SET007 Axioms: SET007+536.ax
%------------------------------------------------------------------------------
% File : SET007+536 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Composition of Functors and Transformations in Alternativ
% 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 : functor3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 75 ( 0 unt; 0 def)
% Number of atoms : 1488 ( 37 equ)
% Maximal formula atoms : 39 ( 19 avg)
% Number of connectives : 1614 ( 201 ~; 5 |; 986 &)
% ( 5 <=>; 417 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 18 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 0 prp; 1-5 aty)
% Number of functors : 34 ( 34 usr; 1 con; 0-9 aty)
% Number of variables : 474 ( 467 !; 7 ?)
% 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_functor3,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A) ) ).
fof(rc2_functor3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v9_functor0(C,A,B)
& v10_functor0(C,A,B)
& v11_functor0(C,A,B)
& v13_functor0(C,A,B)
& v14_functor0(C,A,B) ) ) ).
fof(rc3_functor3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v9_functor0(C,A,B)
& v10_functor0(C,A,B)
& v11_functor0(C,A,B)
& v12_functor0(C,A,B)
& v13_functor0(C,A,B)
& v14_functor0(C,A,B) ) ) ).
fof(rc4_functor3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ? [C] :
( m2_functor0(C,A,B)
& v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v9_functor0(C,A,B)
& v10_functor0(C,A,B)
& v11_functor0(C,A,B)
& v12_functor0(C,A,B)
& v13_functor0(C,A,B)
& v14_functor0(C,A,B)
& v15_functor0(C,A,B)
& v16_functor0(C,A,B) ) ) ).
fof(fc1_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v8_functor0(D,A,B)
& v10_functor0(D,A,B)
& v13_functor0(D,A,B)
& l2_functor0(D,A,B)
& v8_functor0(E,B,C)
& v10_functor0(E,B,C)
& v13_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v6_functor0(k13_functor0(A,B,C,D,E),A,C)
& v8_functor0(k13_functor0(A,B,C,D,E),A,C)
& v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v10_functor0(k13_functor0(A,B,C,D,E),A,C)
& v13_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc2_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v8_functor0(D,A,B)
& v11_functor0(D,A,B)
& v14_functor0(D,A,B)
& l2_functor0(D,A,B)
& v8_functor0(E,B,C)
& v11_functor0(E,B,C)
& v14_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v6_functor0(k13_functor0(A,B,C,D,E),A,C)
& v8_functor0(k13_functor0(A,B,C,D,E),A,C)
& v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v10_functor0(k13_functor0(A,B,C,D,E),A,C)
& v13_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc3_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v8_functor0(D,A,B)
& v10_functor0(D,A,B)
& v13_functor0(D,A,B)
& l2_functor0(D,A,B)
& v8_functor0(E,B,C)
& v11_functor0(E,B,C)
& v14_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v6_functor0(k13_functor0(A,B,C,D,E),A,C)
& v8_functor0(k13_functor0(A,B,C,D,E),A,C)
& v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v11_functor0(k13_functor0(A,B,C,D,E),A,C)
& v14_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc4_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v8_functor0(D,A,B)
& v11_functor0(D,A,B)
& v14_functor0(D,A,B)
& l2_functor0(D,A,B)
& v8_functor0(E,B,C)
& v10_functor0(E,B,C)
& v13_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v6_functor0(k13_functor0(A,B,C,D,E),A,C)
& v8_functor0(k13_functor0(A,B,C,D,E),A,C)
& v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v11_functor0(k13_functor0(A,B,C,D,E),A,C)
& v14_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(t1_functor3,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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,B,C))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,B,E))
=> ! [I] :
( m1_subset_1(I,k1_altcat_1(A,E,D))
=> ( ( k5_altcat_1(A,B,C,D,F,G) = k5_altcat_1(A,B,E,D,H,I)
& k5_altcat_1(A,C,B,C,k1_altcat_3(A,B,C,F),F) = k8_altcat_1(A,C)
& k5_altcat_1(A,E,D,E,I,k1_altcat_3(A,E,D,I)) = k8_altcat_1(A,E) )
=> ( k1_altcat_1(A,B,C) = k1_xboole_0
| k1_altcat_1(A,C,B) = k1_xboole_0
| k1_altcat_1(A,C,D) = k1_xboole_0
| k1_altcat_1(A,D,E) = k1_xboole_0
| k1_altcat_1(A,E,D) = k1_xboole_0
| k5_altcat_1(A,C,B,E,k1_altcat_3(A,B,C,F),H) = k5_altcat_1(A,C,D,E,G,k1_altcat_3(A,E,D,I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_functor3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v8_functor0(D,A,B)
& v10_functor0(D,A,B)
& l2_functor0(D,A,B) )
=> ! [E] :
( l2_functor0(E,B,C)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> k4_functor0(A,C,k13_functor0(A,B,C,D,E),F,G) = k5_relat_1(k5_functor0(A,B,D,F,G),k4_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,G))) ) ) ) ) ) ) ) ).
fof(t3_functor3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v8_functor0(D,A,B)
& v11_functor0(D,A,B)
& l2_functor0(D,A,B) )
=> ! [E] :
( l2_functor0(E,B,C)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> k4_functor0(A,C,k13_functor0(A,B,C,D,E),F,G) = k5_relat_1(k7_functor0(A,B,D,F,G),k4_functor0(B,C,E,k3_functor0(A,B,D,G),k3_functor0(A,B,D,F))) ) ) ) ) ) ) ) ).
fof(t4_functor3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> k13_functor0(A,B,B,C,k11_functor0(B)) = g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) ) ) ) ).
fof(t5_functor3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> k13_functor0(A,A,B,k12_functor0(A),C) = g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) ) ) ) ).
fof(t6_functor3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_altcat_2(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v8_functor0(D,A,B)
& v10_functor0(D,A,B)
& l2_functor0(D,A,B) )
=> ! [E] :
( ( v8_functor0(E,B,C)
& v10_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,F,G))
=> ( k1_altcat_1(A,F,G) != k1_xboole_0
=> k6_functor0(A,C,k13_functor0(A,B,C,D,E),F,G,H) = k6_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,G),k6_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(t7_functor3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_altcat_2(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v8_functor0(D,A,B)
& v11_functor0(D,A,B)
& l2_functor0(D,A,B) )
=> ! [E] :
( ( v8_functor0(E,B,C)
& v11_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,F,G))
=> ( k1_altcat_1(A,F,G) != k1_xboole_0
=> k6_functor0(A,C,k13_functor0(A,B,C,D,E),F,G,H) = k8_functor0(B,C,E,k3_functor0(A,B,D,G),k3_functor0(A,B,D,F),k8_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(t8_functor3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_altcat_2(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v8_functor0(D,A,B)
& v10_functor0(D,A,B)
& l2_functor0(D,A,B) )
=> ! [E] :
( ( v8_functor0(E,B,C)
& v11_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,F,G))
=> ( k1_altcat_1(A,F,G) != k1_xboole_0
=> k8_functor0(A,C,k13_functor0(A,B,C,D,E),F,G,H) = k8_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,G),k6_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(t9_functor3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_altcat_2(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v8_functor0(D,C,B)
& v10_functor0(D,C,B)
& l2_functor0(D,C,B) )
=> ! [E] :
( ( v8_functor0(E,A,C)
& v11_functor0(E,A,C)
& l2_functor0(E,A,C) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,F,G))
=> ( k1_altcat_1(A,F,G) != k1_xboole_0
=> k8_functor0(A,B,k13_functor0(A,C,B,E,D),F,G,H) = k6_functor0(C,B,D,k3_functor0(A,C,E,G),k3_functor0(A,C,E,F),k8_functor0(A,C,E,F,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(t10_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( ( v15_functor0(G,B,C)
& m2_functor0(G,B,C) )
=> ( ( r1_functor2(A,B,D,E)
& r1_functor2(B,C,F,G) )
=> r1_functor2(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G)) ) ) ) ) ) ) ) ) ).
fof(d1_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( m1_functor2(F,A,B,D,E)
=> ! [G] :
( ( v15_functor0(G,B,C)
& m2_functor0(G,B,C) )
=> ( r1_functor2(A,B,D,E)
=> ! [H] :
( m1_functor2(H,A,C,k1_functor3(A,B,C,D,G),k1_functor3(A,B,C,E,G))
=> ( H = k5_functor3(A,B,C,D,E,F,G)
<=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> k1_funct_1(H,I) = k6_functor0(B,C,G,k3_functor0(A,B,D,I),k3_functor0(A,B,E,I),k2_functor2(A,B,D,E,F,I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,C,B)
& m2_functor0(D,C,B) )
=> ! [E] :
( ( v15_functor0(E,C,B)
& m2_functor0(E,C,B) )
=> ! [F] :
( ( v15_functor0(F,B,A)
& m2_functor0(F,B,A) )
=> ! [G] :
( m1_functor2(G,C,B,D,E)
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ( r1_functor2(C,B,D,E)
=> k2_functor2(C,A,k1_functor3(C,B,A,D,F),k1_functor3(C,B,A,E,F),k5_functor3(C,B,A,D,E,G,F),H) = k6_functor0(B,A,F,k3_functor0(C,B,D,H),k3_functor0(C,B,E,H),k2_functor2(C,B,D,E,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(d2_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,B,C)
& m2_functor0(D,B,C) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,A,B)
& m2_functor0(F,A,B) )
=> ! [G] :
( m1_functor2(G,B,C,D,E)
=> ( r1_functor2(B,C,D,E)
=> ! [H] :
( m1_functor2(H,A,C,k1_functor3(A,B,C,F,D),k1_functor3(A,B,C,F,E))
=> ( H = k6_functor3(A,B,C,D,E,F,G)
<=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> k1_funct_1(H,I) = k2_functor2(B,C,D,E,G,k3_functor0(A,B,F,I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,C,A)
& m2_functor0(D,C,A) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( ( v15_functor0(F,A,B)
& m2_functor0(F,A,B) )
=> ! [G] :
( m1_functor2(G,A,B,E,F)
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ( r1_functor2(A,B,E,F)
=> k2_functor2(C,B,k1_functor3(C,A,B,D,E),k1_functor3(C,A,B,D,F),k6_functor3(C,A,B,E,F,D,G),H) = k2_functor2(A,B,E,F,G,k3_functor0(C,A,D,H)) ) ) ) ) ) ) ) ) ) ).
fof(t13_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,B,C)
& m2_functor0(D,B,C) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( ( v15_functor0(G,C,A)
& m2_functor0(G,C,A) )
=> ! [H] :
( m1_functor2(H,B,C,D,E)
=> ! [I] :
( m1_functor2(I,B,C,E,F)
=> ( ( r1_functor2(B,C,D,E)
& r1_functor2(B,C,E,F) )
=> r6_pboole(u1_struct_0(B),k5_functor3(B,C,A,D,F,k3_functor2(B,C,D,E,F,H,I),G),k3_functor2(B,A,k1_functor3(B,C,A,D,G),k1_functor3(B,C,A,E,G),k1_functor3(B,C,A,F,G),k5_functor3(B,C,A,D,E,H,G),k5_functor3(B,C,A,E,F,I,G))) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( ( v15_functor0(G,B,C)
& m2_functor0(G,B,C) )
=> ! [H] :
( m1_functor2(H,B,C,E,F)
=> ! [I] :
( m1_functor2(I,B,C,F,G)
=> ( ( r1_functor2(B,C,E,F)
& r1_functor2(B,C,F,G) )
=> r6_pboole(u1_struct_0(A),k6_functor3(A,B,C,E,G,D,k3_functor2(B,C,E,F,G,H,I)),k3_functor2(A,C,k1_functor3(A,B,C,D,E),k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,D,G),k6_functor3(A,B,C,E,F,D,H),k6_functor3(A,B,C,F,G,D,I))) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_altcat_1(D)
& v12_altcat_1(D)
& l2_altcat_1(D) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( ( v15_functor0(G,C,D)
& m2_functor0(G,C,D) )
=> ! [H] :
( ( v15_functor0(H,C,D)
& m2_functor0(H,C,D) )
=> ! [I] :
( m1_functor2(I,C,D,G,H)
=> ( r1_functor2(C,D,G,H)
=> r6_pboole(u1_struct_0(A),k6_functor3(A,B,D,k1_functor3(B,C,D,F,G),k1_functor3(B,C,D,F,H),E,k6_functor3(B,C,D,G,H,F,I)),k6_functor3(A,C,D,G,H,k1_functor3(A,B,C,E,F),I)) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_altcat_1(D)
& v12_altcat_1(D)
& l2_altcat_1(D) )
=> ! [E] :
( ( v15_functor0(E,A,C)
& m2_functor0(E,A,C) )
=> ! [F] :
( ( v15_functor0(F,C,D)
& m2_functor0(F,C,D) )
=> ! [G] :
( ( v15_functor0(G,C,D)
& m2_functor0(G,C,D) )
=> ! [H] :
( ( v15_functor0(H,D,B)
& m2_functor0(H,D,B) )
=> ! [I] :
( m1_functor2(I,C,D,F,G)
=> ( r1_functor2(C,D,F,G)
=> r6_pboole(u1_struct_0(A),k6_functor3(A,C,B,k1_functor3(C,D,B,F,H),k1_functor3(C,D,B,G,H),E,k5_functor3(C,D,B,F,G,I,H)),k5_functor3(A,D,B,k1_functor3(A,C,D,E,F),k1_functor3(A,C,D,E,G),k6_functor3(A,C,D,F,G,E,I),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t17_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_altcat_1(D)
& v12_altcat_1(D)
& l2_altcat_1(D) )
=> ! [E] :
( ( v15_functor0(E,C,D)
& m2_functor0(E,C,D) )
=> ! [F] :
( ( v15_functor0(F,C,D)
& m2_functor0(F,C,D) )
=> ! [G] :
( ( v15_functor0(G,D,A)
& m2_functor0(G,D,A) )
=> ! [H] :
( ( v15_functor0(H,A,B)
& m2_functor0(H,A,B) )
=> ! [I] :
( m1_functor2(I,C,D,E,F)
=> ( r1_functor2(C,D,E,F)
=> r6_pboole(u1_struct_0(C),k5_functor3(C,D,B,E,F,I,k1_functor3(D,A,B,G,H)),k5_functor3(C,A,B,k1_functor3(C,D,A,E,G),k1_functor3(C,D,A,F,G),k5_functor3(C,D,A,E,F,I,G),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> r6_pboole(u1_struct_0(A),k6_functor3(A,B,C,E,E,D,k4_functor2(B,C,E)),k4_functor2(A,C,k1_functor3(A,B,C,D,E))) ) ) ) ) ) ).
fof(t19_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> r6_pboole(u1_struct_0(A),k5_functor3(A,B,C,D,D,k4_functor2(A,B,D),E),k4_functor2(A,C,k1_functor3(A,B,C,D,E))) ) ) ) ) ) ).
fof(t20_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_functor2(E,A,B,C,D)
=> ( r1_functor2(A,B,C,D)
=> r6_pboole(u1_struct_0(A),k5_functor3(A,B,B,C,D,E,k12_functor0(B)),E) ) ) ) ) ) ) ).
fof(t21_functor3,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,B,A)
& m2_functor0(C,B,A) )
=> ! [D] :
( ( v15_functor0(D,B,A)
& m2_functor0(D,B,A) )
=> ! [E] :
( m1_functor2(E,B,A,C,D)
=> ( r1_functor2(B,A,C,D)
=> r6_pboole(u1_struct_0(B),k6_functor3(B,B,A,C,D,k12_functor0(B),E),E) ) ) ) ) ) ) ).
fof(d3_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( ( v15_functor0(G,B,C)
& m2_functor0(G,B,C) )
=> ! [H] :
( m1_functor2(H,A,B,D,E)
=> ! [I] :
( m1_functor2(I,B,C,F,G)
=> k7_functor3(A,B,C,D,E,F,G,H,I) = k3_functor2(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,F),k1_functor3(A,B,C,E,G),k5_functor3(A,B,C,D,E,H,F),k6_functor3(A,B,C,F,G,E,I)) ) ) ) ) ) ) ) ) ) ).
fof(t22_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,B,C)
& m2_functor0(D,B,C) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,C,A)
& m2_functor0(F,C,A) )
=> ! [G] :
( ( v15_functor0(G,C,A)
& m2_functor0(G,C,A) )
=> ! [H] :
( m1_functor2(H,B,C,D,E)
=> ! [I] :
( m2_functor2(I,C,A,F,G)
=> ( ( r1_functor2(B,C,D,E)
& r2_functor2(C,A,F,G) )
=> r6_pboole(u1_struct_0(B),k7_functor3(B,C,A,D,E,F,G,H,I),k3_functor2(B,A,k1_functor3(B,C,A,D,F),k1_functor3(B,C,A,D,G),k1_functor3(B,C,A,E,G),k6_functor3(B,C,A,F,G,D,I),k5_functor3(B,C,A,D,E,H,G))) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_functor2(E,A,B,C,D)
=> ( r1_functor2(A,B,C,D)
=> r6_pboole(u1_struct_0(A),k7_functor3(A,B,B,C,D,k12_functor0(B),k12_functor0(B),E,k4_functor2(B,B,k12_functor0(B))),E) ) ) ) ) ) ) ).
fof(t24_functor3,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,B,A)
& m2_functor0(C,B,A) )
=> ! [D] :
( ( v15_functor0(D,B,A)
& m2_functor0(D,B,A) )
=> ! [E] :
( m1_functor2(E,B,A,C,D)
=> ( r1_functor2(B,A,C,D)
=> r6_pboole(u1_struct_0(B),k7_functor3(B,B,A,k12_functor0(B),k12_functor0(B),C,D,k4_functor2(B,B,k12_functor0(B)),E),E) ) ) ) ) ) ) ).
fof(t25_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,B,C)
& m2_functor0(D,B,C) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,C,A)
& m2_functor0(F,C,A) )
=> ! [G] :
( m1_functor2(G,B,C,D,E)
=> ( r1_functor2(B,C,D,E)
=> r6_pboole(u1_struct_0(B),k5_functor3(B,C,A,D,E,G,F),k7_functor3(B,C,A,D,E,F,F,G,k4_functor2(C,A,F))) ) ) ) ) ) ) ) ) ).
fof(t26_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( m1_functor2(G,B,C,E,F)
=> ( r1_functor2(B,C,E,F)
=> r6_pboole(u1_struct_0(A),k6_functor3(A,B,C,E,F,D,G),k7_functor3(A,B,C,D,D,E,F,k4_functor2(A,B,D),G)) ) ) ) ) ) ) ) ) ).
fof(t27_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v11_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_altcat_1(D)
& v11_altcat_1(D)
& v12_altcat_1(D)
& l2_altcat_1(D) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( ( v15_functor0(F,A,B)
& m2_functor0(F,A,B) )
=> ! [G] :
( ( v15_functor0(G,B,C)
& m2_functor0(G,B,C) )
=> ! [H] :
( ( v15_functor0(H,B,C)
& m2_functor0(H,B,C) )
=> ! [I] :
( ( v15_functor0(I,C,D)
& m2_functor0(I,C,D) )
=> ! [J] :
( ( v15_functor0(J,C,D)
& m2_functor0(J,C,D) )
=> ! [K] :
( m1_functor2(K,A,B,E,F)
=> ! [L] :
( m1_functor2(L,B,C,G,H)
=> ! [M] :
( m1_functor2(M,C,D,I,J)
=> ( ( r1_functor2(A,B,E,F)
& r1_functor2(B,C,G,H)
& r1_functor2(C,D,I,J) )
=> r6_pboole(u1_struct_0(A),k7_functor3(A,B,D,E,F,k1_functor3(B,C,D,G,I),k1_functor3(B,C,D,H,J),K,k7_functor3(B,C,D,G,H,I,J,L,M)),k7_functor3(A,C,D,k1_functor3(A,B,C,E,G),k1_functor3(A,B,C,F,H),I,J,k7_functor3(A,B,C,E,F,G,H,K,L),M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v11_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,B,C)
& m2_functor0(D,B,C) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,C,A)
& m2_functor0(F,C,A) )
=> ! [G] :
( m2_functor2(G,B,C,D,E)
=> ( r2_functor2(B,C,D,E)
=> m2_functor2(k5_functor3(B,C,A,D,E,G,F),B,A,k1_functor3(B,C,A,D,F),k1_functor3(B,C,A,E,F)) ) ) ) ) ) ) ) ) ).
fof(t29_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v11_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( m2_functor2(G,B,C,E,F)
=> ( r2_functor2(B,C,E,F)
=> m2_functor2(k6_functor3(A,B,C,E,F,D,G),A,C,k1_functor3(A,B,C,D,E),k1_functor3(A,B,C,D,F)) ) ) ) ) ) ) ) ) ).
fof(t30_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v11_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( ( v15_functor0(G,B,C)
& m2_functor0(G,B,C) )
=> ! [H] :
( m2_functor2(H,A,B,D,E)
=> ! [I] :
( m2_functor2(I,B,C,F,G)
=> ( ( r2_functor2(A,B,D,E)
& r2_functor2(B,C,F,G) )
=> ( r2_functor2(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G))
& m2_functor2(k7_functor3(A,B,C,D,E,F,G,H,I),A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v11_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( ( v15_functor0(F,A,B)
& m2_functor0(F,A,B) )
=> ! [G] :
( ( v15_functor0(G,B,C)
& m2_functor0(G,B,C) )
=> ! [H] :
( ( v15_functor0(H,B,C)
& m2_functor0(H,B,C) )
=> ! [I] :
( ( v15_functor0(I,B,C)
& m2_functor0(I,B,C) )
=> ! [J] :
( m2_functor2(J,B,C,G,H)
=> ! [K] :
( m2_functor2(K,B,C,H,I)
=> ! [L] :
( m1_functor2(L,A,B,D,E)
=> ! [M] :
( m1_functor2(M,A,B,E,F)
=> ( ( r2_functor2(A,B,D,E)
& r2_functor2(A,B,E,F)
& r2_functor2(B,C,G,H)
& r2_functor2(B,C,H,I) )
=> r6_pboole(u1_struct_0(A),k7_functor3(A,B,C,D,F,G,I,k3_functor2(A,B,D,E,F,L,M),k5_functor2(B,C,G,H,I,J,K)),k3_functor2(A,C,k1_functor3(A,B,C,D,G),k1_functor3(A,B,C,E,H),k1_functor3(A,B,C,F,I),k7_functor3(A,B,C,D,E,G,H,L,J),k7_functor3(A,B,C,E,F,H,I,M,K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_functor3,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,B,A)
& m2_functor0(C,B,A) )
=> ! [D] :
( ( v15_functor0(D,B,A)
& m2_functor0(D,B,A) )
=> ! [E] :
( m2_functor2(E,B,A,C,D)
=> ( ( r2_functor2(B,A,C,D)
& r1_functor2(B,A,D,C)
& ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> v3_altcat_3(k2_functor2(B,A,C,D,E,F),A,k3_functor0(B,A,C,F),k3_functor0(B,A,D,F)) ) )
=> ( r2_functor2(B,A,D,C)
& ? [F] :
( m2_functor2(F,B,A,D,C)
& ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( k1_funct_1(F,G) = k1_altcat_3(A,k3_functor0(B,A,C,G),k3_functor0(B,A,D,G),k2_functor2(B,A,C,D,E,G))
& v3_altcat_3(k2_functor2(B,A,D,C,F,G),A,k3_functor0(B,A,D,G),k3_functor0(B,A,C,G)) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ( r1_functor3(A,B,C,D)
<=> ( r2_functor2(A,B,C,D)
& r1_functor2(A,B,D,C)
& ? [E] :
( m2_functor2(E,A,B,C,D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> v3_altcat_3(k2_functor2(A,B,C,D,E,F),B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F)) ) ) ) ) ) ) ) ) ).
fof(d5_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ( r1_functor3(A,B,C,D)
=> ! [E] :
( m2_functor2(E,A,B,C,D)
=> ( m1_functor3(E,A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> v3_altcat_3(k2_functor2(A,B,C,D,E,F),B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F)) ) ) ) ) ) ) ) ) ).
fof(t33_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ( ( r1_functor3(A,B,C,D)
& r1_functor3(A,B,D,E) )
=> r1_functor3(A,B,C,E) ) ) ) ) ) ) ).
fof(t34_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( m1_functor3(F,A,B,C,D)
=> ! [G] :
( m1_functor3(G,A,B,D,E)
=> ( ( r1_functor3(A,B,C,D)
& r1_functor3(A,B,D,E) )
=> m1_functor3(k5_functor2(A,B,C,D,E,F,G),A,B,C,E) ) ) ) ) ) ) ) ) ).
fof(t35_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v11_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,B,C)
& m2_functor0(D,B,C) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,C,A)
& m2_functor0(F,C,A) )
=> ! [G] :
( m1_functor3(G,B,C,D,E)
=> ( r1_functor3(B,C,D,E)
=> ( r1_functor3(B,A,k1_functor3(B,C,A,D,F),k1_functor3(B,C,A,E,F))
& m1_functor3(k5_functor3(B,C,A,D,E,G,F),B,A,k1_functor3(B,C,A,D,F),k1_functor3(B,C,A,E,F)) ) ) ) ) ) ) ) ) ) ).
fof(t36_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v11_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( m1_functor3(G,B,C,E,F)
=> ( r1_functor3(B,C,E,F)
=> ( r1_functor3(A,C,k1_functor3(A,B,C,D,E),k1_functor3(A,B,C,D,F))
& m1_functor3(k6_functor3(A,B,C,E,F,D,G),A,C,k1_functor3(A,B,C,D,E),k1_functor3(A,B,C,D,F)) ) ) ) ) ) ) ) ) ) ).
fof(t37_functor3,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] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v11_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ! [G] :
( ( v15_functor0(G,B,C)
& m2_functor0(G,B,C) )
=> ! [H] :
( m1_functor3(H,A,B,D,E)
=> ! [I] :
( m1_functor3(I,B,C,F,G)
=> ( ( r1_functor3(A,B,D,E)
& r1_functor3(B,C,F,G) )
=> ( r1_functor3(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G))
& m1_functor3(k7_functor3(A,B,C,D,E,F,G,H,I),A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_functor3(E,A,B,C,D)
=> ( r1_functor3(A,B,C,D)
=> ! [F] :
( m1_functor3(F,A,B,D,C)
=> ( F = k8_functor3(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> k1_funct_1(F,G) = k1_altcat_3(B,k3_functor0(A,B,C,G),k3_functor0(A,B,D,G),k2_functor2(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) ) ).
fof(t38_functor3,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,B,A)
& m2_functor0(C,B,A) )
=> ! [D] :
( ( v15_functor0(D,B,A)
& m2_functor0(D,B,A) )
=> ! [E] :
( m1_functor3(E,B,A,C,D)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_functor3(B,A,C,D)
=> k2_functor2(B,A,D,C,k8_functor3(B,A,C,D,E),F) = k1_altcat_3(A,k3_functor0(B,A,C,F),k3_functor0(B,A,D,F),k2_functor2(B,A,C,D,E,F)) ) ) ) ) ) ) ) ).
fof(t39_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_functor3(E,A,B,C,D)
=> ( r1_functor3(A,B,C,D)
=> r6_pboole(u1_struct_0(A),k5_functor2(A,B,D,C,D,k8_functor3(A,B,C,D,E),E),k4_functor2(A,B,D)) ) ) ) ) ) ) ).
fof(t40_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_functor3(E,A,B,C,D)
=> ( r1_functor3(A,B,C,D)
=> r6_pboole(u1_struct_0(A),k5_functor2(A,B,C,D,C,E,k8_functor3(A,B,C,D,E)),k4_functor2(A,B,C)) ) ) ) ) ) ) ).
fof(t41_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_functor3(E,A,B,C,D)
=> ( r1_functor3(A,B,C,D)
=> r6_pboole(u1_struct_0(A),k8_functor3(A,B,D,C,k8_functor3(A,B,C,D,E)),E) ) ) ) ) ) ) ).
fof(t42_functor3,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] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( m1_functor3(F,A,B,C,E)
=> ! [G] :
( m1_functor3(G,A,B,E,D)
=> ! [H] :
( m1_functor3(H,A,B,C,D)
=> ( ( r6_pboole(u1_struct_0(A),H,k5_functor2(A,B,C,E,D,F,G))
& r1_functor3(A,B,C,E)
& r1_functor3(A,B,E,D) )
=> r6_pboole(u1_struct_0(A),k8_functor3(A,B,C,D,H),k5_functor2(A,B,D,E,C,k8_functor3(A,B,E,D,G),k8_functor3(A,B,C,E,F))) ) ) ) ) ) ) ) ) ) ).
fof(t43_functor3,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) )
=> r6_pboole(u1_struct_0(A),k8_functor3(A,B,C,C,k9_functor3(A,B,C)),k9_functor3(A,B,C)) ) ) ) ).
fof(dt_m1_functor3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_functor3(E,A,B,C,D)
=> m2_functor2(E,A,B,C,D) ) ) ).
fof(existence_m1_functor3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ? [E] : m1_functor3(E,A,B,C,D) ) ).
fof(symmetry_r1_functor3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ( r1_functor3(A,B,C,D)
=> r1_functor3(A,B,D,C) ) ) ).
fof(reflexivity_r1_functor3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> r1_functor3(A,B,C,C) ) ).
fof(dt_k1_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B)
& v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ( v9_functor0(k1_functor3(A,B,C,D,E),A,C)
& v15_functor0(k1_functor3(A,B,C,D,E),A,C)
& m2_functor0(k1_functor3(A,B,C,D,E),A,C) ) ) ).
fof(redefinition_k1_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B)
& v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> k1_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) ).
fof(dt_k2_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v16_functor0(D,A,B)
& m2_functor0(D,A,B)
& v16_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ( v9_functor0(k2_functor3(A,B,C,D,E),A,C)
& v15_functor0(k2_functor3(A,B,C,D,E),A,C)
& m2_functor0(k2_functor3(A,B,C,D,E),A,C) ) ) ).
fof(redefinition_k2_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v16_functor0(D,A,B)
& m2_functor0(D,A,B)
& v16_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> k2_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) ).
fof(dt_k3_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B)
& v16_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ( v9_functor0(k3_functor3(A,B,C,D,E),A,C)
& v16_functor0(k3_functor3(A,B,C,D,E),A,C)
& m2_functor0(k3_functor3(A,B,C,D,E),A,C) ) ) ).
fof(redefinition_k3_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B)
& v16_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> k3_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) ).
fof(dt_k4_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v16_functor0(D,A,B)
& m2_functor0(D,A,B)
& v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ( v9_functor0(k4_functor3(A,B,C,D,E),A,C)
& v16_functor0(k4_functor3(A,B,C,D,E),A,C)
& m2_functor0(k4_functor3(A,B,C,D,E),A,C) ) ) ).
fof(redefinition_k4_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v16_functor0(D,A,B)
& m2_functor0(D,A,B)
& v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> k4_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) ).
fof(dt_k5_functor3,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B)
& v15_functor0(E,A,B)
& m2_functor0(E,A,B)
& m1_functor2(F,A,B,D,E)
& v15_functor0(G,B,C)
& m2_functor0(G,B,C) )
=> m1_functor2(k5_functor3(A,B,C,D,E,F,G),A,C,k1_functor3(A,B,C,D,G),k1_functor3(A,B,C,E,G)) ) ).
fof(dt_k6_functor3,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v15_functor0(D,B,C)
& m2_functor0(D,B,C)
& v15_functor0(E,B,C)
& m2_functor0(E,B,C)
& v15_functor0(F,A,B)
& m2_functor0(F,A,B)
& m1_functor2(G,B,C,D,E) )
=> m1_functor2(k6_functor3(A,B,C,D,E,F,G),A,C,k1_functor3(A,B,C,F,D),k1_functor3(A,B,C,F,E)) ) ).
fof(dt_k7_functor3,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v2_altcat_1(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B)
& v15_functor0(E,A,B)
& m2_functor0(E,A,B)
& v15_functor0(F,B,C)
& m2_functor0(F,B,C)
& v15_functor0(G,B,C)
& m2_functor0(G,B,C)
& m1_functor2(H,A,B,D,E)
& m1_functor2(I,B,C,F,G) )
=> m1_functor2(k7_functor3(A,B,C,D,E,F,G,H,I),A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,G)) ) ).
fof(dt_k8_functor3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B)
& m1_functor3(E,A,B,C,D) )
=> m1_functor3(k8_functor3(A,B,C,D,E),A,B,D,C) ) ).
fof(dt_k9_functor3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> m1_functor3(k9_functor3(A,B,C),A,B,C,C) ) ).
fof(redefinition_k9_functor3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> k9_functor3(A,B,C) = k1_functor2(A,B,C) ) ).
%------------------------------------------------------------------------------