SET007 Axioms: SET007+434.ax
%------------------------------------------------------------------------------
% File : SET007+434 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Lattice of Subalgebras of a Universal Algebra
% 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 : unialg_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 53 ( 1 unt; 0 def)
% Number of atoms : 518 ( 47 equ)
% Maximal formula atoms : 24 ( 9 avg)
% Number of connectives : 535 ( 70 ~; 0 |; 333 &)
% ( 13 <=>; 119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-3 aty)
% Number of functors : 34 ( 34 usr; 2 con; 0-4 aty)
% Number of variables : 124 ( 118 !; 6 ?)
% 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_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ? [B] :
( m1_unialg_3(B,A)
& ~ v1_xboole_0(B) ) ) ).
fof(cc1_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> v2_unialg_2(B) ) ) ).
fof(fc1_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ( ~ v3_struct_0(k12_unialg_2(A))
& v3_lattices(k12_unialg_2(A))
& v4_lattices(k12_unialg_2(A))
& v5_lattices(k12_unialg_2(A))
& v6_lattices(k12_unialg_2(A))
& v7_lattices(k12_unialg_2(A))
& v8_lattices(k12_unialg_2(A))
& v9_lattices(k12_unialg_2(A))
& v10_lattices(k12_unialg_2(A))
& v13_lattices(k12_unialg_2(A))
& v14_lattices(k12_unialg_2(A))
& v15_lattices(k12_unialg_2(A)) ) ) ).
fof(d1_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_unialg_3(B,A)
<=> ! [C] :
( r2_hidden(C,B)
=> m3_unialg_2(C,A) ) ) ) ).
fof(d2_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_unialg_3(B,A,k1_unialg_3(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = k4_unialg_3(A,B)
<=> ? [D] :
( m3_unialg_2(D,A)
& B = D
& C = u1_struct_0(D) ) ) ) ) ) ).
fof(d3_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A))) )
=> ( B = k5_unialg_3(A)
<=> ! [C] :
( m2_unialg_3(C,A,k1_unialg_3(A))
=> k8_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),B,C) = k4_unialg_3(A,C) ) ) ) ) ).
fof(t1_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( r2_hidden(B,k1_unialg_3(A))
<=> ? [C] :
( v3_unialg_1(C)
& m3_unialg_2(C,A)
& B = C ) ) ) ).
fof(t2_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
=> ( k2_unialg_1(u1_struct_0(A),C) = np__0
=> ( r2_unialg_2(A,B,C)
<=> r2_hidden(k1_funct_1(C,k1_xboole_0),B) ) ) ) ) ) ).
fof(t3_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> r1_tarski(u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(t4_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
=> ( ( r2_unialg_2(A,B,C)
& k2_unialg_1(u1_struct_0(A),C) = np__0 )
=> k2_unialg_2(A,B,C) = C ) ) ) ) ).
fof(t6_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> k6_unialg_2(A) = k6_unialg_2(B) ) ) ).
fof(t7_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ! [C] :
( m3_unialg_2(C,A)
=> k6_unialg_2(B) = k6_unialg_2(C) ) ) ) ).
fof(d4_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A))) )
=> ( B = k6_unialg_3(A)
<=> ! [C] :
( m2_unialg_3(C,A,k1_unialg_3(A))
=> ! [D] :
( m3_unialg_2(D,A)
=> ( C = D
=> k8_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),B,C) = u1_struct_0(D) ) ) ) ) ) ) ).
fof(t8_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& m3_unialg_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(k6_unialg_3(A),B))
<=> r1_rlvect_1(B,C) ) ) ) ) ).
fof(t9_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) )
=> ~ v1_xboole_0(k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B)) ) ) ).
fof(t10_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& m3_unialg_2(B,A) )
=> r1_tarski(k6_unialg_2(A),k1_funct_1(k6_unialg_3(A),B)) ) ) ).
fof(t11_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ! [C] :
( m1_struct_0(C,A,k6_unialg_2(A))
=> r2_hidden(C,u1_struct_0(B)) ) ) ) ).
fof(t12_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) )
=> ( ~ v1_xboole_0(k6_setfam_1(u1_struct_0(A),k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B)))
& m1_subset_1(k6_setfam_1(u1_struct_0(A),k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t13_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> u1_struct_0(k12_unialg_2(A)) = k1_unialg_3(A) ) ).
fof(t14_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = k6_setfam_1(u1_struct_0(A),k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B))
=> v1_unialg_2(C,A) ) ) ) ) ).
fof(d5_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) )
=> ! [C] :
( ( v3_unialg_1(C)
& m3_unialg_2(C,A) )
=> ( C = k7_unialg_3(A,B)
<=> u1_struct_0(C) = k6_setfam_1(u1_struct_0(A),k2_funct_2(k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)),k6_unialg_3(A),B)) ) ) ) ) ).
fof(t15_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k12_unialg_2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k12_unialg_2(A)))
=> ! [D] :
( ( v3_unialg_1(D)
& m3_unialg_2(D,A) )
=> ! [E] :
( ( v3_unialg_1(E)
& m3_unialg_2(E,A) )
=> ( ( B = D
& C = E )
=> k3_lattices(k12_unialg_2(A),B,C) = k8_unialg_2(A,D,E) ) ) ) ) ) ) ).
fof(t16_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k12_unialg_2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k12_unialg_2(A)))
=> ! [D] :
( ( v3_unialg_1(D)
& m3_unialg_2(D,A) )
=> ! [E] :
( ( v3_unialg_1(E)
& m3_unialg_2(E,A) )
=> ( ( B = D
& C = E )
=> k4_lattices(k12_unialg_2(A),B,C) = k5_unialg_2(A,D,E) ) ) ) ) ) ) ).
fof(t17_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k12_unialg_2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k12_unialg_2(A)))
=> ! [D] :
( ( v3_unialg_1(D)
& m3_unialg_2(D,A) )
=> ! [E] :
( ( v3_unialg_1(E)
& m3_unialg_2(E,A) )
=> ( ( B = D
& C = E )
=> ( r3_lattices(k12_unialg_2(A),B,C)
<=> r1_tarski(u1_struct_0(D),u1_struct_0(E)) ) ) ) ) ) ) ) ).
fof(t18_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k12_unialg_2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k12_unialg_2(A)))
=> ! [D] :
( ( v3_unialg_1(D)
& m3_unialg_2(D,A) )
=> ! [E] :
( ( v3_unialg_1(E)
& m3_unialg_2(E,A) )
=> ( ( B = D
& C = E )
=> ( r3_lattices(k12_unialg_2(A),B,C)
<=> m3_unialg_2(D,E) ) ) ) ) ) ) ) ).
fof(t19_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> v15_lattices(k12_unialg_2(A)) ) ).
fof(t20_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& m3_unialg_2(B,A) )
=> k5_unialg_2(A,k7_unialg_2(A,k6_unialg_2(A)),B) = k7_unialg_2(A,k6_unialg_2(A)) ) ) ).
fof(t21_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> k5_lattices(k12_unialg_2(A)) = k7_unialg_2(A,k6_unialg_2(A)) ) ).
fof(t22_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(A)
=> k8_unialg_2(A,k7_unialg_2(A,C),B) = k7_unialg_2(A,C) ) ) ) ) ).
fof(t23_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = u1_struct_0(A)
=> k6_lattices(k12_unialg_2(A)) = k7_unialg_2(A,B) ) ) ) ).
fof(t24_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> k6_lattices(k12_unialg_2(A)) = A ) ).
fof(t25_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> v4_lattice3(k12_unialg_2(A)) ) ).
fof(d6_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& v2_unialg_2(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k12_unialg_2(A)),u1_struct_0(k12_unialg_2(B)))
& m2_relset_1(D,u1_struct_0(k12_unialg_2(A)),u1_struct_0(k12_unialg_2(B))) )
=> ( D = k8_unialg_3(A,B,C)
<=> ! [E] :
( ( v3_unialg_1(E)
& m3_unialg_2(E,A) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ( F = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
=> k1_funct_1(D,E) = k7_unialg_2(B,F) ) ) ) ) ) ) ) ) ).
fof(t26_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( B = k6_relat_1(u1_struct_0(A))
=> k8_unialg_3(A,A,B) = k6_relat_1(u1_struct_0(k12_unialg_2(A))) ) ) ) ).
fof(dt_m1_unialg_3,axiom,
$true ).
fof(existence_m1_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ? [B] : m1_unialg_3(B,A) ) ).
fof(dt_m2_unialg_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& ~ v1_xboole_0(B)
& m1_unialg_3(B,A) )
=> ! [C] :
( m2_unialg_3(C,A,B)
=> m3_unialg_2(C,A) ) ) ).
fof(existence_m2_unialg_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& ~ v1_xboole_0(B)
& m1_unialg_3(B,A) )
=> ? [C] : m2_unialg_3(C,A,B) ) ).
fof(redefinition_m2_unialg_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& ~ v1_xboole_0(B)
& m1_unialg_3(B,A) )
=> ! [C] :
( m2_unialg_3(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_k1_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( ~ v1_xboole_0(k1_unialg_3(A))
& m1_unialg_3(k1_unialg_3(A),A) ) ) ).
fof(redefinition_k1_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k1_unialg_3(A) = k9_unialg_2(A) ) ).
fof(dt_k2_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v1_funct_1(k2_unialg_3(A))
& v1_funct_2(k2_unialg_3(A),k2_zfmisc_1(k1_unialg_3(A),k1_unialg_3(A)),k1_unialg_3(A))
& m2_relset_1(k2_unialg_3(A),k2_zfmisc_1(k1_unialg_3(A),k1_unialg_3(A)),k1_unialg_3(A)) ) ) ).
fof(redefinition_k2_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k2_unialg_3(A) = k10_unialg_2(A) ) ).
fof(dt_k3_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v1_funct_1(k3_unialg_3(A))
& v1_funct_2(k3_unialg_3(A),k2_zfmisc_1(k1_unialg_3(A),k1_unialg_3(A)),k1_unialg_3(A))
& m2_relset_1(k3_unialg_3(A),k2_zfmisc_1(k1_unialg_3(A),k1_unialg_3(A)),k1_unialg_3(A)) ) ) ).
fof(redefinition_k3_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k3_unialg_3(A) = k11_unialg_2(A) ) ).
fof(dt_k4_unialg_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m1_subset_1(B,k1_unialg_3(A)) )
=> m1_subset_1(k4_unialg_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v1_funct_1(k5_unialg_3(A))
& v1_funct_2(k5_unialg_3(A),k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(k5_unialg_3(A),k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(dt_k6_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v1_funct_1(k6_unialg_3(A))
& v1_funct_2(k6_unialg_3(A),k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(k6_unialg_3(A),k1_unialg_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(redefinition_k6_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k6_unialg_3(A) = k5_unialg_3(A) ) ).
fof(dt_k7_unialg_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) )
=> ( v3_unialg_1(k7_unialg_3(A,B))
& m3_unialg_2(k7_unialg_3(A,B),A) ) ) ).
fof(dt_k8_unialg_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A)
& ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& v2_unialg_2(B)
& l1_unialg_1(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k8_unialg_3(A,B,C))
& v1_funct_2(k8_unialg_3(A,B,C),u1_struct_0(k12_unialg_2(A)),u1_struct_0(k12_unialg_2(B)))
& m2_relset_1(k8_unialg_3(A,B,C),u1_struct_0(k12_unialg_2(A)),u1_struct_0(k12_unialg_2(B))) ) ) ).
fof(t5_unialg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k6_unialg_2(A) = a_1_0_unialg_3(A) ) ).
fof(fraenkel_a_1_0_unialg_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( r2_hidden(A,a_1_0_unialg_3(B))
<=> ? [C] :
( m2_unialg_2(C,u1_struct_0(B),k1_unialg_2(B))
& A = k1_funct_1(C,k1_xboole_0)
& k2_unialg_1(u1_struct_0(B),C) = np__0 ) ) ) ).
%------------------------------------------------------------------------------