SET007 Axioms: SET007+682.ax
%------------------------------------------------------------------------------
% File : SET007+682 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Concrete 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 : yellow18 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 107 ( 1 unt; 0 def)
% Number of atoms : 1827 ( 281 equ)
% Maximal formula atoms : 54 ( 17 avg)
% Number of connectives : 2004 ( 284 ~; 3 |;1032 &)
% ( 39 <=>; 646 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 14 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 67 ( 65 usr; 1 prp; 0-5 aty)
% Number of functors : 124 ( 124 usr; 41 con; 0-6 aty)
% Number of variables : 643 ( 558 !; 85 ?)
% 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_yellow18,axiom,
! [A,B,C,D] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ( v1_relat_1(k1_multop_1(A,B,C,D))
& v1_funct_1(k1_multop_1(A,B,C,D)) ) ) ).
fof(fc2_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k1_yellow18(A))
& v2_altcat_1(k1_yellow18(A))
& v6_altcat_1(k1_yellow18(A))
& v11_altcat_1(k1_yellow18(A)) ) ) ).
fof(fc3_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k1_yellow18(A))
& v2_altcat_1(k1_yellow18(A))
& v6_altcat_1(k1_yellow18(A))
& v12_altcat_1(k1_yellow18(A))
& v1_altcat_2(k1_yellow18(A)) ) ) ).
fof(fc4_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v6_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
& v8_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
& v9_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
& v11_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
& v12_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
& v14_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
& v16_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A))
& v21_functor0(k2_yellow18(A,k1_yellow18(A)),A,k1_yellow18(A)) ) ) ).
fof(fc5_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v6_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
& v8_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
& v9_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
& v11_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
& v12_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
& v14_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
& v16_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A)
& v21_functor0(k2_yellow18(k1_yellow18(A),A),k1_yellow18(A),A) ) ) ).
fof(cc1_yellow18,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v8_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A) )
=> ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A) ) ) ) ).
fof(fc6_yellow18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k7_altcat_1(A))
& v2_altcat_1(k7_altcat_1(A))
& v6_altcat_1(k7_altcat_1(A))
& v8_altcat_1(k7_altcat_1(A))
& v9_altcat_1(k7_altcat_1(A))
& v10_altcat_1(k7_altcat_1(A))
& v11_altcat_1(k7_altcat_1(A))
& v12_altcat_1(k7_altcat_1(A))
& v1_altcat_2(k7_altcat_1(A))
& v2_yellow18(k7_altcat_1(A))
& v3_yellow18(k7_altcat_1(A)) ) ) ).
fof(cc2_yellow18,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v4_yellow18(A) )
=> ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A) ) ) ) ).
fof(cc3_yellow18,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& v3_yellow18(A) )
=> ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v4_yellow18(A) ) ) ) ).
fof(rc1_yellow18,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v8_altcat_1(A)
& v9_altcat_1(A)
& v10_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A)
& v4_yellow18(A) ) ).
fof(cc4_yellow18,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ( v1_relat_1(D)
& v1_funct_1(D) ) ) ) ).
fof(fc7_yellow18,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_xboole_0(k3_yellow18(k4_yellow18(A),B)) ) ).
fof(fc8_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v6_functor0(k5_yellow18(A),A,k4_yellow18(A))
& v8_functor0(k5_yellow18(A),A,k4_yellow18(A))
& v9_functor0(k5_yellow18(A),A,k4_yellow18(A))
& v10_functor0(k5_yellow18(A),A,k4_yellow18(A))
& v12_functor0(k5_yellow18(A),A,k4_yellow18(A))
& v13_functor0(k5_yellow18(A),A,k4_yellow18(A))
& v15_functor0(k5_yellow18(A),A,k4_yellow18(A))
& v21_functor0(k5_yellow18(A),A,k4_yellow18(A)) ) ) ).
fof(t1_yellow18,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_subset_1(E,u1_struct_0(A))
=> k3_functor0(A,B,C,E) = k3_functor0(A,B,D,E) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( k1_altcat_1(A,E,F) != k1_xboole_0
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,E,F))
=> k6_functor0(A,B,C,E,F,G) = k6_functor0(A,B,D,E,F,G) ) ) ) ) )
=> g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) = g2_functor0(A,B,u1_functor0(A,B,D),u2_functor0(A,B,D)) ) ) ) ) ) ).
fof(t2_yellow18,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] :
( ( v16_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ( ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k3_functor0(A,B,C,E) = k3_functor0(A,B,D,E) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( k1_altcat_1(A,E,F) != k1_xboole_0
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,E,F))
=> k8_functor0(A,B,C,E,F,G) = k8_functor0(A,B,D,E,F,G) ) ) ) ) )
=> g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) = g2_functor0(A,B,u1_functor0(A,B,D),u2_functor0(A,B,D)) ) ) ) ) ) ).
fof(d1_yellow18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m2_relset_1(D,k2_zfmisc_1(A,B),C) )
=> ( v2_funct_1(D)
<=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,B)
=> ! [H] :
( m1_subset_1(H,B)
=> ( k2_binop_1(A,B,C,D,E,G) = k2_binop_1(A,B,C,D,F,H)
=> ( E = F
& G = H ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_yellow18,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) )
=> ( r1_yellow18(A,B)
<=> ? [C] :
( v15_functor0(C,A,B)
& m2_functor0(C,A,B)
& ? [D] :
( v15_functor0(D,B,A)
& m2_functor0(D,B,A)
& r1_functor3(A,A,k1_functor3(A,B,A,C,D),k12_functor0(A))
& r1_functor3(B,B,k1_functor3(B,A,B,D,C),k12_functor0(B)) ) ) ) ) ) ).
fof(t3_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_altcat_2(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C) )
=> ! [D] :
( ( v8_functor0(D,A,B)
& l2_functor0(D,A,B) )
=> ! [E] :
( ( v8_functor0(E,A,B)
& l2_functor0(E,A,B) )
=> ! [F] :
( l2_functor0(F,B,C)
=> ! [G] :
( l2_functor0(G,B,C)
=> ( ( g2_functor0(A,B,u1_functor0(A,B,D),u2_functor0(A,B,D)) = g2_functor0(A,B,u1_functor0(A,B,E),u2_functor0(A,B,E))
& g2_functor0(B,C,u1_functor0(B,C,F),u2_functor0(B,C,F)) = g2_functor0(B,C,u1_functor0(B,C,G),u2_functor0(B,C,G)) )
=> k13_functor0(A,B,C,D,F) = k13_functor0(A,B,C,E,G) ) ) ) ) ) ) ) ) ).
fof(t4_yellow18,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) )
=> ( ( r1_yellow18(A,B)
& r1_yellow18(B,C) )
=> r1_yellow18(A,C) ) ) ) ) ).
fof(t5_yellow18,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) )
=> ( r1_functor0(A,B)
=> r1_yellow18(A,B) ) ) ) ).
fof(d3_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ( r2_yellow18(A,B)
<=> ( u1_struct_0(B) = u1_struct_0(A)
& u1_altcat_1(B) = k1_altcat_2(u1_struct_0(A),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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ( ( F = C
& G = D
& H = E )
=> k4_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B),F,G,H) = k1_functor0(k1_binop_1(u1_altcat_1(A),D,C),k1_binop_1(u1_altcat_1(A),E,D),k1_binop_1(u1_altcat_1(A),E,C),k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),E,D,C)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ( r2_yellow18(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> m1_subset_1(C,u1_struct_0(B)) ) ) ) ) ).
fof(t7_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ( r2_yellow18(A,B)
=> ! [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))
=> ( ( E = C
& F = D )
=> k1_altcat_1(A,C,D) = k1_altcat_1(B,F,E) ) ) ) ) ) ) ) ) ).
fof(t8_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ( r2_yellow18(A,B)
=> ! [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))
=> ( ( E = C
& F = D )
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
=> m1_subset_1(G,k1_altcat_1(B,F,E)) ) ) ) ) ) ) ) ) ) ).
fof(t9_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& l2_altcat_1(B) )
=> ( r2_yellow18(A,B)
<=> ( u1_struct_0(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,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ( ( F = C
& G = D
& H = E )
=> ( k1_altcat_1(A,C,D) = k1_altcat_1(B,G,F)
& ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,E) != k1_xboole_0
& ? [I] :
( m1_subset_1(I,k1_altcat_1(A,C,D))
& ? [J] :
( m1_subset_1(J,k1_altcat_1(A,D,E))
& ? [K] :
( m1_subset_1(K,k1_altcat_1(B,G,F))
& ? [L] :
( m1_subset_1(L,k1_altcat_1(B,H,G))
& K = I
& L = J
& k5_altcat_1(B,H,G,F,L,K) != k5_altcat_1(A,C,D,E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t10_yellow18,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) )
=> ( r2_yellow18(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( C = D
=> k8_altcat_1(A,C) = k8_altcat_1(B,D) ) ) ) ) ) ) ).
fof(t11_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ? [B] :
( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& l2_altcat_1(B)
& r2_yellow18(A,B) ) ) ).
fof(t12_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& l2_altcat_1(B) )
=> ( ( r2_yellow18(A,B)
& v11_altcat_1(A) )
=> v11_altcat_1(B) ) ) ) ).
fof(t13_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& l2_altcat_1(B) )
=> ( ( r2_yellow18(A,B)
& v12_altcat_1(A) )
=> v12_altcat_1(B) ) ) ) ).
fof(t14_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_altcat_1(C) )
=> ( r2_yellow18(A,B)
=> ( r2_yellow18(A,C)
<=> g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) = g2_altcat_1(u1_struct_0(C),u1_altcat_1(C),u2_altcat_1(C)) ) ) ) ) ) ).
fof(d4_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& l2_altcat_1(B) )
=> ( B = k1_yellow18(A)
<=> r2_yellow18(A,B) ) ) ) ).
fof(d5_yellow18,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) )
=> ( r2_yellow18(A,B)
=> ! [C] :
( ( v9_functor0(C,A,B)
& v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ( C = k2_yellow18(A,B)
<=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_functor0(A,B,C,D) = D )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k1_altcat_1(A,D,E) != k1_xboole_0
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> k8_functor0(A,B,C,D,E,F) = F ) ) ) ) ) ) ) ) ) ) ).
fof(t15_yellow18,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) )
=> ( r2_yellow18(A,B)
=> k2_functor3(B,A,B,k2_yellow18(B,A),k2_yellow18(A,B)) = k12_functor0(B) ) ) ) ).
fof(t16_yellow18,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) )
=> ( r2_yellow18(A,B)
=> v21_functor0(k2_yellow18(A,B),A,B) ) ) ) ).
fof(t17_yellow18,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) )
=> ( r2_yellow18(A,B)
=> r2_functor0(A,B) ) ) ) ).
fof(t18_yellow18,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) )
=> ( r2_yellow18(A,B)
=> ( r1_functor0(A,C)
<=> r2_functor0(B,C) ) ) ) ) ) ).
fof(t19_yellow18,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) )
=> ( ( r2_yellow18(A,B)
& r2_yellow18(C,D)
& r1_functor0(A,C) )
=> r1_functor0(B,D) ) ) ) ) ) ).
fof(t20_yellow18,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) )
=> ( ( r2_yellow18(A,B)
& r2_yellow18(C,D)
& r2_functor0(A,C) )
=> r2_functor0(B,D) ) ) ) ) ) ).
fof(t21_yellow18,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) )
=> ( r2_yellow18(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,C) != k1_xboole_0
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& E = C
& F = D
& ? [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
& ? [H] :
( m1_subset_1(H,k1_altcat_1(B,F,E))
& H = G
& ~ ( v1_altcat_3(G,A,C,D)
<=> v2_altcat_3(H,B,F,E) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_yellow18,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) )
=> ( r2_yellow18(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,C) != k1_xboole_0
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& E = C
& F = D
& ? [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
& ? [H] :
( m1_subset_1(H,k1_altcat_1(B,F,E))
& H = G
& ~ ( v2_altcat_3(G,A,C,D)
<=> v1_altcat_3(H,B,F,E) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_yellow18,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) )
=> ( r2_yellow18(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,C) != k1_xboole_0
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& E = C
& F = D
& ? [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
& ? [H] :
( m1_subset_1(H,k1_altcat_1(B,F,E))
& H = G
& v1_altcat_3(G,A,C,D)
& v2_altcat_3(G,A,C,D)
& k1_altcat_3(B,F,E,H) != k1_altcat_3(A,C,D,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_yellow18,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) )
=> ( r2_yellow18(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,C) != k1_xboole_0
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& E = C
& F = D
& ? [G] :
( m1_subset_1(G,k1_altcat_1(A,C,D))
& ? [H] :
( m1_subset_1(H,k1_altcat_1(B,F,E))
& H = G
& ~ ( v3_altcat_3(G,A,C,D)
<=> v3_altcat_3(H,B,F,E) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_yellow18,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) )
=> ( ( r2_yellow18(A,B)
& r2_yellow18(C,D) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( v15_functor0(F,B,C)
& m2_functor0(F,B,C) )
=> ( r1_functor3(B,C,E,F)
=> r1_functor3(A,D,k2_functor3(A,B,D,k2_yellow18(A,B),k3_functor3(B,C,D,F,k2_yellow18(C,D))),k2_functor3(A,B,D,k2_yellow18(A,B),k3_functor3(B,C,D,E,k2_yellow18(C,D)))) ) ) ) ) ) ) ) ) ).
fof(t26_yellow18,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) )
=> ( ( r2_yellow18(A,B)
& r2_yellow18(C,D)
& r1_yellow18(A,C) )
=> r1_yellow18(B,D) ) ) ) ) ) ).
fof(d6_yellow18,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) )
=> ( r3_yellow18(A,B)
<=> r1_yellow18(A,k1_yellow18(B)) ) ) ) ).
fof(t27_yellow18,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) )
=> ( r2_functor0(A,B)
=> r3_yellow18(A,B) ) ) ) ).
fof(t28_yellow18,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) )
=> ( r2_yellow18(A,B)
=> ( r1_yellow18(A,C)
<=> r3_yellow18(B,C) ) ) ) ) ) ).
fof(t29_yellow18,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) )
=> ( ( r3_yellow18(A,B)
& r1_yellow18(B,C) )
=> r3_yellow18(A,C) ) ) ) ) ).
fof(t30_yellow18,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) )
=> ( ( r3_yellow18(A,B)
& r3_yellow18(B,C) )
=> r1_yellow18(A,C) ) ) ) ) ).
fof(t31_yellow18,axiom,
! [A,B,C] :
( r2_hidden(C,k1_funct_2(A,B))
<=> ( v1_relat_1(C)
& v1_funct_1(C)
& k1_funct_5(C) = A
& r1_tarski(k2_funct_5(C),B) ) ) ).
fof(d7_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v2_yellow18(A)
<=> ? [B] :
( m1_pboole(B,u1_struct_0(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_tarski(k1_altcat_1(A,C,D),k1_funct_2(k1_funct_1(B,C),k1_funct_1(B,D))) ) ) ) ) ) ).
fof(d8_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B,C] :
( ( m1_subset_1(B,u1_struct_0(A))
=> ( C = k3_yellow18(A,B)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& D = B
& C = k1_funct_5(k8_altcat_1(A,D)) ) ) )
& ( ~ m1_subset_1(B,u1_struct_0(A))
=> ( C = k3_yellow18(A,B)
<=> C = k1_xboole_0 ) ) ) ) ).
fof(d9_yellow18,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))
=> k3_yellow18(A,B) = k1_funct_5(k8_altcat_1(A,B)) ) ) ).
fof(t32_yellow18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_altcat_1(A)))
=> k8_altcat_1(k7_altcat_1(A),B) = k6_partfun1(B) ) ) ).
fof(t33_yellow18,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_altcat_1(A)))
=> k3_yellow18(k7_altcat_1(A),B) = B ) ) ).
fof(d10_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v3_yellow18(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k8_altcat_1(A,B) = k6_partfun1(k3_yellow18(A,B)) ) ) ) ).
fof(d11_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v4_yellow18(A)
<=> ( v2_yellow18(A)
& v9_altcat_1(A)
& v3_yellow18(A) ) ) ) ).
fof(t34_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v2_yellow18(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_tarski(k1_altcat_1(A,B,C),k1_funct_2(k3_yellow18(A,B),k3_yellow18(A,C))) ) ) ) ) ).
fof(t35_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_altcat_1(A,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ( v1_funct_1(D)
& v1_funct_2(D,k3_yellow18(A,B),k3_yellow18(A,C))
& m2_relset_1(D,k3_yellow18(A,B),k3_yellow18(A,C)) ) ) ) ) ) ) ).
fof(t36_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_altcat_1(A,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ( k1_relat_1(D) = k3_yellow18(A,B)
& r1_tarski(k2_relat_1(D),k3_yellow18(A,C)) ) ) ) ) ) ) ).
fof(t37_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_yellow18(A,B) = k1_relat_1(k8_altcat_1(A,B)) ) ) ).
fof(t38_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(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))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,D) != k1_xboole_0
& ~ ! [E] :
( m1_subset_1(E,k1_altcat_1(A,B,C))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,C,D))
=> k5_altcat_1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ) ) ) ) ) ) ).
fof(t39_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r2_hidden(k6_partfun1(k3_yellow18(A,B)),k1_altcat_1(A,B,B))
=> k8_altcat_1(A,B) = k6_partfun1(k3_yellow18(A,B)) ) ) ) ).
fof(t40_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v4_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,B) != k1_xboole_0
& ? [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
& v1_altcat_3(D,A,B,C)
& k2_relat_1(D) != k3_yellow18(A,C) ) ) ) ) ) ).
fof(t41_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v4_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,B) != k1_xboole_0
& ? [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
& v2_altcat_3(D,A,B,C)
& ~ v2_funct_1(D) ) ) ) ) ) ).
fof(t42_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v4_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,B) != k1_xboole_0
& ? [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
& v3_altcat_3(D,A,B,C)
& ~ ( v2_funct_1(D)
& k2_relat_1(D) = k3_yellow18(A,C) ) ) ) ) ) ) ).
fof(t43_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_altcat_1(A,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ( ( v2_funct_1(D)
& r2_hidden(k2_funct_1(D),k1_altcat_1(A,C,B)) )
=> v3_altcat_3(D,A,B,C) ) ) ) ) ) ) ).
fof(t44_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v4_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,B) != k1_xboole_0
& ? [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
& v3_altcat_3(D,A,B,C)
& k1_altcat_3(A,B,C,D) != k2_funct_1(D) ) ) ) ) ) ).
fof(d12_yellow18,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)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v4_yellow18(B)
& l2_altcat_1(B) )
=> ( B = k4_yellow18(A)
<=> ( u1_struct_0(B) = u1_struct_0(A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( r2_hidden(D,k3_yellow18(B,C))
<=> ( r2_hidden(D,k3_card_3(k2_card_3(u1_altcat_1(A))))
& C = k20_mcart_1(D) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
<=> ( r2_hidden(E,k1_funct_2(k3_yellow18(B,C),k3_yellow18(B,D)))
& ? [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))
& F = C
& G = D
& k1_altcat_1(A,F,G) != k1_xboole_0
& ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( k1_altcat_1(A,I,F) != k1_xboole_0
=> ! [J] :
( m1_subset_1(J,k1_altcat_1(A,I,F))
=> k1_funct_1(E,k4_tarski(J,k4_tarski(I,F))) = k4_tarski(k5_altcat_1(A,I,F,G,J,H),k4_tarski(I,G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_yellow18,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] :
( r2_hidden(C,k3_yellow18(k4_yellow18(A),B))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,k1_altcat_1(A,D,B))
& k1_altcat_1(A,D,B) != k1_xboole_0
& C = k4_tarski(E,k4_tarski(D,B)) ) ) ) ) ) ).
fof(t46_yellow18,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))
=> ( k1_altcat_1(A,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k3_yellow18(k4_yellow18(A),B),k3_yellow18(k4_yellow18(A),C))
& m2_relset_1(E,k3_yellow18(k4_yellow18(A),B),k3_yellow18(k4_yellow18(A),C))
& r2_hidden(E,k1_binop_1(u1_altcat_1(k4_yellow18(A)),B,C))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,F,B))
=> ( k1_altcat_1(A,F,B) != k1_xboole_0
=> k1_funct_1(E,k4_tarski(G,k4_tarski(F,B))) = k4_tarski(k5_altcat_1(A,F,B,C,G,D),k4_tarski(F,C)) ) ) ) ) ) ) ) ) ) ).
fof(t47_yellow18,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))
=> ( k1_altcat_1(A,B,C) != k1_xboole_0
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( ( r2_hidden(D,k1_binop_1(u1_altcat_1(k4_yellow18(A)),B,C))
& r2_hidden(E,k1_binop_1(u1_altcat_1(k4_yellow18(A)),B,C))
& k1_funct_1(D,k4_tarski(k8_altcat_1(A,B),k4_tarski(B,B))) = k1_funct_1(E,k4_tarski(k8_altcat_1(A,B),k4_tarski(B,B))) )
=> D = E ) ) ) ) ) ) ) ).
fof(d13_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( v9_functor0(B,A,k4_yellow18(A))
& v15_functor0(B,A,k4_yellow18(A))
& m2_functor0(B,A,k4_yellow18(A)) )
=> ( B = k5_yellow18(A)
<=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k3_functor0(A,k4_yellow18(A),B,C) = C )
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( k1_altcat_1(A,C,D) != k1_xboole_0
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,C,D))
=> k1_funct_1(k6_functor0(A,k4_yellow18(A),B,C,D,E),k4_tarski(k8_altcat_1(A,C),k4_tarski(C,C))) = k4_tarski(E,k4_tarski(C,D)) ) ) ) ) ) ) ) ) ).
fof(t48_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> r1_functor0(A,k4_yellow18(A)) ) ).
fof(s1_yellow18,axiom,
( ! [A] :
( m1_subset_1(A,f1_s1_yellow18)
=> ! [B] :
( m1_subset_1(B,f1_s1_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s1_yellow18)
=> ! [D,E] :
( ( r2_hidden(D,f2_s1_yellow18(A,B))
& r2_hidden(E,f2_s1_yellow18(B,C)) )
=> r2_hidden(f3_s1_yellow18(A,B,C,D,E),f2_s1_yellow18(A,C)) ) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& l2_altcat_1(A)
& u1_struct_0(A) = f1_s1_yellow18
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_altcat_1(A,B,C) = f2_s1_yellow18(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,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,D) != k1_xboole_0
& ~ ! [E] :
( m1_subset_1(E,k1_altcat_1(A,B,C))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,C,D))
=> k5_altcat_1(A,B,C,D,E,F) = f3_s1_yellow18(B,C,D,E,F) ) ) ) ) ) ) ) ) ).
fof(s2_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s2_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s2_yellow18))
=> ~ ( k1_altcat_1(f1_s2_yellow18,A,B) != k1_xboole_0
& k1_altcat_1(f1_s2_yellow18,B,C) != k1_xboole_0
& ~ ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s2_yellow18,A,B))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(f1_s2_yellow18,B,C))
=> k5_altcat_1(f1_s2_yellow18,A,B,C,D,E) = f2_s2_yellow18(A,B,C,D,E) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s2_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s2_yellow18))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(f1_s2_yellow18))
=> ! [E,F,G] :
( ( r2_hidden(E,k1_altcat_1(f1_s2_yellow18,A,B))
& r2_hidden(F,k1_altcat_1(f1_s2_yellow18,B,C))
& r2_hidden(G,k1_altcat_1(f1_s2_yellow18,C,D)) )
=> f2_s2_yellow18(A,C,D,f2_s2_yellow18(A,B,C,E,F),G) = f2_s2_yellow18(A,B,D,E,f2_s2_yellow18(B,C,D,F,G)) ) ) ) ) ) )
=> v11_altcat_1(f1_s2_yellow18) ) ).
fof(s3_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s3_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s3_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s3_yellow18))
=> ~ ( k1_altcat_1(f1_s3_yellow18,A,B) != k1_xboole_0
& k1_altcat_1(f1_s3_yellow18,B,C) != k1_xboole_0
& ~ ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s3_yellow18,A,B))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(f1_s3_yellow18,B,C))
=> k5_altcat_1(f1_s3_yellow18,A,B,C,D,E) = f2_s3_yellow18(A,B,C,D,E) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s3_yellow18))
=> ? [B] :
( r2_hidden(B,k1_altcat_1(f1_s3_yellow18,A,A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s3_yellow18))
=> ! [D] :
( r2_hidden(D,k1_altcat_1(f1_s3_yellow18,A,C))
=> f2_s3_yellow18(A,A,C,B,D) = D ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s3_yellow18))
=> ? [B] :
( r2_hidden(B,k1_altcat_1(f1_s3_yellow18,A,A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s3_yellow18))
=> ! [D] :
( r2_hidden(D,k1_altcat_1(f1_s3_yellow18,C,A))
=> f2_s3_yellow18(C,A,A,D,B) = D ) ) ) ) )
=> v12_altcat_1(f1_s3_yellow18) ) ).
fof(s4_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s4_yellow18)
=> ! [B] :
( m1_subset_1(B,f1_s4_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s4_yellow18)
=> ! [D,E] :
( ( r2_hidden(D,f2_s4_yellow18(A,B))
& r2_hidden(E,f2_s4_yellow18(B,C)) )
=> r2_hidden(f3_s4_yellow18(A,B,C,D,E),f2_s4_yellow18(A,C)) ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s4_yellow18)
=> ! [B] :
( m1_subset_1(B,f1_s4_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s4_yellow18)
=> ! [D] :
( m1_subset_1(D,f1_s4_yellow18)
=> ! [E,F,G] :
( ( r2_hidden(E,f2_s4_yellow18(A,B))
& r2_hidden(F,f2_s4_yellow18(B,C))
& r2_hidden(G,f2_s4_yellow18(C,D)) )
=> f3_s4_yellow18(A,C,D,f3_s4_yellow18(A,B,C,E,F),G) = f3_s4_yellow18(A,B,D,E,f3_s4_yellow18(B,C,D,F,G)) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s4_yellow18)
=> ? [B] :
( r2_hidden(B,f2_s4_yellow18(A,A))
& ! [C] :
( m1_subset_1(C,f1_s4_yellow18)
=> ! [D] :
( r2_hidden(D,f2_s4_yellow18(A,C))
=> f3_s4_yellow18(A,A,C,B,D) = D ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s4_yellow18)
=> ? [B] :
( r2_hidden(B,f2_s4_yellow18(A,A))
& ! [C] :
( m1_subset_1(C,f1_s4_yellow18)
=> ! [D] :
( r2_hidden(D,f2_s4_yellow18(C,A))
=> f3_s4_yellow18(C,A,A,D,B) = D ) ) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& u1_struct_0(A) = f1_s4_yellow18
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_altcat_1(A,B,C) = f2_s4_yellow18(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,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,D) != k1_xboole_0
& ~ ! [E] :
( m1_subset_1(E,k1_altcat_1(A,B,C))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,C,D))
=> k5_altcat_1(A,B,C,D,E,F) = f3_s4_yellow18(B,C,D,E,F) ) ) ) ) ) ) ) ) ).
fof(s5_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& l2_altcat_1(B) )
=> ( ( u1_struct_0(A) = f1_s5_yellow18
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_altcat_1(A,C,D) = f2_s5_yellow18(C,D) ) )
& ! [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))
=> ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,E) != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k1_altcat_1(A,C,D))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,D,E))
=> k5_altcat_1(A,C,D,E,F,G) = f3_s5_yellow18(C,D,E,F,G) ) ) ) ) ) )
& u1_struct_0(B) = f1_s5_yellow18
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k1_altcat_1(B,C,D) = f2_s5_yellow18(C,D) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ~ ( k1_altcat_1(B,C,D) != k1_xboole_0
& k1_altcat_1(B,D,E) != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k1_altcat_1(B,C,D))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(B,D,E))
=> k5_altcat_1(B,C,D,E,F,G) = f3_s5_yellow18(C,D,E,F,G) ) ) ) ) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) ).
fof(s6_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s6_yellow18)
=> ! [B] :
( m1_subset_1(B,f1_s6_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s6_yellow18)
=> ! [D,E] :
( ( r2_hidden(D,f2_s6_yellow18(A,B))
& p1_s6_yellow18(A,B,D)
& r2_hidden(E,f2_s6_yellow18(B,C))
& p1_s6_yellow18(B,C,E) )
=> ( r2_hidden(f3_s6_yellow18(A,B,C,D,E),f2_s6_yellow18(A,C))
& p1_s6_yellow18(A,C,f3_s6_yellow18(A,B,C,D,E)) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s6_yellow18)
=> ! [B] :
( m1_subset_1(B,f1_s6_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s6_yellow18)
=> ! [D] :
( m1_subset_1(D,f1_s6_yellow18)
=> ! [E,F,G] :
( ( r2_hidden(E,f2_s6_yellow18(A,B))
& p1_s6_yellow18(A,B,E)
& r2_hidden(F,f2_s6_yellow18(B,C))
& p1_s6_yellow18(B,C,F)
& r2_hidden(G,f2_s6_yellow18(C,D))
& p1_s6_yellow18(C,D,G) )
=> f3_s6_yellow18(A,C,D,f3_s6_yellow18(A,B,C,E,F),G) = f3_s6_yellow18(A,B,D,E,f3_s6_yellow18(B,C,D,F,G)) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s6_yellow18)
=> ? [B] :
( r2_hidden(B,f2_s6_yellow18(A,A))
& p1_s6_yellow18(A,A,B)
& ! [C] :
( m1_subset_1(C,f1_s6_yellow18)
=> ! [D] :
( ( r2_hidden(D,f2_s6_yellow18(A,C))
& p1_s6_yellow18(A,C,D) )
=> f3_s6_yellow18(A,A,C,B,D) = D ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s6_yellow18)
=> ? [B] :
( r2_hidden(B,f2_s6_yellow18(A,A))
& p1_s6_yellow18(A,A,B)
& ! [C] :
( m1_subset_1(C,f1_s6_yellow18)
=> ! [D] :
( ( r2_hidden(D,f2_s6_yellow18(C,A))
& p1_s6_yellow18(C,A,D) )
=> f3_s6_yellow18(C,A,A,D,B) = D ) ) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& u1_struct_0(A) = f1_s6_yellow18
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( r2_hidden(D,k1_altcat_1(A,B,C))
<=> ( r2_hidden(D,f2_s6_yellow18(B,C))
& p1_s6_yellow18(B,C,D) ) ) ) )
& ! [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))
=> ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
& k1_altcat_1(A,C,D) != k1_xboole_0
& ~ ! [E] :
( m1_subset_1(E,k1_altcat_1(A,B,C))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,C,D))
=> k5_altcat_1(A,B,C,D,E,F) = f3_s6_yellow18(B,C,D,E,F) ) ) ) ) ) ) ) ) ).
fof(s7_yellow18,axiom,
( ( ? [A] :
( m1_subset_1(A,u1_struct_0(f1_s7_yellow18))
& p1_s7_yellow18(A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s7_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s7_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s7_yellow18))
=> ( ( p1_s7_yellow18(A)
& p1_s7_yellow18(B)
& p1_s7_yellow18(C) )
=> ( k1_altcat_1(f1_s7_yellow18,A,B) = k1_xboole_0
| k1_altcat_1(f1_s7_yellow18,B,C) = k1_xboole_0
| ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s7_yellow18,A,B))
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(f1_s7_yellow18,B,C))
=> ( ( p2_s7_yellow18(A,B,D)
& p2_s7_yellow18(B,C,E) )
=> p2_s7_yellow18(A,C,k5_altcat_1(f1_s7_yellow18,A,B,C,D,E)) ) ) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s7_yellow18))
=> ( p1_s7_yellow18(A)
=> p2_s7_yellow18(A,A,k8_altcat_1(f1_s7_yellow18,A)) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v3_altcat_2(A,f1_s7_yellow18)
& m1_altcat_2(A,f1_s7_yellow18)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s7_yellow18))
=> ( m1_subset_1(B,u1_struct_0(A))
<=> p1_s7_yellow18(B) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s7_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s7_yellow18))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( D = B
& E = C )
=> ( k1_altcat_1(f1_s7_yellow18,B,C) = k1_xboole_0
| ! [F] :
( m1_subset_1(F,k1_altcat_1(f1_s7_yellow18,B,C))
=> ( r2_hidden(F,k1_altcat_1(A,D,E))
<=> p2_s7_yellow18(B,C,F) ) ) ) ) ) ) ) ) ) ) ).
fof(s8_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s8_yellow18))
=> m1_subset_1(f3_s8_yellow18(A),u1_struct_0(f2_s8_yellow18)) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s8_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s8_yellow18))
=> ( k1_altcat_1(f1_s8_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s8_yellow18,A,B))
=> r2_hidden(f4_s8_yellow18(A,B,C),k1_binop_1(u1_altcat_1(f2_s8_yellow18),f3_s8_yellow18(A),f3_s8_yellow18(B))) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s8_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s8_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s8_yellow18))
=> ~ ( k1_altcat_1(f1_s8_yellow18,A,B) != k1_xboole_0
& k1_altcat_1(f1_s8_yellow18,B,C) != k1_xboole_0
& ? [D] :
( m1_subset_1(D,k1_altcat_1(f1_s8_yellow18,A,B))
& ? [E] :
( m1_subset_1(E,k1_altcat_1(f1_s8_yellow18,B,C))
& ? [F] :
( m1_subset_1(F,u1_struct_0(f2_s8_yellow18))
& ? [G] :
( m1_subset_1(G,u1_struct_0(f2_s8_yellow18))
& ? [H] :
( m1_subset_1(H,u1_struct_0(f2_s8_yellow18))
& F = f3_s8_yellow18(A)
& G = f3_s8_yellow18(B)
& H = f3_s8_yellow18(C)
& ? [I] :
( m1_subset_1(I,k1_altcat_1(f2_s8_yellow18,F,G))
& ? [J] :
( m1_subset_1(J,k1_altcat_1(f2_s8_yellow18,G,H))
& I = f4_s8_yellow18(A,B,D)
& J = f4_s8_yellow18(B,C,E)
& f4_s8_yellow18(A,C,k5_altcat_1(f1_s8_yellow18,A,B,C,D,E)) != k5_altcat_1(f2_s8_yellow18,F,G,H,I,J) ) ) ) ) ) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s8_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s8_yellow18))
=> ( B = f3_s8_yellow18(A)
=> f4_s8_yellow18(A,A,k8_altcat_1(f1_s8_yellow18,A)) = k8_altcat_1(f2_s8_yellow18,B) ) ) ) )
=> ? [A] :
( v9_functor0(A,f1_s8_yellow18,f2_s8_yellow18)
& v15_functor0(A,f1_s8_yellow18,f2_s8_yellow18)
& m2_functor0(A,f1_s8_yellow18,f2_s8_yellow18)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s8_yellow18))
=> k3_functor0(f1_s8_yellow18,f2_s8_yellow18,A,B) = f3_s8_yellow18(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s8_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s8_yellow18))
=> ( k1_altcat_1(f1_s8_yellow18,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s8_yellow18,B,C))
=> k6_functor0(f1_s8_yellow18,f2_s8_yellow18,A,B,C,D) = f4_s8_yellow18(B,C,D) ) ) ) ) ) ) ).
fof(s9_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s9_yellow18))
=> m1_subset_1(f3_s9_yellow18(A),u1_struct_0(f2_s9_yellow18)) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s9_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s9_yellow18))
=> ( k1_altcat_1(f1_s9_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s9_yellow18,A,B))
=> r2_hidden(f4_s9_yellow18(A,B,C),k1_binop_1(u1_altcat_1(f2_s9_yellow18),f3_s9_yellow18(B),f3_s9_yellow18(A))) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s9_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s9_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s9_yellow18))
=> ~ ( k1_altcat_1(f1_s9_yellow18,A,B) != k1_xboole_0
& k1_altcat_1(f1_s9_yellow18,B,C) != k1_xboole_0
& ? [D] :
( m1_subset_1(D,k1_altcat_1(f1_s9_yellow18,A,B))
& ? [E] :
( m1_subset_1(E,k1_altcat_1(f1_s9_yellow18,B,C))
& ? [F] :
( m1_subset_1(F,u1_struct_0(f2_s9_yellow18))
& ? [G] :
( m1_subset_1(G,u1_struct_0(f2_s9_yellow18))
& ? [H] :
( m1_subset_1(H,u1_struct_0(f2_s9_yellow18))
& F = f3_s9_yellow18(A)
& G = f3_s9_yellow18(B)
& H = f3_s9_yellow18(C)
& ? [I] :
( m1_subset_1(I,k1_altcat_1(f2_s9_yellow18,G,F))
& ? [J] :
( m1_subset_1(J,k1_altcat_1(f2_s9_yellow18,H,G))
& I = f4_s9_yellow18(A,B,D)
& J = f4_s9_yellow18(B,C,E)
& f4_s9_yellow18(A,C,k5_altcat_1(f1_s9_yellow18,A,B,C,D,E)) != k5_altcat_1(f2_s9_yellow18,H,G,F,J,I) ) ) ) ) ) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s9_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s9_yellow18))
=> ( B = f3_s9_yellow18(A)
=> f4_s9_yellow18(A,A,k8_altcat_1(f1_s9_yellow18,A)) = k8_altcat_1(f2_s9_yellow18,B) ) ) ) )
=> ? [A] :
( v9_functor0(A,f1_s9_yellow18,f2_s9_yellow18)
& v16_functor0(A,f1_s9_yellow18,f2_s9_yellow18)
& m2_functor0(A,f1_s9_yellow18,f2_s9_yellow18)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s9_yellow18))
=> k3_functor0(f1_s9_yellow18,f2_s9_yellow18,A,B) = f3_s9_yellow18(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s9_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s9_yellow18))
=> ( k1_altcat_1(f1_s9_yellow18,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s9_yellow18,B,C))
=> k8_functor0(f1_s9_yellow18,f2_s9_yellow18,A,B,C,D) = f4_s9_yellow18(B,C,D) ) ) ) ) ) ) ).
fof(s10_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s10_yellow18))
=> k3_functor0(f1_s10_yellow18,f2_s10_yellow18,f3_s10_yellow18,A) = f4_s10_yellow18(A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s10_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s10_yellow18))
=> ( k1_altcat_1(f1_s10_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s10_yellow18,A,B))
=> k6_functor0(f1_s10_yellow18,f2_s10_yellow18,f3_s10_yellow18,A,B,C) = f5_s10_yellow18(A,B,C) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s10_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s10_yellow18))
=> ( f4_s10_yellow18(A) = f4_s10_yellow18(B)
=> A = B ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s10_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s10_yellow18))
=> ( k1_altcat_1(f1_s10_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s10_yellow18,A,B))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s10_yellow18,A,B))
=> ( f5_s10_yellow18(A,B,C) = f5_s10_yellow18(A,B,D)
=> C = D ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s10_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s10_yellow18))
=> ( k1_altcat_1(f2_s10_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f2_s10_yellow18,A,B))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(f1_s10_yellow18))
& ? [E] :
( m1_subset_1(E,u1_struct_0(f1_s10_yellow18))
& ? [F] :
( m1_subset_1(F,k1_altcat_1(f1_s10_yellow18,D,E))
& A = f4_s10_yellow18(D)
& B = f4_s10_yellow18(E)
& k1_altcat_1(f1_s10_yellow18,D,E) != k1_xboole_0
& C = f5_s10_yellow18(D,E,F) ) ) ) ) ) ) ) )
=> v21_functor0(f3_s10_yellow18,f1_s10_yellow18,f2_s10_yellow18) ) ).
fof(s11_yellow18,axiom,
( ( ? [A] :
( v15_functor0(A,f1_s11_yellow18,f2_s11_yellow18)
& m2_functor0(A,f1_s11_yellow18,f2_s11_yellow18)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s11_yellow18))
=> k3_functor0(f1_s11_yellow18,f2_s11_yellow18,A,B) = f3_s11_yellow18(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s11_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s11_yellow18))
=> ( k1_altcat_1(f1_s11_yellow18,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s11_yellow18,B,C))
=> k6_functor0(f1_s11_yellow18,f2_s11_yellow18,A,B,C,D) = f4_s11_yellow18(B,C,D) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s11_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s11_yellow18))
=> ( f3_s11_yellow18(A) = f3_s11_yellow18(B)
=> A = B ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s11_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s11_yellow18))
=> ( k1_altcat_1(f1_s11_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s11_yellow18,A,B))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s11_yellow18,A,B))
=> ( f4_s11_yellow18(A,B,C) = f4_s11_yellow18(A,B,D)
=> C = D ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s11_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s11_yellow18))
=> ( k1_altcat_1(f2_s11_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f2_s11_yellow18,A,B))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(f1_s11_yellow18))
& ? [E] :
( m1_subset_1(E,u1_struct_0(f1_s11_yellow18))
& ? [F] :
( m1_subset_1(F,k1_altcat_1(f1_s11_yellow18,D,E))
& A = f3_s11_yellow18(D)
& B = f3_s11_yellow18(E)
& k1_altcat_1(f1_s11_yellow18,D,E) != k1_xboole_0
& C = f4_s11_yellow18(D,E,F) ) ) ) ) ) ) ) )
=> r1_functor0(f1_s11_yellow18,f2_s11_yellow18) ) ).
fof(s12_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s12_yellow18))
=> k3_functor0(f1_s12_yellow18,f2_s12_yellow18,f3_s12_yellow18,A) = f4_s12_yellow18(A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s12_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s12_yellow18))
=> ( k1_altcat_1(f1_s12_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s12_yellow18,A,B))
=> k8_functor0(f1_s12_yellow18,f2_s12_yellow18,f3_s12_yellow18,A,B,C) = f5_s12_yellow18(A,B,C) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s12_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s12_yellow18))
=> ( f4_s12_yellow18(A) = f4_s12_yellow18(B)
=> A = B ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s12_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s12_yellow18))
=> ( k1_altcat_1(f1_s12_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s12_yellow18,A,B))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s12_yellow18,A,B))
=> ( f5_s12_yellow18(A,B,C) = f5_s12_yellow18(A,B,D)
=> C = D ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s12_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s12_yellow18))
=> ( k1_altcat_1(f2_s12_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f2_s12_yellow18,A,B))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(f1_s12_yellow18))
& ? [E] :
( m1_subset_1(E,u1_struct_0(f1_s12_yellow18))
& ? [F] :
( m1_subset_1(F,k1_altcat_1(f1_s12_yellow18,D,E))
& B = f4_s12_yellow18(D)
& A = f4_s12_yellow18(E)
& k1_altcat_1(f1_s12_yellow18,D,E) != k1_xboole_0
& C = f5_s12_yellow18(D,E,F) ) ) ) ) ) ) ) )
=> v21_functor0(f3_s12_yellow18,f1_s12_yellow18,f2_s12_yellow18) ) ).
fof(s13_yellow18,axiom,
( ( ? [A] :
( v16_functor0(A,f1_s13_yellow18,f2_s13_yellow18)
& m2_functor0(A,f1_s13_yellow18,f2_s13_yellow18)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s13_yellow18))
=> k3_functor0(f1_s13_yellow18,f2_s13_yellow18,A,B) = f3_s13_yellow18(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s13_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s13_yellow18))
=> ( k1_altcat_1(f1_s13_yellow18,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s13_yellow18,B,C))
=> k8_functor0(f1_s13_yellow18,f2_s13_yellow18,A,B,C,D) = f4_s13_yellow18(B,C,D) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s13_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s13_yellow18))
=> ( f3_s13_yellow18(A) = f3_s13_yellow18(B)
=> A = B ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s13_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s13_yellow18))
=> ( k1_altcat_1(f1_s13_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s13_yellow18,A,B))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s13_yellow18,A,B))
=> ( f4_s13_yellow18(A,B,C) = f4_s13_yellow18(A,B,D)
=> C = D ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s13_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s13_yellow18))
=> ( k1_altcat_1(f2_s13_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f2_s13_yellow18,A,B))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(f1_s13_yellow18))
& ? [E] :
( m1_subset_1(E,u1_struct_0(f1_s13_yellow18))
& ? [F] :
( m1_subset_1(F,k1_altcat_1(f1_s13_yellow18,D,E))
& B = f3_s13_yellow18(D)
& A = f3_s13_yellow18(E)
& k1_altcat_1(f1_s13_yellow18,D,E) != k1_xboole_0
& C = f4_s13_yellow18(D,E,F) ) ) ) ) ) ) ) )
=> r2_functor0(f1_s13_yellow18,f2_s13_yellow18) ) ).
fof(s14_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s14_yellow18))
=> r2_hidden(f5_s14_yellow18(A),k1_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,A))) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s14_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s14_yellow18))
=> ( k1_altcat_1(f1_s14_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s14_yellow18,A,B))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,A)))
=> ( D = f5_s14_yellow18(A)
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,B),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,B)))
=> ( E = f5_s14_yellow18(B)
=> k5_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,B),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,B),k6_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A,B,C),E) = k5_altcat_1(f2_s14_yellow18,k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,A),k3_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,B),D,k6_functor0(f1_s14_yellow18,f2_s14_yellow18,f4_s14_yellow18,A,B,C)) ) ) ) ) ) ) ) ) )
=> ? [A] :
( m2_functor2(A,f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,f4_s14_yellow18)
& r2_functor2(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,f4_s14_yellow18)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s14_yellow18))
=> k2_functor2(f1_s14_yellow18,f2_s14_yellow18,f3_s14_yellow18,f4_s14_yellow18,A,B) = f5_s14_yellow18(B) ) ) ) ).
fof(s15_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s15_yellow18))
=> ( r2_hidden(f5_s15_yellow18(A),k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A)))
& k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A)) != k1_xboole_0
& ! [B] :
( m1_subset_1(B,k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A)))
=> ( B = f5_s15_yellow18(A)
=> v3_altcat_3(B,f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A)) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s15_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s15_yellow18))
=> ( k1_altcat_1(f1_s15_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s15_yellow18,A,B))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A)))
=> ( D = f5_s15_yellow18(A)
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,B),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,B)))
=> ( E = f5_s15_yellow18(B)
=> k5_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,B),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,B),k6_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A,B,C),E) = k5_altcat_1(f2_s15_yellow18,k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A),k3_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,B),D,k6_functor0(f1_s15_yellow18,f2_s15_yellow18,f4_s15_yellow18,A,B,C)) ) ) ) ) ) ) ) ) )
=> ? [A] :
( m1_functor3(A,f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,f4_s15_yellow18)
& r1_functor3(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,f4_s15_yellow18)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s15_yellow18))
=> k2_functor2(f1_s15_yellow18,f2_s15_yellow18,f3_s15_yellow18,f4_s15_yellow18,A,B) = f5_s15_yellow18(B) ) ) ) ).
fof(s16_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s16_yellow18)
=> ! [B] :
( m1_subset_1(B,f1_s16_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s16_yellow18)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( ( r2_hidden(D,f2_s16_yellow18(A,B))
& r2_hidden(E,f2_s16_yellow18(B,C)) )
=> r2_hidden(k5_relat_1(D,E),f2_s16_yellow18(A,C)) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s16_yellow18)
=> ! [B] :
( m1_subset_1(B,f1_s16_yellow18)
=> r1_tarski(f2_s16_yellow18(A,B),k1_funct_2(f3_s16_yellow18(A),f3_s16_yellow18(B))) ) )
& ! [A] :
( m1_subset_1(A,f1_s16_yellow18)
=> r2_hidden(k6_partfun1(f3_s16_yellow18(A)),f2_s16_yellow18(A,A)) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v4_yellow18(A)
& l2_altcat_1(A)
& u1_struct_0(A) = f1_s16_yellow18
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_yellow18(A,B) = f3_s16_yellow18(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_altcat_1(A,B,C) = f2_s16_yellow18(B,C) ) ) ) ) ).
fof(s17_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s17_yellow18)
=> ! [B] :
( m1_subset_1(B,f1_s17_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s17_yellow18)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( ( p1_s17_yellow18(A,B,D)
& p1_s17_yellow18(B,C,E) )
=> p1_s17_yellow18(A,C,k5_relat_1(D,E)) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s17_yellow18)
=> p1_s17_yellow18(A,A,k6_partfun1(f2_s17_yellow18(A))) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v4_yellow18(A)
& l2_altcat_1(A)
& u1_struct_0(A) = f1_s17_yellow18
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_yellow18(A,B) = f2_s17_yellow18(B) )
& ! [B] :
( m1_subset_1(B,f1_s17_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s17_yellow18)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r2_hidden(D,k1_binop_1(u1_altcat_1(A),B,C))
<=> ( r2_hidden(D,k1_funct_2(f2_s17_yellow18(B),f2_s17_yellow18(C)))
& p1_s17_yellow18(B,C,D) ) ) ) ) ) ) ) ).
fof(s18_yellow18,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s18_yellow18)
=> ! [B] :
( m1_subset_1(B,f1_s18_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s18_yellow18)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( ( p2_s18_yellow18(A,B,D)
& p2_s18_yellow18(B,C,E) )
=> p2_s18_yellow18(A,C,k5_relat_1(D,E)) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s18_yellow18)
=> ! [B] :
( ! [C] :
( r2_hidden(C,B)
<=> ( r2_hidden(C,f2_s18_yellow18(A))
& p1_s18_yellow18(A,C) ) )
=> p2_s18_yellow18(A,A,k6_partfun1(B)) ) ) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v4_yellow18(A)
& l2_altcat_1(A)
& u1_struct_0(A) = f1_s18_yellow18
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r2_hidden(C,k3_yellow18(A,B))
<=> ( r2_hidden(C,f2_s18_yellow18(B))
& p1_s18_yellow18(B,C) ) ) )
& ! [B] :
( m1_subset_1(B,f1_s18_yellow18)
=> ! [C] :
( m1_subset_1(C,f1_s18_yellow18)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r2_hidden(D,k1_binop_1(u1_altcat_1(A),B,C))
<=> ( r2_hidden(D,k1_funct_2(k3_yellow18(A,B),k3_yellow18(A,C)))
& p2_s18_yellow18(B,C,D) ) ) ) ) ) ) ) ).
fof(s19_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v2_yellow18(B)
& l2_altcat_1(B) )
=> ( ( u1_struct_0(A) = f1_s19_yellow18
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_altcat_1(A,C,D) = f2_s19_yellow18(C,D) ) )
& u1_struct_0(B) = f1_s19_yellow18
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k1_altcat_1(B,C,D) = f2_s19_yellow18(C,D) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) ).
fof(s20_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v2_yellow18(B)
& l2_altcat_1(B) )
=> ( ( u1_struct_0(A) = f1_s20_yellow18
& ! [C] :
( m1_subset_1(C,f1_s20_yellow18)
=> ! [D] :
( m1_subset_1(D,f1_s20_yellow18)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(A),C,D))
<=> ( r2_hidden(E,k1_funct_2(f2_s20_yellow18(C),f2_s20_yellow18(D)))
& p1_s20_yellow18(C,D,E) ) ) ) ) )
& u1_struct_0(B) = f1_s20_yellow18
& ! [C] :
( m1_subset_1(C,f1_s20_yellow18)
=> ! [D] :
( m1_subset_1(D,f1_s20_yellow18)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
<=> ( r2_hidden(E,k1_funct_2(f2_s20_yellow18(C),f2_s20_yellow18(D)))
& p1_s20_yellow18(C,D,E) ) ) ) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) ).
fof(s21_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v2_yellow18(B)
& l2_altcat_1(B) )
=> ( ( u1_struct_0(A) = f1_s21_yellow18
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( r2_hidden(D,k3_yellow18(A,C))
<=> ( r2_hidden(D,f2_s21_yellow18(C))
& p1_s21_yellow18(C,D) ) ) )
& ! [C] :
( m1_subset_1(C,f1_s21_yellow18)
=> ! [D] :
( m1_subset_1(D,f1_s21_yellow18)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(A),C,D))
<=> ( r2_hidden(E,k1_funct_2(k3_yellow18(A,C),k3_yellow18(A,D)))
& p2_s21_yellow18(C,D,E) ) ) ) ) )
& u1_struct_0(B) = f1_s21_yellow18
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( r2_hidden(D,k3_yellow18(B,C))
<=> ( r2_hidden(D,f2_s21_yellow18(C))
& p1_s21_yellow18(C,D) ) ) )
& ! [C] :
( m1_subset_1(C,f1_s21_yellow18)
=> ! [D] :
( m1_subset_1(D,f1_s21_yellow18)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
<=> ( r2_hidden(E,k1_funct_2(k3_yellow18(B,C),k3_yellow18(B,D)))
& p2_s21_yellow18(C,D,E) ) ) ) ) ) )
=> g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) ).
fof(s22_yellow18,axiom,
( ( ? [A] :
( v15_functor0(A,f1_s22_yellow18,f2_s22_yellow18)
& m2_functor0(A,f1_s22_yellow18,f2_s22_yellow18)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s22_yellow18))
=> k3_functor0(f1_s22_yellow18,f2_s22_yellow18,A,B) = f3_s22_yellow18(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s22_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f1_s22_yellow18))
=> ( k1_altcat_1(f1_s22_yellow18,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f1_s22_yellow18,B,C))
=> k6_functor0(f1_s22_yellow18,f2_s22_yellow18,A,B,C,D) = f5_s22_yellow18(B,C,D) ) ) ) ) )
& ? [A] :
( v15_functor0(A,f2_s22_yellow18,f1_s22_yellow18)
& m2_functor0(A,f2_s22_yellow18,f1_s22_yellow18)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s22_yellow18))
=> k3_functor0(f2_s22_yellow18,f1_s22_yellow18,A,B) = f4_s22_yellow18(B) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s22_yellow18))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f2_s22_yellow18))
=> ( k1_altcat_1(f2_s22_yellow18,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(f2_s22_yellow18,B,C))
=> k6_functor0(f2_s22_yellow18,f1_s22_yellow18,A,B,C,D) = f6_s22_yellow18(B,C,D) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s22_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s22_yellow18))
=> ( A = f4_s22_yellow18(f3_s22_yellow18(B))
=> ( r2_hidden(f7_s22_yellow18(B),k1_altcat_1(f1_s22_yellow18,A,B))
& r2_hidden(k2_funct_1(f7_s22_yellow18(B)),k1_altcat_1(f1_s22_yellow18,B,A))
& v2_funct_1(f7_s22_yellow18(B)) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s22_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s22_yellow18))
=> ( B = f3_s22_yellow18(f4_s22_yellow18(A))
=> ( r2_hidden(f8_s22_yellow18(A),k1_altcat_1(f2_s22_yellow18,A,B))
& r2_hidden(k2_funct_1(f8_s22_yellow18(A)),k1_altcat_1(f2_s22_yellow18,B,A))
& v2_funct_1(f8_s22_yellow18(A)) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s22_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s22_yellow18))
=> ( k1_altcat_1(f1_s22_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f1_s22_yellow18,A,B))
=> k5_relat_1(f6_s22_yellow18(f3_s22_yellow18(A),f3_s22_yellow18(B),f5_s22_yellow18(A,B,C)),f7_s22_yellow18(B)) = k5_relat_1(f7_s22_yellow18(A),C) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s22_yellow18))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s22_yellow18))
=> ( k1_altcat_1(f2_s22_yellow18,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,k1_altcat_1(f2_s22_yellow18,A,B))
=> k5_relat_1(f8_s22_yellow18(A),f5_s22_yellow18(f4_s22_yellow18(A),f4_s22_yellow18(B),f6_s22_yellow18(A,B,C))) = k5_relat_1(C,f8_s22_yellow18(B)) ) ) ) ) )
=> r1_yellow18(f1_s22_yellow18,f2_s22_yellow18) ) ).
fof(s23_yellow18,axiom,
( ! [A,B] :
~ ( r2_hidden(A,f1_s23_yellow18)
& r2_hidden(B,k1_funct_1(f2_s23_yellow18,A))
& ! [C] :
~ ( r2_hidden(C,k1_funct_1(f3_s23_yellow18,A))
& p1_s23_yellow18(A,B,C) ) )
=> ? [A] :
( m3_pboole(A,f1_s23_yellow18,f2_s23_yellow18,f3_s23_yellow18)
& ! [B,C] :
( ( r2_hidden(B,f1_s23_yellow18)
& r2_hidden(C,k1_funct_1(f2_s23_yellow18,B)) )
=> ( r2_hidden(k1_funct_1(k1_funct_1(A,B),C),k1_funct_1(f3_s23_yellow18,B))
& p1_s23_yellow18(B,C,k1_funct_1(k1_funct_1(A,B),C)) ) ) ) ) ).
fof(redefinition_v1_yellow18,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C) )
=> ( v1_yellow18(D,A,B,C)
<=> v2_funct_1(D) ) ) ).
fof(symmetry_r1_yellow18,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) )
=> ( r1_yellow18(A,B)
=> r1_yellow18(B,A) ) ) ).
fof(reflexivity_r1_yellow18,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) )
=> r1_yellow18(A,A) ) ).
fof(symmetry_r2_yellow18,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ( r2_yellow18(A,B)
=> r2_yellow18(B,A) ) ) ).
fof(symmetry_r3_yellow18,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) )
=> ( r3_yellow18(A,B)
=> r3_yellow18(B,A) ) ) ).
fof(dt_k1_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ( ~ v3_struct_0(k1_yellow18(A))
& v2_altcat_1(k1_yellow18(A))
& v6_altcat_1(k1_yellow18(A))
& l2_altcat_1(k1_yellow18(A)) ) ) ).
fof(dt_k2_yellow18,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) )
=> ( v9_functor0(k2_yellow18(A,B),A,B)
& v16_functor0(k2_yellow18(A,B),A,B)
& m2_functor0(k2_yellow18(A,B),A,B) ) ) ).
fof(dt_k3_yellow18,axiom,
$true ).
fof(dt_k4_yellow18,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_yellow18(A))
& v2_altcat_1(k4_yellow18(A))
& v6_altcat_1(k4_yellow18(A))
& v11_altcat_1(k4_yellow18(A))
& v12_altcat_1(k4_yellow18(A))
& v4_yellow18(k4_yellow18(A))
& l2_altcat_1(k4_yellow18(A)) ) ) ).
fof(dt_k5_yellow18,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v9_functor0(k5_yellow18(A),A,k4_yellow18(A))
& v15_functor0(k5_yellow18(A),A,k4_yellow18(A))
& m2_functor0(k5_yellow18(A),A,k4_yellow18(A)) ) ) ).
%------------------------------------------------------------------------------