbtree_2ELf(A_27a)),V0ts)) = ap(c_2Elbtree_2Ebf__flatten(A_27a),V0ts) )
& ! [V1a] :
( mem(V1a,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4ts] :
( mem(V4ts,ty_2Elist_2Elist(ty_2Elbtree_2Elbtree(A_27a)))
=> ap(c_2Elbtree_2Ebf__flatten(A_27a),ap(ap(c_2Elist_2ECONS(ty_2Elbtree_2Elbtree(A_27a)),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1a),V2t1),V3t2)),V4ts)) = ap(ap(c_2Ellist_2ELCONS(A_27a),V1a),ap(c_2Elbtree_2Ebf__flatten(A_27a),ap(ap(c_2Elist_2EAPPEND(ty_2Elbtree_2Elbtree(A_27a)),V4ts),ap(ap(c_2Elist_2ECONS(ty_2Elbtree_2Elbtree(A_27a)),V2t1),ap(ap(c_2Elist_2ECONS(ty_2Elbtree_2Elbtree(A_27a)),V3t2),c_2Elist_2ENIL(ty_2Elbtree_2Elbtree(A_27a))))))) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Ebf__flatten__eq__lnil,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Elbtree_2Elbtree(A_27a)))
=> ( ap(c_2Elbtree_2Ebf__flatten(A_27a),V0l) = c_2Ellist_2ELNIL(A_27a)
<=> p(ap(ap(c_2Elist_2EEVERY(ty_2Elbtree_2Elbtree(A_27a)),ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),c_2Elbtree_2ELf(A_27a))),V0l)) ) ) ) ).
fof(conj_thm_2Elbtree_2Ebf__flatten__append,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l2] :
( mem(V0l2,ty_2Elist_2Elist(ty_2Elbtree_2Elbtree(A_27a)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(ty_2Elbtree_2Elbtree(A_27a)))
=> ( p(ap(ap(c_2Elist_2EEVERY(ty_2Elbtree_2Elbtree(A_27a)),ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),c_2Elbtree_2ELf(A_27a))),V1l1))
=> ap(c_2Elbtree_2Ebf__flatten(A_27a),ap(ap(c_2Elist_2EAPPEND(ty_2Elbtree_2Elbtree(A_27a)),V1l1),V0l2)) = ap(c_2Elbtree_2Ebf__flatten(A_27a),V0l2) ) ) ) ) ).
fof(conj_thm_2Elbtree_2EEXISTS__FIRST,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_2Elist_2EEXISTS(A_27a),V0P),V1l))
=> ? [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
& ? [V3x] :
( mem(V3x,A_27a)
& ? [V4l2] :
( mem(V4l2,ty_2Elist_2Elist(A_27a))
& V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),ap(ap(c_2Elist_2ECONS(A_27a),V3x),V4l2))
& p(ap(ap(c_2Elist_2EEVERY(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V2l1))
& p(ap(V0P,V3x)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Eexists__bf__flatten,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1tlist] :
( mem(V1tlist,ty_2Elist_2Elist(ty_2Elbtree_2Elbtree(A_27a)))
=> ( p(ap(ap(c_2Ellist_2Eexists(A_27a),ap(c_2Emin_2E_3D(A_27a),V0x)),ap(c_2Elbtree_2Ebf__flatten(A_27a),V1tlist)))
=> p(ap(ap(c_2Elist_2EEXISTS(ty_2Elbtree_2Elbtree(A_27a)),ap(c_2Elbtree_2Emem(A_27a),V0x)),V1tlist)) ) ) ) ) ).
fof(lameq_f1994,axiom,
! [A_27a,V4a0] :
( mem(V4a0,A_27a)
=> ! [V7t1] :
( mem(V7t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V8t2] : ap(f1994(A_27a,V4a0,V7t1,V5a1,V6a2),V8t2) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),V5a1),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V4a0),V7t1),V8t2))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6a2),c_2Enum_2E0)) ) ) ) ) ).
fof(lameq_f1995,axiom,
! [A_27a,V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V7t1] : ap(f1995(A_27a,V6a2,V5a1,V4a0),V7t1) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1994(A_27a,V4a0,V7t1,V5a1,V6a2)) ) ) ) ).
fof(lameq_f1996,axiom,
! [A_27a,V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V9m] :
( mem(V9m,ty_2Enum_2Enum)
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V11t1] :
( mem(V11t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V10a] :
( mem(V10a,A_27a)
=> ! [V12t2] : ap(f1996(A_27a,V6a2,V9m,V3depth_27,V4a0,V5a1,V11t1,V10a),V12t2) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),V5a1),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V10a),V11t1),V12t2))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6a2),ap(c_2Enum_2ESUC,V9m))),ap(ap(ap(V3depth_27,V4a0),V11t1),V9m))) ) ) ) ) ) ) ) ).
fof(lameq_f1997,axiom,
! [A_27a,V10a] :
( mem(V10a,A_27a)
=> ! [V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V9m] :
( mem(V9m,ty_2Enum_2Enum)
=> ! [V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V11t1] : ap(f1997(A_27a,V10a,V5a1,V4a0,V3depth_27,V9m,V6a2),V11t1) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1996(A_27a,V6a2,V9m,V3depth_27,V4a0,V5a1,V11t1,V10a)) ) ) ) ) ) ) ).
fof(lameq_f1998,axiom,
! [A_27a,V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V9m] :
( mem(V9m,ty_2Enum_2Enum)
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V10a] : ap(f1998(A_27a,V6a2,V9m,V3depth_27,V4a0,V5a1),V10a) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1997(A_27a,V10a,V5a1,V4a0,V3depth_27,V9m,V6a2)) ) ) ) ) ) ).
fof(lameq_f1999,axiom,
! [A_27a,V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V9m] : ap(f1999(A_27a,V5a1,V4a0,V3depth_27,V6a2),V9m) = ap(c_2Ebool_2E_3F(A_27a),f1998(A_27a,V6a2,V9m,V3depth_27,V4a0,V5a1)) ) ) ) ) ).
fof(lameq_f2000,axiom,
! [A_27a,V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V13m] :
( mem(V13m,ty_2Enum_2Enum)
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V15t1] :
( mem(V15t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V14a] :
( mem(V14a,A_27a)
=> ! [V16t2] : ap(f2000(A_27a,V6a2,V13m,V3depth_27,V4a0,V5a1,V15t1,V14a),V16t2) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Elbtree_2Elbtree(A_27a)),V5a1),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V14a),V15t1),V16t2))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6a2),ap(c_2Enum_2ESUC,V13m))),ap(ap(ap(V3depth_27,V4a0),V16t2),V13m))) ) ) ) ) ) ) ) ).
fof(lameq_f2001,axiom,
! [A_27a,V14a] :
( mem(V14a,A_27a)
=> ! [V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V13m] :
( mem(V13m,ty_2Enum_2Enum)
=> ! [V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V15t1] : ap(f2001(A_27a,V14a,V5a1,V4a0,V3depth_27,V13m,V6a2),V15t1) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f2000(A_27a,V6a2,V13m,V3depth_27,V4a0,V5a1,V15t1,V14a)) ) ) ) ) ) ) ).
fof(lameq_f2002,axiom,
! [A_27a,V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V13m] :
( mem(V13m,ty_2Enum_2Enum)
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V14a] : ap(f2002(A_27a,V6a2,V13m,V3depth_27,V4a0,V5a1),V14a) = ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f2001(A_27a,V14a,V5a1,V4a0,V3depth_27,V13m,V6a2)) ) ) ) ) ) ).
fof(lameq_f2003,axiom,
! [A_27a,V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V6a2] :
( mem(V6a2,ty_2Enum_2Enum)
=> ! [V13m] : ap(f2003(A_27a,V5a1,V4a0,V3depth_27,V6a2),V13m) = ap(c_2Ebool_2E_3F(A_27a),f2002(A_27a,V6a2,V13m,V3depth_27,V4a0,V5a1)) ) ) ) ) ).
fof(lameq_f2004,axiom,
! [A_27a,V5a1] :
( mem(V5a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V4a0] :
( mem(V4a0,A_27a)
=> ! [V6a2] : ap(f2004(A_27a,V5a1,V3depth_27,V4a0),V6a2) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(ty_2Elbtree_2Elbtree(A_27a)),f1995(A_27a,V6a2,V5a1,V4a0))),ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f1999(A_27a,V5a1,V4a0,V3depth_27,V6a2))),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f2003(A_27a,V5a1,V4a0,V3depth_27,V6a2))))),ap(ap(ap(V3depth_27,V4a0),V5a1),V6a2)) ) ) ) ).
fof(lameq_f2005,axiom,
! [A_27a,V4a0] :
( mem(V4a0,A_27a)
=> ! [V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V5a1] : ap(f2005(A_27a,V4a0,V3depth_27),V5a1) = ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f2004(A_27a,V5a1,V3depth_27,V4a0)) ) ) ).
fof(lameq_f2006,axiom,
! [A_27a,V3depth_27] :
( mem(V3depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ! [V4a0] : ap(f2006(A_27a,V3depth_27),V4a0) = ap(c_2Ebool_2E_21(ty_2Elbtree_2Elbtree(A_27a)),f2005(A_27a,V4a0,V3depth_27)) ) ).
fof(lameq_f2007,axiom,
! [A_27a,V2a2] :
( mem(V2a2,ty_2Enum_2Enum)
=> ! [V0a0] :
( mem(V0a0,A_27a)
=> ! [V1a1] :
( mem(V1a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3depth_27] : ap(f2007(A_27a,V2a2,V0a0,V1a1),V3depth_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(A_27a),f2006(A_27a,V3depth_27))),ap(ap(ap(V3depth_27,V0a0),V1a1),V2a2)) ) ) ) ).
fof(lameq_f2008,axiom,
! [A_27a,V1a1] :
( mem(V1a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V0a0] :
( mem(V0a0,A_27a)
=> ! [V2a2] : ap(f2008(A_27a,V1a1,V0a0),V2a2) = ap(c_2Ebool_2E_21(arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool)))),f2007(A_27a,V2a2,V0a0,V1a1)) ) ) ).
fof(lameq_f2009,axiom,
! [A_27a,V0a0] :
( mem(V0a0,A_27a)
=> ! [V1a1] : ap(f2009(A_27a,V0a0),V1a1) = f2008(A_27a,V1a1,V0a0) ) ).
fof(lameq_f2010,axiom,
! [A_27a,V0a0] : ap(f2010(A_27a),V0a0) = f2009(A_27a,V0a0) ).
fof(ax_thm_2Elbtree_2Edepth__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Elbtree_2Edepth(A_27a) = f2010(A_27a) ) ).
fof(conj_thm_2Elbtree_2Edepth__rules,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1t1] :
( mem(V1t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V2t2] :
( mem(V2t2,ty_2Elbtree_2Elbtree(A_27a))
=> p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V0x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V0x),V1t1),V2t2)),c_2Enum_2E0)) ) ) )
& ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5a] :
( mem(V5a,A_27a)
=> ! [V6t1] :
( mem(V6t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V7t2] :
( mem(V7t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V4x),V6t1),V3m))
=> p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V4x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V5a),V6t1),V7t2)),ap(c_2Enum_2ESUC,V3m))) ) ) ) ) ) )
& ! [V8m] :
( mem(V8m,ty_2Enum_2Enum)
=> ! [V9x] :
( mem(V9x,A_27a)
=> ! [V10a] :
( mem(V10a,A_27a)
=> ! [V11t1] :
( mem(V11t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V12t2] :
( mem(V12t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V9x),V12t2),V8m))
=> p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V9x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V10a),V11t1),V12t2)),ap(c_2Enum_2ESUC,V8m))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Edepth__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0depth_27] :
( mem(V0depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ( ( ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> p(ap(ap(ap(V0depth_27,V1x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1x),V2t1),V3t2)),c_2Enum_2E0)) ) ) )
& ! [V4m] :
( mem(V4m,ty_2Enum_2Enum)
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6a] :
( mem(V6a,A_27a)
=> ! [V7t1] :
( mem(V7t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V8t2] :
( mem(V8t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(ap(V0depth_27,V5x),V7t1),V4m))
=> p(ap(ap(ap(V0depth_27,V5x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V6a),V7t1),V8t2)),ap(c_2Enum_2ESUC,V4m))) ) ) ) ) ) )
& ! [V9m] :
( mem(V9m,ty_2Enum_2Enum)
=> ! [V10x] :
( mem(V10x,A_27a)
=> ! [V11a] :
( mem(V11a,A_27a)
=> ! [V12t1] :
( mem(V12t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V13t2] :
( mem(V13t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(ap(V0depth_27,V10x),V13t2),V9m))
=> p(ap(ap(ap(V0depth_27,V10x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V11a),V12t1),V13t2)),ap(c_2Enum_2ESUC,V9m))) ) ) ) ) ) ) )
=> ! [V14a0] :
( mem(V14a0,A_27a)
=> ! [V15a1] :
( mem(V15a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V16a2] :
( mem(V16a2,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V14a0),V15a1),V16a2))
=> p(ap(ap(ap(V0depth_27,V14a0),V15a1),V16a2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Edepth__strongind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0depth_27] :
( mem(V0depth_27,arr(A_27a,arr(ty_2Elbtree_2Elbtree(A_27a),arr(ty_2Enum_2Enum,bool))))
=> ( ( ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> p(ap(ap(ap(V0depth_27,V1x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1x),V2t1),V3t2)),c_2Enum_2E0)) ) ) )
& ! [V4m] :
( mem(V4m,ty_2Enum_2Enum)
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6a] :
( mem(V6a,A_27a)
=> ! [V7t1] :
( mem(V7t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V8t2] :
( mem(V8t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ( p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V5x),V7t1),V4m))
& p(ap(ap(ap(V0depth_27,V5x),V7t1),V4m)) )
=> p(ap(ap(ap(V0depth_27,V5x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V6a),V7t1),V8t2)),ap(c_2Enum_2ESUC,V4m))) ) ) ) ) ) )
& ! [V9m] :
( mem(V9m,ty_2Enum_2Enum)
=> ! [V10x] :
( mem(V10x,A_27a)
=> ! [V11a] :
( mem(V11a,A_27a)
=> ! [V12t1] :
( mem(V12t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V13t2] :
( mem(V13t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ( p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V10x),V13t2),V9m))
& p(ap(ap(ap(V0depth_27,V10x),V13t2),V9m)) )
=> p(ap(ap(ap(V0depth_27,V10x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V11a),V12t1),V13t2)),ap(c_2Enum_2ESUC,V9m))) ) ) ) ) ) ) )
=> ! [V14a0] :
( mem(V14a0,A_27a)
=> ! [V15a1] :
( mem(V15a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V16a2] :
( mem(V16a2,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V14a0),V15a1),V16a2))
=> p(ap(ap(ap(V0depth_27,V14a0),V15a1),V16a2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Edepth__cases,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a0] :
( mem(V0a0,A_27a)
=> ! [V1a1] :
( mem(V1a1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V2a2] :
( mem(V2a2,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V0a0),V1a1),V2a2))
<=> ( ? [V3t1] :
( mem(V3t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V4t2] :
( mem(V4t2,ty_2Elbtree_2Elbtree(A_27a))
& V1a1 = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V0a0),V3t1),V4t2)
& V2a2 = c_2Enum_2E0 ) )
| ? [V5m] :
( mem(V5m,ty_2Enum_2Enum)
& ? [V6a] :
( mem(V6a,A_27a)
& ? [V7t1] :
( mem(V7t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V8t2] :
( mem(V8t2,ty_2Elbtree_2Elbtree(A_27a))
& V1a1 = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V6a),V7t1),V8t2)
& V2a2 = ap(c_2Enum_2ESUC,V5m)
& p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V0a0),V7t1),V5m)) ) ) ) )
| ? [V9m] :
( mem(V9m,ty_2Enum_2Enum)
& ? [V10a] :
( mem(V10a,A_27a)
& ? [V11t1] :
( mem(V11t1,ty_2Elbtree_2Elbtree(A_27a))
& ? [V12t2] :
( mem(V12t2,ty_2Elbtree_2Elbtree(A_27a))
& V1a1 = ap(ap(ap(c_2Elbtree_2ENd(A_27a),V10a),V11t1),V12t2)
& V2a2 = ap(c_2Enum_2ESUC,V9m)
& p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V0a0),V12t2),V9m)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emem__depth,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V0x),V1t))
=> ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V0x),V1t),V2n)) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Edepth__mem,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V0x),V1t),V2n))
=> p(ap(ap(c_2Elbtree_2Emem(A_27a),V0x),V1t)) ) ) ) ) ) ).
fof(lameq_f2011,axiom,
! [A_27a,V1t] :
( mem(V1t,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V2n] : ap(f2011(A_27a,V1t,V0x),V2n) = ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V0x),V1t),V2n) ) ) ).
fof(ax_thm_2Elbtree_2Emindepth__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elbtree_2Elbtree(A_27a))
=> ap(ap(c_2Elbtree_2Emindepth(A_27a),V0x),V1t) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(ty_2Enum_2Enum)),ap(ap(c_2Elbtree_2Emem(A_27a),V0x),V1t)),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),ap(c_2Ewhile_2ELEAST,f2011(A_27a,V1t,V0x)))),c_2Eoption_2ENONE(ty_2Enum_2Enum)) ) ) ) ).
fof(conj_thm_2Elbtree_2Eoptmin__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Eoption_2Eoption(ty_2Enum_2Enum),arr(ty_2Eoption_2Eoption(ty_2Enum_2Enum),bool)))
=> ( ( p(ap(ap(V0P,c_2Eoption_2ENONE(ty_2Enum_2Enum)),c_2Eoption_2ENONE(ty_2Enum_2Enum)))
& ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> p(ap(ap(V0P,ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V1x)),c_2Eoption_2ENONE(ty_2Enum_2Enum))) )
& ! [V2y] :
( mem(V2y,ty_2Enum_2Enum)
=> p(ap(ap(V0P,c_2Eoption_2ENONE(ty_2Enum_2Enum)),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V2y))) )
& ! [V3x] :
( mem(V3x,ty_2Enum_2Enum)
=> ! [V4y] :
( mem(V4y,ty_2Enum_2Enum)
=> p(ap(ap(V0P,ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V3x)),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V4y))) ) ) )
=> ! [V5v] :
( mem(V5v,ty_2Eoption_2Eoption(ty_2Enum_2Enum))
=> ! [V6v1] :
( mem(V6v1,ty_2Eoption_2Eoption(ty_2Enum_2Enum))
=> p(ap(ap(V0P,V5v),V6v1)) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Eoptmin__def,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1y] :
( mem(V1y,ty_2Enum_2Enum)
=> ( ap(ap(c_2Elbtree_2Eoptmin,c_2Eoption_2ENONE(ty_2Enum_2Enum)),c_2Eoption_2ENONE(ty_2Enum_2Enum)) = c_2Eoption_2ENONE(ty_2Enum_2Enum)
& ap(ap(c_2Elbtree_2Eoptmin,ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V0x)),c_2Eoption_2ENONE(ty_2Enum_2Enum)) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V0x)
& ap(ap(c_2Elbtree_2Eoptmin,c_2Eoption_2ENONE(ty_2Enum_2Enum)),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V1y)) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V1y)
& ap(ap(c_2Elbtree_2Eoptmin,ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V0x)),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V1y)) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EMIN,V0x),V1y)) ) ) ) ).
fof(conj_thm_2Elbtree_2Emindepth__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1a] :
( mem(V1a,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V3t2] :
( mem(V3t2,ty_2Elbtree_2Elbtree(A_27a))
=> ( ap(ap(c_2Elbtree_2Emindepth(A_27a),V0x),c_2Elbtree_2ELf(A_27a)) = c_2Eoption_2ENONE(ty_2Enum_2Enum)
& ap(ap(c_2Elbtree_2Emindepth(A_27a),V0x),ap(ap(ap(c_2Elbtree_2ENd(A_27a),V1a),V2t1),V3t2)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(A_27a),V0x),V1a)),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),c_2Enum_2E0)),ap(ap(c_2Eoption_2EOPTION__MAP(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2ESUC),ap(ap(c_2Elbtree_2Eoptmin,ap(ap(c_2Elbtree_2Emindepth(A_27a),V0x),V2t1)),ap(ap(c_2Elbtree_2Emindepth(A_27a),V0x),V3t2)))) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emem__mindepth,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elbtree_2Elbtree(A_27a))
=> ( p(ap(ap(c_2Elbtree_2Emem(A_27a),V0x),V1t))
=> ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& ap(ap(c_2Elbtree_2Emindepth(A_27a),V0x),V1t) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V2n) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emindepth__depth,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elbtree_2Elbtree(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Elbtree_2Emindepth(A_27a),V0x),V1t) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V2n)
=> p(ap(ap(ap(c_2Elbtree_2Edepth(A_27a),V0x),V1t),V2n)) ) ) ) ) ) ).
fof(ax_thm_2Elbtree_2Eis__mmindex__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(ty_2Enum_2Enum)))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3d] :
( mem(V3d,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(ap(c_2Elbtree_2Eis__mmindex(A_27a),V0f),V1l),V2n),V3d))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V1l)))
& ap(V0f,ap(ap(c_2Elist_2EEL(A_27a),V2n),V1l)) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V3d)
& ! [V4i] :
( mem(V4i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V4i),ap(c_2Elist_2ELENGTH(A_27a),V1l)))
=> ( ap(V0f,ap(ap(c_2Elist_2EEL(A_27a),V4i),V1l)) = c_2Eoption_2ENONE(ty_2Enum_2Enum)
| ? [V5d_27] :
( mem(V5d_27,ty_2Enum_2Enum)
& ap(V0f,ap(ap(c_2Elist_2EEL(A_27a),V4i),V1l)) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V5d_27)
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V3d),V5d_27))
& ( p(ap(ap(c_2Eprim__rec_2E_3C,V4i),V2n))
=> p(ap(ap(c_2Eprim__rec_2E_3C,V3d),V5d_27)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f2012,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(ty_2Enum_2Enum)))
=> ! [V2e] :
( mem(V2e,A_27a)
=> ! [V3n] : ap(f2012(A_27a,V0f,V2e),V3n) = ap(ap(c_2Emin_2E_3D(ty_2Eoption_2Eoption(ty_2Enum_2Enum)),ap(V0f,V2e)),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V3n)) ) ) ).
fof(lameq_f2013,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(ty_2Enum_2Enum)))
=> ! [V2e] : ap(f2013(A_27a,V0f),V2e) = ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f2012(A_27a,V0f,V2e)) ) ).
fof(conj_thm_2Elbtree_2Emmindex__EXISTS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(ty_2Enum_2Enum)))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),f2013(A_27a,V0f)),V1l))
=> ? [V4i] :
( mem(V4i,ty_2Enum_2Enum)
& ? [V5m] :
( mem(V5m,ty_2Enum_2Enum)
& p(ap(ap(ap(ap(c_2Elbtree_2Eis__mmindex(A_27a),V0f),V1l),V4i),V5m)) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emmindex__unique,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(ty_2Enum_2Enum)))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ! [V3m] :
( mem(V3m,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(ap(c_2Elbtree_2Eis__mmindex(A_27a),V0f),V1l),V2i),V3m))
=> ! [V4j] :
( mem(V4j,ty_2Enum_2Enum)
=> ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ( p(ap(ap(ap(ap(c_2Elbtree_2Eis__mmindex(A_27a),V0f),V1l),V4j),V5n))
<=> ( V4j = V2i
& V5n = V3m ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elbtree_2Emem__bf__flatten,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1tlist] :
( mem(V1tlist,ty_2Elist_2Elist(ty_2Elbtree_2Elbtree(A_27a)))
=> ( p(ap(ap(c_2Ellist_2Eexists(A_27a),ap(c_2Emin_2E_3D(A_27a),V0x)),ap(c_2Elbtree_2Ebf__flatten(A_27a),V1tlist)))
<=> p(ap(ap(c_2Elist_2EEXISTS(ty_2Elbtree_2Elbtree(A_27a)),ap(c_2Elbtree_2Emem(A_27a),V0x)),V1tlist)) ) ) ) ) ).
%------------------------------------------------------------------------------