SET007 Axioms: SET007+202.ax
%------------------------------------------------------------------------------
% File : SET007+202 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Categories and 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 : cat_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 196 ( 42 unt; 0 def)
% Number of atoms : 1211 ( 240 equ)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 1068 ( 53 ~; 25 |; 371 &)
% ( 27 <=>; 592 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-4 aty)
% Number of functors : 39 ( 39 usr; 1 con; 0-6 aty)
% Number of variables : 644 ( 620 !; 24 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_cat_1,axiom,
? [A] :
( l1_cat_1(A)
& v1_cat_1(A) ) ).
fof(rc2_cat_1,axiom,
? [A] :
( l1_cat_1(A)
& v2_cat_1(A) ) ).
fof(rc3_cat_1,axiom,
? [A] :
( l1_cat_1(A)
& v1_cat_1(A)
& v2_cat_1(A) ) ).
fof(t1_cat_1,axiom,
$true ).
fof(t2_cat_1,axiom,
$true ).
fof(t3_cat_1,axiom,
$true ).
fof(t4_cat_1,axiom,
! [A,B,C,D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,D)
& m2_relset_1(E,A,D) )
=> ( ( r1_tarski(B,A)
& r1_tarski(k2_funct_2(A,D,E,B),C) )
=> ( v1_funct_1(k2_partfun1(A,D,E,B))
& v1_funct_2(k2_partfun1(A,D,E,B),B,C)
& m2_relset_1(k2_partfun1(A,D,E,B),B,C) ) ) ) ) ).
fof(d1_cat_1,axiom,
! [A,B,C] : k1_cat_1(A,B,C) = k3_cqc_lang(k4_tarski(A,B),C) ).
fof(t5_cat_1,axiom,
$true ).
fof(t6_cat_1,axiom,
$true ).
fof(t7_cat_1,axiom,
! [A,B,C] :
( k1_relat_1(k1_cat_1(A,B,C)) = k1_tarski(k4_tarski(A,B))
& k1_relat_1(k1_cat_1(A,B,C)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) ) ).
fof(t8_cat_1,axiom,
! [A,B,C] : k1_funct_1(k1_cat_1(A,B,C),k4_tarski(A,B)) = C ).
fof(t9_cat_1,axiom,
! [A,B,C,D] :
( m1_subset_1(D,k1_tarski(A))
=> ! [E] :
( m1_subset_1(E,k1_tarski(B))
=> k1_funct_1(k1_cat_1(A,B,C),k4_tarski(D,E)) = C ) ) ).
fof(d2_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) ) ) ).
fof(d3_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k3_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) ) ) ).
fof(d4_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A)))
=> k4_cat_1(A,B,C) = k1_funct_1(u5_cat_1(A),k4_tarski(C,B)) ) ) ) ) ).
fof(d5_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k5_cat_1(A,B) = k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) ) ) ).
fof(t10_cat_1,axiom,
$true ).
fof(t11_cat_1,axiom,
$true ).
fof(t12_cat_1,axiom,
$true ).
fof(t13_cat_1,axiom,
$true ).
fof(t14_cat_1,axiom,
$true ).
fof(t15_cat_1,axiom,
$true ).
fof(t16_cat_1,axiom,
$true ).
fof(t17_cat_1,axiom,
$true ).
fof(t18_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( r2_hidden(D,k6_cat_1(A,B,C))
<=> ( k2_cat_1(A,D) = B
& k3_cat_1(A,D) = C ) ) ) ) ) ) ).
fof(t19_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,B)) != k1_xboole_0 ) ) ).
fof(d7_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k6_cat_1(A,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( m1_cat_1(D,A,B,C)
<=> r2_hidden(D,k6_cat_1(A,B,C)) ) ) ) ) ) ) ).
fof(t20_cat_1,axiom,
$true ).
fof(t21_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( r2_hidden(D,k6_cat_1(A,B,C))
=> m1_cat_1(D,A,B,C) ) ) ) ) ).
fof(t22_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> m1_cat_1(B,A,k2_cat_1(A,B),k3_cat_1(A,B)) ) ) ).
fof(t23_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( k6_cat_1(A,B,C) != k1_xboole_0
=> ( k2_cat_1(A,D) = B
& k3_cat_1(A,D) = C ) ) ) ) ) ) ).
fof(t24_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_cat_1(F,A,B,C)
=> ! [G] :
( m1_cat_1(G,A,D,E)
=> ( F = G
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,D,E) = k1_xboole_0
| ( B = D
& C = E ) ) ) ) ) ) ) ) ) ) ).
fof(t25_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( k6_cat_1(A,B,C) = k1_tarski(D)
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> D = E ) ) ) ) ) ) ).
fof(t26_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( ! [E] :
( m1_cat_1(E,A,B,C)
=> D = E )
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,B,C) = k1_tarski(D) ) ) ) ) ) ) ).
fof(t27_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_cat_1(F,A,B,C)
=> ~ ( r2_tarski(k6_cat_1(A,B,C),k6_cat_1(A,D,E))
& k6_cat_1(A,B,C) = k1_tarski(F)
& ! [G] :
( m1_cat_1(G,A,D,E)
=> k6_cat_1(A,D,E) != k1_tarski(G) ) ) ) ) ) ) ) ) ).
fof(d8_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( v2_cat_1(A)
<=> ( ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A)))
<=> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) ) ) )
& ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B)
=> ( k1_funct_1(u3_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B)
& k1_funct_1(u4_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) ) ) ) )
& ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C)
& k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) )
=> k1_funct_1(u5_cat_1(A),k4_tarski(D,k1_funct_1(u5_cat_1(A),k4_tarski(C,B)))) = k1_funct_1(u5_cat_1(A),k4_tarski(k1_funct_1(u5_cat_1(A),k4_tarski(D,C)),B)) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B
& k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B
& ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = B
=> k1_funct_1(u5_cat_1(A),k4_tarski(k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),C)) = C ) )
& ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = B
=> k1_funct_1(u5_cat_1(A),k4_tarski(C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))) = C ) ) ) ) ) ) ) ).
fof(t28_cat_1,axiom,
$true ).
fof(t29_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( ( ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A)))
<=> k2_cat_1(A,C) = k3_cat_1(A,B) ) ) )
& ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k2_cat_1(A,C) = k3_cat_1(A,B)
=> ( k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B)
& k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) ) ) ) )
& ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( ( k2_cat_1(A,D) = k3_cat_1(A,C)
& k2_cat_1(A,C) = k3_cat_1(A,B) )
=> k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D)) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( k2_cat_1(A,k5_cat_1(A,B)) = B
& k3_cat_1(A,k5_cat_1(A,B)) = B
& ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k3_cat_1(A,C) = B
=> k4_cat_1(A,C,k5_cat_1(A,B)) = C ) )
& ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k2_cat_1(A,C) = B
=> k4_cat_1(A,k5_cat_1(A,B),C) = C ) ) ) ) )
=> v2_cat_1(A) ) ) ).
fof(d9_cat_1,axiom,
! [A,B] : k8_cat_1(A,B) = g1_cat_1(k1_tarski(A),k1_tarski(B),k7_cat_1(B,A),k7_cat_1(B,A),k1_cat_1(B,B,B),k7_cat_1(A,B)) ).
fof(t30_cat_1,axiom,
$true ).
fof(t31_cat_1,axiom,
$true ).
fof(t32_cat_1,axiom,
! [A,B] : m1_subset_1(A,u1_cat_1(k8_cat_1(A,B))) ).
fof(t33_cat_1,axiom,
! [A,B] : m1_subset_1(A,u2_cat_1(k8_cat_1(B,A))) ).
fof(t34_cat_1,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
=> C = A ) ).
fof(t35_cat_1,axiom,
! [A,B,C] :
( m1_subset_1(C,u2_cat_1(k8_cat_1(A,B)))
=> C = B ) ).
fof(t36_cat_1,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k8_cat_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k8_cat_1(A,B)))
=> r2_hidden(E,k6_cat_1(k8_cat_1(A,B),C,D)) ) ) ) ).
fof(t37_cat_1,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k8_cat_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k8_cat_1(A,B)))
=> m1_cat_1(E,k8_cat_1(A,B),C,D) ) ) ) ).
fof(t38_cat_1,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k8_cat_1(A,B)))
=> k6_cat_1(k8_cat_1(A,B),C,D) != k1_xboole_0 ) ) ).
fof(t39_cat_1,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k8_cat_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k8_cat_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(k8_cat_1(A,B)))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(k8_cat_1(A,B)))
=> ! [G] :
( m1_cat_1(G,k8_cat_1(A,B),C,D)
=> ! [H] :
( m1_cat_1(H,k8_cat_1(A,B),E,F)
=> G = H ) ) ) ) ) ) ).
fof(t40_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k2_cat_1(A,B) = k3_cat_1(A,C)
<=> r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A))) ) ) ) ) ).
fof(t41_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k2_cat_1(A,B) = k3_cat_1(A,C)
=> k4_cat_1(A,C,B) = k1_funct_1(u5_cat_1(A),k4_tarski(B,C)) ) ) ) ) ).
fof(t42_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k2_cat_1(A,C) = k3_cat_1(A,B)
=> ( k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B)
& k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) ) ) ) ) ) ).
fof(t43_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( ( k2_cat_1(A,D) = k3_cat_1(A,C)
& k2_cat_1(A,C) = k3_cat_1(A,B) )
=> k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D)) ) ) ) ) ) ).
fof(t44_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( k2_cat_1(A,k5_cat_1(A,B)) = B
& k3_cat_1(A,k5_cat_1(A,B)) = B ) ) ) ).
fof(t45_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k5_cat_1(A,B) = k5_cat_1(A,C)
=> B = C ) ) ) ) ).
fof(t46_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k3_cat_1(A,C) = B
=> k4_cat_1(A,C,k5_cat_1(A,B)) = C ) ) ) ) ).
fof(t47_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k2_cat_1(A,C) = B
=> k4_cat_1(A,k5_cat_1(A,B),C) = C ) ) ) ) ).
fof(d10_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v3_cat_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( ( k2_cat_1(A,C) = k2_cat_1(A,D)
& k3_cat_1(A,C) = k2_cat_1(A,B)
& k3_cat_1(A,D) = k2_cat_1(A,B)
& k4_cat_1(A,C,B) = k4_cat_1(A,D,B) )
=> C = D ) ) ) ) ) ) ).
fof(d11_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v4_cat_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( ( k2_cat_1(A,C) = k3_cat_1(A,B)
& k2_cat_1(A,D) = k3_cat_1(A,B)
& k3_cat_1(A,C) = k3_cat_1(A,D)
& k4_cat_1(A,B,C) = k4_cat_1(A,B,D) )
=> C = D ) ) ) ) ) ) ).
fof(d12_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v5_cat_1(B,A)
<=> ? [C] :
( m1_subset_1(C,u2_cat_1(A))
& k2_cat_1(A,C) = k3_cat_1(A,B)
& k3_cat_1(A,C) = k2_cat_1(A,B)
& k4_cat_1(A,C,B) = k5_cat_1(A,k3_cat_1(A,B))
& k4_cat_1(A,B,C) = k5_cat_1(A,k2_cat_1(A,B)) ) ) ) ) ).
fof(t48_cat_1,axiom,
$true ).
fof(t49_cat_1,axiom,
$true ).
fof(t50_cat_1,axiom,
$true ).
fof(t51_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,D) != k1_xboole_0
& ~ r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D)) ) ) ) ) ) ) ) ).
fof(t52_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,D) != k1_xboole_0
& k6_cat_1(A,B,D) = k1_xboole_0 ) ) ) ) ) ).
fof(d13_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,D) != k1_xboole_0
& k9_cat_1(A,B,C,D,E,F) != k4_cat_1(A,E,F) ) ) ) ) ) ) ) ).
fof(t53_cat_1,axiom,
$true ).
fof(t54_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_cat_1(F,A,B,C)
=> ! [G] :
( m1_cat_1(G,A,C,D)
=> ! [H] :
( m1_cat_1(H,A,D,E)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,D) != k1_xboole_0
& k6_cat_1(A,D,E) != k1_xboole_0
& k9_cat_1(A,B,C,E,F,k9_cat_1(A,C,D,E,G,H)) != k9_cat_1(A,B,D,E,k9_cat_1(A,B,C,D,F,G),H) ) ) ) ) ) ) ) ) ) ).
fof(t55_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> r2_hidden(k5_cat_1(A,B),k6_cat_1(A,B,B)) ) ) ).
fof(t56_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k6_cat_1(A,B,B) != k1_xboole_0 ) ) ).
fof(t57_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( k6_cat_1(A,B,C) != k1_xboole_0
=> k9_cat_1(A,B,C,C,D,k10_cat_1(A,C)) = D ) ) ) ) ) ).
fof(t58_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( k6_cat_1(A,B,C) != k1_xboole_0
=> k9_cat_1(A,B,B,C,k10_cat_1(A,B),D) = D ) ) ) ) ) ).
fof(t59_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k9_cat_1(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)) = k10_cat_1(A,B) ) ) ).
fof(t60_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( k6_cat_1(A,B,C) != k1_xboole_0
=> ( v3_cat_1(D,A)
<=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_cat_1(F,A,E,B)
=> ! [G] :
( m1_cat_1(G,A,E,B)
=> ( k9_cat_1(A,E,B,C,F,D) = k9_cat_1(A,E,B,C,G,D)
=> ( k6_cat_1(A,E,B) = k1_xboole_0
| F = G ) ) ) ) ) ) ) ) ) ) ) ).
fof(t61_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ( ( v3_cat_1(E,A)
& v3_cat_1(F,A) )
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,C,D) = k1_xboole_0
| v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) ) ) ) ) ) ) ) ) ).
fof(t62_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ( v3_cat_1(k9_cat_1(A,B,C,D,E,F),A)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,C,D) = k1_xboole_0
| v3_cat_1(E,A) ) ) ) ) ) ) ) ) ).
fof(t63_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ! [E] :
( m1_cat_1(E,A,C,B)
=> ( k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,C,B) = k1_xboole_0
| v3_cat_1(E,A) ) ) ) ) ) ) ) ).
fof(t64_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> v3_cat_1(k10_cat_1(A,B),A) ) ) ).
fof(t65_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( k6_cat_1(A,B,C) != k1_xboole_0
=> ( v4_cat_1(D,A)
<=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_cat_1(F,A,C,E)
=> ! [G] :
( m1_cat_1(G,A,C,E)
=> ( k9_cat_1(A,B,C,E,D,F) = k9_cat_1(A,B,C,E,D,G)
=> ( k6_cat_1(A,C,E) = k1_xboole_0
| F = G ) ) ) ) ) ) ) ) ) ) ) ).
fof(t66_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ( ( v4_cat_1(E,A)
& v4_cat_1(F,A) )
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,C,D) = k1_xboole_0
| v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) ) ) ) ) ) ) ) ) ).
fof(t67_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ( v4_cat_1(k9_cat_1(A,B,C,D,E,F),A)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,C,D) = k1_xboole_0
| v4_cat_1(F,A) ) ) ) ) ) ) ) ) ).
fof(t68_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ! [E] :
( m1_cat_1(E,A,C,B)
=> ( k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,C,B) = k1_xboole_0
| v4_cat_1(D,A) ) ) ) ) ) ) ) ).
fof(t69_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> v4_cat_1(k10_cat_1(A,B),A) ) ) ).
fof(t70_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( k6_cat_1(A,B,C) != k1_xboole_0
=> ( v5_cat_1(D,A)
<=> ( k6_cat_1(A,C,B) != k1_xboole_0
& ? [E] :
( m1_cat_1(E,A,C,B)
& k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C)
& k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) ) ) ) ) ) ) ) ) ).
fof(t71_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,B) != k1_xboole_0
& ? [E] :
( m1_cat_1(E,A,C,B)
& ? [F] :
( m1_cat_1(F,A,C,B)
& k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C)
& k9_cat_1(A,B,C,B,D,F) = k10_cat_1(A,B)
& E != F ) ) ) ) ) ) ) ).
fof(d14_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( v5_cat_1(D,A)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| ! [E] :
( m1_cat_1(E,A,C,B)
=> ( E = k11_cat_1(A,B,C,D)
<=> ( k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C)
& k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) ) ) ) ) ) ) ) ) ) ).
fof(t72_cat_1,axiom,
$true ).
fof(t73_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( v5_cat_1(D,A)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| ( v3_cat_1(D,A)
& v4_cat_1(D,A) ) ) ) ) ) ) ) ).
fof(t74_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> v5_cat_1(k10_cat_1(A,B),A) ) ) ).
fof(t75_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ( ( v5_cat_1(E,A)
& v5_cat_1(F,A) )
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,C,D) = k1_xboole_0
| v5_cat_1(k9_cat_1(A,B,C,D,E,F),A) ) ) ) ) ) ) ) ) ).
fof(t76_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( v5_cat_1(D,A)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| v5_cat_1(k11_cat_1(A,B,C,D),A) ) ) ) ) ) ) ).
fof(t77_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ( ( v5_cat_1(E,A)
& v5_cat_1(F,A) )
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,C,D) = k1_xboole_0
| k11_cat_1(A,B,D,k9_cat_1(A,B,C,D,E,F)) = k9_cat_1(A,D,C,B,k11_cat_1(A,C,D,F),k11_cat_1(A,B,C,E)) ) ) ) ) ) ) ) ) ).
fof(d15_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( v6_cat_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k6_cat_1(A,C,B) != k1_xboole_0
& ? [D] :
( m1_cat_1(D,A,C,B)
& ! [E] :
( m1_cat_1(E,A,C,B)
=> D = E ) ) ) ) ) ) ) ).
fof(d16_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( v7_cat_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k6_cat_1(A,B,C) != k1_xboole_0
& ? [D] :
( m1_cat_1(D,A,B,C)
& ! [E] :
( m1_cat_1(E,A,B,C)
=> D = E ) ) ) ) ) ) ) ).
fof(d17_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( r1_cat_1(A,B,C)
<=> ( k6_cat_1(A,B,C) != k1_xboole_0
& ? [D] :
( m1_cat_1(D,A,B,C)
& v5_cat_1(D,A) ) ) ) ) ) ) ).
fof(t78_cat_1,axiom,
$true ).
fof(t79_cat_1,axiom,
$true ).
fof(t80_cat_1,axiom,
$true ).
fof(t81_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( r1_cat_1(A,B,C)
<=> ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,B) != k1_xboole_0
& ? [D] :
( m1_cat_1(D,A,B,C)
& ? [E] :
( m1_cat_1(E,A,C,B)
& k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C)
& k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) ) ) ) ) ) ) ) ).
fof(t82_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( v7_cat_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ? [D] :
( m1_cat_1(D,A,B,C)
& k6_cat_1(A,B,C) = k1_tarski(D) ) ) ) ) ) ).
fof(t83_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( v7_cat_1(B,A)
=> ! [C] :
( m1_cat_1(C,A,B,B)
=> k10_cat_1(A,B) = C ) ) ) ) ).
fof(t84_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( ( v7_cat_1(B,A)
& v7_cat_1(C,A) )
=> r1_cat_1(A,B,C) ) ) ) ) ).
fof(t85_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( ( v7_cat_1(B,A)
& r1_cat_1(A,B,C) )
=> v7_cat_1(C,A) ) ) ) ) ).
fof(t86_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( v6_cat_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ? [D] :
( m1_cat_1(D,A,C,B)
& k6_cat_1(A,C,B) = k1_tarski(D) ) ) ) ) ) ).
fof(t87_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( v6_cat_1(B,A)
=> ! [C] :
( m1_cat_1(C,A,B,B)
=> k10_cat_1(A,B) = C ) ) ) ) ).
fof(t88_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( ( v6_cat_1(B,A)
& v6_cat_1(C,A) )
=> r1_cat_1(A,B,C) ) ) ) ) ).
fof(t89_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( ( v6_cat_1(B,A)
& r1_cat_1(A,C,B) )
=> v6_cat_1(C,A) ) ) ) ) ).
fof(t90_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> ( v6_cat_1(B,A)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| v3_cat_1(D,A) ) ) ) ) ) ) ).
fof(t91_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> r1_cat_1(A,B,B) ) ) ).
fof(t92_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( r1_cat_1(A,B,C)
=> r1_cat_1(A,C,B) ) ) ) ) ).
fof(t93_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ( ( r1_cat_1(A,B,C)
& r1_cat_1(A,C,D) )
=> r1_cat_1(A,B,D) ) ) ) ) ) ).
fof(d18_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( m2_cat_1(C,A,B)
<=> ( ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ? [E] :
( m1_subset_1(E,u1_cat_1(B))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) ) )
& ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u3_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u4_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) )
& ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ( r2_hidden(k4_tarski(E,D),k1_relat_1(u5_cat_1(A)))
=> k1_funct_1(C,k1_funct_1(u5_cat_1(A),k4_tarski(E,D))) = k1_funct_1(u5_cat_1(B),k4_tarski(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) ) ) ) ) ) ) ) ).
fof(t94_cat_1,axiom,
$true ).
fof(t95_cat_1,axiom,
$true ).
fof(t96_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ? [E] :
( m1_subset_1(E,u1_cat_1(B))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) )
& ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) )
& ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ( k2_cat_1(A,E) = k3_cat_1(A,D)
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) )
=> m2_cat_1(C,A,B) ) ) ) ) ).
fof(t97_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ? [E] :
( m1_subset_1(E,u1_cat_1(B))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) ) ) ) ) ).
fof(t98_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) ) ) ) ) ).
fof(t99_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ( k2_cat_1(A,E) = k3_cat_1(A,D)
=> ( k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) ) ) ) ) ).
fof(t100_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_cat_1(A),u1_cat_1(B))
& m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) )
=> ( ( ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,E)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E)) )
& ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ( k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k2_cat_1(A,E)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E))
& k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k3_cat_1(A,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) )
& ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ( k2_cat_1(A,F) = k3_cat_1(A,E)
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,E,F)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)) ) ) ) )
=> m2_cat_1(C,A,B) ) ) ) ) ) ).
fof(d19_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ? [E] :
( m1_subset_1(E,u1_cat_1(B))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) ) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_cat_1(A),u1_cat_1(B))
& m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) )
=> ( D = k12_cat_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),E)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),F)
=> k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E) = F ) ) ) ) ) ) ) ) ) ).
fof(t101_cat_1,axiom,
$true ).
fof(t102_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ? [E] :
( m1_subset_1(E,u1_cat_1(B))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) )
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(B))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E)
=> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E ) ) ) ) ) ) ) ).
fof(t103_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(B))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E)
=> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E ) ) ) ) ) ) ).
fof(t104_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) ) ) ) ) ).
fof(t105_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))
& k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ) ).
fof(d20_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k13_cat_1(A,B,C,D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) ) ) ) ) ).
fof(t106_cat_1,axiom,
$true ).
fof(t107_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(B))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E)
=> k13_cat_1(A,B,C,D) = E ) ) ) ) ) ) ).
fof(t108_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k13_cat_1(A,B,C,D)) ) ) ) ) ).
fof(t109_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k13_cat_1(A,B,C,k2_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))
& k13_cat_1(A,B,C,k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ) ).
fof(t110_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> m2_cat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C) ) ) ) ) ) ).
fof(t111_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> m2_cat_1(k6_partfun1(u2_cat_1(A)),A,A) ) ).
fof(t112_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k14_cat_1(A,B,C,D,E)),F) = k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,E),k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F)) ) ) ) ) ) ) ).
fof(t113_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> k13_cat_1(A,C,k14_cat_1(A,B,C,D,E),F) = k13_cat_1(B,C,E,k13_cat_1(A,B,D,F)) ) ) ) ) ) ) ).
fof(d21_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> k15_cat_1(A) = k6_partfun1(u2_cat_1(A)) ) ).
fof(t114_cat_1,axiom,
$true ).
fof(t115_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(A),k15_cat_1(A),B) = B ) ) ).
fof(t116_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(A),u1_cat_1(A),k12_cat_1(A,A,k15_cat_1(A)),B) = B ) ) ).
fof(t117_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> k12_cat_1(A,A,k15_cat_1(A)) = k6_partfun1(u1_cat_1(A)) ) ).
fof(t118_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k13_cat_1(A,A,k15_cat_1(A),B) = B ) ) ).
fof(d22_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ( v8_cat_1(C,A,B)
<=> ( v2_funct_1(C)
& k2_relat_1(C) = u2_cat_1(B)
& k2_relat_1(k12_cat_1(A,B,C)) = u1_cat_1(B) ) ) ) ) ) ).
fof(d23_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ( v9_cat_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ( k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) != k1_xboole_0
=> ! [F] :
( m1_cat_1(F,B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))
=> ( k6_cat_1(A,D,E) != k1_xboole_0
& ? [G] :
( m1_cat_1(G,A,D,E)
& F = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) ) ) ) ) ) ) ) ) ) ) ).
fof(d24_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ( v10_cat_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ( k6_cat_1(A,D,E) != k1_xboole_0
=> ! [F] :
( m1_cat_1(F,A,D,E)
=> ! [G] :
( m1_cat_1(G,A,D,E)
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G)
=> F = G ) ) ) ) ) ) ) ) ) ) ).
fof(t119_cat_1,axiom,
$true ).
fof(t120_cat_1,axiom,
$true ).
fof(t121_cat_1,axiom,
$true ).
fof(t122_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> v8_cat_1(k15_cat_1(A),A,A) ) ).
fof(t123_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( r2_hidden(F,k6_cat_1(A,D,E))
=> r2_hidden(k1_funct_1(C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) ) ) ) ) ) ) ).
fof(t124_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ( k6_cat_1(A,D,E) != k1_xboole_0
=> ! [F] :
( m1_cat_1(F,A,D,E)
=> r2_hidden(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) ) ) ) ) ) ) ) ).
fof(t125_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ( k6_cat_1(A,D,E) != k1_xboole_0
=> ! [F] :
( m1_cat_1(F,A,D,E)
=> m1_cat_1(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) ) ) ) ) ) ) ) ).
fof(t126_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ~ ( k6_cat_1(A,D,E) != k1_xboole_0
& k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) = k1_xboole_0 ) ) ) ) ) ) ).
fof(t127_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ( ( v9_cat_1(D,A,B)
& v9_cat_1(E,B,C) )
=> v9_cat_1(k14_cat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) ).
fof(t128_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ( ( v10_cat_1(D,A,B)
& v10_cat_1(E,B,C) )
=> v10_cat_1(k14_cat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) ).
fof(t129_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> r1_tarski(k2_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) ) ) ) ) ) ).
fof(d25_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> k16_cat_1(A,B,C,D,E) = k2_partfun1(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)) ) ) ) ) ) ).
fof(t130_cat_1,axiom,
$true ).
fof(t131_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ( k6_cat_1(A,D,E) != k1_xboole_0
=> ! [F] :
( m1_cat_1(F,A,D,E)
=> k1_funct_1(k16_cat_1(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) ) ) ) ) ) ) ) ).
fof(t132_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ( v9_cat_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> k2_relat_1(k16_cat_1(A,B,C,D,E)) = k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) ) ) ) ) ) ) ).
fof(t133_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ( v10_cat_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> v2_funct_1(k16_cat_1(A,B,C,D,E)) ) ) ) ) ) ) ).
fof(dt_m1_cat_1,axiom,
! [A,B,C] :
( ( l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> m1_subset_1(D,u2_cat_1(A)) ) ) ).
fof(existence_m1_cat_1,axiom,
! [A,B,C] :
( ( l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> ? [D] : m1_cat_1(D,A,B,C) ) ).
fof(dt_m2_cat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) ) ) ) ).
fof(existence_m2_cat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ? [C] : m2_cat_1(C,A,B) ) ).
fof(dt_l1_cat_1,axiom,
$true ).
fof(existence_l1_cat_1,axiom,
? [A] : l1_cat_1(A) ).
fof(abstractness_v1_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( v1_cat_1(A)
=> A = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ) ).
fof(dt_k1_cat_1,axiom,
! [A,B,C] :
( v1_funct_1(k1_cat_1(A,B,C))
& m2_relset_1(k1_cat_1(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) ) ).
fof(dt_k2_cat_1,axiom,
! [A,B] :
( ( l1_cat_1(A)
& m1_subset_1(B,u2_cat_1(A)) )
=> m1_subset_1(k2_cat_1(A,B),u1_cat_1(A)) ) ).
fof(dt_k3_cat_1,axiom,
! [A,B] :
( ( l1_cat_1(A)
& m1_subset_1(B,u2_cat_1(A)) )
=> m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)) ) ).
fof(dt_k4_cat_1,axiom,
! [A,B,C] :
( ( l1_cat_1(A)
& m1_subset_1(B,u2_cat_1(A))
& m1_subset_1(C,u2_cat_1(A)) )
=> m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)) ) ).
fof(dt_k5_cat_1,axiom,
! [A,B] :
( ( l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)) ) ).
fof(dt_k6_cat_1,axiom,
! [A,B,C] :
( ( l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))) ) ).
fof(dt_k7_cat_1,axiom,
! [A,B] :
( v1_funct_1(k7_cat_1(A,B))
& v1_funct_2(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B))
& m2_relset_1(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)) ) ).
fof(redefinition_k7_cat_1,axiom,
! [A,B] : k7_cat_1(A,B) = k3_cqc_lang(A,B) ).
fof(dt_k8_cat_1,axiom,
! [A,B] :
( v1_cat_1(k8_cat_1(A,B))
& v2_cat_1(k8_cat_1(A,B))
& l1_cat_1(k8_cat_1(A,B)) ) ).
fof(dt_k9_cat_1,axiom,
! [A,B,C,D,E,F] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A))
& m1_subset_1(D,u1_cat_1(A))
& m1_cat_1(E,A,B,C)
& m1_cat_1(F,A,C,D) )
=> m1_cat_1(k9_cat_1(A,B,C,D,E,F),A,B,D) ) ).
fof(dt_k10_cat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_cat_1(k10_cat_1(A,B),A,B,B) ) ).
fof(redefinition_k10_cat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> k10_cat_1(A,B) = k5_cat_1(A,B) ) ).
fof(dt_k11_cat_1,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A))
& m1_cat_1(D,A,B,C) )
=> m1_cat_1(k11_cat_1(A,B,C,D),A,C,B) ) ).
fof(dt_k12_cat_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( v1_funct_1(k12_cat_1(A,B,C))
& v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B))
& m2_relset_1(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) ) ) ).
fof(dt_k13_cat_1,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& m2_cat_1(C,A,B)
& m1_subset_1(D,u1_cat_1(A)) )
=> m1_subset_1(k13_cat_1(A,B,C,D),u1_cat_1(B)) ) ).
fof(dt_k14_cat_1,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,B,C) )
=> m2_cat_1(k14_cat_1(A,B,C,D,E),A,C) ) ).
fof(redefinition_k14_cat_1,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,B,C) )
=> k14_cat_1(A,B,C,D,E) = k5_relat_1(D,E) ) ).
fof(dt_k15_cat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> m2_cat_1(k15_cat_1(A),A,A) ) ).
fof(dt_k16_cat_1,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& m2_cat_1(C,A,B)
& m1_subset_1(D,u1_cat_1(A))
& m1_subset_1(E,u1_cat_1(A)) )
=> ( v1_funct_1(k16_cat_1(A,B,C,D,E))
& v1_funct_2(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))
& m2_relset_1(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) ) ) ).
fof(dt_u1_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ~ v1_xboole_0(u1_cat_1(A)) ) ).
fof(dt_u2_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ~ v1_xboole_0(u2_cat_1(A)) ) ).
fof(dt_u3_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( v1_funct_1(u3_cat_1(A))
& v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ).
fof(dt_u4_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( v1_funct_1(u4_cat_1(A))
& v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
& m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ).
fof(dt_u5_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( v1_funct_1(u5_cat_1(A))
& m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A)) ) ) ).
fof(dt_u6_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ( v1_funct_1(u6_cat_1(A))
& v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A))
& m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) ) ) ).
fof(dt_g1_cat_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,A)
& m1_relset_1(C,B,A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& v1_funct_1(E)
& m1_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(F)
& v1_funct_2(F,A,B)
& m1_relset_1(F,A,B) )
=> ( v1_cat_1(g1_cat_1(A,B,C,D,E,F))
& l1_cat_1(g1_cat_1(A,B,C,D,E,F)) ) ) ).
fof(free_g1_cat_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,A)
& m1_relset_1(C,B,A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& v1_funct_1(E)
& m1_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(F)
& v1_funct_2(F,A,B)
& m1_relset_1(F,A,B) )
=> ! [G,H,I,J,K,L] :
( g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L)
=> ( A = G
& B = H
& C = I
& D = J
& E = K
& F = L ) ) ) ).
fof(d6_cat_1,axiom,
! [A] :
( l1_cat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k6_cat_1(A,B,C) = a_3_0_cat_1(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_cat_1,axiom,
! [A,B,C,D] :
( ( l1_cat_1(B)
& m1_subset_1(C,u1_cat_1(B))
& m1_subset_1(D,u1_cat_1(B)) )
=> ( r2_hidden(A,a_3_0_cat_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u2_cat_1(B))
& A = E
& k2_cat_1(B,E) = C
& k3_cat_1(B,E) = D ) ) ) ).
%------------------------------------------------------------------------------