SET007 Axioms: SET007+293.ax
%------------------------------------------------------------------------------
% File : SET007+293 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Opposite Categories and Contravariant Functors
% 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 : oppcat_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 95 ( 0 unt; 0 def)
% Number of atoms : 630 ( 83 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 547 ( 12 ~; 0 |; 243 &)
% ( 11 <=>; 281 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 0 prp; 1-4 aty)
% Number of functors : 31 ( 31 usr; 1 con; 0-6 aty)
% Number of variables : 293 ( 291 !; 2 ?)
% 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(t1_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ( v2_cat_1(g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A)))
& l1_cat_1(g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))) ) ) ).
fof(d1_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> k2_oppcat_1(A) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A)) ) ).
fof(t2_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> k2_oppcat_1(k2_oppcat_1(A)) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ).
fof(d2_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k3_oppcat_1(A,B) = B ) ) ).
fof(d3_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
=> k4_oppcat_1(A,B) = k3_oppcat_1(k2_oppcat_1(A),B) ) ) ).
fof(t3_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k3_oppcat_1(k2_oppcat_1(A),k3_oppcat_1(A,B)) = B ) ) ).
fof(t4_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k4_oppcat_1(A,k3_oppcat_1(A,B)) = B ) ) ).
fof(t5_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
=> k3_oppcat_1(A,k4_oppcat_1(A,B)) = B ) ) ).
fof(d4_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k5_oppcat_1(A,B) = B ) ) ).
fof(d5_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
=> k6_oppcat_1(A,B) = k5_oppcat_1(k2_oppcat_1(A),B) ) ) ).
fof(t6_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k5_oppcat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = B ) ) ).
fof(t7_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k6_oppcat_1(A,k5_oppcat_1(A,B)) = B ) ) ).
fof(t8_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
=> k5_oppcat_1(A,k6_oppcat_1(A,B)) = B ) ) ).
fof(t9_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k3_cat_1(A,B)
& k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k2_cat_1(A,B) ) ) ) ).
fof(t10_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
=> ( k2_cat_1(A,k6_oppcat_1(A,B)) = k3_cat_1(k2_oppcat_1(A),B)
& k3_cat_1(A,k6_oppcat_1(A,B)) = k2_cat_1(k2_oppcat_1(A),B) ) ) ) ).
fof(t11_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( k3_oppcat_1(A,k2_cat_1(A,B)) = k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B))
& k3_oppcat_1(A,k3_cat_1(A,B)) = k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) ) ) ) ).
fof(t12_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
=> ( k4_oppcat_1(A,k2_cat_1(k2_oppcat_1(A),B)) = k3_cat_1(A,k6_oppcat_1(A,B))
& k4_oppcat_1(A,k3_cat_1(k2_oppcat_1(A),B)) = k2_cat_1(A,k6_oppcat_1(A,B)) ) ) ) ).
fof(t13_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( r2_hidden(D,k6_cat_1(A,B,C))
<=> r2_hidden(k5_oppcat_1(A,D),k6_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B))) ) ) ) ) ) ).
fof(t14_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(k2_oppcat_1(A)))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k2_oppcat_1(A)))
=> ( r2_hidden(D,k6_cat_1(k2_oppcat_1(A),B,C))
<=> r2_hidden(k6_oppcat_1(A,D),k6_cat_1(A,k4_oppcat_1(A,C),k4_oppcat_1(A,B))) ) ) ) ) ) ).
fof(t15_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( k6_cat_1(A,B,C) != k1_xboole_0
=> m1_cat_1(k5_oppcat_1(A,D),k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B)) ) ) ) ) ) ).
fof(t16_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(k2_oppcat_1(A)))
=> ! [D] :
( m1_cat_1(D,k2_oppcat_1(A),B,C)
=> ( k6_cat_1(k2_oppcat_1(A),B,C) != k1_xboole_0
=> m1_cat_1(k6_oppcat_1(A,D),A,k4_oppcat_1(A,C),k4_oppcat_1(A,B)) ) ) ) ) ) ).
fof(t17_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k2_cat_1(A,C) = k3_cat_1(A,B)
=> k5_oppcat_1(A,k4_cat_1(A,B,C)) = k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C),k5_oppcat_1(A,B)) ) ) ) ) ).
fof(t18_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C)) = k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B))
=> k5_oppcat_1(A,k4_cat_1(A,B,C)) = k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C),k5_oppcat_1(A,B)) ) ) ) ) ).
fof(t19_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(k2_oppcat_1(A)))
=> ( k2_cat_1(k2_oppcat_1(A),C) = k3_cat_1(k2_oppcat_1(A),B)
=> k6_oppcat_1(A,k4_cat_1(k2_oppcat_1(A),B,C)) = k4_cat_1(A,k6_oppcat_1(A,C),k6_oppcat_1(A,B)) ) ) ) ) ).
fof(t20_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,D) != k1_xboole_0
& k5_oppcat_1(A,k9_cat_1(A,B,C,D,E,F)) != k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,F),k5_oppcat_1(A,E)) ) ) ) ) ) ) ) ).
fof(t21_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k5_oppcat_1(A,k10_cat_1(A,B)) = k10_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,B)) ) ) ).
fof(t22_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
=> k6_oppcat_1(A,k10_cat_1(k2_oppcat_1(A),B)) = k10_cat_1(A,k4_oppcat_1(A,B)) ) ) ).
fof(t23_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v3_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A))
<=> v4_cat_1(B,A) ) ) ) ).
fof(t24_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v4_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A))
<=> v3_cat_1(B,A) ) ) ) ).
fof(t25_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v5_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A))
<=> v5_cat_1(B,A) ) ) ) ).
fof(t26_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( v7_cat_1(B,A)
<=> v6_cat_1(k3_oppcat_1(A,B),k2_oppcat_1(A)) ) ) ) ).
fof(t27_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( v7_cat_1(k3_oppcat_1(A,B),k2_oppcat_1(A))
<=> v6_cat_1(B,A) ) ) ) ).
fof(d6_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) )
=> ( D = k7_oppcat_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),D,E) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),C,k5_oppcat_1(A,E)) ) ) ) ) ) ) ).
fof(t28_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k2_oppcat_1(A)))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),k7_oppcat_1(A,B,C),k6_oppcat_1(A,D)) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),C,D) ) ) ) ) ).
fof(t29_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,k2_oppcat_1(A),B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),k3_oppcat_1(A,D)) ) ) ) ) ).
fof(t30_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,k2_oppcat_1(A),B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k2_oppcat_1(A)))
=> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),k4_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),D) ) ) ) ) ).
fof(d7_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( m1_oppcat_1(C,A,B)
<=> ( ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ? [E] :
( m1_subset_1(E,u1_cat_1(B))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) )
& ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) )
& ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ( k2_cat_1(A,E) = k3_cat_1(A,D)
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ) ) ) ) ).
fof(t31_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(B))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E)
=> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E ) ) ) ) ) ) ).
fof(t32_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) ).
fof(t33_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))
& k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ) ).
fof(t34_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ( k2_cat_1(A,E) = k3_cat_1(A,D)
=> k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) ) ) ) ).
fof(t35_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,k2_oppcat_1(A),B)
=> m1_oppcat_1(k7_oppcat_1(A,B,C),A,B) ) ) ) ).
fof(t36_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_oppcat_1(D,A,B)
=> ! [E] :
( m1_oppcat_1(E,B,C)
=> m2_cat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C) ) ) ) ) ) ).
fof(t37_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,k2_oppcat_1(A),B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),k3_oppcat_1(A,D)) ) ) ) ) ).
fof(t38_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,k2_oppcat_1(A),B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k2_oppcat_1(A)))
=> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),k4_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),D) ) ) ) ) ).
fof(t39_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,k2_oppcat_1(A),B)
=> m2_cat_1(k7_oppcat_1(A,B,C),A,B) ) ) ) ).
fof(d8_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
& m2_relset_1(D,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
=> ( D = k8_oppcat_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u2_cat_1(k2_oppcat_1(A)))
=> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),D,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_oppcat_1(A,E)) ) ) ) ) ) ) ).
fof(d9_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_cat_1(A),u2_cat_1(k2_oppcat_1(B)))
& m2_relset_1(D,u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) )
=> ( D = k9_oppcat_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(k2_oppcat_1(B)),D,E) = k5_oppcat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) ) ) ) ).
fof(t40_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),k8_oppcat_1(A,B,C),k5_oppcat_1(A,D)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D) ) ) ) ) ).
fof(t41_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k2_oppcat_1(A)))
=> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k4_oppcat_1(A,D)) ) ) ) ) ).
fof(t42_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k3_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) ) ) ) ) ).
fof(t43_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)),D) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) ).
fof(t44_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k2_oppcat_1(A)))
=> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k4_oppcat_1(A,D)) ) ) ) ) ).
fof(t45_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k3_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) ) ) ) ) ).
fof(t46_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)),D) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) ).
fof(t47_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(B)),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k5_oppcat_1(A,D)) = k5_oppcat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ).
fof(t48_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> k7_oppcat_1(A,B,k8_oppcat_1(A,B,C)) = C ) ) ) ).
fof(t49_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
=> k8_oppcat_1(A,B,k7_oppcat_1(A,B,C)) = C ) ) ) ).
fof(t50_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)) = k8_oppcat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)) ) ) ) ).
fof(t51_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v1_cat_1(B)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> k9_oppcat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)) = C ) ) ) ).
fof(t52_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v1_cat_1(B)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(B),u2_cat_1(A))
& m2_relset_1(C,u2_cat_1(B),u2_cat_1(A)) )
=> k8_oppcat_1(k2_oppcat_1(B),A,k8_oppcat_1(B,A,C)) = C ) ) ) ).
fof(t53_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u2_cat_1(B),u2_cat_1(C))
& m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) )
=> k8_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E)) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),u2_cat_1(C),k8_oppcat_1(A,B,D),E) ) ) ) ) ) ).
fof(t54_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u2_cat_1(B),u2_cat_1(C))
& m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) )
=> k9_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E)) = k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(k2_oppcat_1(C)),D,k9_oppcat_1(B,C,E)) ) ) ) ) ) ).
fof(t55_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u2_cat_1(B),u2_cat_1(C))
& m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) )
=> k9_oppcat_1(k2_oppcat_1(A),C,k8_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E))) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(B)),u2_cat_1(k2_oppcat_1(C)),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,D)),k9_oppcat_1(k2_oppcat_1(B),C,k8_oppcat_1(B,C,E))) ) ) ) ) ) ).
fof(t56_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> m2_cat_1(k8_oppcat_1(A,B,C),k2_oppcat_1(A),B) ) ) ) ).
fof(t57_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> m2_cat_1(k9_oppcat_1(A,B,C),A,k2_oppcat_1(B)) ) ) ) ).
fof(t58_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> m1_oppcat_1(k8_oppcat_1(A,B,C),k2_oppcat_1(A),B) ) ) ) ).
fof(t59_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> m1_oppcat_1(k9_oppcat_1(A,B,C),A,k2_oppcat_1(B)) ) ) ) ).
fof(t60_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_oppcat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> m1_oppcat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C) ) ) ) ) ) ).
fof(t61_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m1_oppcat_1(E,B,C)
=> m1_oppcat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C) ) ) ) ) ) ).
fof(t62_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(k2_oppcat_1(A),k2_oppcat_1(B),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C))),k3_oppcat_1(A,D)) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) ).
fof(t63_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(k2_oppcat_1(A),k2_oppcat_1(B),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C))),k3_oppcat_1(A,D)) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) ).
fof(t64_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> m2_cat_1(k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k2_oppcat_1(A),k2_oppcat_1(B)) ) ) ) ).
fof(t65_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> m1_oppcat_1(k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k2_oppcat_1(A),k2_oppcat_1(B)) ) ) ) ).
fof(d10_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> k10_oppcat_1(A) = k9_oppcat_1(A,A,k15_cat_1(A)) ) ).
fof(d11_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> k11_oppcat_1(A) = k8_oppcat_1(A,A,k15_cat_1(A)) ) ).
fof(t66_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(k2_oppcat_1(A)),k10_oppcat_1(A),B) = k5_oppcat_1(A,B) ) ) ).
fof(t67_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(A)),k12_cat_1(A,k2_oppcat_1(A),k10_oppcat_1(A)),B) = k3_oppcat_1(A,B) ) ) ).
fof(t68_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
=> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(A),k11_oppcat_1(A),B) = k6_oppcat_1(A,B) ) ) ).
fof(t69_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
=> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(A),k12_cat_1(k2_oppcat_1(A),A,k11_oppcat_1(A)),B) = k4_oppcat_1(A,B) ) ) ).
fof(t70_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( k8_oppcat_1(A,B,C) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(A),u2_cat_1(B),k11_oppcat_1(A),C)
& k9_oppcat_1(A,B,C) = k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(k2_oppcat_1(B)),C,k10_oppcat_1(B)) ) ) ) ) ).
fof(dt_m1_oppcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_oppcat_1(C,A,B)
=> ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) ) ) ) ).
fof(existence_m1_oppcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ? [C] : m1_oppcat_1(C,A,B) ) ).
fof(dt_k1_oppcat_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& m1_relset_1(D,k2_zfmisc_1(A,B),C) )
=> ( v1_funct_1(k1_oppcat_1(A,B,C,D))
& m2_relset_1(k1_oppcat_1(A,B,C,D),k2_zfmisc_1(B,A),C) ) ) ).
fof(redefinition_k1_oppcat_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& m1_relset_1(D,k2_zfmisc_1(A,B),C) )
=> k1_oppcat_1(A,B,C,D) = k2_funct_4(D) ) ).
fof(dt_k2_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ( v1_cat_1(k2_oppcat_1(A))
& v2_cat_1(k2_oppcat_1(A))
& l1_cat_1(k2_oppcat_1(A)) ) ) ).
fof(dt_k3_oppcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_subset_1(k3_oppcat_1(A,B),u1_cat_1(k2_oppcat_1(A))) ) ).
fof(dt_k4_oppcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) )
=> m1_subset_1(k4_oppcat_1(A,B),u1_cat_1(A)) ) ).
fof(dt_k5_oppcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u2_cat_1(A)) )
=> m1_subset_1(k5_oppcat_1(A,B),u2_cat_1(k2_oppcat_1(A))) ) ).
fof(dt_k6_oppcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) )
=> m1_subset_1(k6_oppcat_1(A,B),u2_cat_1(A)) ) ).
fof(dt_k7_oppcat_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
& m1_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) )
=> ( v1_funct_1(k7_oppcat_1(A,B,C))
& v1_funct_2(k7_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(k7_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(B)) ) ) ).
fof(dt_k8_oppcat_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( v1_funct_1(k8_oppcat_1(A,B,C))
& v1_funct_2(k8_oppcat_1(A,B,C),u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B))
& m2_relset_1(k8_oppcat_1(A,B,C),u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) ) ) ).
fof(dt_k9_oppcat_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( v1_funct_1(k9_oppcat_1(A,B,C))
& v1_funct_2(k9_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(k2_oppcat_1(B)))
& m2_relset_1(k9_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) ) ) ).
fof(dt_k10_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> m1_oppcat_1(k10_oppcat_1(A),A,k2_oppcat_1(A)) ) ).
fof(dt_k11_oppcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> m1_oppcat_1(k11_oppcat_1(A),k2_oppcat_1(A),A) ) ).
%------------------------------------------------------------------------------