SET007 Axioms: SET007+620.ax
%------------------------------------------------------------------------------
% File : SET007+620 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : A Characterization of Concept Lattices. Dual Concept Lattices
% 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 : conlat_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 50 ( 0 unt; 0 def)
% Number of atoms : 351 ( 47 equ)
% Maximal formula atoms : 19 ( 7 avg)
% Number of connectives : 382 ( 81 ~; 0 |; 209 &)
% ( 14 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 35 ( 34 usr; 0 prp; 1-3 aty)
% Number of functors : 46 ( 46 usr; 0 con; 1-4 aty)
% Number of variables : 115 ( 96 !; 19 ?)
% 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(fc1_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_struct_0(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& v4_lattices(k11_conlat_1(A))
& v5_lattices(k11_conlat_1(A))
& v6_lattices(k11_conlat_1(A))
& v7_lattices(k11_conlat_1(A))
& v8_lattices(k11_conlat_1(A))
& v9_lattices(k11_conlat_1(A))
& v10_lattices(k11_conlat_1(A))
& v13_lattices(k11_conlat_1(A))
& v14_lattices(k11_conlat_1(A))
& v15_lattices(k11_conlat_1(A))
& v4_lattice3(k11_conlat_1(A)) ) ) ).
fof(fc2_conlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ( ~ v3_struct_0(k1_lattice2(A))
& v3_lattices(k1_lattice2(A))
& v4_lattices(k1_lattice2(A))
& v5_lattices(k1_lattice2(A))
& v6_lattices(k1_lattice2(A))
& v7_lattices(k1_lattice2(A))
& v8_lattices(k1_lattice2(A))
& v9_lattices(k1_lattice2(A))
& v10_lattices(k1_lattice2(A))
& v4_lattice3(k1_lattice2(A)) ) ) ).
fof(d1_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> k1_conlat_2(A,B) = B ) ) ).
fof(t1_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( k5_lattices(k11_conlat_1(A)) = k6_conlat_1(A)
& k6_lattices(k11_conlat_1(A)) = k5_conlat_1(A) ) ) ).
fof(t4_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
=> ( ~ v7_conlat_1(k16_lattice3(k11_conlat_1(A),B),A)
& v9_conlat_1(k16_lattice3(k11_conlat_1(A),B),A)
& l3_conlat_1(k16_lattice3(k11_conlat_1(A),B),A)
& ~ v7_conlat_1(k15_lattice3(k11_conlat_1(A),B),A)
& v9_conlat_1(k15_lattice3(k11_conlat_1(A),B),A)
& l3_conlat_1(k15_lattice3(k11_conlat_1(A),B),A) ) ) ) ).
fof(d2_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
=> k2_conlat_2(A,B) = k16_lattice3(k11_conlat_1(A),B) ) ) ).
fof(d3_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
=> k3_conlat_2(A,B) = k15_lattice3(k11_conlat_1(A),B) ) ) ).
fof(t5_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( k3_conlat_2(A,k1_pre_topc(k11_conlat_1(A))) = k6_conlat_1(A)
& k2_conlat_2(A,k1_pre_topc(k11_conlat_1(A))) = k5_conlat_1(A) ) ) ).
fof(t6_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( k3_conlat_2(A,k2_subset_1(u1_struct_0(k11_conlat_1(A)))) = k5_conlat_1(A)
& k2_conlat_2(A,k2_subset_1(u1_struct_0(k11_conlat_1(A)))) = k6_conlat_1(A) ) ) ).
fof(d4_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
& m2_relset_1(B,u1_conlat_1(A),u1_struct_0(k11_conlat_1(A))) )
=> ( B = k4_conlat_2(A)
<=> ! [C] :
( m1_subset_1(C,u1_conlat_1(A))
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(A)))
& ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(A)))
& k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),B,C) = g3_conlat_1(A,D,E)
& D = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k6_domain_1(u1_conlat_1(A),C)))
& E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k6_domain_1(u1_conlat_1(A),C)) ) ) ) ) ) ) ).
fof(d5_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
& m2_relset_1(B,u2_conlat_1(A),u1_struct_0(k11_conlat_1(A))) )
=> ( B = k5_conlat_2(A)
<=> ! [C] :
( m1_subset_1(C,u2_conlat_1(A))
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(A)))
& ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(A)))
& k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),B,C) = g3_conlat_1(A,D,E)
& D = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k6_domain_1(u2_conlat_1(A),C))
& E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k6_domain_1(u2_conlat_1(A),C))) ) ) ) ) ) ) ).
fof(t11_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_conlat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_conlat_1(A))
=> ( ~ v7_conlat_1(k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A)
& v9_conlat_1(k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A)
& l3_conlat_1(k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A)
& ~ v7_conlat_1(k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A)
& v9_conlat_1(k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A)
& l3_conlat_1(k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A) ) ) ) ) ).
fof(t12_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v8_lattice6(k5_relset_1(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A)),k11_conlat_1(A))
& v9_lattice6(k5_relset_1(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A)),k11_conlat_1(A)) ) ) ).
fof(t13_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_conlat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_conlat_1(A))
=> ( r1_conlat_1(A,B,C)
<=> r3_lattices(k11_conlat_1(A),k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C)) ) ) ) ) ).
fof(t14_conlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B) )
=> ( r1_filter_1(k11_conlat_1(B),A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_conlat_1(B),u1_struct_0(A))
& m2_relset_1(C,u1_conlat_1(B),u1_struct_0(A))
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u2_conlat_1(B),u1_struct_0(A))
& m2_relset_1(D,u2_conlat_1(B),u1_struct_0(A))
& v8_lattice6(k5_relset_1(u1_conlat_1(B),u1_struct_0(A),C),A)
& v9_lattice6(k5_relset_1(u2_conlat_1(B),u1_struct_0(A),D),A)
& ! [E] :
( m1_subset_1(E,u1_conlat_1(B))
=> ! [F] :
( m1_subset_1(F,u2_conlat_1(B))
=> ( r1_conlat_1(B,E,F)
<=> r3_lattices(A,k8_funct_2(u1_conlat_1(B),u1_struct_0(A),C,E),k8_funct_2(u2_conlat_1(B),u1_struct_0(A),D,F)) ) ) ) ) ) ) ) ) ).
fof(d6_conlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> k6_conlat_2(A) = g2_conlat_1(u1_struct_0(A),u1_struct_0(A),k2_lattice3(A)) ) ).
fof(t15_conlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_lattice3(A)
& l3_lattices(A) )
=> r1_filter_1(k11_conlat_1(k6_conlat_2(A)),A) ) ).
fof(t16_conlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v4_lattice3(A)
<=> ? [B] :
( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& r1_filter_1(k11_conlat_1(B),A) ) ) ) ).
fof(d7_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> k7_conlat_2(A) = g2_conlat_1(u2_conlat_1(A),u1_conlat_1(A),k6_relset_1(u1_conlat_1(A),u2_conlat_1(A),u3_conlat_1(A))) ) ).
fof(t17_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& v4_conlat_1(A)
& l2_conlat_1(A) )
=> k7_conlat_2(k7_conlat_2(A)) = A ) ).
fof(t18_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
=> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B) = k1_funct_1(k2_conlat_1(k7_conlat_2(A)),B) ) ) ).
fof(t19_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
=> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B) = k1_funct_1(k1_conlat_1(k7_conlat_2(A)),B) ) ) ).
fof(d8_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( l3_conlat_1(B,A)
=> ! [C] :
( ( v6_conlat_1(C,k7_conlat_2(A))
& l3_conlat_1(C,k7_conlat_2(A)) )
=> ( C = k8_conlat_2(A,B)
<=> ( u4_conlat_1(k7_conlat_2(A),C) = u5_conlat_1(A,B)
& u5_conlat_1(k7_conlat_2(A),C) = u4_conlat_1(A,B) ) ) ) ) ) ).
fof(t20_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& v4_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> k9_conlat_2(k7_conlat_2(A),k9_conlat_2(A,B)) = B ) ) ).
fof(d9_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_lattice4(B,k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A)))
=> ( B = k10_conlat_2(A)
<=> ! [C] :
( ( v6_conlat_1(C,A)
& ~ v7_conlat_1(C,A)
& v9_conlat_1(C,A)
& l3_conlat_1(C,A) )
=> k1_funct_1(B,C) = k9_conlat_2(A,C) ) ) ) ) ).
fof(t21_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> v3_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A))) ) ).
fof(t22_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> r1_filter_1(k11_conlat_1(k7_conlat_2(A)),k1_lattice2(k11_conlat_1(A))) ) ).
fof(dt_k1_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> m1_subset_1(k1_conlat_2(A,B),u1_struct_0(k11_conlat_1(A))) ) ).
fof(dt_k2_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ( ~ v7_conlat_1(k2_conlat_2(A,B),A)
& v9_conlat_1(k2_conlat_2(A,B),A)
& l3_conlat_1(k2_conlat_2(A,B),A) ) ) ).
fof(dt_k3_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ( ~ v7_conlat_1(k3_conlat_2(A,B),A)
& v9_conlat_1(k3_conlat_2(A,B),A)
& l3_conlat_1(k3_conlat_2(A,B),A) ) ) ).
fof(dt_k4_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k4_conlat_2(A))
& v1_funct_2(k4_conlat_2(A),u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
& m2_relset_1(k4_conlat_2(A),u1_conlat_1(A),u1_struct_0(k11_conlat_1(A))) ) ) ).
fof(dt_k5_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k5_conlat_2(A))
& v1_funct_2(k5_conlat_2(A),u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
& m2_relset_1(k5_conlat_2(A),u2_conlat_1(A),u1_struct_0(k11_conlat_1(A))) ) ) ).
fof(dt_k6_conlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ~ v3_conlat_1(k6_conlat_2(A))
& v4_conlat_1(k6_conlat_2(A))
& l2_conlat_1(k6_conlat_2(A)) ) ) ).
fof(dt_k7_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_conlat_1(k7_conlat_2(A))
& v4_conlat_1(k7_conlat_2(A))
& l2_conlat_1(k7_conlat_2(A)) ) ) ).
fof(dt_k8_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& l3_conlat_1(B,A) )
=> ( v6_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A))
& l3_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) ) ) ).
fof(dt_k9_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> ( v6_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
& ~ v7_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
& v9_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
& l3_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A)) ) ) ).
fof(redefinition_k9_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> k9_conlat_2(A,B) = k8_conlat_2(A,B) ) ).
fof(dt_k10_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> m1_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A))) ) ).
fof(t2_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_conlat_1(A)))) )
=> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k5_setfam_1(u1_conlat_1(A),B)) = k1_setfam_1(a_2_0_conlat_2(A,B)) ) ) ).
fof(t3_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u2_conlat_1(A)))) )
=> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k5_setfam_1(u2_conlat_1(A),B)) = k1_setfam_1(a_2_1_conlat_2(A,B)) ) ) ).
fof(t7_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ( u4_conlat_1(A,k3_conlat_2(A,B)) = k1_funct_1(k2_conlat_1(A),k1_funct_1(k1_conlat_1(A),k3_tarski(a_2_2_conlat_2(A,B))))
& u5_conlat_1(A,k3_conlat_2(A,B)) = k1_setfam_1(a_2_3_conlat_2(A,B)) ) ) ) ).
fof(t8_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ( u4_conlat_1(A,k2_conlat_2(A,B)) = k1_setfam_1(a_2_2_conlat_2(A,B))
& u5_conlat_1(A,k2_conlat_2(A,B)) = k1_funct_1(k1_conlat_1(A),k1_funct_1(k2_conlat_1(A),k3_tarski(a_2_3_conlat_2(A,B)))) ) ) ) ).
fof(t9_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> k15_lattice3(k11_conlat_1(A),a_2_4_conlat_2(A,B)) = B ) ) ).
fof(t10_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> k16_lattice3(k11_conlat_1(A),a_2_5_conlat_2(A,B)) = B ) ) ).
fof(fraenkel_a_2_0_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_conlat_1(B)))) )
=> ( r2_hidden(A,a_2_0_conlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
& A = k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_1_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u2_conlat_1(B)))) )
=> ( r2_hidden(A,a_2_1_conlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(B)))
& A = k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_2_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) )
=> ( r2_hidden(A,a_2_2_conlat_2(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
& m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
& A = u4_conlat_1(B,g3_conlat_1(B,D,E))
& r2_hidden(g3_conlat_1(B,D,E),C) ) ) ) ).
fof(fraenkel_a_2_3_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) )
=> ( r2_hidden(A,a_2_3_conlat_2(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
& m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
& A = u5_conlat_1(B,g3_conlat_1(B,D,E))
& r2_hidden(g3_conlat_1(B,D,E),C) ) ) ) ).
fof(fraenkel_a_2_4_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& v6_conlat_1(C,B)
& ~ v7_conlat_1(C,B)
& v9_conlat_1(C,B)
& l3_conlat_1(C,B) )
=> ( r2_hidden(A,a_2_4_conlat_2(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
& m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
& A = g3_conlat_1(B,D,E)
& ? [F] :
( m1_subset_1(F,u1_conlat_1(B))
& r2_hidden(F,u4_conlat_1(B,C))
& D = k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),k6_domain_1(u1_conlat_1(B),F)))
& E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),k6_domain_1(u1_conlat_1(B),F)) ) ) ) ) ).
fof(fraenkel_a_2_5_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& v6_conlat_1(C,B)
& ~ v7_conlat_1(C,B)
& v9_conlat_1(C,B)
& l3_conlat_1(C,B) )
=> ( r2_hidden(A,a_2_5_conlat_2(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
& m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
& A = g3_conlat_1(B,D,E)
& ? [F] :
( m1_subset_1(F,u2_conlat_1(B))
& r2_hidden(F,u5_conlat_1(B,C))
& D = k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),k6_domain_1(u2_conlat_1(B),F))
& E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),k6_domain_1(u2_conlat_1(B),F))) ) ) ) ) ).
%------------------------------------------------------------------------------