SET007 Axioms: SET007+10.ax
%------------------------------------------------------------------------------
% File : SET007+10 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Relations and Their Basic Properties
% 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 : relat_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 234 ( 46 unt; 0 def)
% Number of atoms : 630 ( 124 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 415 ( 19 ~; 1 |; 68 &)
% ( 36 <=>; 291 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-2 aty)
% Number of variables : 462 ( 451 !; 11 ?)
% 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_relat_1,axiom,
? [A] :
( v1_xboole_0(A)
& v1_relat_1(A) ) ).
fof(fc1_relat_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_relat_1(B) )
=> v1_relat_1(k3_xboole_0(A,B)) ) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_relat_1(B) )
=> v1_relat_1(k2_xboole_0(A,B)) ) ).
fof(fc3_relat_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_relat_1(B) )
=> v1_relat_1(k4_xboole_0(A,B)) ) ).
fof(cc1_relat_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_relat_1(A) ) ).
fof(fc4_relat_1,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0) ) ).
fof(rc2_relat_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A) ) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A) )
=> ~ v1_xboole_0(k1_relat_1(A)) ) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A) )
=> ~ v1_xboole_0(k2_relat_1(A)) ) ).
fof(fc7_relat_1,axiom,
! [A] :
( v1_xboole_0(A)
=> ( v1_xboole_0(k1_relat_1(A))
& v1_relat_1(k1_relat_1(A)) ) ) ).
fof(fc8_relat_1,axiom,
! [A] :
( v1_xboole_0(A)
=> ( v1_xboole_0(k2_relat_1(A))
& v1_relat_1(k2_relat_1(A)) ) ) ).
fof(fc9_relat_1,axiom,
! [A,B] :
( ( v1_xboole_0(A)
& v1_relat_1(B) )
=> ( v1_xboole_0(k5_relat_1(A,B))
& v1_relat_1(k5_relat_1(A,B)) ) ) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( v1_xboole_0(A)
& v1_relat_1(B) )
=> ( v1_xboole_0(k5_relat_1(B,A))
& v1_relat_1(k5_relat_1(B,A)) ) ) ).
fof(fc11_relat_1,axiom,
! [A] :
( v1_xboole_0(A)
=> ( v1_xboole_0(k4_relat_1(A))
& v1_relat_1(k4_relat_1(A)) ) ) ).
fof(fc12_relat_1,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0) ) ).
fof(rc3_relat_1,axiom,
? [A] :
( v1_relat_1(A)
& v3_relat_1(A) ) ).
fof(fc13_relat_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v3_relat_1(A) )
=> ( v1_relat_1(k7_relat_1(A,B))
& v3_relat_1(k7_relat_1(A,B)) ) ) ).
fof(d1_relat_1,axiom,
! [A] :
( v1_relat_1(A)
<=> ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D] : B != k4_tarski(C,D) ) ) ).
fof(t1_relat_1,axiom,
$true ).
fof(t2_relat_1,axiom,
$true ).
fof(t3_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(A,B)
=> v1_relat_1(A) ) ) ).
fof(t4_relat_1,axiom,
! [A,B] : v1_relat_1(k1_tarski(k4_tarski(A,B))) ).
fof(t5_relat_1,axiom,
! [A,B,C,D] : v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) ).
fof(t6_relat_1,axiom,
! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)) ).
fof(d2_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( A = B
<=> ! [C,D] :
( r2_hidden(k4_tarski(C,D),A)
<=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ).
fof(d3_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( r1_tarski(A,B)
<=> ! [C,D] :
( r2_hidden(k4_tarski(C,D),A)
=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ).
fof(t7_relat_1,axiom,
$true ).
fof(t8_relat_1,axiom,
$true ).
fof(t9_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> v1_relat_1(k3_xboole_0(A,B)) ) ).
fof(t10_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> v1_relat_1(k4_xboole_0(B,A)) ) ).
fof(d4_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( B = k1_relat_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ).
fof(t11_relat_1,axiom,
$true ).
fof(t12_relat_1,axiom,
$true ).
fof(t13_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) ) ) ).
fof(t14_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) ) ) ).
fof(t15_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> r1_tarski(k4_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(k4_xboole_0(A,B))) ) ) ).
fof(d5_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( B = k2_relat_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) ) ).
fof(t16_relat_1,axiom,
$true ).
fof(t17_relat_1,axiom,
$true ).
fof(t18_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ~ ( r2_hidden(A,k1_relat_1(B))
& ! [C] : ~ r2_hidden(C,k2_relat_1(B)) ) ) ).
fof(t19_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ~ ( r2_hidden(A,k2_relat_1(B))
& ! [C] : ~ r2_hidden(C,k1_relat_1(B)) ) ) ).
fof(t20_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r2_hidden(k4_tarski(A,B),C)
=> ( r2_hidden(A,k1_relat_1(C))
& r2_hidden(B,k2_relat_1(C)) ) ) ) ).
fof(t21_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) ) ).
fof(t22_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) = A ) ).
fof(t23_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( C = k1_tarski(k4_tarski(A,B))
=> ( k1_relat_1(C) = k1_tarski(A)
& k2_relat_1(C) = k1_tarski(B) ) ) ) ).
fof(t24_relat_1,axiom,
! [A,B,C,D,E] :
( v1_relat_1(E)
=> ( E = k2_tarski(k4_tarski(A,B),k4_tarski(C,D))
=> ( k1_relat_1(E) = k2_tarski(A,C)
& k2_relat_1(E) = k2_tarski(B,D) ) ) ) ).
fof(t25_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( r1_tarski(A,B)
=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
& r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) ) ).
fof(t26_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ).
fof(t27_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> r1_tarski(k2_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k2_relat_1(A),k2_relat_1(B))) ) ) ).
fof(t28_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> r1_tarski(k4_xboole_0(k2_relat_1(A),k2_relat_1(B)),k2_relat_1(k4_xboole_0(A,B))) ) ) ).
fof(d6_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ).
fof(t29_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( r1_tarski(k1_relat_1(A),k3_relat_1(A))
& r1_tarski(k2_relat_1(A),k3_relat_1(A)) ) ) ).
fof(t30_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r2_hidden(k4_tarski(A,B),C)
=> ( r2_hidden(A,k3_relat_1(C))
& r2_hidden(B,k3_relat_1(C)) ) ) ) ).
fof(t31_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( r1_tarski(A,B)
=> r1_tarski(k3_relat_1(A),k3_relat_1(B)) ) ) ) ).
fof(t32_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( C = k1_tarski(k4_tarski(A,B))
=> k3_relat_1(C) = k2_tarski(A,B) ) ) ).
fof(t33_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)) ) ) ).
fof(t34_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> r1_tarski(k3_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k3_relat_1(A),k3_relat_1(B))) ) ) ).
fof(d7_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( B = k4_relat_1(A)
<=> ! [C,D] :
( r2_hidden(k4_tarski(C,D),B)
<=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) ).
fof(t35_relat_1,axiom,
$true ).
fof(t36_relat_1,axiom,
$true ).
fof(t37_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( k2_relat_1(A) = k1_relat_1(k4_relat_1(A))
& k1_relat_1(A) = k2_relat_1(k4_relat_1(A)) ) ) ).
fof(t38_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k3_relat_1(A) = k3_relat_1(k4_relat_1(A)) ) ).
fof(t39_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k4_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k4_relat_1(A),k4_relat_1(B)) ) ) ).
fof(t40_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)) ) ) ).
fof(t41_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k4_relat_1(k4_xboole_0(A,B)) = k4_xboole_0(k4_relat_1(A),k4_relat_1(B)) ) ) ).
fof(d8_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( C = k5_relat_1(A,B)
<=> ! [D,E] :
( r2_hidden(k4_tarski(D,E),C)
<=> ? [F] :
( r2_hidden(k4_tarski(D,F),A)
& r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) ).
fof(t42_relat_1,axiom,
$true ).
fof(t43_relat_1,axiom,
$true ).
fof(t44_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)) ) ) ).
fof(t45_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)) ) ) ).
fof(t46_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
=> k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ).
fof(t47_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( r1_tarski(k1_relat_1(A),k2_relat_1(B))
=> k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) ) ) ) ).
fof(t48_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) ) ).
fof(t49_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C)) ) ) ) ) ).
fof(t50_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ! [D] :
( v1_relat_1(D)
=> ( ( r1_tarski(A,B)
& r1_tarski(C,D) )
=> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D)) ) ) ) ) ) ).
fof(t51_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)) ) ) ) ).
fof(t52_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k5_relat_1(A,k3_xboole_0(B,C)),k3_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C))) ) ) ) ).
fof(t53_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k4_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)),k5_relat_1(A,k4_xboole_0(B,C))) ) ) ) ).
fof(t54_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k4_relat_1(k5_relat_1(A,B)) = k5_relat_1(k4_relat_1(B),k4_relat_1(A)) ) ) ).
fof(t55_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ).
fof(t56_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( ! [B,C] : ~ r2_hidden(k4_tarski(B,C),A)
=> A = k1_xboole_0 ) ) ).
fof(t57_relat_1,axiom,
$true ).
fof(t58_relat_1,axiom,
$true ).
fof(t59_relat_1,axiom,
$true ).
fof(t60_relat_1,axiom,
( k1_relat_1(k1_xboole_0) = k1_xboole_0
& k2_relat_1(k1_xboole_0) = k1_xboole_0 ) ).
fof(t61_relat_1,axiom,
$true ).
fof(t62_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( k5_relat_1(k1_xboole_0,A) = k1_xboole_0
& k5_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ) ).
fof(t63_relat_1,axiom,
$true ).
fof(t64_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( ( k1_relat_1(A) = k1_xboole_0
| k2_relat_1(A) = k1_xboole_0 )
=> A = k1_xboole_0 ) ) ).
fof(t65_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( k1_relat_1(A) = k1_xboole_0
<=> k2_relat_1(A) = k1_xboole_0 ) ) ).
fof(t66_relat_1,axiom,
k4_relat_1(k1_xboole_0) = k1_xboole_0 ).
fof(t67_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( r1_xboole_0(k2_relat_1(A),k1_relat_1(B))
=> k5_relat_1(A,B) = k1_xboole_0 ) ) ) ).
fof(d9_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( v2_relat_1(A)
<=> ~ r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) ).
fof(d10_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( B = k6_relat_1(A)
<=> ! [C,D] :
( r2_hidden(k4_tarski(C,D),B)
<=> ( r2_hidden(C,A)
& C = D ) ) ) ) ).
fof(t68_relat_1,axiom,
$true ).
fof(t69_relat_1,axiom,
$true ).
fof(t70_relat_1,axiom,
$true ).
fof(t71_relat_1,axiom,
! [A] :
( k1_relat_1(k6_relat_1(A)) = A
& k2_relat_1(k6_relat_1(A)) = A ) ).
fof(t72_relat_1,axiom,
! [A] : k4_relat_1(k6_relat_1(A)) = k6_relat_1(A) ).
fof(t73_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( ! [C] :
( r2_hidden(C,A)
=> r2_hidden(k4_tarski(C,C),B) )
=> r1_tarski(k6_relat_1(A),B) ) ) ).
fof(t74_relat_1,axiom,
! [A,B,C,D] :
( v1_relat_1(D)
=> ( r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D))
<=> ( r2_hidden(A,C)
& r2_hidden(k4_tarski(A,B),D) ) ) ) ).
fof(t75_relat_1,axiom,
! [A,B,C,D] :
( v1_relat_1(D)
=> ( r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))
<=> ( r2_hidden(B,C)
& r2_hidden(k4_tarski(A,B),D) ) ) ) ).
fof(t76_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(k5_relat_1(B,k6_relat_1(A)),B)
& r1_tarski(k5_relat_1(k6_relat_1(A),B),B) ) ) ).
fof(t77_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(k1_relat_1(B),A)
=> k5_relat_1(k6_relat_1(A),B) = B ) ) ).
fof(t78_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A ) ).
fof(t79_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(k2_relat_1(B),A)
=> k5_relat_1(B,k6_relat_1(A)) = B ) ) ).
fof(t80_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A ) ).
fof(t81_relat_1,axiom,
k6_relat_1(k1_xboole_0) = k1_xboole_0 ).
fof(t82_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ! [D] :
( v1_relat_1(D)
=> ( ( k1_relat_1(B) = A
& r1_tarski(k2_relat_1(C),A)
& k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D))
& k5_relat_1(B,D) = k6_relat_1(A) )
=> D = C ) ) ) ) ).
fof(d11_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B,C] :
( v1_relat_1(C)
=> ( C = k7_relat_1(A,B)
<=> ! [D,E] :
( r2_hidden(k4_tarski(D,E),C)
<=> ( r2_hidden(D,B)
& r2_hidden(k4_tarski(D,E),A) ) ) ) ) ) ).
fof(t83_relat_1,axiom,
$true ).
fof(t84_relat_1,axiom,
$true ).
fof(t85_relat_1,axiom,
$true ).
fof(t86_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))
<=> ( r2_hidden(A,B)
& r2_hidden(A,k1_relat_1(C)) ) ) ) ).
fof(t87_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k1_relat_1(k7_relat_1(B,A)),A) ) ).
fof(t88_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k7_relat_1(B,A),B) ) ).
fof(t89_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) ) ).
fof(t90_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ).
fof(t91_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(A,k1_relat_1(B))
=> k1_relat_1(k7_relat_1(B,A)) = A ) ) ).
fof(t92_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k5_relat_1(k7_relat_1(B,A),C),k5_relat_1(B,C)) ) ) ).
fof(t93_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k5_relat_1(B,k7_relat_1(C,A)),k5_relat_1(B,C)) ) ) ).
fof(t94_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B) ) ).
fof(t95_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( k7_relat_1(B,A) = k1_xboole_0
<=> r1_xboole_0(k1_relat_1(B),A) ) ) ).
fof(t96_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))) ) ).
fof(t97_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(k1_relat_1(B),A)
=> k7_relat_1(B,A) = B ) ) ).
fof(t98_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k7_relat_1(A,k1_relat_1(A)) = A ) ).
fof(t99_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ).
fof(t100_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)) ) ).
fof(t101_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A) ) ).
fof(t102_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A) ) ) ).
fof(t103_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A) ) ) ).
fof(t104_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B)) ) ) ).
fof(t105_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(B,C)
=> r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A)) ) ) ) ).
fof(t106_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ! [D] :
( v1_relat_1(D)
=> ( ( r1_tarski(C,D)
& r1_tarski(A,B) )
=> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B)) ) ) ) ).
fof(t107_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) ) ).
fof(t108_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k7_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) ) ).
fof(t109_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k7_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) ) ).
fof(t110_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k7_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ).
fof(t111_relat_1,axiom,
! [A] : k7_relat_1(k1_xboole_0,A) = k1_xboole_0 ).
fof(t112_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C) ) ) ).
fof(d12_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( C = k8_relat_1(A,B)
<=> ! [D,E] :
( r2_hidden(k4_tarski(D,E),C)
<=> ( r2_hidden(E,A)
& r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ).
fof(t113_relat_1,axiom,
$true ).
fof(t114_relat_1,axiom,
$true ).
fof(t115_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r2_hidden(A,k2_relat_1(k8_relat_1(B,C)))
<=> ( r2_hidden(A,B)
& r2_hidden(A,k2_relat_1(C)) ) ) ) ).
fof(t116_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k2_relat_1(k8_relat_1(A,B)),A) ) ).
fof(t117_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k8_relat_1(A,B),B) ) ).
fof(t118_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)) ) ).
fof(t119_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k2_relat_1(k8_relat_1(A,B)) = k3_xboole_0(k2_relat_1(B),A) ) ).
fof(t120_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(A,k2_relat_1(B))
=> k2_relat_1(k8_relat_1(A,B)) = A ) ) ).
fof(t121_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)) ) ) ).
fof(t122_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)) ) ) ).
fof(t123_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k8_relat_1(A,B) = k5_relat_1(B,k6_relat_1(A)) ) ).
fof(t124_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k8_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)) ) ).
fof(t125_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(k2_relat_1(B),A)
=> k8_relat_1(A,B) = B ) ) ).
fof(t126_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k8_relat_1(k2_relat_1(A),A) = A ) ).
fof(t127_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C) ) ).
fof(t128_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k8_relat_1(A,k8_relat_1(A,B)) = k8_relat_1(A,B) ) ).
fof(t129_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C) ) ) ).
fof(t130_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C) ) ) ).
fof(t131_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,C)) ) ) ).
fof(t132_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(B,C)
=> r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C)) ) ) ) ).
fof(t133_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ! [D] :
( v1_relat_1(D)
=> ( ( r1_tarski(C,D)
& r1_tarski(A,B) )
=> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D)) ) ) ) ).
fof(t134_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k8_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) ) ).
fof(t135_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k8_relat_1(k3_xboole_0(A,B),C) = k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) ) ).
fof(t136_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k8_relat_1(k4_xboole_0(A,B),C) = k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) ) ).
fof(t137_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k8_relat_1(k1_xboole_0,A) = k1_xboole_0 ) ).
fof(t138_relat_1,axiom,
! [A] : k8_relat_1(A,k1_xboole_0) = k1_xboole_0 ).
fof(t139_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> k8_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(B,k8_relat_1(A,C)) ) ) ).
fof(t140_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k7_relat_1(k8_relat_1(A,C),B) = k8_relat_1(A,k7_relat_1(C,B)) ) ).
fof(d13_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B,C] :
( C = k9_relat_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( r2_hidden(k4_tarski(E,D),A)
& r2_hidden(E,B) ) ) ) ) ).
fof(t141_relat_1,axiom,
$true ).
fof(t142_relat_1,axiom,
$true ).
fof(t143_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r2_hidden(A,k9_relat_1(C,B))
<=> ? [D] :
( r2_hidden(D,k1_relat_1(C))
& r2_hidden(k4_tarski(D,A),C)
& r2_hidden(D,B) ) ) ) ).
fof(t144_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) ).
fof(t145_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k9_relat_1(B,A) = k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) ) ).
fof(t146_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ).
fof(t147_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k9_relat_1(B,A),k9_relat_1(B,k1_relat_1(B))) ) ).
fof(t148_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A) ) ).
fof(t149_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k9_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ).
fof(t150_relat_1,axiom,
! [A] : k9_relat_1(k1_xboole_0,A) = k1_xboole_0 ).
fof(t151_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( k9_relat_1(B,A) = k1_xboole_0
<=> r1_xboole_0(k1_relat_1(B),A) ) ) ).
fof(t152_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ~ ( A != k1_xboole_0
& r1_tarski(A,k1_relat_1(B))
& k9_relat_1(B,A) = k1_xboole_0 ) ) ).
fof(t153_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) ) ).
fof(t154_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> r1_tarski(k9_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))) ) ).
fof(t155_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> r1_tarski(k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)),k9_relat_1(C,k4_xboole_0(A,B))) ) ).
fof(t156_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ) ).
fof(t157_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(B,C)
=> r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ) ) ).
fof(t158_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ! [D] :
( v1_relat_1(D)
=> ( ( r1_tarski(C,D)
& r1_tarski(A,B) )
=> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B)) ) ) ) ).
fof(t159_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)) ) ) ).
fof(t160_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)) ) ) ).
fof(t161_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> r1_tarski(k9_relat_1(k7_relat_1(C,A),B),k9_relat_1(C,B)) ) ).
fof(t162_relat_1,axiom,
$true ).
fof(t163_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k3_xboole_0(k1_relat_1(B),A),k9_relat_1(k4_relat_1(B),k9_relat_1(B,A))) ) ).
fof(d14_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B,C] :
( C = k10_relat_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( r2_hidden(k4_tarski(D,E),A)
& r2_hidden(E,B) ) ) ) ) ).
fof(t164_relat_1,axiom,
$true ).
fof(t165_relat_1,axiom,
$true ).
fof(t166_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r2_hidden(A,k10_relat_1(C,B))
<=> ? [D] :
( r2_hidden(D,k2_relat_1(C))
& r2_hidden(k4_tarski(A,D),C)
& r2_hidden(D,B) ) ) ) ).
fof(t167_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k10_relat_1(B,A),k1_relat_1(B)) ) ).
fof(t168_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) ) ).
fof(t169_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A) ) ).
fof(t170_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k10_relat_1(B,A),k10_relat_1(B,k2_relat_1(B))) ) ).
fof(t171_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k10_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ).
fof(t172_relat_1,axiom,
! [A] : k10_relat_1(k1_xboole_0,A) = k1_xboole_0 ).
fof(t173_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( k10_relat_1(B,A) = k1_xboole_0
<=> r1_xboole_0(k2_relat_1(B),A) ) ) ).
fof(t174_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ~ ( A != k1_xboole_0
& r1_tarski(A,k2_relat_1(B))
& k10_relat_1(B,A) = k1_xboole_0 ) ) ).
fof(t175_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> k10_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) ) ).
fof(t176_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> r1_tarski(k10_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B))) ) ).
fof(t177_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> r1_tarski(k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)),k10_relat_1(C,k4_xboole_0(A,B))) ) ).
fof(t178_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) ) ) ).
fof(t179_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(B,C)
=> r1_tarski(k10_relat_1(B,A),k10_relat_1(C,A)) ) ) ) ).
fof(t180_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ! [D] :
( v1_relat_1(D)
=> ( ( r1_tarski(C,D)
& r1_tarski(A,B) )
=> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B)) ) ) ) ).
fof(t181_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> k10_relat_1(k5_relat_1(B,C),A) = k10_relat_1(B,k10_relat_1(C,A)) ) ) ).
fof(t182_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k1_relat_1(k5_relat_1(A,B)) = k10_relat_1(A,k1_relat_1(B)) ) ) ).
fof(t183_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> r1_tarski(k3_xboole_0(k2_relat_1(B),A),k10_relat_1(k4_relat_1(B),k10_relat_1(B,A))) ) ).
fof(d15_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( v3_relat_1(A)
<=> r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0)) ) ) ).
fof(t184_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( v3_relat_1(A)
<=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
=> B = k1_xboole_0 ) ) ) ).
fof(t185_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C,D] :
( ( k7_relat_1(A,C) = k7_relat_1(B,C)
& k7_relat_1(A,D) = k7_relat_1(B,D) )
=> k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)) ) ) ) ).
fof(t186_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( ( r1_tarski(k1_relat_1(C),A)
& r1_tarski(C,B) )
=> r1_tarski(C,k7_relat_1(B,A)) ) ) ) ).
fof(t187_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( r1_xboole_0(B,k1_relat_1(A))
=> k7_relat_1(A,B) = k1_xboole_0 ) ) ).
fof(t188_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ! [C,D] :
( ( r1_tarski(C,D)
& k7_relat_1(A,D) = k7_relat_1(B,D) )
=> k7_relat_1(A,C) = k7_relat_1(B,C) ) ) ) ).
fof(t189_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k7_relat_1(A,k1_relat_1(B)) = k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))) ) ) ).
fof(t190_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ~ ( ~ v3_relat_1(k7_relat_1(B,A))
& v3_relat_1(B) ) ) ).
fof(s1_relat_1,axiom,
? [A] :
( v1_relat_1(A)
& ! [B,C] :
( r2_hidden(k4_tarski(B,C),A)
<=> ( r2_hidden(B,f1_s1_relat_1)
& r2_hidden(C,f2_s1_relat_1)
& p1_s1_relat_1(B,C) ) ) ) ).
fof(dt_k1_relat_1,axiom,
$true ).
fof(dt_k2_relat_1,axiom,
$true ).
fof(dt_k3_relat_1,axiom,
$true ).
fof(dt_k4_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> v1_relat_1(k4_relat_1(A)) ) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( v1_relat_1(A)
=> k4_relat_1(k4_relat_1(A)) = A ) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_relat_1(B) )
=> v1_relat_1(k5_relat_1(A,B)) ) ).
fof(dt_k6_relat_1,axiom,
! [A] : v1_relat_1(k6_relat_1(A)) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( v1_relat_1(A)
=> v1_relat_1(k7_relat_1(A,B)) ) ).
fof(dt_k8_relat_1,axiom,
! [A,B] :
( v1_relat_1(B)
=> v1_relat_1(k8_relat_1(A,B)) ) ).
fof(dt_k9_relat_1,axiom,
$true ).
fof(dt_k10_relat_1,axiom,
$true ).
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