SET007 Axioms: SET007+513.ax
%------------------------------------------------------------------------------
% File : SET007+513 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Category of Functors between Alternative Categories
% 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 : functor2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 43 ( 4 unt; 0 def)
% Number of atoms : 643 ( 29 equ)
% Maximal formula atoms : 42 ( 14 avg)
% Number of connectives : 682 ( 82 ~; 0 |; 404 &)
% ( 15 <=>; 181 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 14 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 1 prp; 0-5 aty)
% Number of functors : 20 ( 20 usr; 1 con; 0-7 aty)
% Number of variables : 213 ( 208 !; 5 ?)
% 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(cc1_functor2,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)
=> ( v8_functor0(C,A,B)
& v12_functor0(C,A,B) ) ) ) ).
fof(cc2_functor2,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)
=> ( v15_functor0(C,A,B)
=> ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v10_functor0(C,A,B)
& v12_functor0(C,A,B)
& v13_functor0(C,A,B) ) ) ) ) ).
fof(cc3_functor2,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)
=> ( ( v10_functor0(C,A,B)
& v13_functor0(C,A,B) )
=> ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v12_functor0(C,A,B)
& v15_functor0(C,A,B) ) ) ) ) ).
fof(cc4_functor2,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)
=> ( v16_functor0(C,A,B)
=> ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v11_functor0(C,A,B)
& v12_functor0(C,A,B)
& v14_functor0(C,A,B) ) ) ) ) ).
fof(cc5_functor2,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)
=> ( ( v11_functor0(C,A,B)
& v14_functor0(C,A,B) )
=> ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v12_functor0(C,A,B)
& v16_functor0(C,A,B) ) ) ) ) ).
fof(t1_functor2,axiom,
$true ).
fof(t2_functor2,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))
=> k6_functor0(A,B,C,D,D,k8_altcat_1(A,D)) = k8_altcat_1(B,k3_functor0(A,B,C,D)) ) ) ) ) ).
fof(d1_functor2,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) )
=> ( r1_functor2(A,B,C,D)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,D,E)) != k1_xboole_0 ) ) ) ) ) ) ).
fof(t3_functor2,axiom,
$true ).
fof(t4_functor2,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] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ( ( r1_functor2(A,B,C,D)
& r1_functor2(A,B,D,E) )
=> r1_functor2(A,B,C,E) ) ) ) ) ) ) ).
fof(d2_functor2,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) )
=> ( r1_functor2(A,B,C,D)
=> ! [E] :
( m1_pboole(E,u1_struct_0(A))
=> ( m1_functor2(E,A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> m1_subset_1(k1_funct_1(E,F),k1_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F))) ) ) ) ) ) ) ) ) ).
fof(d3_functor2,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_functor2(D,A,B,C,C)
=> ( D = k1_functor2(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_funct_1(D,E) = k8_altcat_1(B,k3_functor0(A,B,C,E)) ) ) ) ) ) ) ).
fof(d4_functor2,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) )
=> ( r1_functor2(A,B,C,D)
=> ! [E] :
( m1_functor2(E,A,B,C,D)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F)))
=> ( G = k2_functor2(A,B,C,D,E,F)
<=> G = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ) ).
fof(d5_functor2,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] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ( ( r1_functor2(A,B,C,D)
& r1_functor2(A,B,D,E) )
=> ! [F] :
( m1_functor2(F,A,B,C,D)
=> ! [G] :
( m1_functor2(G,A,B,D,E)
=> ! [H] :
( m1_functor2(H,A,B,C,E)
=> ( H = k3_functor2(A,B,C,D,E,F,G)
<=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> k2_functor2(A,B,C,E,H,I) = k5_altcat_1(B,k3_functor0(A,B,C,I),k3_functor0(A,B,D,I),k3_functor0(A,B,E,I),k2_functor2(A,B,C,D,F,I),k2_functor2(A,B,D,E,G,I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_functor2,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) )
=> ( r1_functor2(A,B,C,D)
=> ! [E] :
( m1_functor2(E,A,B,C,D)
=> ! [F] :
( m1_functor2(F,A,B,C,D)
=> ( ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> k2_functor2(A,B,C,D,E,G) = k2_functor2(A,B,C,D,F,G) )
=> r6_pboole(u1_struct_0(A),E,F) ) ) ) ) ) ) ) ) ).
fof(t6_functor2,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))
=> k2_functor2(A,B,C,C,k1_functor2(A,B,C),D) = k8_altcat_1(B,k3_functor0(A,B,C,D)) ) ) ) ) ).
fof(t7_functor2,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) )
=> ( r1_functor2(A,B,C,D)
=> ! [E] :
( m1_functor2(E,A,B,C,D)
=> ( r6_pboole(u1_struct_0(A),k3_functor2(A,B,C,D,D,E,k1_functor2(A,B,D)),E)
& r6_pboole(u1_struct_0(A),k3_functor2(A,B,C,C,D,k1_functor2(A,B,C),E),E) ) ) ) ) ) ) ) ).
fof(t8_functor2,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] :
( ( v15_functor0(F,A,B)
& m2_functor0(F,A,B) )
=> ( ( r1_functor2(A,B,C,D)
& r1_functor2(A,B,D,E)
& r1_functor2(A,B,E,F) )
=> ! [G] :
( m1_functor2(G,A,B,C,D)
=> ! [H] :
( m1_functor2(H,A,B,D,E)
=> ! [I] :
( m1_functor2(I,A,B,E,F)
=> r6_pboole(u1_struct_0(A),k3_functor2(A,B,C,D,F,G,k3_functor2(A,B,D,E,F,H,I)),k3_functor2(A,B,C,E,F,k3_functor2(A,B,C,D,E,G,H),I)) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_functor2,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) )
=> ( r2_functor2(A,B,C,D)
<=> ( r1_functor2(A,B,C,D)
& ? [E] :
( m1_functor2(E,A,B,C,D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( k1_altcat_1(A,F,G) != k1_xboole_0
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,F,G))
=> k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,G),k3_functor0(A,B,D,G),k6_functor0(A,B,C,F,G,H),k2_functor2(A,B,C,D,E,G)) = k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F),k3_functor0(A,B,D,G),k2_functor2(A,B,C,D,E,F),k6_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_functor2,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) )
=> r2_functor2(A,B,C,C) ) ) ) ).
fof(t10_functor2,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) )
=> ( ( r2_functor2(A,B,C,D)
& r2_functor2(A,B,D,E) )
=> r2_functor2(A,B,C,E) ) ) ) ) ) ) ).
fof(d7_functor2,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) )
=> ( r2_functor2(A,B,C,D)
=> ! [E] :
( m1_functor2(E,A,B,C,D)
=> ( m2_functor2(E,A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( k1_altcat_1(A,F,G) != k1_xboole_0
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,F,G))
=> k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,G),k3_functor0(A,B,D,G),k6_functor0(A,B,C,F,G,H),k2_functor2(A,B,C,D,E,G)) = k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F),k3_functor0(A,B,D,G),k2_functor2(A,B,C,D,E,F),k6_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_functor2,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) )
=> ( ( r2_functor2(A,B,C,D)
& r2_functor2(A,B,D,E) )
=> ! [F] :
( m2_functor2(F,A,B,C,D)
=> ! [G] :
( m2_functor2(G,A,B,D,E)
=> ! [H] :
( m2_functor2(H,A,B,C,E)
=> ( H = k5_functor2(A,B,C,D,E,F,G)
<=> r6_pboole(u1_struct_0(A),H,k3_functor2(A,B,C,D,E,F,G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_functor2,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) )
=> ( r2_functor2(A,B,C,D)
=> ! [E] :
( m2_functor2(E,A,B,C,D)
=> ( r6_pboole(u1_struct_0(A),k3_functor2(A,B,C,D,D,E,k4_functor2(A,B,D)),E)
& r6_pboole(u1_struct_0(A),k3_functor2(A,B,C,C,D,k4_functor2(A,B,C),E),E) ) ) ) ) ) ) ) ).
fof(t12_functor2,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] :
( ( v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ( ( r2_functor2(A,B,C,D)
& r2_functor2(A,B,D,E) )
=> ! [F] :
( m2_functor2(F,A,B,C,D)
=> ! [G] :
( m2_functor2(G,A,B,D,E)
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> k2_functor2(A,B,C,E,k3_functor2(A,B,C,D,E,F,G),H) = k5_altcat_1(B,k3_functor0(A,B,C,H),k3_functor0(A,B,D,H),k3_functor0(A,B,E,H),k2_functor2(A,B,C,D,F,H),k2_functor2(A,B,D,E,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(t13_functor2,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] :
( ( v15_functor0(F,A,B)
& m2_functor0(F,A,B) )
=> ! [G] :
( m2_functor2(G,A,B,C,D)
=> ! [H] :
( m2_functor2(H,A,B,D,E)
=> ( ( r2_functor2(A,B,C,D)
& r2_functor2(A,B,D,E)
& r2_functor2(A,B,E,F) )
=> ! [I] :
( m2_functor2(I,A,B,E,F)
=> r6_pboole(u1_struct_0(A),k5_functor2(A,B,C,D,F,G,k5_functor2(A,B,D,E,F,H,I)),k5_functor2(A,B,C,E,F,k5_functor2(A,B,C,D,E,G,H),I)) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_functor2,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( ( ! [E] :
( ( r2_hidden(E,A)
& k1_funct_1(C,E) = k1_xboole_0 )
=> k1_funct_1(B,E) = k1_xboole_0 )
=> ( D = k6_functor2(A,B,C)
<=> ! [E] :
( r2_hidden(E,D)
<=> m3_pboole(E,A,B,C) ) ) )
& ( ? [E] :
( r2_hidden(E,A)
& k1_funct_1(C,E) = k1_xboole_0
& k1_funct_1(B,E) != k1_xboole_0 )
=> ( D = k6_functor2(A,B,C)
<=> D = k1_xboole_0 ) ) ) ) ) ).
fof(d10_functor2,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] :
( C = k7_functor2(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( v9_functor0(D,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) ) ) ) ) ) ).
fof(d11_functor2,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)
& v6_altcat_1(C)
& l2_altcat_1(C) )
=> ( C = k8_functor2(A,B)
<=> ( u1_struct_0(C) = k7_functor2(A,B)
& ! [D] :
( ( v9_functor0(D,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v9_functor0(E,A,B)
& v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( r2_hidden(F,k1_binop_1(u1_altcat_1(C),D,E))
<=> ( r2_functor2(A,B,D,E)
& m2_functor2(F,A,B,D,E) ) ) ) )
& ! [D] :
( ( v9_functor0(D,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v9_functor0(E,A,B)
& v15_functor0(E,A,B)
& m2_functor0(E,A,B) )
=> ! [F] :
( ( v9_functor0(F,A,B)
& v15_functor0(F,A,B)
& m2_functor0(F,A,B) )
=> ( ( r2_functor2(A,B,D,E)
& r2_functor2(A,B,E,F) )
=> ! [G] :
( m2_functor2(G,A,B,D,E)
=> ! [H] :
( m2_functor2(H,A,B,E,F)
=> ? [I] :
( v1_relat_1(I)
& v1_funct_1(I)
& I = k1_multop_1(u2_altcat_1(C),D,E,F)
& k1_binop_1(I,H,G) = k5_functor2(A,B,D,E,F,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m1_functor2,axiom,
! [A,B,C,D] :
( ( ~ 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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_functor2(E,A,B,C,D)
=> m1_pboole(E,u1_struct_0(A)) ) ) ).
fof(existence_m1_functor2,axiom,
! [A,B,C,D] :
( ( ~ 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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ? [E] : m1_functor2(E,A,B,C,D) ) ).
fof(dt_m2_functor2,axiom,
! [A,B,C,D] :
( ( ~ 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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m2_functor2(E,A,B,C,D)
=> m1_functor2(E,A,B,C,D) ) ) ).
fof(existence_m2_functor2,axiom,
! [A,B,C,D] :
( ( ~ 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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ? [E] : m2_functor2(E,A,B,C,D) ) ).
fof(reflexivity_r1_functor2,axiom,
! [A,B,C,D] :
( ( ~ 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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> r1_functor2(A,B,C,C) ) ).
fof(dt_k1_functor2,axiom,
! [A,B,C] :
( ( ~ 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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> m1_functor2(k1_functor2(A,B,C),A,B,C,C) ) ).
fof(dt_k2_functor2,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B)
& m1_functor2(E,A,B,C,D)
& m1_subset_1(F,u1_struct_0(A)) )
=> m1_subset_1(k2_functor2(A,B,C,D,E,F),k1_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F))) ) ).
fof(dt_k3_functor2,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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& 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,C,D)
& m1_functor2(G,A,B,D,E) )
=> m1_functor2(k3_functor2(A,B,C,D,E,F,G),A,B,C,E) ) ).
fof(dt_k4_functor2,axiom,
! [A,B,C] :
( ( ~ 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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> m2_functor2(k4_functor2(A,B,C),A,B,C,C) ) ).
fof(redefinition_k4_functor2,axiom,
! [A,B,C] :
( ( ~ 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)
& v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> k4_functor2(A,B,C) = k1_functor2(A,B,C) ) ).
fof(dt_k5_functor2,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ 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)
& v15_functor0(E,A,B)
& m2_functor0(E,A,B)
& m2_functor2(F,A,B,C,D)
& m2_functor2(G,A,B,D,E) )
=> m2_functor2(k5_functor2(A,B,C,D,E,F,G),A,B,C,E) ) ).
fof(dt_k6_functor2,axiom,
$true ).
fof(dt_k7_functor2,axiom,
$true ).
fof(dt_k8_functor2,axiom,
! [A,B] :
( ( ~ 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) )
=> ( ~ v3_struct_0(k8_functor2(A,B))
& v2_altcat_1(k8_functor2(A,B))
& v6_altcat_1(k8_functor2(A,B))
& l2_altcat_1(k8_functor2(A,B)) ) ) ).
%------------------------------------------------------------------------------