SET007 Axioms: SET007+292.ax
%------------------------------------------------------------------------------
% File : SET007+292 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Preliminaries to the Lambek Calculus
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : prelamb [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 88 ( 3 unt; 0 def)
% Number of atoms : 810 ( 143 equ)
% Maximal formula atoms : 93 ( 9 avg)
% Number of connectives : 849 ( 127 ~; 1 |; 399 &)
% ( 30 <=>; 292 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 10 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 36 ( 34 usr; 1 prp; 0-3 aty)
% Number of functors : 50 ( 50 usr; 11 con; 0-6 aty)
% Number of variables : 379 ( 322 !; 57 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_prelamb,axiom,
? [A] :
( l1_prelamb(A)
& v1_prelamb(A) ) ).
fof(rc2_prelamb,axiom,
? [A] :
( l1_prelamb(A)
& ~ v3_struct_0(A)
& v1_prelamb(A) ) ).
fof(rc3_prelamb,axiom,
? [A] :
( l2_prelamb(A)
& v9_prelamb(A) ) ).
fof(rc4_prelamb,axiom,
? [A] :
( l2_prelamb(A)
& ~ v3_struct_0(A)
& v9_prelamb(A) ) ).
fof(rc5_prelamb,axiom,
? [A] :
( l2_prelamb(A)
& ~ v3_struct_0(A)
& v10_prelamb(A) ) ).
fof(d1_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_prelamb(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_prelamb(A),B,C) ) ) ) ).
fof(d2_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_prelamb(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_prelamb(A),B,C) ) ) ) ).
fof(d3_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k3_prelamb(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u3_prelamb(A),B,C) ) ) ) ).
fof(d4_prelamb,axiom,
$true ).
fof(d5_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_finset_1(B)
& v3_trees_2(B)
& m3_trees_2(B,k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers)) )
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ( ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__0
=> ( v2_prelamb(C,A,B)
<=> ( k10_trees_2(k1_relat_1(B),C) = np__0
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k12_finseq_1(u1_struct_0(A),D),D) ) ) ) )
& ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__1
=> ( v2_prelamb(C,A,B)
<=> ( k10_trees_2(k1_relat_1(B),C) = np__1
& ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(D,k2_prelamb(A,E,F))
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),D,k12_finseq_1(u1_struct_0(A),F)),E) ) ) ) ) ) )
& ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__2
=> ( v2_prelamb(C,A,B)
<=> ( k10_trees_2(k1_relat_1(B),C) = np__1
& ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(D,k1_prelamb(A,F,E))
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),F),D),E) ) ) ) ) ) )
& ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__3
=> ( v2_prelamb(C,A,B)
<=> ( k10_trees_2(k1_relat_1(B),C) = np__2
& ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& ? [E] :
( m2_finseq_1(E,u1_struct_0(A))
& ? [F] :
( m2_finseq_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& ? [I] :
( m1_subset_1(I,u1_struct_0(A))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,G,H))),D),F),I)
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(D,H)
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F),I) ) ) ) ) ) ) ) ) )
& ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__4
=> ( v2_prelamb(C,A,B)
<=> ( k10_trees_2(k1_relat_1(B),C) = np__2
& ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& ? [E] :
( m2_finseq_1(E,u1_struct_0(A))
& ? [F] :
( m2_finseq_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& ? [I] :
( m1_subset_1(I,u1_struct_0(A))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,D),k12_finseq_1(u1_struct_0(A),k1_prelamb(A,H,G))),F),I)
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(D,H)
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F),I) ) ) ) ) ) ) ) ) )
& ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__5
=> ( v2_prelamb(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( k10_trees_2(k1_relat_1(B),C) = np__1
& ? [E] :
( m2_finseq_1(E,u1_struct_0(A))
& ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m2_finseq_1(H,u1_struct_0(A))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),k3_prelamb(A,F,G))),H),D)
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),F)),k12_finseq_1(u1_struct_0(A),G)),H),D) ) ) ) ) ) ) ) )
& ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__6
=> ( v2_prelamb(C,A,B)
<=> ( k10_trees_2(k1_relat_1(B),C) = np__2
& ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& ? [E] :
( m2_finseq_1(E,u1_struct_0(A))
& ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),D,E),k3_prelamb(A,F,G))
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(D,F)
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)))) = k4_tarski(E,G) ) ) ) ) ) ) )
& ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__7
=> ( v2_prelamb(C,A,B)
<=> ( k10_trees_2(k1_relat_1(B),C) = np__2
& ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& ? [E] :
( m2_finseq_1(E,u1_struct_0(A))
& ? [F] :
( m2_finseq_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,D),F),H)
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)))) = k4_tarski(D,G)
& k1_mcart_1(k1_funct_1(B,k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)))) = k4_tarski(k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F),H) ) ) ) ) ) ) ) )
& ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__0
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__1
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__2
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__3
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__4
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__5
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__6
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__7
& ~ ( v2_prelamb(C,A,B)
<=> ~ $true ) ) ) ) ) ) ).
fof(d6_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v3_prelamb(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& B = k1_prelamb(A,C,D) ) ) ) ) ) ).
fof(d7_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v4_prelamb(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& B = k2_prelamb(A,C,D) ) ) ) ) ) ).
fof(d8_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v5_prelamb(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& B = k3_prelamb(A,C,D) ) ) ) ) ) ).
fof(d9_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v6_prelamb(B,A)
<=> ( ~ v3_prelamb(B,A)
& ~ v4_prelamb(B,A)
& ~ v5_prelamb(B,A) ) ) ) ) ).
fof(d10_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_finset_1(B)
& v3_trees_2(B)
& m3_trees_2(B,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_prelamb(A,B,C)
<=> ( v1_finset_1(k1_relat_1(B))
& ! [D] :
( m1_trees_1(D,k1_relat_1(B))
=> ( ( k10_trees_2(k1_relat_1(B),D) = np__0
| k10_trees_2(k1_relat_1(B),D) = np__2 )
& ( k10_trees_2(k1_relat_1(B),D) = np__0
=> v6_prelamb(k4_prelamb(A,B,D),A) )
& ~ ( k10_trees_2(k1_relat_1(B),D) = np__2
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( ~ ( k4_prelamb(A,B,D) != k2_prelamb(A,E,F)
& k4_prelamb(A,B,D) != k1_prelamb(A,E,F)
& k4_prelamb(A,B,D) != k3_prelamb(A,E,F) )
& k1_funct_1(B,k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,np__0))) = E
& k1_funct_1(B,k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,np__1))) = F ) ) ) ) ) ) ) ) ) ) ) ).
fof(d11_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ( v7_prelamb(A)
<=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ~ ( v3_prelamb(B,A)
& v4_prelamb(B,A) )
& ~ ( v3_prelamb(B,A)
& v5_prelamb(B,A) )
& ~ ( v4_prelamb(B,A)
& v5_prelamb(B,A) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( v1_funct_1(C)
& v1_finset_1(C)
& v3_trees_2(C)
& m3_trees_2(C,u1_struct_0(A))
& ! [D] :
( ( v1_funct_1(D)
& v1_finset_1(D)
& v3_trees_2(D)
& m3_trees_2(D,u1_struct_0(A)) )
=> ( r1_prelamb(A,D,B)
<=> C = D ) ) ) ) ) ) ) ).
fof(d12_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v7_prelamb(A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_finset_1(C)
& v3_trees_2(C)
& m3_trees_2(C,u1_struct_0(A)) )
=> ( C = k5_prelamb(A,B)
<=> ! [D] :
( ( v1_funct_1(D)
& v1_finset_1(D)
& v3_trees_2(D)
& m3_trees_2(D,u1_struct_0(A)) )
=> ( r1_prelamb(A,D,B)
<=> C = D ) ) ) ) ) ) ) ).
fof(d13_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_finset_1(B)
& v3_trees_2(B)
& m3_trees_2(B,k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers)) )
=> ( m1_prelamb(B,A)
<=> ( v1_finset_1(k1_relat_1(B))
& ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> v2_prelamb(C,A,B) ) ) ) ) ) ).
fof(t1_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ( k10_trees_2(k1_relat_1(B),C) = np__1
=> r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)),k1_relat_1(B)) ) ) ) ) ).
fof(t2_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ( k10_trees_2(k1_relat_1(B),C) = np__2
=> ( r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0)),k1_relat_1(B))
& r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1)),k1_relat_1(B)) ) ) ) ) ) ).
fof(t3_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__0
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != k6_prelamb(A,k12_finseq_1(u1_struct_0(A),D),D) ) ) ) ) ) ).
fof(t4_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__1
& ! [D] :
( m1_trees_1(D,k1_relat_1(B))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,E,k2_prelamb(A,F,G))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F) ) ) ) ) ) ) ) ) ) ).
fof(t5_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__2
& ! [D] :
( m1_trees_1(D,k1_relat_1(B))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,E,k1_prelamb(A,G,F))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),G),E),F) ) ) ) ) ) ) ) ) ) ).
fof(t6_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__3
& ! [D] :
( m1_trees_1(D,k1_relat_1(B))
=> ! [E] :
( m1_trees_1(E,k1_relat_1(B))
=> ! [F] :
( m2_finseq_1(F,u1_struct_0(A))
=> ! [G] :
( m2_finseq_1(G,u1_struct_0(A))
=> ! [H] :
( m2_finseq_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
& E = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,I,J))),F),H),K)
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,F,J)
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,E)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,k12_finseq_1(u1_struct_0(A),I)),H),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__4
& ! [D] :
( m1_trees_1(D,k1_relat_1(B))
=> ! [E] :
( m1_trees_1(E,k1_relat_1(B))
=> ! [F] :
( m2_finseq_1(F,u1_struct_0(A))
=> ! [G] :
( m2_finseq_1(G,u1_struct_0(A))
=> ! [H] :
( m2_finseq_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
& E = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,F),k12_finseq_1(u1_struct_0(A),k1_prelamb(A,J,I))),H),K)
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,F,J)
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,E)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,k12_finseq_1(u1_struct_0(A),I)),H),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_prelamb(C,A)
=> ! [D] :
( m1_trees_1(D,k1_relat_1(C))
=> ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),C,D)) = np__5
& ! [E] :
( m1_trees_1(E,k1_relat_1(C))
=> ! [F] :
( m2_finseq_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m2_finseq_1(I,u1_struct_0(A))
=> ~ ( E = k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,np__0))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),C,D)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),F,k12_finseq_1(u1_struct_0(A),k3_prelamb(A,G,H))),I),B)
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),C,E)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),F,k12_finseq_1(u1_struct_0(A),G)),k12_finseq_1(u1_struct_0(A),H)),I),B) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__6
& ! [D] :
( m1_trees_1(D,k1_relat_1(B))
=> ! [E] :
( m1_trees_1(E,k1_relat_1(B))
=> ! [F] :
( m2_finseq_1(F,u1_struct_0(A))
=> ! [G] :
( m2_finseq_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
& E = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),F,G),k3_prelamb(A,H,I))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,F,H)
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,E)) = k6_prelamb(A,G,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t10_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = np__7
& ! [D] :
( m1_trees_1(D,k1_relat_1(B))
=> ! [E] :
( m1_trees_1(E,k1_relat_1(B))
=> ! [F] :
( m2_finseq_1(F,u1_struct_0(A))
=> ! [G] :
( m2_finseq_1(G,u1_struct_0(A))
=> ! [H] :
( m2_finseq_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ~ ( D = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__0))
& E = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,np__1))
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,F),H),J)
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,D)) = k6_prelamb(A,F,I)
& k1_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,E)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,k12_finseq_1(u1_struct_0(A),I)),H),J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> ~ ( k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__0
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__1
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__2
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__3
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__4
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__5
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__6
& k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__7 ) ) ) ) ).
fof(d14_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_finset_1(B)
& v3_trees_2(B)
& m3_trees_2(B,k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers)) )
=> ( v8_prelamb(B,A)
<=> ! [C] :
( m1_trees_1(C,k1_relat_1(B))
=> k2_mcart_1(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers),B,C)) != np__7 ) ) ) ) ).
fof(d15_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k5_numbers)
& m2_relset_1(B,u1_struct_0(A),k5_numbers) )
=> ( B = k7_prelamb(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),k5_numbers,B,C) = k4_card_1(k1_relat_1(k5_prelamb(A,C))) ) ) ) ) ).
fof(d16_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( k2_mcart_1(k1_funct_1(B,k1_xboole_0)) = np__7
=> ( C = k9_prelamb(A,B)
<=> ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& ? [E] :
( m2_finseq_1(E,u1_struct_0(A))
& ? [F] :
( m2_finseq_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& k1_mcart_1(k1_funct_1(B,k1_xboole_0)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,D),F),H)
& k1_mcart_1(k1_funct_1(B,k12_finseq_1(k5_numbers,np__0))) = k6_prelamb(A,D,G)
& k1_mcart_1(k1_funct_1(B,k12_finseq_1(k5_numbers,np__1))) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F),H)
& C = k3_real_1(k1_nat_1(k8_funct_2(u1_struct_0(A),k5_numbers,k7_prelamb(A),G),k8_funct_2(u1_struct_0(A),k5_numbers,k7_prelamb(A),H)),k15_rvsum_1(k8_prelamb(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),E,D),F),k7_prelamb(A)))) ) ) ) ) ) ) )
& ( k2_mcart_1(k1_funct_1(B,k1_xboole_0)) != np__7
=> ( C = k9_prelamb(A,B)
<=> C = np__0 ) ) ) ) ) ) ).
fof(d18_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_prelamb(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_prelamb(A,B,C)
<=> r2_hidden(k6_prelamb(A,B,C),u4_prelamb(A)) ) ) ) ) ).
fof(d19_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_prelamb(A) )
=> ( v10_prelamb(A)
<=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),B) )
& ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_prelamb(A,k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),D)),C)
=> r2_prelamb(A,B,k2_prelamb(A,C,D)) ) ) ) )
& ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),D),B),C)
=> r2_prelamb(A,B,k1_prelamb(A,D,C)) ) ) ) )
& ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_prelamb(A,B,F)
& r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),C,k12_finseq_1(u1_struct_0(A),E)),D),G) )
=> r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),C,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,E,F))),B),D),G) ) ) ) ) ) ) )
& ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_prelamb(A,B,F)
& r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),C,k12_finseq_1(u1_struct_0(A),E)),D),G) )
=> r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),C,B),k12_finseq_1(u1_struct_0(A),k1_prelamb(A,F,E))),D),G) ) ) ) ) ) ) )
& ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),D)),k12_finseq_1(u1_struct_0(A),E)),C),F)
=> r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),k3_prelamb(A,D,E))),C),F) ) ) ) ) ) )
& ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_prelamb(A,B,D)
& r2_prelamb(A,C,E) )
=> r2_prelamb(A,k8_finseq_1(u1_struct_0(A),B,C),k3_prelamb(A,D,E)) ) ) ) ) ) ) ) ) ).
fof(t12_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,C)),k12_finseq_1(u1_struct_0(A),C)),B)
& r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),C),k12_finseq_1(u1_struct_0(A),k1_prelamb(A,C,B))),B) ) ) ) ) ).
fof(t13_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),k2_prelamb(A,C,k1_prelamb(A,B,C)))
& r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),k1_prelamb(A,k2_prelamb(A,C,B),C)) ) ) ) ) ).
fof(t14_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,C)),k2_prelamb(A,k2_prelamb(A,B,D),k2_prelamb(A,C,D))) ) ) ) ) ).
fof(t15_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k1_prelamb(A,B,C)),k1_prelamb(A,k1_prelamb(A,D,B),k1_prelamb(A,D,C))) ) ) ) ) ).
fof(t16_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),C)
=> ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,D)),k2_prelamb(A,C,D))
& r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k1_prelamb(A,D,B)),k1_prelamb(A,D,C)) ) ) ) ) ) ) ).
fof(t17_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),C)
=> ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,D,C)),k2_prelamb(A,D,B))
& r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k1_prelamb(A,C,D)),k1_prelamb(A,B,D)) ) ) ) ) ) ) ).
fof(t18_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,k1_prelamb(A,k2_prelamb(A,B,C),B))),k2_prelamb(A,B,C)) ) ) ) ).
fof(t19_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),C)
=> ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,C,B))
& r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,B,C)) ) ) ) ) ) ).
fof(t20_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,B,B))
& r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,B,B)) ) ) ) ).
fof(t21_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,k2_prelamb(A,B,k1_prelamb(A,C,B)),C))
& r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,C,k1_prelamb(A,k2_prelamb(A,B,C),B))) ) ) ) ) ).
fof(t22_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,k2_prelamb(A,k2_prelamb(A,B,C),k2_prelamb(A,D,C)),k2_prelamb(A,B,D)))
& r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,k1_prelamb(A,D,B),k1_prelamb(A,k1_prelamb(A,C,D),k1_prelamb(A,C,B)))) ) ) ) ) ) ).
fof(t23_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),B)
=> ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,C,k2_prelamb(A,C,B)))
& r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,k1_prelamb(A,B,C),C)) ) ) ) ) ) ).
fof(t24_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,B,k2_prelamb(A,C,C))),B) ) ) ) ).
fof(d20_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_prelamb(A,B,C)
<=> ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),C)
& r2_prelamb(A,k12_finseq_1(u1_struct_0(A),C),B) ) ) ) ) ) ).
fof(t25_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r3_prelamb(A,B,B) ) ) ).
fof(t26_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r3_prelamb(A,k2_prelamb(A,B,C),k2_prelamb(A,B,k1_prelamb(A,k2_prelamb(A,B,C),B))) ) ) ) ).
fof(t27_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r3_prelamb(A,k2_prelamb(A,B,k3_prelamb(A,C,D)),k2_prelamb(A,k2_prelamb(A,B,D),C)) ) ) ) ) ).
fof(t28_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k3_prelamb(A,B,k2_prelamb(A,C,D))),k2_prelamb(A,k3_prelamb(A,B,C),D)) ) ) ) ) ).
fof(t29_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),k2_prelamb(A,k3_prelamb(A,B,C),C))
& r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),k1_prelamb(A,C,k3_prelamb(A,C,B))) ) ) ) ) ).
fof(t30_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_prelamb(A)
& l2_prelamb(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r3_prelamb(A,k3_prelamb(A,k3_prelamb(A,B,C),D),k3_prelamb(A,B,k3_prelamb(A,C,D))) ) ) ) ) ).
fof(dt_m1_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( m1_prelamb(B,A)
=> ( v1_funct_1(B)
& v1_finset_1(B)
& v3_trees_2(B)
& m3_trees_2(B,k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k5_numbers)) ) ) ) ).
fof(existence_m1_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ? [B] : m1_prelamb(B,A) ) ).
fof(dt_m2_prelamb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& ~ v1_xboole_0(B) )
=> ! [C] :
( m2_prelamb(C,A,B)
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)))
& m2_relset_1(C,u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B))) ) ) ) ).
fof(existence_m2_prelamb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& ~ v1_xboole_0(B) )
=> ? [C] : m2_prelamb(C,A,B) ) ).
fof(dt_l1_prelamb,axiom,
! [A] :
( l1_prelamb(A)
=> l1_struct_0(A) ) ).
fof(existence_l1_prelamb,axiom,
? [A] : l1_prelamb(A) ).
fof(dt_l2_prelamb,axiom,
! [A] :
( l2_prelamb(A)
=> l1_prelamb(A) ) ).
fof(existence_l2_prelamb,axiom,
? [A] : l2_prelamb(A) ).
fof(abstractness_v1_prelamb,axiom,
! [A] :
( l1_prelamb(A)
=> ( v1_prelamb(A)
=> A = g1_prelamb(u1_struct_0(A),u1_prelamb(A),u2_prelamb(A),u3_prelamb(A)) ) ) ).
fof(abstractness_v9_prelamb,axiom,
! [A] :
( l2_prelamb(A)
=> ( v9_prelamb(A)
=> A = g2_prelamb(u1_struct_0(A),u1_prelamb(A),u2_prelamb(A),u3_prelamb(A),u4_prelamb(A)) ) ) ).
fof(dt_k1_prelamb,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k1_prelamb(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k2_prelamb,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k2_prelamb(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k3_prelamb,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k3_prelamb(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k4_prelamb,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& v1_funct_1(B)
& v1_finset_1(B)
& v3_trees_2(B)
& m3_trees_2(B,u1_struct_0(A))
& m1_subset_1(C,k1_relat_1(B)) )
=> m1_subset_1(k4_prelamb(A,B,C),u1_struct_0(A)) ) ).
fof(redefinition_k4_prelamb,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& v1_funct_1(B)
& v1_finset_1(B)
& v3_trees_2(B)
& m3_trees_2(B,u1_struct_0(A))
& m1_subset_1(C,k1_relat_1(B)) )
=> k4_prelamb(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k5_prelamb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_funct_1(k5_prelamb(A,B))
& v1_finset_1(k5_prelamb(A,B))
& v3_trees_2(k5_prelamb(A,B))
& m3_trees_2(k5_prelamb(A,B),u1_struct_0(A)) ) ) ).
fof(dt_k6_prelamb,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& m1_finseq_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k6_prelamb(A,B,C),k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A))) ) ).
fof(redefinition_k6_prelamb,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& m1_finseq_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k6_prelamb(A,B,C) = k4_tarski(B,C) ) ).
fof(dt_k7_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ( v1_funct_1(k7_prelamb(A))
& v1_funct_2(k7_prelamb(A),u1_struct_0(A),k5_numbers)
& m2_relset_1(k7_prelamb(A),u1_struct_0(A),k5_numbers) ) ) ).
fof(dt_k8_prelamb,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,A,k5_numbers)
& m1_relset_1(C,A,k5_numbers) )
=> m2_finseq_1(k8_prelamb(A,B,C),k1_numbers) ) ).
fof(redefinition_k8_prelamb,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,A,k5_numbers)
& m1_relset_1(C,A,k5_numbers) )
=> k8_prelamb(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k9_prelamb,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A)
& m1_prelamb(B,A) )
=> m2_subset_1(k9_prelamb(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_u1_prelamb,axiom,
! [A] :
( l1_prelamb(A)
=> ( v1_funct_1(u1_prelamb(A))
& v1_funct_2(u1_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(u1_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_u2_prelamb,axiom,
! [A] :
( l1_prelamb(A)
=> ( v1_funct_1(u2_prelamb(A))
& v1_funct_2(u2_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(u2_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_u3_prelamb,axiom,
! [A] :
( l1_prelamb(A)
=> ( v1_funct_1(u3_prelamb(A))
& v1_funct_2(u3_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(u3_prelamb(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_u4_prelamb,axiom,
! [A] :
( l2_prelamb(A)
=> m2_relset_1(u4_prelamb(A),k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)) ) ).
fof(dt_g1_prelamb,axiom,
! [A,B,C,D] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m1_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( v1_prelamb(g1_prelamb(A,B,C,D))
& l1_prelamb(g1_prelamb(A,B,C,D)) ) ) ).
fof(free_g1_prelamb,axiom,
! [A,B,C,D] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m1_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E,F,G,H] :
( g1_prelamb(A,B,C,D) = g1_prelamb(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
fof(dt_g2_prelamb,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m1_relset_1(D,k2_zfmisc_1(A,A),A)
& m1_relset_1(E,k3_finseq_2(A),A) )
=> ( v9_prelamb(g2_prelamb(A,B,C,D,E))
& l2_prelamb(g2_prelamb(A,B,C,D,E)) ) ) ).
fof(free_g2_prelamb,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m1_relset_1(D,k2_zfmisc_1(A,A),A)
& m1_relset_1(E,k3_finseq_2(A),A) )
=> ! [F,G,H,I,J] :
( g2_prelamb(A,B,C,D,E) = g2_prelamb(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(d17_prelamb,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_prelamb(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)))
& m2_relset_1(C,u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B))) )
=> ( m2_prelamb(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)),C,k3_prelamb(A,D,E)) = a_5_0_prelamb(A,B,C,D,E)
& k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)),C,k2_prelamb(A,D,E)) = a_5_1_prelamb(A,B,C,D,E)
& k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_finseq_2(B)),C,k1_prelamb(A,E,D)) = a_5_2_prelamb(A,B,C,D,E) ) ) ) ) ) ) ) ).
fof(fraenkel_a_5_0_prelamb,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(B)
& l1_prelamb(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
& m2_relset_1(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B)) )
=> ( r2_hidden(A,a_5_0_prelamb(B,C,D,E,F))
<=> ? [G,H] :
( m2_finseq_2(G,C,k3_finseq_2(C))
& m2_finseq_2(H,C,k3_finseq_2(C))
& A = k8_finseq_1(C,G,H)
& r2_hidden(G,k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,E))
& r2_hidden(H,k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,F)) ) ) ) ).
fof(fraenkel_a_5_1_prelamb,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(B)
& l1_prelamb(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
& m2_relset_1(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B)) )
=> ( r2_hidden(A,a_5_1_prelamb(B,C,D,E,F))
<=> ? [G] :
( m2_finseq_2(G,C,k3_finseq_2(C))
& A = G
& ! [H] :
( m2_finseq_2(H,C,k3_finseq_2(C))
=> ( r2_hidden(H,k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,F))
=> r2_hidden(k8_finseq_1(C,G,H),k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,E)) ) ) ) ) ) ).
fof(fraenkel_a_5_2_prelamb,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(B)
& l1_prelamb(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
& m2_relset_1(D,u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B)) )
=> ( r2_hidden(A,a_5_2_prelamb(B,C,D,E,F))
<=> ? [G] :
( m2_finseq_2(G,C,k3_finseq_2(C))
& A = G
& ! [H] :
( m2_finseq_2(H,C,k3_finseq_2(C))
=> ( r2_hidden(H,k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,F))
=> r2_hidden(k8_finseq_1(C,H,G),k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k3_finseq_2(C)),D,E)) ) ) ) ) ) ).
%------------------------------------------------------------------------------