SET007 Axioms: SET007+697.ax
%------------------------------------------------------------------------------
% File : SET007+697 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Miscellaneous Facts about Functors
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : yellow20 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 79 ( 0 unt; 0 def)
% Number of atoms : 1240 ( 148 equ)
% Maximal formula atoms : 46 ( 15 avg)
% Number of connectives : 1318 ( 157 ~; 9 |; 676 &)
% ( 22 <=>; 454 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 15 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 52 ( 51 usr; 0 prp; 1-5 aty)
% Number of functors : 59 ( 59 usr; 18 con; 0-6 aty)
% Number of variables : 423 ( 403 !; 20 ?)
% 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_yellow20,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ( v1_relat_1(k1_binop_1(A,B,C))
& v1_funct_1(k1_binop_1(A,B,C)) ) ) ).
fof(fc2_yellow20,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)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ( v6_functor0(k10_functor0(A,B),B,A)
& v8_functor0(k10_functor0(A,B),B,A)
& v9_functor0(k10_functor0(A,B),B,A)
& v10_functor0(k10_functor0(A,B),B,A)
& v12_functor0(k10_functor0(A,B),B,A)
& v13_functor0(k10_functor0(A,B),B,A) ) ) ).
fof(fc3_yellow20,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)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ( v6_functor0(k10_functor0(A,B),B,A)
& v8_functor0(k10_functor0(A,B),B,A)
& v9_functor0(k10_functor0(A,B),B,A)
& v10_functor0(k10_functor0(A,B),B,A)
& v12_functor0(k10_functor0(A,B),B,A)
& v13_functor0(k10_functor0(A,B),B,A) ) ) ).
fof(t1_yellow20,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] :
( ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( ( v7_functor0(C,A,B)
& v21_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( k3_functor0(A,B,C,D) = E
<=> k3_functor0(B,A,k15_functor0(A,B,C),E) = D ) ) ) ) ) ) ) ).
fof(t2_yellow20,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] :
( ( v8_functor0(C,A,B)
& v10_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ! [D] :
( ( v8_functor0(D,B,A)
& v10_functor0(D,B,A)
& l2_functor0(D,B,A) )
=> ( ( v21_functor0(C,A,B)
& D = k15_functor0(A,B,C) )
=> ! [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))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F)))
=> ( k6_functor0(A,B,C,E,F,G) = H
<=> k6_functor0(B,A,D,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),H) = G ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_yellow20,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] :
( ( v8_functor0(C,A,B)
& v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ! [D] :
( ( v8_functor0(D,B,A)
& v11_functor0(D,B,A)
& l2_functor0(D,B,A) )
=> ( ( v21_functor0(C,A,B)
& D = k15_functor0(A,B,C) )
=> ! [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))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E)))
=> ( k8_functor0(A,B,C,E,F,G) = H
<=> k8_functor0(B,A,D,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E),H) = G ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_yellow20,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] :
( m2_functor0(C,A,B)
=> ( v21_functor0(C,A,B)
=> ! [D] :
( m2_functor0(D,B,A)
=> ( k13_functor0(B,A,B,D,C) = k12_functor0(B)
=> g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) ).
fof(t5_yellow20,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] :
( m2_functor0(C,A,B)
=> ( v21_functor0(C,A,B)
=> ! [D] :
( m2_functor0(D,B,A)
=> ( k13_functor0(A,B,A,C,D) = k12_functor0(A)
=> g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) ).
fof(t6_yellow20,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) )
=> ( v21_functor0(C,A,B)
=> ! [D] :
( ( v15_functor0(D,B,A)
& m2_functor0(D,B,A) )
=> ( ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k3_functor0(A,B,C,k3_functor0(B,A,D,E)) = E )
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( k1_altcat_1(B,E,F) != k1_xboole_0
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(B,E,F))
=> k6_functor0(A,B,C,k3_functor0(B,A,D,E),k3_functor0(B,A,D,F),k6_functor0(B,A,D,E,F,G)) = G ) ) ) ) )
=> g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) ).
fof(t7_yellow20,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) )
=> ( v21_functor0(C,A,B)
=> ! [D] :
( ( v16_functor0(D,B,A)
& m2_functor0(D,B,A) )
=> ( ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k3_functor0(A,B,C,k3_functor0(B,A,D,E)) = E )
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( k1_altcat_1(B,E,F) != k1_xboole_0
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(B,E,F))
=> k8_functor0(A,B,C,k3_functor0(B,A,D,F),k3_functor0(B,A,D,E),k8_functor0(B,A,D,E,F,G)) = G ) ) ) ) )
=> g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) ).
fof(t8_yellow20,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) )
=> ( v21_functor0(C,A,B)
=> ! [D] :
( ( v15_functor0(D,B,A)
& m2_functor0(D,B,A) )
=> ( ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k3_functor0(B,A,D,k3_functor0(A,B,C,E)) = 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(B,A,D,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),k6_functor0(A,B,C,E,F,G)) = G ) ) ) ) )
=> g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) ).
fof(t9_yellow20,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) )
=> ( v21_functor0(C,A,B)
=> ! [D] :
( ( v16_functor0(D,B,A)
& m2_functor0(D,B,A) )
=> ( ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k3_functor0(B,A,D,k3_functor0(A,B,C,E)) = 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(B,A,D,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E),k8_functor0(A,B,C,E,F,G)) = G ) ) ) ) )
=> g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) ).
fof(d1_yellow20,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( l2_altcat_1(B)
=> ( r1_yellow20(A,B)
<=> ! [C,D,E] : r1_partfun1(k1_funct_1(u2_altcat_1(A),k3_mcart_1(C,D,E)),k1_funct_1(u2_altcat_1(B),k3_mcart_1(C,D,E))) ) ) ) ).
fof(t10_yellow20,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( l2_altcat_1(B)
=> ( r1_yellow20(A,B)
<=> ! [C,D,E,F] :
( ( r2_hidden(F,k1_relat_1(k1_funct_1(u2_altcat_1(A),k3_mcart_1(C,D,E))))
& r2_hidden(F,k1_relat_1(k1_funct_1(u2_altcat_1(B),k3_mcart_1(C,D,E)))) )
=> k1_funct_1(k1_funct_1(u2_altcat_1(A),k3_mcart_1(C,D,E)),F) = k1_funct_1(k1_funct_1(u2_altcat_1(B),k3_mcart_1(C,D,E)),F) ) ) ) ) ).
fof(t11_yellow20,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) )
=> ( r1_yellow20(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(A))
=> ~ ( k1_altcat_1(A,C,D) != k1_xboole_0
& k1_altcat_1(A,D,E) != k1_xboole_0
& ? [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))
& k1_altcat_1(B,F,G) != k1_xboole_0
& k1_altcat_1(B,G,H) != k1_xboole_0
& F = C
& G = D
& H = E
& ? [I] :
( m1_subset_1(I,k1_altcat_1(A,C,D))
& ? [J] :
( m1_subset_1(J,k1_altcat_1(B,F,G))
& J = I
& ? [K] :
( m1_subset_1(K,k1_altcat_1(A,D,E))
& ? [L] :
( m1_subset_1(L,k1_altcat_1(B,G,H))
& L = K
& k5_altcat_1(A,C,D,E,I,K) != k5_altcat_1(B,F,G,H,J,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_yellow20,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) )
=> r1_yellow20(A,B) ) ) ).
fof(d2_yellow20,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( C = k1_yellow20(A,B)
<=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
& ! [D] :
( r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))
=> k1_funct_1(C,D) = k3_xboole_0(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ).
fof(t13_yellow20,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> k1_yellow20(B,C) = k3_pboole(A,B,C) ) ) ).
fof(t14_yellow20,axiom,
! [A,B,C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,B)
=> m1_pboole(k1_yellow20(C,D),k3_xboole_0(A,B)) ) ) ).
fof(t15_yellow20,axiom,
! [A,B,C] :
( m1_pboole(C,A)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( m1_pboole(E,B)
=> ( E = k1_yellow20(C,D)
=> r2_altcat_2(B,A,E,C) ) ) ) ) ).
fof(t16_yellow20,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,C,D)
& m2_relset_1(F,C,D) )
=> ( r1_partfun1(E,F)
=> ( v1_funct_1(k3_xboole_0(E,F))
& v1_funct_2(k3_xboole_0(E,F),k3_xboole_0(A,C),k3_xboole_0(B,D))
& m2_relset_1(k3_xboole_0(E,F),k3_xboole_0(A,C),k3_xboole_0(B,D)) ) ) ) ) ).
fof(t17_yellow20,axiom,
! [A,B,C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,B)
=> ! [F] :
( m1_pboole(F,B)
=> ! [G] :
( m1_pboole(G,k3_xboole_0(A,B))
=> ! [H] :
( m1_pboole(H,k3_xboole_0(A,B))
=> ( ( G = k1_yellow20(C,E)
& H = k1_yellow20(D,F) )
=> ! [I] :
( m3_pboole(I,A,C,D)
=> ! [J] :
( m3_pboole(J,B,E,F)
=> ( ! [K] :
( ( r2_hidden(K,k1_relat_1(I))
& r2_hidden(K,k1_relat_1(J)) )
=> r1_partfun1(k1_funct_1(I,K),k1_funct_1(J,K)) )
=> m3_pboole(k1_yellow20(I,J),k3_xboole_0(A,B),G,H) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_yellow20,axiom,
! [A,B,C] :
( m1_pboole(C,k2_zfmisc_1(A,A))
=> ! [D] :
( m1_pboole(D,k2_zfmisc_1(B,B))
=> ? [E] :
( m1_pboole(E,k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(A,B)))
& E = k1_yellow20(C,D)
& k1_yellow20(k2_altcat_1(A,C),k2_altcat_1(B,D)) = k2_altcat_1(k3_xboole_0(A,B),E) ) ) ) ).
fof(t19_yellow20,axiom,
! [A,B,C] :
( m1_pboole(C,k2_zfmisc_1(A,A))
=> ! [D] :
( m1_pboole(D,k2_zfmisc_1(A,A))
=> ! [E] :
( m1_pboole(E,k2_zfmisc_1(B,B))
=> ! [F] :
( m1_pboole(F,k2_zfmisc_1(B,B))
=> ? [G] :
( m1_pboole(G,k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(A,B)))
& ? [H] :
( m1_pboole(H,k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(A,B)))
& G = k1_yellow20(C,E)
& H = k1_yellow20(D,F)
& k1_yellow20(k3_altcat_1(A,C,D),k3_altcat_1(B,E,F)) = k3_altcat_1(k3_xboole_0(A,B),G,H) ) ) ) ) ) ) ).
fof(d3_yellow20,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( l2_altcat_1(B)
=> ( r1_yellow20(A,B)
=> ! [C] :
( ( v6_altcat_1(C)
& l2_altcat_1(C) )
=> ( C = k2_yellow20(A,B)
<=> ( u1_struct_0(C) = k3_xboole_0(u1_struct_0(A),u1_struct_0(B))
& u1_altcat_1(C) = k1_yellow20(u1_altcat_1(A),u1_altcat_1(B))
& u2_altcat_1(C) = k1_yellow20(u2_altcat_1(A),u2_altcat_1(B)) ) ) ) ) ) ) ).
fof(t20_yellow20,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( l2_altcat_1(B)
=> ( r1_yellow20(A,B)
=> k2_yellow20(A,B) = k2_yellow20(B,A) ) ) ) ).
fof(t21_yellow20,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( l2_altcat_1(B)
=> ( r1_yellow20(A,B)
=> m1_altcat_2(k2_yellow20(A,B),A) ) ) ) ).
fof(t22_yellow20,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( l2_altcat_1(B)
=> ( r1_yellow20(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))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_yellow20(A,B)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_yellow20(A,B)))
=> ( ( G = C
& G = E
& H = D
& H = F )
=> k1_altcat_1(k2_yellow20(A,B),G,H) = k3_xboole_0(k1_altcat_1(A,C,D),k1_altcat_1(B,E,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_yellow20,axiom,
! [A] :
( ( v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( v2_altcat_1(B)
& l2_altcat_1(B) )
=> ( r1_yellow20(A,B)
=> v2_altcat_1(k2_yellow20(A,B)) ) ) ) ).
fof(t24_yellow20,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( l2_altcat_1(B)
=> ( r1_yellow20(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))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_yellow20(A,B)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_yellow20(A,B)))
=> ( ( G = C
& G = E
& H = D
& H = F )
=> ( k1_altcat_1(A,C,D) = k1_xboole_0
| k1_altcat_1(B,E,F) = k1_xboole_0
| ! [I] :
( m1_subset_1(I,k1_altcat_1(A,C,D))
=> ! [J] :
( m1_subset_1(J,k1_altcat_1(B,E,F))
=> ( I = J
=> r2_hidden(I,k1_altcat_1(k2_yellow20(A,B),G,H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ( r1_yellow20(A,B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_yellow20(A,B)))
=> ( ( E = C
& E = D
& k8_altcat_1(A,C) = k8_altcat_1(B,D) )
=> r2_hidden(k8_altcat_1(A,C),k1_altcat_1(k2_yellow20(A,B),E,E)) ) ) ) ) ) ) ) ).
fof(t26_yellow20,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_yellow20(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) ) ) ) )
=> ( v3_struct_0(k2_yellow20(A,B))
| ( v2_altcat_1(k2_yellow20(A,B))
& v3_altcat_2(k2_yellow20(A,B),A)
& m1_altcat_2(k2_yellow20(A,B),A) ) ) ) ) ) ).
fof(t27_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_altcat_2(B,A) )
=> ( v2_altcat_2(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( E = C
& F = D )
=> k1_altcat_1(B,E,F) = k1_altcat_1(A,C,D) ) ) ) ) ) ) ) ) ).
fof(t28_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( k1_altcat_1(B,C,D) != k1_xboole_0
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(B,C,D))
=> k6_functor0(B,A,k10_functor0(A,B),C,D,E) = E ) ) ) ) ) ) ).
fof(t29_yellow20,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)
& v3_altcat_2(C,A)
& m1_altcat_2(C,A) )
=> ! [D] :
( l2_functor0(D,A,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ( F = E
=> k3_functor0(C,B,k14_functor0(A,B,C,D),F) = k3_functor0(A,B,D,E) ) ) ) ) ) ) ) ).
fof(t30_yellow20,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)
& v3_altcat_2(C,A)
& m1_altcat_2(C,A) )
=> ! [D] :
( ( v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ( ( G = E
& H = F )
=> ( k1_altcat_1(C,G,H) = k1_xboole_0
| ! [I] :
( m1_subset_1(I,k1_altcat_1(A,E,F))
=> ! [J] :
( m1_subset_1(J,k1_altcat_1(C,G,H))
=> ( J = I
=> k6_functor0(C,B,k4_yellow20(A,B,C,D),G,H,J) = k6_functor0(A,B,D,E,F,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_yellow20,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)
& v3_altcat_2(C,A)
& m1_altcat_2(C,A) )
=> ! [D] :
( ( v16_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ( ( G = E
& H = F )
=> ( k1_altcat_1(C,G,H) = k1_xboole_0
| ! [I] :
( m1_subset_1(I,k1_altcat_1(A,E,F))
=> ! [J] :
( m1_subset_1(J,k1_altcat_1(C,G,H))
=> ( J = I
=> k8_functor0(C,B,k5_yellow20(A,B,C,D),G,H,J) = k8_functor0(A,B,D,E,F,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ( ( v10_functor0(C,A,B)
& v4_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k3_functor0(A,B,C,D) = k3_functor0(A,B,C,E)
=> D = E ) ) ) ) ) ) ) ).
fof(t33_yellow20,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] :
( ( v8_functor0(C,A,B)
& v10_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v17_functor0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k1_altcat_1(A,D,E) != k1_xboole_0
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,D,E))
=> ( k6_functor0(A,B,C,D,E,F) = k6_functor0(A,B,C,D,E,G)
=> F = G ) ) ) ) ) ) ) ) ) ) ).
fof(t34_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( v10_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v20_functor0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( k1_altcat_1(B,D,E) != k1_xboole_0
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(B,D,E))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& ? [I] :
( m1_subset_1(I,k1_altcat_1(A,G,H))
& D = k3_functor0(A,B,C,G)
& E = k3_functor0(A,B,C,H)
& k1_altcat_1(A,G,H) != k1_xboole_0
& F = k6_functor0(A,B,C,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ( ( v11_functor0(C,A,B)
& v4_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k3_functor0(A,B,C,D) = k3_functor0(A,B,C,E)
=> D = E ) ) ) ) ) ) ) ).
fof(t36_yellow20,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] :
( ( v8_functor0(C,A,B)
& v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v17_functor0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k1_altcat_1(A,D,E) != k1_xboole_0
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,D,E))
=> ( k8_functor0(A,B,C,D,E,F) = k8_functor0(A,B,C,D,E,G)
=> F = G ) ) ) ) ) ) ) ) ) ) ).
fof(t37_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v20_functor0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( k1_altcat_1(B,D,E) != k1_xboole_0
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(B,D,E))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& ? [I] :
( m1_subset_1(I,k1_altcat_1(A,G,H))
& E = k3_functor0(A,B,C,G)
& D = k3_functor0(A,B,C,H)
& k1_altcat_1(A,G,H) != k1_xboole_0
& F = k8_functor0(A,B,C,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_yellow20,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] :
( l2_functor0(C,A,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_altcat_1(D)
& v11_altcat_1(D)
& v12_altcat_1(D)
& l2_altcat_1(D) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v2_altcat_1(E)
& v11_altcat_1(E)
& v12_altcat_1(E)
& l2_altcat_1(E) )
=> ( r2_yellow20(A,B,C,D,E)
<=> ( v2_altcat_1(D)
& v3_altcat_2(D,A)
& m1_altcat_2(D,A)
& v2_altcat_1(E)
& v3_altcat_2(E,B)
& m1_altcat_2(E,B)
& ? [F] :
( v15_functor0(F,D,E)
& m2_functor0(F,D,E)
& v21_functor0(F,D,E)
& ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( G = H
=> k3_functor0(D,E,F,G) = k3_functor0(A,B,C,H) ) ) )
& ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(D))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( ( G = I
& H = J )
=> ( k1_altcat_1(D,G,H) = k1_xboole_0
| ! [K] :
( m1_subset_1(K,k1_altcat_1(D,G,H))
=> ! [L] :
( m1_subset_1(L,k1_altcat_1(A,I,J))
=> ( K = L
=> k6_functor0(D,E,F,G,H,K) = k1_funct_1(k4_functor0(A,B,C,I,J),L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_yellow20,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] :
( l2_functor0(C,A,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_altcat_1(D)
& v11_altcat_1(D)
& v12_altcat_1(D)
& l2_altcat_1(D) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v2_altcat_1(E)
& v11_altcat_1(E)
& v12_altcat_1(E)
& l2_altcat_1(E) )
=> ( r3_yellow20(A,B,C,D,E)
<=> ( v2_altcat_1(D)
& v3_altcat_2(D,A)
& m1_altcat_2(D,A)
& v2_altcat_1(E)
& v3_altcat_2(E,B)
& m1_altcat_2(E,B)
& ? [F] :
( v16_functor0(F,D,E)
& m2_functor0(F,D,E)
& v21_functor0(F,D,E)
& ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( G = H
=> k3_functor0(D,E,F,G) = k3_functor0(A,B,C,H) ) ) )
& ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(D))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( ( G = I
& H = J )
=> ( k1_altcat_1(D,G,H) = k1_xboole_0
| ! [K] :
( m1_subset_1(K,k1_altcat_1(D,G,H))
=> ! [L] :
( m1_subset_1(L,k1_altcat_1(A,I,J))
=> ( K = L
=> k8_functor0(D,E,F,G,H,K) = k1_funct_1(k4_functor0(A,B,C,I,J),L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_yellow20,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] :
( l2_functor0(E,A,B)
=> ( r2_yellow20(A,B,E,C,D)
=> r1_functor0(C,D) ) ) ) ) ) ) ).
fof(t39_yellow20,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] :
( l2_functor0(E,A,B)
=> ( r3_yellow20(A,B,E,C,D)
=> r2_functor0(C,D) ) ) ) ) ) ) ).
fof(t40_yellow20,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) )
=> ( r2_yellow20(A,B,C,A,B)
=> v21_functor0(C,A,B) ) ) ) ) ).
fof(t41_yellow20,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) )
=> ( r3_yellow20(A,B,C,A,B)
=> v21_functor0(C,A,B) ) ) ) ) ).
fof(t42_yellow20,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) )
=> ( v21_functor0(C,A,B)
=> r2_yellow20(A,B,C,A,B) ) ) ) ) ).
fof(t43_yellow20,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) )
=> ( v21_functor0(C,A,B)
=> r3_yellow20(A,B,C,A,B) ) ) ) ) ).
fof(t44_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> r2_yellow20(A,A,k12_functor0(A),B,B) ) ) ).
fof(t45_yellow20,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r1_tarski(A,B)
=> r1_tarski(k2_funct_4(A),k2_funct_4(B)) ) ) ) ).
fof(t46_yellow20,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( ( v1_relat_1(k1_relat_1(A))
& r1_tarski(k2_funct_4(A),k2_funct_4(B)) )
=> r1_tarski(A,B) ) ) ) ).
fof(t47_yellow20,axiom,
! [A,B,C] :
( m1_pboole(C,k2_zfmisc_1(A,A))
=> ! [D] :
( m1_pboole(D,k2_zfmisc_1(B,B))
=> ( r2_altcat_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),C,D)
=> r2_altcat_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k1_altcat_2(A,C),k1_altcat_2(B,D)) ) ) ) ).
fof(t48_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& m1_altcat_2(B,A) )
=> m1_altcat_2(k1_yellow18(B),k1_yellow18(A)) ) ) ).
fof(t49_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ( v2_altcat_1(k1_yellow18(B))
& v3_altcat_2(k1_yellow18(B),k1_yellow18(A))
& m1_altcat_2(k1_yellow18(B),k1_yellow18(A)) ) ) ) ).
fof(t50_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> r3_yellow20(A,k1_yellow18(A),k2_yellow18(A,k1_yellow18(A)),B,k1_yellow18(B)) ) ) ).
fof(t51_yellow20,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) )
=> ( v21_functor0(C,A,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_altcat_1(D)
& v3_altcat_2(D,A)
& m1_altcat_2(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v2_altcat_1(E)
& v3_altcat_2(E,B)
& m1_altcat_2(E,B) )
=> ( r2_yellow20(A,B,C,D,E)
=> r2_yellow20(B,A,k15_functor0(A,B,C),E,D) ) ) ) ) ) ) ) ).
fof(t52_yellow20,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) )
=> ( v21_functor0(C,A,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_altcat_1(D)
& v3_altcat_2(D,A)
& m1_altcat_2(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v2_altcat_1(E)
& v3_altcat_2(E,B)
& m1_altcat_2(E,B) )
=> ( r3_yellow20(A,B,C,D,E)
=> r3_yellow20(B,A,k15_functor0(A,B,C),E,D) ) ) ) ) ) ) ) ).
fof(t53_yellow20,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] :
( ( ~ v3_struct_0(F)
& v2_altcat_1(F)
& v3_altcat_2(F,A)
& m1_altcat_2(F,A) )
=> ! [G] :
( ( ~ v3_struct_0(G)
& v2_altcat_1(G)
& v3_altcat_2(G,B)
& m1_altcat_2(G,B) )
=> ! [H] :
( ( ~ v3_struct_0(H)
& v2_altcat_1(H)
& v3_altcat_2(H,C)
& m1_altcat_2(H,C) )
=> ( ( r2_yellow20(A,B,D,F,G)
& r2_yellow20(B,C,E,G,H) )
=> r2_yellow20(A,C,k1_functor3(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) ).
fof(t54_yellow20,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] :
( ( v16_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v15_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& v2_altcat_1(F)
& v3_altcat_2(F,A)
& m1_altcat_2(F,A) )
=> ! [G] :
( ( ~ v3_struct_0(G)
& v2_altcat_1(G)
& v3_altcat_2(G,B)
& m1_altcat_2(G,B) )
=> ! [H] :
( ( ~ v3_struct_0(H)
& v2_altcat_1(H)
& v3_altcat_2(H,C)
& m1_altcat_2(H,C) )
=> ( ( r3_yellow20(A,B,D,F,G)
& r2_yellow20(B,C,E,G,H) )
=> r3_yellow20(A,C,k4_functor3(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) ).
fof(t55_yellow20,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] :
( ( v16_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& v2_altcat_1(F)
& v3_altcat_2(F,A)
& m1_altcat_2(F,A) )
=> ! [G] :
( ( ~ v3_struct_0(G)
& v2_altcat_1(G)
& v3_altcat_2(G,B)
& m1_altcat_2(G,B) )
=> ! [H] :
( ( ~ v3_struct_0(H)
& v2_altcat_1(H)
& v3_altcat_2(H,C)
& m1_altcat_2(H,C) )
=> ( ( r2_yellow20(A,B,D,F,G)
& r3_yellow20(B,C,E,G,H) )
=> r3_yellow20(A,C,k3_functor3(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) ).
fof(t56_yellow20,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] :
( ( v16_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ! [E] :
( ( v16_functor0(E,B,C)
& m2_functor0(E,B,C) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& v2_altcat_1(F)
& v3_altcat_2(F,A)
& m1_altcat_2(F,A) )
=> ! [G] :
( ( ~ v3_struct_0(G)
& v2_altcat_1(G)
& v3_altcat_2(G,B)
& m1_altcat_2(G,B) )
=> ! [H] :
( ( ~ v3_struct_0(H)
& v2_altcat_1(H)
& v3_altcat_2(H,C)
& m1_altcat_2(H,C) )
=> ( ( r3_yellow20(A,B,D,F,G)
& r3_yellow20(B,C,E,G,H) )
=> r2_yellow20(A,C,k2_functor3(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) ).
fof(s1_yellow20,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_yellow20))
=> ( m1_subset_1(A,u1_struct_0(f2_s1_yellow20))
<=> p1_s1_yellow20(A) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_yellow20))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_yellow20))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f2_s1_yellow20))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(f2_s1_yellow20))
=> ( ( C = A
& D = B )
=> ( k1_altcat_1(f1_s1_yellow20,A,B) = k1_xboole_0
| ! [E] :
( m1_subset_1(E,k1_altcat_1(f1_s1_yellow20,A,B))
=> ( r2_hidden(E,k1_altcat_1(f2_s1_yellow20,C,D))
<=> p2_s1_yellow20(A,B,E) ) ) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_yellow20))
=> ( m1_subset_1(A,u1_struct_0(f3_s1_yellow20))
<=> p1_s1_yellow20(A) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s1_yellow20))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_yellow20))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f3_s1_yellow20))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(f3_s1_yellow20))
=> ( ( C = A
& D = B )
=> ( k1_altcat_1(f1_s1_yellow20,A,B) = k1_xboole_0
| ! [E] :
( m1_subset_1(E,k1_altcat_1(f1_s1_yellow20,A,B))
=> ( r2_hidden(E,k1_altcat_1(f3_s1_yellow20,C,D))
<=> p2_s1_yellow20(A,B,E) ) ) ) ) ) ) ) ) )
=> g2_altcat_1(u1_struct_0(f2_s1_yellow20),u1_altcat_1(f2_s1_yellow20),u2_altcat_1(f2_s1_yellow20)) = g2_altcat_1(u1_struct_0(f3_s1_yellow20),u1_altcat_1(f3_s1_yellow20),u2_altcat_1(f3_s1_yellow20)) ) ).
fof(s2_yellow20,axiom,
( ? [A] :
( m1_subset_1(A,u1_struct_0(f1_s2_yellow20))
& p1_s2_yellow20(A) )
=> ? [A] :
( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v2_altcat_2(A,f1_s2_yellow20)
& v3_altcat_2(A,f1_s2_yellow20)
& m1_altcat_2(A,f1_s2_yellow20)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_yellow20))
=> ( m1_subset_1(B,u1_struct_0(A))
<=> p1_s2_yellow20(B) ) ) ) ) ).
fof(s3_yellow20,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s3_yellow20))
=> ( m1_subset_1(A,u1_struct_0(f2_s3_yellow20))
<=> p1_s3_yellow20(A) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s3_yellow20))
=> ( m1_subset_1(A,u1_struct_0(f3_s3_yellow20))
<=> p1_s3_yellow20(A) ) ) )
=> g2_altcat_1(u1_struct_0(f2_s3_yellow20),u1_altcat_1(f2_s3_yellow20),u2_altcat_1(f2_s3_yellow20)) = g2_altcat_1(u1_struct_0(f3_s3_yellow20),u1_altcat_1(f3_s3_yellow20),u2_altcat_1(f3_s3_yellow20)) ) ).
fof(s4_yellow20,axiom,
( ( v21_functor0(f3_s4_yellow20,f1_s4_yellow20,f2_s4_yellow20)
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s4_yellow20))
=> ( m1_subset_1(A,u1_struct_0(f4_s4_yellow20))
<=> m1_subset_1(k3_functor0(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,A),u1_struct_0(f5_s4_yellow20)) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s4_yellow20))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s4_yellow20))
=> ( k1_altcat_1(f1_s4_yellow20,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f4_s4_yellow20))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(f4_s4_yellow20))
=> ( ( C = A
& D = B )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(f5_s4_yellow20))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(f5_s4_yellow20))
=> ( ( E = k3_functor0(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,A)
& F = k3_functor0(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,B) )
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(f1_s4_yellow20,A,B))
=> ( r2_hidden(G,k1_altcat_1(f4_s4_yellow20,C,D))
<=> r2_hidden(k6_functor0(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,A,B,G),k1_altcat_1(f5_s4_yellow20,E,F)) ) ) ) ) ) ) ) ) ) ) ) )
=> r2_yellow20(f1_s4_yellow20,f2_s4_yellow20,f3_s4_yellow20,f4_s4_yellow20,f5_s4_yellow20) ) ).
fof(s5_yellow20,axiom,
( ( v21_functor0(f3_s5_yellow20,f1_s5_yellow20,f2_s5_yellow20)
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s5_yellow20))
=> ( m1_subset_1(A,u1_struct_0(f4_s5_yellow20))
<=> m1_subset_1(k3_functor0(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,A),u1_struct_0(f5_s5_yellow20)) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s5_yellow20))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s5_yellow20))
=> ( k1_altcat_1(f1_s5_yellow20,A,B) != k1_xboole_0
=> ! [C] :
( m1_subset_1(C,u1_struct_0(f4_s5_yellow20))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(f4_s5_yellow20))
=> ( ( C = A
& D = B )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(f5_s5_yellow20))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(f5_s5_yellow20))
=> ( ( E = k3_functor0(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,A)
& F = k3_functor0(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,B) )
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(f1_s5_yellow20,A,B))
=> ( r2_hidden(G,k1_altcat_1(f4_s5_yellow20,C,D))
<=> r2_hidden(k8_functor0(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,A,B,G),k1_altcat_1(f5_s5_yellow20,F,E)) ) ) ) ) ) ) ) ) ) ) ) )
=> r3_yellow20(f1_s5_yellow20,f2_s5_yellow20,f3_s5_yellow20,f4_s5_yellow20,f5_s5_yellow20) ) ).
fof(symmetry_r1_yellow20,axiom,
! [A,B] :
( ( l2_altcat_1(A)
& l2_altcat_1(B) )
=> ( r1_yellow20(A,B)
=> r1_yellow20(B,A) ) ) ).
fof(dt_k1_yellow20,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B) )
=> ( v1_relat_1(k1_yellow20(A,B))
& v1_funct_1(k1_yellow20(A,B)) ) ) ).
fof(commutativity_k1_yellow20,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B) )
=> k1_yellow20(A,B) = k1_yellow20(B,A) ) ).
fof(dt_k2_yellow20,axiom,
! [A,B] :
( ( l2_altcat_1(A)
& l2_altcat_1(B) )
=> ( v6_altcat_1(k2_yellow20(A,B))
& l2_altcat_1(k2_yellow20(A,B)) ) ) ).
fof(dt_k3_yellow20,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)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> ( v9_functor0(k3_yellow20(A,B),B,A)
& v15_functor0(k3_yellow20(A,B),B,A)
& m2_functor0(k3_yellow20(A,B),B,A) ) ) ).
fof(redefinition_k3_yellow20,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)
& v3_altcat_2(B,A)
& m1_altcat_2(B,A) )
=> k3_yellow20(A,B) = k10_functor0(A,B) ) ).
fof(dt_k4_yellow20,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)
& ~ v3_struct_0(C)
& v2_altcat_1(C)
& v3_altcat_2(C,A)
& m1_altcat_2(C,A)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ( v9_functor0(k4_yellow20(A,B,C,D),C,B)
& v15_functor0(k4_yellow20(A,B,C,D),C,B)
& m2_functor0(k4_yellow20(A,B,C,D),C,B) ) ) ).
fof(redefinition_k4_yellow20,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)
& ~ v3_struct_0(C)
& v2_altcat_1(C)
& v3_altcat_2(C,A)
& m1_altcat_2(C,A)
& v15_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> k4_yellow20(A,B,C,D) = k14_functor0(A,B,C,D) ) ).
fof(dt_k5_yellow20,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)
& ~ v3_struct_0(C)
& v2_altcat_1(C)
& v3_altcat_2(C,A)
& m1_altcat_2(C,A)
& v16_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> ( v9_functor0(k5_yellow20(A,B,C,D),C,B)
& v16_functor0(k5_yellow20(A,B,C,D),C,B)
& m2_functor0(k5_yellow20(A,B,C,D),C,B) ) ) ).
fof(redefinition_k5_yellow20,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)
& ~ v3_struct_0(C)
& v2_altcat_1(C)
& v3_altcat_2(C,A)
& m1_altcat_2(C,A)
& v16_functor0(D,A,B)
& m2_functor0(D,A,B) )
=> k5_yellow20(A,B,C,D) = k14_functor0(A,B,C,D) ) ).
%------------------------------------------------------------------------------