SET007 Axioms: SET007+22.ax
%------------------------------------------------------------------------------
% File : SET007+22 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Domains and Their Cartesian Products
% 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 : domain_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 140 ( 34 unt; 0 def)
% Number of atoms : 731 ( 112 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 813 ( 222 ~; 2 |; 295 &)
% ( 50 <=>; 244 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-4 aty)
% Number of functors : 95 ( 95 usr; 13 con; 0-9 aty)
% Number of variables : 524 ( 453 !; 71 ?)
% 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(t1_domain_1,axiom,
$true ).
fof(t2_domain_1,axiom,
$true ).
fof(t3_domain_1,axiom,
$true ).
fof(t4_domain_1,axiom,
$true ).
fof(t5_domain_1,axiom,
$true ).
fof(t6_domain_1,axiom,
$true ).
fof(t7_domain_1,axiom,
$true ).
fof(t8_domain_1,axiom,
$true ).
fof(t9_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ~ ( r2_hidden(A,k2_zfmisc_1(B,C))
& ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( m1_subset_1(E,C)
=> A != k4_tarski(D,E) ) ) ) ) ) ).
fof(t10_domain_1,axiom,
$true ).
fof(t11_domain_1,axiom,
$true ).
fof(t12_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(A,B))
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(A,B))
=> ( ( k1_mcart_1(C) = k1_mcart_1(D)
& k2_mcart_1(C) = k2_mcart_1(D) )
=> C = D ) ) ) ) ) ).
fof(t13_domain_1,axiom,
$true ).
fof(t14_domain_1,axiom,
$true ).
fof(t15_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( r2_hidden(A,k3_zfmisc_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& ? [F] :
( m1_subset_1(F,C)
& ? [G] :
( m1_subset_1(G,D)
& A = k3_mcart_1(E,F,G) ) ) ) ) ) ) ) ).
fof(t16_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( ! [E] :
( r2_hidden(E,A)
<=> ? [F] :
( m1_subset_1(F,B)
& ? [G] :
( m1_subset_1(G,C)
& ? [H] :
( m1_subset_1(H,D)
& E = k3_mcart_1(F,G,H) ) ) ) )
=> A = k3_zfmisc_1(B,C,D) ) ) ) ) ) ).
fof(t17_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( A = k3_zfmisc_1(B,C,D)
<=> ! [E] :
( r2_hidden(E,A)
<=> ? [F] :
( m1_subset_1(F,B)
& ? [G] :
( m1_subset_1(G,C)
& ? [H] :
( m1_subset_1(H,D)
& E = k3_mcart_1(F,G,H) ) ) ) ) ) ) ) ) ) ).
fof(t18_domain_1,axiom,
$true ).
fof(t19_domain_1,axiom,
$true ).
fof(t20_domain_1,axiom,
$true ).
fof(t21_domain_1,axiom,
$true ).
fof(t22_domain_1,axiom,
$true ).
fof(t23_domain_1,axiom,
$true ).
fof(t24_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(B,C,D))
=> ( A = k5_mcart_1(B,C,D,E)
<=> ! [F] :
( m1_subset_1(F,B)
=> ! [G] :
( m1_subset_1(G,C)
=> ! [H] :
( m1_subset_1(H,D)
=> ( E = k4_domain_1(B,C,D,F,G,H)
=> A = F ) ) ) ) ) ) ) ) ) ).
fof(t25_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(B,C,D))
=> ( A = k6_mcart_1(B,C,D,E)
<=> ! [F] :
( m1_subset_1(F,B)
=> ! [G] :
( m1_subset_1(G,C)
=> ! [H] :
( m1_subset_1(H,D)
=> ( E = k4_domain_1(B,C,D,F,G,H)
=> A = G ) ) ) ) ) ) ) ) ) ).
fof(t26_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(B,C,D))
=> ( A = k7_mcart_1(B,C,D,E)
<=> ! [F] :
( m1_subset_1(F,B)
=> ! [G] :
( m1_subset_1(G,C)
=> ! [H] :
( m1_subset_1(H,D)
=> ( E = k4_domain_1(B,C,D,F,G,H)
=> A = H ) ) ) ) ) ) ) ) ) ).
fof(t27_domain_1,axiom,
$true ).
fof(t28_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k3_zfmisc_1(A,B,C))
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(A,B,C))
=> ( ( k5_mcart_1(A,B,C,D) = k5_mcart_1(A,B,C,E)
& k6_mcart_1(A,B,C,D) = k6_mcart_1(A,B,C,E)
& k7_mcart_1(A,B,C,D) = k7_mcart_1(A,B,C,E) )
=> D = E ) ) ) ) ) ) ).
fof(t29_domain_1,axiom,
$true ).
fof(t30_domain_1,axiom,
$true ).
fof(t31_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ( r2_hidden(A,k4_zfmisc_1(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,B)
& ? [G] :
( m1_subset_1(G,C)
& ? [H] :
( m1_subset_1(H,D)
& ? [I] :
( m1_subset_1(I,E)
& A = k4_mcart_1(F,G,H,I) ) ) ) ) ) ) ) ) ) ).
fof(t32_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ( ! [F] :
( r2_hidden(F,A)
<=> ? [G] :
( m1_subset_1(G,B)
& ? [H] :
( m1_subset_1(H,C)
& ? [I] :
( m1_subset_1(I,D)
& ? [J] :
( m1_subset_1(J,E)
& F = k4_mcart_1(G,H,I,J) ) ) ) ) )
=> A = k4_zfmisc_1(B,C,D,E) ) ) ) ) ) ) ).
fof(t33_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ( A = k4_zfmisc_1(B,C,D,E)
<=> ! [F] :
( r2_hidden(F,A)
<=> ? [G] :
( m1_subset_1(G,B)
& ? [H] :
( m1_subset_1(H,C)
& ? [I] :
( m1_subset_1(I,D)
& ? [J] :
( m1_subset_1(J,E)
& F = k4_mcart_1(G,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_domain_1,axiom,
$true ).
fof(t35_domain_1,axiom,
$true ).
fof(t36_domain_1,axiom,
$true ).
fof(t37_domain_1,axiom,
$true ).
fof(t38_domain_1,axiom,
$true ).
fof(t39_domain_1,axiom,
$true ).
fof(t40_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ! [F] :
( m1_subset_1(F,k4_zfmisc_1(B,C,D,E))
=> ( A = k8_mcart_1(B,C,D,E,F)
<=> ! [G] :
( m1_subset_1(G,B)
=> ! [H] :
( m1_subset_1(H,C)
=> ! [I] :
( m1_subset_1(I,D)
=> ! [J] :
( m1_subset_1(J,E)
=> ( F = k5_domain_1(B,C,D,E,G,H,I,J)
=> A = G ) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ! [F] :
( m1_subset_1(F,k4_zfmisc_1(B,C,D,E))
=> ( A = k9_mcart_1(B,C,D,E,F)
<=> ! [G] :
( m1_subset_1(G,B)
=> ! [H] :
( m1_subset_1(H,C)
=> ! [I] :
( m1_subset_1(I,D)
=> ! [J] :
( m1_subset_1(J,E)
=> ( F = k5_domain_1(B,C,D,E,G,H,I,J)
=> A = H ) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ! [F] :
( m1_subset_1(F,k4_zfmisc_1(B,C,D,E))
=> ( A = k10_mcart_1(B,C,D,E,F)
<=> ! [G] :
( m1_subset_1(G,B)
=> ! [H] :
( m1_subset_1(H,C)
=> ! [I] :
( m1_subset_1(I,D)
=> ! [J] :
( m1_subset_1(J,E)
=> ( F = k5_domain_1(B,C,D,E,G,H,I,J)
=> A = I ) ) ) ) ) ) ) ) ) ) ) ).
fof(t43_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ! [F] :
( m1_subset_1(F,k4_zfmisc_1(B,C,D,E))
=> ( A = k11_mcart_1(B,C,D,E,F)
<=> ! [G] :
( m1_subset_1(G,B)
=> ! [H] :
( m1_subset_1(H,C)
=> ! [I] :
( m1_subset_1(I,D)
=> ! [J] :
( m1_subset_1(J,E)
=> ( F = k5_domain_1(B,C,D,E,G,H,I,J)
=> A = J ) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_domain_1,axiom,
$true ).
fof(t45_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
=> ! [F] :
( m1_subset_1(F,k4_zfmisc_1(A,B,C,D))
=> ( ( k8_mcart_1(A,B,C,D,E) = k8_mcart_1(A,B,C,D,F)
& k9_mcart_1(A,B,C,D,E) = k9_mcart_1(A,B,C,D,F)
& k10_mcart_1(A,B,C,D,E) = k10_mcart_1(A,B,C,D,F)
& k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) )
=> E = F ) ) ) ) ) ) ) ).
fof(t46_domain_1,axiom,
$true ).
fof(t47_domain_1,axiom,
$true ).
fof(dt_k1_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,A)
& m1_subset_1(D,B) )
=> m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ).
fof(redefinition_k1_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,A)
& m1_subset_1(D,B) )
=> k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ).
fof(dt_k2_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,k2_zfmisc_1(A,B)) )
=> m1_subset_1(k2_domain_1(A,B,C),A) ) ).
fof(redefinition_k2_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,k2_zfmisc_1(A,B)) )
=> k2_domain_1(A,B,C) = k1_mcart_1(C) ) ).
fof(dt_k3_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,k2_zfmisc_1(A,B)) )
=> m1_subset_1(k3_domain_1(A,B,C),B) ) ).
fof(redefinition_k3_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,k2_zfmisc_1(A,B)) )
=> k3_domain_1(A,B,C) = k2_mcart_1(C) ) ).
fof(dt_k4_domain_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,A)
& m1_subset_1(E,B)
& m1_subset_1(F,C) )
=> m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)) ) ).
fof(redefinition_k4_domain_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,A)
& m1_subset_1(E,B)
& m1_subset_1(F,C) )
=> k4_domain_1(A,B,C,D,E,F) = k3_mcart_1(D,E,F) ) ).
fof(dt_k5_domain_1,axiom,
! [A,B,C,D,E,F,G,H] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ~ v1_xboole_0(D)
& m1_subset_1(E,A)
& m1_subset_1(F,B)
& m1_subset_1(G,C)
& m1_subset_1(H,D) )
=> m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)) ) ).
fof(redefinition_k5_domain_1,axiom,
! [A,B,C,D,E,F,G,H] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ~ v1_xboole_0(D)
& m1_subset_1(E,A)
& m1_subset_1(F,B)
& m1_subset_1(G,C)
& m1_subset_1(H,D) )
=> k5_domain_1(A,B,C,D,E,F,G,H) = k4_mcart_1(E,F,G,H) ) ).
fof(dt_k6_domain_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A) )
=> m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ).
fof(redefinition_k6_domain_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A) )
=> k6_domain_1(A,B) = k1_tarski(B) ) ).
fof(dt_k7_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A) )
=> m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)) ) ).
fof(commutativity_k7_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A) )
=> k7_domain_1(A,B,C) = k7_domain_1(A,C,B) ) ).
fof(redefinition_k7_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A) )
=> k7_domain_1(A,B,C) = k2_tarski(B,C) ) ).
fof(dt_k8_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A) )
=> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)) ) ).
fof(redefinition_k8_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A) )
=> k8_domain_1(A,B,C,D) = k1_enumset1(B,C,D) ) ).
fof(dt_k9_domain_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A) )
=> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)) ) ).
fof(redefinition_k9_domain_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A) )
=> k9_domain_1(A,B,C,D,E) = k2_enumset1(B,C,D,E) ) ).
fof(dt_k10_domain_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A) )
=> m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)) ) ).
fof(redefinition_k10_domain_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A) )
=> k10_domain_1(A,B,C,D,E,F) = k3_enumset1(B,C,D,E,F) ) ).
fof(dt_k11_domain_1,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& m1_subset_1(G,A) )
=> m1_subset_1(k11_domain_1(A,B,C,D,E,F,G),k1_zfmisc_1(A)) ) ).
fof(redefinition_k11_domain_1,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& m1_subset_1(G,A) )
=> k11_domain_1(A,B,C,D,E,F,G) = k4_enumset1(B,C,D,E,F,G) ) ).
fof(dt_k12_domain_1,axiom,
! [A,B,C,D,E,F,G,H] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& m1_subset_1(G,A)
& m1_subset_1(H,A) )
=> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)) ) ).
fof(redefinition_k12_domain_1,axiom,
! [A,B,C,D,E,F,G,H] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& m1_subset_1(G,A)
& m1_subset_1(H,A) )
=> k12_domain_1(A,B,C,D,E,F,G,H) = k5_enumset1(B,C,D,E,F,G,H) ) ).
fof(dt_k13_domain_1,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& m1_subset_1(G,A)
& m1_subset_1(H,A)
& m1_subset_1(I,A) )
=> m1_subset_1(k13_domain_1(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(A)) ) ).
fof(redefinition_k13_domain_1,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& m1_subset_1(G,A)
& m1_subset_1(H,A)
& m1_subset_1(I,A) )
=> k13_domain_1(A,B,C,D,E,F,G,H,I) = k6_enumset1(B,C,D,E,F,G,H,I) ) ).
fof(dt_k14_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) )
=> m1_subset_1(k14_domain_1(A,B,C,D),A) ) ).
fof(redefinition_k14_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) )
=> k14_domain_1(A,B,C,D) = k17_mcart_1(D) ) ).
fof(dt_k15_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) )
=> m1_subset_1(k15_domain_1(A,B,C,D),B) ) ).
fof(redefinition_k15_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) )
=> k15_domain_1(A,B,C,D) = k18_mcart_1(D) ) ).
fof(dt_k16_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) )
=> m1_subset_1(k16_domain_1(A,B,C,D),B) ) ).
fof(redefinition_k16_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) )
=> k16_domain_1(A,B,C,D) = k19_mcart_1(D) ) ).
fof(dt_k17_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) )
=> m1_subset_1(k17_domain_1(A,B,C,D),C) ) ).
fof(redefinition_k17_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) )
=> k17_domain_1(A,B,C,D) = k20_mcart_1(D) ) ).
fof(t48_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> A = a_1_0_domain_1(A) ) ).
fof(t49_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> k2_zfmisc_1(A,B) = a_2_0_domain_1(A,B) ) ) ).
fof(t50_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> k3_zfmisc_1(A,B,C) = a_3_0_domain_1(A,B,C) ) ) ) ).
fof(t51_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> k4_zfmisc_1(A,B,C,D) = a_4_0_domain_1(A,B,C,D) ) ) ) ) ).
fof(t52_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> B = a_2_1_domain_1(A,B) ) ) ).
fof(t53_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> k12_mcart_1(A,B,C,D) = a_4_1_domain_1(A,B,C,D) ) ) ) ) ).
fof(t54_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(B))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(C))
=> k13_mcart_1(A,B,C,D,E,F) = a_6_0_domain_1(A,B,C,D,E,F) ) ) ) ) ) ) ).
fof(t55_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(A))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(B))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(C))
=> ! [H] :
( m1_subset_1(H,k1_zfmisc_1(D))
=> k14_mcart_1(A,B,C,D,E,F,G,H) = a_8_0_domain_1(A,B,C,D,E,F,G,H) ) ) ) ) ) ) ) ) ).
fof(t56_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k1_subset_1(A) = a_1_1_domain_1(A) ) ).
fof(t57_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> k3_subset_1(A,B) = a_2_2_domain_1(A,B) ) ) ).
fof(t58_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> k5_subset_1(A,B,C) = a_3_1_domain_1(A,B,C) ) ) ) ).
fof(t59_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> k4_subset_1(A,B,C) = a_3_2_domain_1(A,B,C) ) ) ) ).
fof(t60_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> k6_subset_1(A,B,C) = a_3_3_domain_1(A,B,C) ) ) ) ).
fof(t61_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> k7_subset_1(A,B,C) = a_3_4_domain_1(A,B,C) ) ) ) ).
fof(t62_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> k7_subset_1(A,B,C) = a_3_5_domain_1(A,B,C) ) ) ) ).
fof(t63_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> k7_subset_1(A,B,C) = a_3_6_domain_1(A,B,C) ) ) ) ).
fof(t64_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> k7_subset_1(A,B,C) = a_3_7_domain_1(A,B,C) ) ) ) ).
fof(s1_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> m1_subset_1(a_1_2_domain_1(A),k1_zfmisc_1(A)) ) ).
fof(s2_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> m1_subset_1(a_2_3_domain_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) ).
fof(s3_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> m1_subset_1(a_3_8_domain_1(A,B,C),k1_zfmisc_1(k3_zfmisc_1(A,B,C))) ) ) ) ).
fof(s4_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> m1_subset_1(a_4_2_domain_1(A,B,C,D),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))) ) ) ) ) ).
fof(s5_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ! [B] :
( m1_subset_1(B,A)
=> ( p1_s5_domain_1(B)
=> p2_s5_domain_1(B) ) )
=> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A)) ) ) ).
fof(s6_domain_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ! [B] :
( m1_subset_1(B,A)
=> ( p1_s6_domain_1(B)
<=> p2_s6_domain_1(B) ) )
=> a_1_5_domain_1(A) = a_1_6_domain_1(A) ) ) ).
fof(s7_domain_1,axiom,
m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(f1_s7_domain_1)) ).
fof(s8_domain_1,axiom,
m1_subset_1(a_0_1_domain_1,k1_zfmisc_1(f2_s8_domain_1)) ).
fof(s9_domain_1,axiom,
m1_subset_1(a_0_2_domain_1,k1_zfmisc_1(f3_s9_domain_1)) ).
fof(s10_domain_1,axiom,
a_0_3_domain_1 = k3_xboole_0(a_0_4_domain_1,a_0_5_domain_1) ).
fof(fraenkel_a_1_0_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_0_domain_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = C ) ) ) ).
fof(fraenkel_a_2_0_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C) )
=> ( r2_hidden(A,a_2_0_domain_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,B)
& m1_subset_1(E,C)
& A = k1_domain_1(B,C,D,E) ) ) ) ).
fof(fraenkel_a_3_0_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ~ v1_xboole_0(D) )
=> ( r2_hidden(A,a_3_0_domain_1(B,C,D))
<=> ? [E,F,G] :
( m1_subset_1(E,B)
& m1_subset_1(F,C)
& m1_subset_1(G,D)
& A = k4_domain_1(B,C,D,E,F,G) ) ) ) ).
fof(fraenkel_a_4_0_domain_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ~ v1_xboole_0(D)
& ~ v1_xboole_0(E) )
=> ( r2_hidden(A,a_4_0_domain_1(B,C,D,E))
<=> ? [F,G,H,I] :
( m1_subset_1(F,B)
& m1_subset_1(G,C)
& m1_subset_1(H,D)
& m1_subset_1(I,E)
& A = k5_domain_1(B,C,D,E,F,G,H,I) ) ) ) ).
fof(fraenkel_a_2_1_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_2_1_domain_1(B,C))
<=> ? [D] :
( m1_subset_1(D,B)
& A = D
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_4_1_domain_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,k1_zfmisc_1(B))
& m1_subset_1(E,k1_zfmisc_1(C)) )
=> ( r2_hidden(A,a_4_1_domain_1(B,C,D,E))
<=> ? [F,G] :
( m1_subset_1(F,B)
& m1_subset_1(G,C)
& A = k1_domain_1(B,C,F,G)
& r2_hidden(F,D)
& r2_hidden(G,E) ) ) ) ).
fof(fraenkel_a_6_0_domain_1,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ~ v1_xboole_0(D)
& m1_subset_1(E,k1_zfmisc_1(B))
& m1_subset_1(F,k1_zfmisc_1(C))
& m1_subset_1(G,k1_zfmisc_1(D)) )
=> ( r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G))
<=> ? [H,I,J] :
( m1_subset_1(H,B)
& m1_subset_1(I,C)
& m1_subset_1(J,D)
& A = k4_domain_1(B,C,D,H,I,J)
& r2_hidden(H,E)
& r2_hidden(I,F)
& r2_hidden(J,G) ) ) ) ).
fof(fraenkel_a_8_0_domain_1,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ~ v1_xboole_0(D)
& ~ v1_xboole_0(E)
& m1_subset_1(F,k1_zfmisc_1(B))
& m1_subset_1(G,k1_zfmisc_1(C))
& m1_subset_1(H,k1_zfmisc_1(D))
& m1_subset_1(I,k1_zfmisc_1(E)) )
=> ( r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I))
<=> ? [J,K,L,M] :
( m1_subset_1(J,B)
& m1_subset_1(K,C)
& m1_subset_1(L,D)
& m1_subset_1(M,E)
& A = k5_domain_1(B,C,D,E,J,K,L,M)
& r2_hidden(J,F)
& r2_hidden(K,G)
& r2_hidden(L,H)
& r2_hidden(M,I) ) ) ) ).
fof(fraenkel_a_1_1_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_1_domain_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = C
& ~ $true ) ) ) ).
fof(fraenkel_a_2_2_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_2_2_domain_1(B,C))
<=> ? [D] :
( m1_subset_1(D,B)
& A = D
& ~ r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_3_1_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(C,k1_zfmisc_1(B))
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_3_1_domain_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& A = E
& r2_hidden(E,C)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_3_2_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(C,k1_zfmisc_1(B))
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_3_2_domain_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& A = E
& ( r2_hidden(E,C)
| r2_hidden(E,D) ) ) ) ) ).
fof(fraenkel_a_3_3_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(C,k1_zfmisc_1(B))
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_3_3_domain_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& A = E
& r2_hidden(E,C)
& ~ r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_3_4_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(C,k1_zfmisc_1(B))
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_3_4_domain_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& A = E
& ( ( r2_hidden(E,C)
& ~ r2_hidden(E,D) )
| ( ~ r2_hidden(E,C)
& r2_hidden(E,D) ) ) ) ) ) ).
fof(fraenkel_a_3_5_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(C,k1_zfmisc_1(B))
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_3_5_domain_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& A = E
& ( ~ r2_hidden(E,C)
<=> r2_hidden(E,D) ) ) ) ) ).
fof(fraenkel_a_3_6_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(C,k1_zfmisc_1(B))
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_3_6_domain_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& A = E
& ( r2_hidden(E,C)
<=> ~ r2_hidden(E,D) ) ) ) ) ).
fof(fraenkel_a_3_7_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(C,k1_zfmisc_1(B))
& m1_subset_1(D,k1_zfmisc_1(B)) )
=> ( r2_hidden(A,a_3_7_domain_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& A = E
& ~ ( r2_hidden(E,C)
<=> r2_hidden(E,D) ) ) ) ) ).
fof(fraenkel_a_1_2_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_2_domain_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = C
& p1_s1_domain_1(C) ) ) ) ).
fof(fraenkel_a_2_3_domain_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C) )
=> ( r2_hidden(A,a_2_3_domain_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,B)
& m1_subset_1(E,C)
& A = k1_domain_1(B,C,D,E)
& p1_s2_domain_1(D,E) ) ) ) ).
fof(fraenkel_a_3_8_domain_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ~ v1_xboole_0(D) )
=> ( r2_hidden(A,a_3_8_domain_1(B,C,D))
<=> ? [E,F,G] :
( m1_subset_1(E,B)
& m1_subset_1(F,C)
& m1_subset_1(G,D)
& A = k4_domain_1(B,C,D,E,F,G)
& p1_s3_domain_1(E,F,G) ) ) ) ).
fof(fraenkel_a_4_2_domain_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ~ v1_xboole_0(D)
& ~ v1_xboole_0(E) )
=> ( r2_hidden(A,a_4_2_domain_1(B,C,D,E))
<=> ? [F,G,H,I] :
( m1_subset_1(F,B)
& m1_subset_1(G,C)
& m1_subset_1(H,D)
& m1_subset_1(I,E)
& A = k5_domain_1(B,C,D,E,F,G,H,I)
& p1_s4_domain_1(F,G,H,I) ) ) ) ).
fof(fraenkel_a_1_3_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_3_domain_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = C
& p1_s5_domain_1(C) ) ) ) ).
fof(fraenkel_a_1_4_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_4_domain_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = C
& p2_s5_domain_1(C) ) ) ) ).
fof(fraenkel_a_1_5_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_5_domain_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = C
& p1_s6_domain_1(C) ) ) ) ).
fof(fraenkel_a_1_6_domain_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_6_domain_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = C
& p2_s6_domain_1(C) ) ) ) ).
fof(fraenkel_a_0_0_domain_1,axiom,
! [A] :
( r2_hidden(A,a_0_0_domain_1)
<=> ? [B] :
( m1_subset_1(B,f1_s7_domain_1)
& A = B
& p1_s7_domain_1(B) ) ) ).
fof(fraenkel_a_0_1_domain_1,axiom,
! [A] :
( r2_hidden(A,a_0_1_domain_1)
<=> ? [B] :
( m1_subset_1(B,f1_s8_domain_1)
& A = f3_s8_domain_1(B)
& p1_s8_domain_1(B) ) ) ).
fof(fraenkel_a_0_2_domain_1,axiom,
! [A] :
( r2_hidden(A,a_0_2_domain_1)
<=> ? [B,C] :
( m1_subset_1(B,f1_s9_domain_1)
& m1_subset_1(C,f2_s9_domain_1)
& A = f4_s9_domain_1(B,C)
& p1_s9_domain_1(B,C) ) ) ).
fof(fraenkel_a_0_3_domain_1,axiom,
! [A] :
( r2_hidden(A,a_0_3_domain_1)
<=> ? [B] :
( m1_subset_1(B,f1_s10_domain_1)
& A = B
& p1_s10_domain_1(B)
& p2_s10_domain_1(B) ) ) ).
fof(fraenkel_a_0_4_domain_1,axiom,
! [A] :
( r2_hidden(A,a_0_4_domain_1)
<=> ? [B] :
( m1_subset_1(B,f1_s10_domain_1)
& A = B
& p1_s10_domain_1(B) ) ) ).
fof(fraenkel_a_0_5_domain_1,axiom,
! [A] :
( r2_hidden(A,a_0_5_domain_1)
<=> ? [B] :
( m1_subset_1(B,f1_s10_domain_1)
& A = B
& p2_s10_domain_1(B) ) ) ).
%------------------------------------------------------------------------------