SET007 Axioms: SET007+525.ax
%------------------------------------------------------------------------------
% File : SET007+525 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Categories Without Uniqueness of cod and dom
% Version : [Urb08] axioms.
% English : Some Properties of the Morphisms and the Functors
% 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 : altcat_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 78 ( 0 unt; 0 def)
% Number of atoms : 1030 ( 116 equ)
% Maximal formula atoms : 31 ( 13 avg)
% Number of connectives : 1103 ( 151 ~; 47 |; 541 &)
% ( 12 <=>; 352 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 12 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 37 ( 36 usr; 0 prp; 1-5 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-6 aty)
% Number of variables : 303 ( 302 !; 1 ?)
% 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_altcat_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ~ v1_xboole_0(k1_altcat_1(A,B,B)) ) ).
fof(fc2_altcat_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_altcat_3(k8_altcat_1(A,B),A,B,B)
& v2_altcat_3(k8_altcat_1(A,B),A,B,B)
& v4_altcat_3(k8_altcat_1(A,B),A,B,B)
& v5_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) ).
fof(fc3_altcat_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_altcat_3(k8_altcat_1(A,B),A,B,B)
& v2_altcat_3(k8_altcat_1(A,B),A,B,B)
& v3_altcat_3(k8_altcat_1(A,B),A,B,B)
& v4_altcat_3(k8_altcat_1(A,B),A,B,B)
& v5_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) ).
fof(rc1_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ? [B] :
( m1_altcat_2(B,A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v2_altcat_2(B,A)
& v3_altcat_2(B,A) ) ) ).
fof(fc4_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k1_altcat_4(A))
& v2_altcat_1(k1_altcat_4(A))
& v6_altcat_1(k1_altcat_4(A))
& v11_altcat_1(k1_altcat_4(A))
& v12_altcat_1(k1_altcat_4(A))
& v1_altcat_2(k1_altcat_4(A))
& v3_altcat_2(k1_altcat_4(A),A) ) ) ).
fof(fc5_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k2_altcat_4(A))
& v2_altcat_1(k2_altcat_4(A))
& v6_altcat_1(k2_altcat_4(A))
& v11_altcat_1(k2_altcat_4(A))
& v12_altcat_1(k2_altcat_4(A))
& v1_altcat_2(k2_altcat_4(A))
& v3_altcat_2(k2_altcat_4(A),A) ) ) ).
fof(fc6_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k3_altcat_4(A))
& v2_altcat_1(k3_altcat_4(A))
& v6_altcat_1(k3_altcat_4(A))
& v11_altcat_1(k3_altcat_4(A))
& v12_altcat_1(k3_altcat_4(A))
& v1_altcat_2(k3_altcat_4(A))
& v3_altcat_2(k3_altcat_4(A),A) ) ) ).
fof(fc7_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k4_altcat_4(A))
& v2_altcat_1(k4_altcat_4(A))
& v6_altcat_1(k4_altcat_4(A))
& v11_altcat_1(k4_altcat_4(A))
& v12_altcat_1(k4_altcat_4(A))
& v1_altcat_2(k4_altcat_4(A))
& v3_altcat_2(k4_altcat_4(A),A) ) ) ).
fof(fc8_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k5_altcat_4(A))
& v2_altcat_1(k5_altcat_4(A))
& v6_altcat_1(k5_altcat_4(A))
& v11_altcat_1(k5_altcat_4(A))
& v12_altcat_1(k5_altcat_4(A))
& v1_altcat_2(k5_altcat_4(A))
& v3_altcat_2(k5_altcat_4(A),A) ) ) ).
fof(t1_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(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))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,B,C))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,B,D))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
=> ( ( F = k5_altcat_1(A,B,C,D,E,G)
& k5_altcat_1(A,C,D,C,G,k1_altcat_3(A,C,D,G)) = k8_altcat_1(A,C) )
=> ( k1_altcat_1(A,B,C) = k1_xboole_0
| k1_altcat_1(A,C,D) = k1_xboole_0
| k1_altcat_1(A,D,C) = k1_xboole_0
| E = k5_altcat_1(A,B,D,C,F,k1_altcat_3(A,C,D,G)) ) ) ) ) ) ) ) ) ) ).
fof(t2_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(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))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,B,C))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,C))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,D,B))
=> ( ( F = k5_altcat_1(A,D,B,C,G,E)
& k5_altcat_1(A,B,D,B,k1_altcat_3(A,D,B,G),G) = k8_altcat_1(A,B) )
=> ( k1_altcat_1(A,D,B) = k1_xboole_0
| k1_altcat_1(A,B,D) = k1_xboole_0
| k1_altcat_1(A,B,C) = k1_xboole_0
| E = k5_altcat_1(A,B,D,C,k1_altcat_3(A,D,B,G),F) ) ) ) ) ) ) ) ) ) ).
fof(t3_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ( v3_altcat_3(D,A,B,C)
=> ( k1_altcat_1(A,B,C) = k1_xboole_0
| k1_altcat_1(A,C,B) = k1_xboole_0
| v3_altcat_3(k1_altcat_3(A,B,C,D),A,C,B) ) ) ) ) ) ) ).
fof(t4_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v5_altcat_3(k8_altcat_1(A,B),A,B,B)
& v4_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) ) ).
fof(t5_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,C,B))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,C,B))
=> ( ( k5_altcat_1(A,B,C,B,D,F) = k8_altcat_1(A,B)
& k5_altcat_1(A,C,B,C,E,D) = k8_altcat_1(A,C) )
=> ( k1_altcat_1(A,B,C) = k1_xboole_0
| k1_altcat_1(A,C,B) = k1_xboole_0
| E = F ) ) ) ) ) ) ) ) ).
fof(t6_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> v2_altcat_3(D,A,B,C) ) ) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,B) != k1_xboole_0
& ~ v3_altcat_3(D,A,B,C) ) ) ) ) ) ) ).
fof(t7_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,B,C))
=> ( ( v9_altcat_3(D,A,B,C)
& v9_altcat_3(E,A,B,C) )
=> ( ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ v8_altcat_3(F,A) )
| D = E ) ) ) ) ) ) ) ).
fof(t8_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ( v7_altcat_3(B,A)
=> v4_altcat_3(D,A,B,C) ) ) ) ) ) ).
fof(t9_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,C,B))
=> ( v6_altcat_3(B,A)
=> v5_altcat_3(D,A,C,B) ) ) ) ) ) ).
fof(t10_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v7_altcat_3(B,A)
& r2_altcat_3(A,C,B) )
=> v7_altcat_3(C,A) ) ) ) ) ).
fof(t11_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v6_altcat_3(B,A)
& r2_altcat_3(A,B,C) )
=> v6_altcat_3(C,A) ) ) ) ) ).
fof(t12_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v6_altcat_3(B,A)
& v7_altcat_3(C,A) )
=> ( k1_altcat_1(A,C,B) = k1_xboole_0
| ( v6_altcat_3(C,A)
& v7_altcat_3(B,A) ) ) ) ) ) ) ).
fof(t13_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_functor0(A,B,C,D,D,k8_altcat_1(A,D)) = k8_altcat_1(B,k3_functor0(A,B,C,D)) ) ) ) ) ).
fof(t14_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v18_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> v2_funct_2(k7_functor0(A,B,C,E,D),k1_altcat_1(A,E,D),k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E))) ) ) ) ) ) ) ).
fof(t15_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v17_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> v2_funct_1(k7_functor0(A,B,C,E,D)) ) ) ) ) ) ) ).
fof(t16_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v10_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& v18_functor0(C,A,B)
& v8_functor0(C,A,B)
& ! [G] :
( m1_subset_1(G,k1_altcat_1(A,D,E))
=> F != k6_functor0(A,B,C,D,E,G) ) ) ) ) ) ) ) ) ).
fof(t17_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& v18_functor0(C,A,B)
& v8_functor0(C,A,B)
& ! [G] :
( m1_subset_1(G,k1_altcat_1(A,D,E))
=> F != k8_functor0(A,B,C,D,E,G) ) ) ) ) ) ) ) ) ).
fof(t18_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( v1_altcat_3(F,A,D,E)
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v1_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) ) ) ) ).
fof(t19_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( v2_altcat_3(F,A,D,E)
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v2_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) ) ) ) ).
fof(t20_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( v3_altcat_3(F,A,D,E)
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v3_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) ) ) ) ).
fof(t21_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_altcat_3(A,D,E)
=> r2_altcat_3(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) ) ).
fof(t22_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( v1_altcat_3(F,A,D,E)
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v2_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) ) ) ) ).
fof(t23_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( v2_altcat_3(F,A,D,E)
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v1_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) ) ) ) ).
fof(t24_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( v3_altcat_3(F,A,D,E)
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v3_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) ) ) ) ).
fof(t25_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_altcat_3(A,D,E)
=> r2_altcat_3(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) ) ).
fof(t26_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( ( v18_functor0(C,A,B)
& v17_functor0(C,A,B)
& v1_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) )
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v1_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) ).
fof(t27_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( ( v18_functor0(C,A,B)
& v17_functor0(C,A,B)
& v2_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) )
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v2_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) ).
fof(t28_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( ( v18_functor0(C,A,B)
& v17_functor0(C,A,B)
& v3_altcat_3(k6_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) )
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v3_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) ).
fof(t29_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( v18_functor0(C,A,B)
& v17_functor0(C,A,B)
& r2_altcat_3(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) )
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| r2_altcat_3(A,D,E) ) ) ) ) ) ) ) ).
fof(t30_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( ( v18_functor0(C,A,B)
& v17_functor0(C,A,B)
& v1_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) )
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v2_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) ).
fof(t31_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( ( v18_functor0(C,A,B)
& v17_functor0(C,A,B)
& v2_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) )
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v1_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) ).
fof(t32_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ( ( v18_functor0(C,A,B)
& v17_functor0(C,A,B)
& v3_altcat_3(k8_functor0(A,B,C,D,E,F),B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) )
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| v3_altcat_3(F,A,D,E) ) ) ) ) ) ) ) ) ).
fof(t33_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( v18_functor0(C,A,B)
& v17_functor0(C,A,B)
& r2_altcat_3(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) )
=> ( k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| r2_altcat_3(A,D,E) ) ) ) ) ) ) ) ).
fof(t34_altcat_4,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& u1_altcat_1(A) = u1_altcat_1(B) )
=> v2_altcat_2(B,A) ) ) ) ).
fof(t35_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& u1_altcat_1(A) = u1_altcat_1(B) )
=> ( v2_altcat_2(B,A)
& v3_altcat_2(B,A) ) ) ) ) ).
fof(t36_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v3_altcat_2(C,B)
& m1_altcat_2(C,B) )
=> ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v3_altcat_2(C,A)
& m1_altcat_2(C,A) ) ) ) ) ).
fof(t37_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& m1_altcat_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(B,E,F))
=> ( ( E = C
& F = D
& G = H )
=> ( k1_altcat_1(B,E,F) = k1_xboole_0
| ( ( v4_altcat_3(G,A,C,D)
=> v4_altcat_3(H,B,E,F) )
& ( v5_altcat_3(G,A,C,D)
=> v5_altcat_3(H,B,E,F) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,D,C))
=> ! [I] :
( m1_subset_1(I,k1_altcat_1(B,E,F))
=> ! [J] :
( m1_subset_1(J,k1_altcat_1(B,F,E))
=> ( ( E = C
& F = D
& G = I
& H = J )
=> ( k1_altcat_1(B,E,F) = k1_xboole_0
| k1_altcat_1(B,F,E) = k1_xboole_0
| ( ( r1_altcat_3(A,C,D,G,H)
=> r1_altcat_3(B,E,F,I,J) )
& ( r1_altcat_3(B,E,F,I,J)
=> r1_altcat_3(A,C,D,G,H) )
& ( r1_altcat_3(A,D,C,H,G)
=> r1_altcat_3(B,F,E,J,I) )
& ( r1_altcat_3(B,F,E,J,I)
=> r1_altcat_3(A,D,C,H,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v2_altcat_2(B,A)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(B,E,F))
=> ( ( E = C
& F = D
& G = H )
=> ( k1_altcat_1(B,E,F) = k1_xboole_0
| k1_altcat_1(B,F,E) = k1_xboole_0
| ( ( v1_altcat_3(G,A,C,D)
=> v1_altcat_3(H,B,E,F) )
& ( v2_altcat_3(G,A,C,D)
=> v2_altcat_3(H,B,E,F) )
& ( v3_altcat_3(G,A,C,D)
=> v3_altcat_3(H,B,E,F) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(B,E,F))
=> ( ( E = C
& F = D
& G = H )
=> ( k1_altcat_1(B,E,F) = k1_xboole_0
| k1_altcat_1(B,F,E) = k1_xboole_0
| ( ( v1_altcat_3(H,B,E,F)
=> v1_altcat_3(G,A,C,D) )
& ( v2_altcat_3(H,B,E,F)
=> v2_altcat_3(G,A,C,D) )
& ( v3_altcat_3(H,B,E,F)
=> v3_altcat_3(G,A,C,D) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& m1_altcat_2(B,A) )
=> ( B = k1_altcat_4(A)
<=> ( u1_struct_0(B) = u1_struct_0(A)
& r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,C,D))
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
<=> ( k1_altcat_1(A,C,D) != k1_xboole_0
& v4_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) ).
fof(d2_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& m1_altcat_2(B,A) )
=> ( B = k2_altcat_4(A)
<=> ( u1_struct_0(B) = u1_struct_0(A)
& r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,C,D))
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
<=> ( k1_altcat_1(A,C,D) != k1_xboole_0
& v5_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) ).
fof(d3_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& m1_altcat_2(B,A) )
=> ( B = k3_altcat_4(A)
<=> ( u1_struct_0(B) = u1_struct_0(A)
& r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,C,D))
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
<=> ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,C) != k1_xboole_0
& v1_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) ).
fof(d4_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& m1_altcat_2(B,A) )
=> ( B = k4_altcat_4(A)
<=> ( u1_struct_0(B) = u1_struct_0(A)
& r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,C,D))
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
<=> ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,C) != k1_xboole_0
& v2_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) ).
fof(d5_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& m1_altcat_2(B,A) )
=> ( B = k5_altcat_4(A)
<=> ( u1_struct_0(B) = u1_struct_0(A)
& r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,C,D))
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
<=> ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,C) != k1_xboole_0
& v3_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) ).
fof(t41_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k5_altcat_4(A))
& v2_altcat_1(k5_altcat_4(A))
& v3_altcat_2(k5_altcat_4(A),k3_altcat_4(A))
& m1_altcat_2(k5_altcat_4(A),k3_altcat_4(A)) ) ) ).
fof(t42_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k5_altcat_4(A))
& v2_altcat_1(k5_altcat_4(A))
& v3_altcat_2(k5_altcat_4(A),k4_altcat_4(A))
& m1_altcat_2(k5_altcat_4(A),k4_altcat_4(A)) ) ) ).
fof(t43_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k4_altcat_4(A))
& v2_altcat_1(k4_altcat_4(A))
& v3_altcat_2(k4_altcat_4(A),k1_altcat_4(A))
& m1_altcat_2(k4_altcat_4(A),k1_altcat_4(A)) ) ) ).
fof(t44_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k3_altcat_4(A))
& v2_altcat_1(k3_altcat_4(A))
& v3_altcat_2(k3_altcat_4(A),k2_altcat_4(A))
& m1_altcat_2(k3_altcat_4(A),k2_altcat_4(A)) ) ) ).
fof(t45_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> v4_altcat_3(D,A,B,C) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k1_altcat_4(A) ) ) ).
fof(t46_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> v5_altcat_3(D,A,B,C) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k2_altcat_4(A) ) ) ).
fof(t47_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ( v1_altcat_3(D,A,B,C)
& k1_altcat_1(A,C,B) != k1_xboole_0 ) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k3_altcat_4(A) ) ) ).
fof(t48_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ( v2_altcat_3(D,A,B,C)
& k1_altcat_1(A,C,B) != k1_xboole_0 ) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k4_altcat_4(A) ) ) ).
fof(t49_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ( v3_altcat_3(D,A,B,C)
& k1_altcat_1(A,C,B) != k1_xboole_0 ) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = k5_altcat_4(A) ) ) ).
fof(t50_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_altcat_4(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_altcat_4(A)))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(k1_altcat_4(A),B,C))
=> ( k1_altcat_1(k1_altcat_4(A),B,C) != k1_xboole_0
=> v4_altcat_3(D,k1_altcat_4(A),B,C) ) ) ) ) ) ).
fof(t51_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_altcat_4(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_altcat_4(A)))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(k2_altcat_4(A),B,C))
=> ( k1_altcat_1(k2_altcat_4(A),B,C) != k1_xboole_0
=> v5_altcat_3(D,k2_altcat_4(A),B,C) ) ) ) ) ) ).
fof(t52_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_altcat_4(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_altcat_4(A)))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(k5_altcat_4(A),B,C))
=> ( k1_altcat_1(k5_altcat_4(A),B,C) != k1_xboole_0
=> ( v3_altcat_3(D,k5_altcat_4(A),B,C)
& r2_hidden(k1_altcat_3(k5_altcat_4(A),B,C,D),k1_altcat_1(k5_altcat_4(A),C,B)) ) ) ) ) ) ) ).
fof(t53_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> k1_altcat_4(k1_altcat_4(A)) = k1_altcat_4(A) ) ).
fof(t54_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> k2_altcat_4(k2_altcat_4(A)) = k2_altcat_4(A) ) ).
fof(t55_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> k5_altcat_4(k5_altcat_4(A)) = k5_altcat_4(A) ) ).
fof(t56_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> k5_altcat_4(k1_altcat_4(A)) = k5_altcat_4(A) ) ).
fof(t57_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> k5_altcat_4(k2_altcat_4(A)) = k5_altcat_4(A) ) ).
fof(t58_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> k5_altcat_4(k3_altcat_4(A)) = k5_altcat_4(A) ) ).
fof(t59_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> k5_altcat_4(k4_altcat_4(A)) = k5_altcat_4(A) ) ).
fof(dt_k1_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k1_altcat_4(A))
& v2_altcat_1(k1_altcat_4(A))
& v6_altcat_1(k1_altcat_4(A))
& m1_altcat_2(k1_altcat_4(A),A) ) ) ).
fof(dt_k2_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k2_altcat_4(A))
& v2_altcat_1(k2_altcat_4(A))
& v6_altcat_1(k2_altcat_4(A))
& m1_altcat_2(k2_altcat_4(A),A) ) ) ).
fof(dt_k3_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k3_altcat_4(A))
& v2_altcat_1(k3_altcat_4(A))
& v6_altcat_1(k3_altcat_4(A))
& m1_altcat_2(k3_altcat_4(A),A) ) ) ).
fof(dt_k4_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k4_altcat_4(A))
& v2_altcat_1(k4_altcat_4(A))
& v6_altcat_1(k4_altcat_4(A))
& m1_altcat_2(k4_altcat_4(A),A) ) ) ).
fof(dt_k5_altcat_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k5_altcat_4(A))
& v2_altcat_1(k5_altcat_4(A))
& v6_altcat_1(k5_altcat_4(A))
& m1_altcat_2(k5_altcat_4(A),A) ) ) ).
%------------------------------------------------------------------------------