SET007 Axioms: SET007+898.ax
%------------------------------------------------------------------------------
% File : SET007+898 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Stirling Numbers of the Second Kind
% 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 : stirl2_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 123 ( 1 unt; 0 def)
% Number of atoms : 908 ( 164 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 870 ( 85 ~; 10 |; 407 &)
% ( 22 <=>; 346 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 35 ( 34 usr; 0 prp; 1-3 aty)
% Number of functors : 109 ( 109 usr; 41 con; 0-6 aty)
% Number of variables : 354 ( 333 !; 21 ?)
% 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(cc1_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v4_ordinal2(B)
& v1_xcmplx_0(B)
& v1_finset_1(B)
& v1_xreal_0(B)
& ~ v3_xreal_0(B)
& v1_int_1(B) ) ) ) ).
fof(fc1_stirl2_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> ( v4_ordinal2(k1_funct_1(C,D))
& v1_xcmplx_0(k1_funct_1(C,D))
& v1_finset_1(k1_funct_1(C,D))
& v1_xreal_0(k1_funct_1(C,D))
& ~ v3_xreal_0(k1_funct_1(C,D))
& v1_int_1(k1_funct_1(C,D)) ) ) ).
fof(t1_stirl2_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
=> k10_cqc_sim1(A) = k1_henmodel(A) ) ).
fof(t2_stirl2_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
=> k3_square_1(k10_cqc_sim1(A),k10_cqc_sim1(B)) = k10_cqc_sim1(k4_subset_1(k5_numbers,A,B)) ) ) ).
fof(t3_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
=> r1_xreal_0(k3_square_1(k1_henmodel(A),k1_henmodel(B)),k1_henmodel(k4_subset_1(k5_numbers,A,B))) ) ) ).
fof(t4_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
=> ( ~ r2_hidden(k1_henmodel(A),k5_subset_1(k5_numbers,A,B))
=> k1_henmodel(A) = k1_henmodel(k6_subset_1(k5_numbers,A,B)) ) ) ) ).
fof(t5_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k1_henmodel(k1_stirl2_1(A)) = A
& k10_cqc_sim1(k1_stirl2_1(A)) = A ) ) ).
fof(t6_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k1_henmodel(k2_stirl2_1(A,B)) = k3_square_1(A,B)
& k10_cqc_sim1(k2_stirl2_1(A,B)) = k3_square_1(A,B) ) ) ) ).
fof(t7_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_henmodel(k3_stirl2_1(A,B,C)) = k3_square_1(A,k3_square_1(B,C)) ) ) ) ).
fof(t8_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> m1_subset_1(A,k1_zfmisc_1(k5_numbers)) ) ).
fof(t9_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
=> ( r1_tarski(B,A)
=> m2_subset_1(k10_binop_2(A,np__1),k1_numbers,k5_numbers) ) ) ) ).
fof(t10_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(A,B)
=> ( r1_xreal_0(A,k10_binop_2(B,np__1))
& m2_subset_1(k10_binop_2(B,np__1),k1_numbers,k5_numbers) ) ) ) ) ).
fof(t11_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_henmodel(A) = np__0 ) ).
fof(t12_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
=> ( r1_tarski(B,A)
=> r1_xreal_0(k1_henmodel(B),k10_binop_2(A,np__1)) ) ) ) ).
fof(t13_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
=> ~ ( r1_tarski(B,A)
& B != k2_setwiseo(k1_numbers,k10_binop_2(A,np__1))
& r1_xreal_0(k10_binop_2(A,np__1),k1_henmodel(B)) ) ) ) ).
fof(t14_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
=> ( r1_tarski(B,A)
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(k1_henmodel(B),k10_binop_2(A,np__1)) ) ) ) ) ).
fof(d1_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v1_stirl2_1(C,A,B)
<=> ( ( A = np__0
=> B = np__0 )
& ( B = np__0
=> A = np__0 )
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k5_relset_1(A,B,C))
& r2_hidden(E,k5_relset_1(A,B,C))
& ~ r1_xreal_0(E,D)
& r1_xreal_0(k1_henmodel(k4_stirl2_1(A,B,C,k1_stirl2_1(E))),k1_henmodel(k4_stirl2_1(A,B,C,k1_stirl2_1(D)))) ) ) ) ) ) ) ) ) ).
fof(t15_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( A = np__0
& B = np__0 )
=> ( v2_funct_2(C,A,B)
& v1_stirl2_1(C,A,B) ) ) ) ) ) ).
fof(t16_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ( ~ r1_xreal_0(B,np__0)
=> r1_xreal_0(k1_henmodel(k4_stirl2_1(B,A,D,k1_stirl2_1(C))),k10_binop_2(B,np__1)) ) ) ) ) ) ).
fof(t17_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v2_funct_2(C,A,B)
=> r1_xreal_0(B,A) ) ) ) ) ).
fof(t18_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( v2_funct_2(C,A,B)
& v1_stirl2_1(C,A,B) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,D)
=> r1_xreal_0(D,k1_henmodel(k4_stirl2_1(A,B,C,k1_stirl2_1(D)))) ) ) ) ) ) ) ).
fof(t19_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,A)
& m2_relset_1(C,B,A) )
=> ( ( v2_funct_2(C,B,A)
& v1_stirl2_1(C,B,A) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,D)
=> r1_xreal_0(k1_henmodel(k4_stirl2_1(B,A,C,k1_stirl2_1(D))),k9_binop_2(k10_binop_2(B,A),D)) ) ) ) ) ) ) ).
fof(t20_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( v2_funct_2(C,A,B)
& v1_stirl2_1(C,A,B)
& A = B )
=> C = k6_partfun1(A) ) ) ) ) ).
fof(t21_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,A)
& m2_relset_1(C,B,A) )
=> ( C = k6_partfun1(B)
=> ( r1_xreal_0(B,np__0)
| v1_stirl2_1(C,B,A) ) ) ) ) ) ).
fof(t22_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ( A = np__0
=> B = np__0 )
& ( B = np__0
=> A = np__0 )
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ~ v1_stirl2_1(C,A,B) ) ) ) ) ).
fof(t23_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ( A = np__0
=> B = np__0 )
& ( B = np__0
=> A = np__0 )
& r1_xreal_0(B,A)
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ~ ( v2_funct_2(C,A,B)
& v1_stirl2_1(C,A,B) ) ) ) ) ) ).
fof(t26_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k6_stirl2_1(A,A) = k4_ordinal2 ) ).
fof(t27_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( A != np__0
=> k6_stirl2_1(np__0,A) = np__0 ) ) ).
fof(t28_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k6_stirl2_1(np__0,A) = k4_ordinal2
<=> A = np__0 ) ) ).
fof(t29_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,A)
=> k6_stirl2_1(A,B) = np__0 ) ) ) ).
fof(t30_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k6_stirl2_1(A,np__0) = k4_ordinal2
<=> A = np__0 ) ) ).
fof(t31_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( A != np__0
=> k6_stirl2_1(A,np__0) = np__0 ) ) ).
fof(t32_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( A != np__0
=> k6_stirl2_1(A,np__1) = k4_ordinal2 ) ) ).
fof(t33_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ ( ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B) )
| A = B )
& r1_xreal_0(k6_stirl2_1(B,A),np__0) )
& ~ ( ~ r1_xreal_0(k6_stirl2_1(B,A),np__0)
& ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B) )
& A != B ) ) ) ) ).
fof(t34_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
& m2_relset_1(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1)) )
=> ( ( v2_funct_2(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
& v1_stirl2_1(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
& k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,k2_setwiseo(k23_binop_2(B,np__1),k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A))) = k1_stirl2_1(A) )
=> k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A) = B ) ) ) ) ).
fof(t35_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k23_binop_2(A,np__1),B)
& m2_relset_1(C,k23_binop_2(A,np__1),B) )
=> ~ ( B != np__0
& k4_stirl2_1(k23_binop_2(A,np__1),B,C,k1_tarski(k5_stirl2_1(k23_binop_2(A,np__1),B,C,A))) != k1_stirl2_1(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_stirl2_1(k23_binop_2(A,np__1),B,C,k1_tarski(k5_stirl2_1(k23_binop_2(A,np__1),B,C,A))))
& D != A ) ) ) ) ) ) ).
fof(t36_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k23_binop_2(A,C),k23_binop_2(B,D))
& m2_relset_1(F,k23_binop_2(A,C),k23_binop_2(B,D)) )
=> ( ( v1_stirl2_1(F,k23_binop_2(A,C),k23_binop_2(B,D))
& E = k2_partfun1(k23_binop_2(A,C),k23_binop_2(B,D),F,A) )
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(G,k5_relset_1(A,B,E))
& r2_hidden(H,k5_relset_1(A,B,E))
& ~ r1_xreal_0(H,G)
& r1_xreal_0(k1_henmodel(k4_stirl2_1(A,B,E,k1_stirl2_1(H))),k1_henmodel(k4_stirl2_1(A,B,E,k1_stirl2_1(G)))) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
& m2_relset_1(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1)) )
=> ( ( v2_funct_2(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
& v1_stirl2_1(C,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
& k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,k2_setwiseo(k23_binop_2(B,np__1),k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A))) = k1_stirl2_1(A) )
=> ( r1_tarski(k5_relset_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),k2_partfun1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A)),B)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( D = k2_partfun1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),C,A)
=> ( v2_funct_2(D,A,B)
& v1_stirl2_1(D,A,B) ) ) ) ) ) ) ) ) ).
fof(t38_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k23_binop_2(A,np__1),B)
& m2_relset_1(C,k23_binop_2(A,np__1),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( ( v2_funct_2(C,k23_binop_2(A,np__1),B)
& v1_stirl2_1(C,k23_binop_2(A,np__1),B)
& k2_partfun1(k23_binop_2(A,np__1),B,C,A) = D )
=> ( k4_stirl2_1(k23_binop_2(A,np__1),B,C,k1_tarski(k5_stirl2_1(k23_binop_2(A,np__1),B,C,A))) = k1_stirl2_1(A)
| ( v2_funct_2(D,A,B)
& v1_stirl2_1(D,A,B) ) ) ) ) ) ) ) ).
fof(t39_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k23_binop_2(A,np__1),k23_binop_2(B,C))
& m2_relset_1(E,k23_binop_2(A,np__1),k23_binop_2(B,C)) )
=> ( ( v2_funct_2(D,A,B)
& v1_stirl2_1(D,A,B)
& D = k2_partfun1(k23_binop_2(A,np__1),k23_binop_2(B,C),E,A) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(F,k5_relset_1(k23_binop_2(A,np__1),k23_binop_2(B,C),E))
& r2_hidden(G,k5_relset_1(k23_binop_2(A,np__1),k23_binop_2(B,C),E))
& ~ r1_xreal_0(G,F)
& r1_xreal_0(k1_henmodel(k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,C),E,k1_stirl2_1(G))),k1_henmodel(k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,C),E,k1_stirl2_1(F)))) ) ) ) ) ) ) ) ) ) ).
fof(t40_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
& m2_relset_1(D,k23_binop_2(A,np__1),k23_binop_2(B,np__1)) )
=> ( ( v2_funct_2(C,A,B)
& v1_stirl2_1(C,A,B)
& C = k2_partfun1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),D,A)
& k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),D,A) = B )
=> ( v2_funct_2(D,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
& v1_stirl2_1(D,k23_binop_2(A,np__1),k23_binop_2(B,np__1))
& k4_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),D,k2_setwiseo(k23_binop_2(B,np__1),k5_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1),D,A))) = k1_stirl2_1(A) ) ) ) ) ) ) ).
fof(t41_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k23_binop_2(A,np__1),B)
& m2_relset_1(D,k23_binop_2(A,np__1),B) )
=> ( ( v2_funct_2(C,A,B)
& v1_stirl2_1(C,A,B)
& C = k2_partfun1(k23_binop_2(A,np__1),B,D,A) )
=> ( r1_xreal_0(B,k5_stirl2_1(k23_binop_2(A,np__1),B,D,A))
| ( v2_funct_2(D,k23_binop_2(A,np__1),B)
& v1_stirl2_1(D,k23_binop_2(A,np__1),B)
& k4_stirl2_1(k23_binop_2(A,np__1),B,D,k1_tarski(k5_stirl2_1(k23_binop_2(A,np__1),B,D,A))) != k1_stirl2_1(A) ) ) ) ) ) ) ) ).
fof(d3_stirl2_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_finset_1(B)
& m1_ordinal1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( ( v1_setwiseo(C,A)
| r1_xreal_0(np__1,k1_afinsq_1(B)) )
=> ! [D] :
( m1_subset_1(D,A)
=> ( ( ( v1_setwiseo(C,A)
& k1_afinsq_1(B) = np__0 )
=> ( D = k7_stirl2_1(A,B,C)
<=> D = k3_binop_1(A,C) ) )
& ( ~ ( v1_setwiseo(C,A)
& k1_afinsq_1(B) = np__0 )
=> ( D = k7_stirl2_1(A,B,C)
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,A)
& m2_relset_1(E,k5_numbers,A)
& k8_funct_2(k5_numbers,A,E,np__0) = k1_funct_1(B,np__0)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k1_afinsq_1(B),k23_binop_2(F,np__1))
=> k8_funct_2(k5_numbers,A,E,k23_binop_2(F,np__1)) = k1_binop_1(C,k8_funct_2(k5_numbers,A,E,F),k1_funct_1(B,k23_binop_2(F,np__1))) ) )
& D = k1_funct_1(E,k10_binop_2(k1_afinsq_1(B),np__1)) ) ) ) ) ) ) ) ) ) ).
fof(t44_stirl2_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m1_subset_1(C,A)
=> k7_stirl2_1(A,k9_afinsq_1(A,C),B) = C ) ) ) ).
fof(t45_stirl2_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_finset_1(B)
& m1_ordinal1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( m1_subset_1(D,A)
=> ( ~ ( ~ v1_setwiseo(C,A)
& r1_xreal_0(k1_afinsq_1(B),np__0) )
=> k7_stirl2_1(A,k5_afinsq_1(A,B,k9_afinsq_1(A,D)),C) = k2_binop_1(A,A,A,C,k7_stirl2_1(A,B,C),D) ) ) ) ) ) ).
fof(t46_stirl2_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_finset_1(B)
& m1_ordinal1(B,A) )
=> ~ ( B != k4_afinsq_1(A)
& ! [C] :
( ( v1_finset_1(C)
& m1_ordinal1(C,A) )
=> ! [D] :
( m1_subset_1(D,A)
=> B != k5_afinsq_1(A,C,k9_afinsq_1(A,D)) ) ) ) ) ) ).
fof(t47_stirl2_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_finset_1(B)
& m1_ordinal1(B,A) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_ordinal1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( v2_binop_1(D,A)
=> ( ( ~ v1_setwiseo(D,A)
& ~ ( r1_xreal_0(np__1,k1_afinsq_1(B))
& r1_xreal_0(np__1,k1_afinsq_1(C)) ) )
| k7_stirl2_1(A,k5_afinsq_1(A,B,C),D) = k2_binop_1(A,A,A,D,k7_stirl2_1(A,B,D),k7_stirl2_1(A,C,D)) ) ) ) ) ) ) ).
fof(t48_stirl2_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> k7_stirl2_1(A,k8_stirl2_1(A,C,D),B) = k2_binop_1(A,A,A,B,C,D) ) ) ) ) ).
fof(t49_stirl2_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> k7_stirl2_1(A,k9_stirl2_1(A,C,D,E),B) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E) ) ) ) ) ) ).
fof(d4_stirl2_1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_ordinal1(A,k5_numbers) )
=> k10_stirl2_1(A) = k7_stirl2_1(k5_numbers,A,k47_binop_2) ) ).
fof(t50_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_finset_1(B)
& m1_ordinal1(B,k5_numbers) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k2_afinsq_1(B))
=> r1_xreal_0(k11_stirl2_1(B,C),A) ) )
=> r1_xreal_0(k10_stirl2_1(B),k24_binop_2(k1_afinsq_1(B),A)) ) ) ) ).
fof(t51_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_finset_1(B)
& m1_ordinal1(B,k5_numbers) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k2_afinsq_1(B))
=> r1_xreal_0(A,k11_stirl2_1(B,C)) ) )
=> r1_xreal_0(k24_binop_2(k1_afinsq_1(B),A),k10_stirl2_1(B)) ) ) ) ).
fof(t52_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_finset_1(B)
& m1_ordinal1(B,k5_numbers) )
=> ~ ( ~ r1_xreal_0(k1_afinsq_1(B),np__0)
& ? [C] :
( r2_hidden(C,k2_afinsq_1(B))
& k11_stirl2_1(B,C) = A )
& ~ r1_xreal_0(A,k10_stirl2_1(B)) ) ) ) ).
fof(t53_stirl2_1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_ordinal1(A,k5_numbers) )
=> ( k10_stirl2_1(A) = np__0
<=> ( k1_afinsq_1(A) = np__0
| ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k2_afinsq_1(A))
=> k11_stirl2_1(A,B) = np__0 ) ) ) ) ) ).
fof(t54_stirl2_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_xboole_0(k3_tarski(k2_relat_1(k7_relat_1(A,B))),k1_funct_1(A,B)) = k3_tarski(k2_relat_1(k7_relat_1(A,k23_binop_2(B,np__1)))) ) ) ).
fof(t56_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k6_stirl2_1(k23_binop_2(A,np__1),k23_binop_2(B,np__1)) = k23_binop_2(k24_binop_2(k23_binop_2(B,np__1),k6_stirl2_1(A,k23_binop_2(B,np__1))),k6_stirl2_1(A,B)) ) ) ).
fof(t57_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,A)
=> k6_stirl2_1(A,np__2) = k11_binop_2(k12_binop_2(np__1,np__2),k10_binop_2(k3_newton(np__2,A),np__2)) ) ) ).
fof(t58_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__2,A)
=> k6_stirl2_1(A,np__3) = k11_binop_2(k12_binop_2(np__1,np__6),k9_binop_2(k10_binop_2(k3_newton(np__3,A),k11_binop_2(np__3,k3_newton(np__2,A))),np__3)) ) ) ).
fof(t59_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__3,A)
=> k6_stirl2_1(A,np__4) = k11_binop_2(k12_binop_2(np__1,np__24),k10_binop_2(k9_binop_2(k10_binop_2(k3_newton(np__4,A),k11_binop_2(np__4,k3_newton(np__3,A))),k11_binop_2(np__6,k3_newton(np__2,A))),np__4)) ) ) ).
fof(t60_stirl2_1,axiom,
( k11_newton(np__3) = np__6
& k11_newton(np__4) = np__24 ) ).
fof(t61_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k8_newton(np__1,A) = A
& k8_newton(np__2,A) = k12_binop_2(k11_binop_2(A,k10_binop_2(A,np__1)),np__2)
& k8_newton(np__3,A) = k12_binop_2(k11_binop_2(k11_binop_2(A,k10_binop_2(A,np__1)),k10_binop_2(A,np__2)),np__6)
& k8_newton(np__4,A) = k12_binop_2(k11_binop_2(k11_binop_2(k11_binop_2(A,k10_binop_2(A,np__1)),k10_binop_2(A,np__2)),k10_binop_2(A,np__3)),np__24) ) ) ).
fof(t62_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k6_stirl2_1(k23_binop_2(A,np__1),A) = k8_newton(np__2,k23_binop_2(A,np__1)) ) ).
fof(t63_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k6_stirl2_1(k23_binop_2(A,np__2),A) = k9_binop_2(k11_binop_2(np__3,k8_newton(np__4,k23_binop_2(A,np__2))),k8_newton(np__3,k23_binop_2(A,np__2))) ) ).
fof(t64_stirl2_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(B))))) = k4_xboole_0(k2_relat_1(A),k1_tarski(B))
& ! [C] :
( C != B
=> k10_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(B)))),k1_tarski(C)) = k10_relat_1(A,k1_tarski(C)) ) ) ) ).
fof(t65_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( k1_card_1(B) = k23_binop_2(A,np__1)
& r2_hidden(C,B) )
=> k1_card_1(k4_xboole_0(B,k1_tarski(C))) = A ) ) ).
fof(t66_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ~ ( v1_finset_1(A)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r2_hidden(C,A)
& ~ r1_xreal_0(C,B) ) ) ) ) ).
fof(t67_stirl2_1,axiom,
! [A,B,C,D] :
~ ( ( v1_xboole_0(B)
=> v1_xboole_0(A) )
& ~ r2_hidden(C,A)
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B)
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)))
& m2_relset_1(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) )
=> ~ ( k2_partfun1(k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)),F,A) = E
& k1_funct_1(F,C) = D ) ) ) ) ).
fof(t68_stirl2_1,axiom,
! [A,B,C,D] :
( ( v1_xboole_0(B)
=> v1_xboole_0(A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)))
& m2_relset_1(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) )
=> ( ( k2_partfun1(k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D)),F,A) = E
& k1_funct_1(F,C) = D )
=> ( ( v2_funct_2(E,A,B)
=> v2_funct_2(F,k2_xboole_0(A,k1_tarski(C)),k2_xboole_0(B,k1_tarski(D))) )
& ( v2_funct_1(E)
=> ( r2_hidden(D,B)
| v2_funct_1(F) ) ) ) ) ) ) ) ).
fof(t69_stirl2_1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,A,k4_card_1(A))
& m2_relset_1(B,A,k4_card_1(A))
& v3_funct_2(B,A,k4_card_1(A))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(C,k4_relset_1(A,k4_card_1(A),B))
& r2_hidden(D,k4_relset_1(A,k4_card_1(A),B))
& ~ r1_xreal_0(D,C)
& r1_xreal_0(k5_stirl2_1(A,k4_card_1(A),B,D),k5_stirl2_1(A,k4_card_1(A),B,C)) ) ) ) ) ) ).
fof(t70_stirl2_1,axiom,
! [A] :
( v1_finset_1(A)
=> ! [B] :
( v1_finset_1(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( k4_card_1(A) = k4_card_1(B)
=> ( v2_funct_2(C,A,B)
<=> v2_funct_1(C) ) ) ) ) ) ).
fof(t71_stirl2_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
~ ( r2_hidden(C,k2_relat_1(k5_relat_1(A,B)))
& v2_funct_1(B)
& ! [D] :
~ ( r2_hidden(D,k1_relat_1(B))
& r2_hidden(D,k2_relat_1(A))
& k10_relat_1(B,k1_tarski(C)) = k1_tarski(D)
& k10_relat_1(A,k1_tarski(D)) = k10_relat_1(k5_relat_1(A,B),k1_tarski(C)) ) ) ) ) ).
fof(d5_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v2_stirl2_1(C,A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k5_relset_1(A,B,C))
& r2_hidden(E,k5_relset_1(A,B,C))
& ~ r1_xreal_0(E,D)
& r1_xreal_0(k1_henmodel(k3_funct_2(A,B,C,k1_stirl2_1(E))),k1_henmodel(k3_funct_2(A,B,C,k1_stirl2_1(D)))) ) ) ) ) ) ) ) ).
fof(t72_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v2_stirl2_1(C,A,B)
=> k1_henmodel(k5_relset_1(A,B,C)) = k1_funct_1(C,k1_henmodel(k4_relset_1(A,B,C))) ) ) ) ) ).
fof(t73_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ~ ( v1_finset_1(k5_relset_1(A,B,C))
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
& v3_funct_2(E,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
& m2_relset_1(E,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) )
=> ~ ( C = k1_partfun1(A,B,k5_relset_1(A,B,C),k5_relset_1(A,B,C),D,E)
& k5_relset_1(A,B,C) = k5_relset_1(A,B,D)
& v2_stirl2_1(D,A,B) ) ) ) ) ) ) ) ).
fof(t74_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k5_numbers))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( v1_finset_1(k5_relset_1(A,B,D))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,C)
& m2_relset_1(F,A,C) )
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ( ( v2_funct_1(G)
& v2_funct_1(H)
& k5_relset_1(A,C,E) = k5_relset_1(A,C,F)
& k5_relset_1(A,C,E) = k1_relat_1(G)
& k1_relat_1(G) = k1_relat_1(H)
& D = k5_relat_1(E,G)
& D = k5_relat_1(F,H)
& v2_stirl2_1(E,A,C)
& v2_stirl2_1(F,A,C) )
=> ( G = H
& E = F ) ) ) ) ) ) ) ) ) ) ) ).
fof(t75_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_numbers))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v1_finset_1(k5_relset_1(A,B,C))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
& v3_funct_2(F,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
& m2_relset_1(F,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
& v3_funct_2(G,k5_relset_1(A,B,C),k5_relset_1(A,B,C))
& m2_relset_1(G,k5_relset_1(A,B,C),k5_relset_1(A,B,C)) )
=> ( ( C = k1_partfun1(A,B,k5_relset_1(A,B,C),k5_relset_1(A,B,C),D,F)
& C = k1_partfun1(A,B,k5_relset_1(A,B,C),k5_relset_1(A,B,C),E,G)
& k5_relset_1(A,B,C) = k5_relset_1(A,B,D)
& k5_relset_1(A,B,C) = k5_relset_1(A,B,E)
& v2_stirl2_1(D,A,B)
& v2_stirl2_1(E,A,B) )
=> ( F = G
& D = E ) ) ) ) ) ) ) ) ) ) ).
fof(s2_stirl2_1,axiom,
( ( ! [A] :
( r2_hidden(A,k4_xboole_0(f3_s2_stirl2_1,f1_s2_stirl2_1))
=> r2_hidden(f6_s2_stirl2_1(A),f4_s2_stirl2_1) )
& r1_tarski(f1_s2_stirl2_1,f3_s2_stirl2_1)
& r1_tarski(f2_s2_stirl2_1,f4_s2_stirl2_1)
& ( v1_xboole_0(f2_s2_stirl2_1)
=> v1_xboole_0(f1_s2_stirl2_1) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f3_s2_stirl2_1,f4_s2_stirl2_1)
& m2_relset_1(A,f3_s2_stirl2_1,f4_s2_stirl2_1)
& k2_partfun1(f3_s2_stirl2_1,f4_s2_stirl2_1,A,f1_s2_stirl2_1) = f5_s2_stirl2_1
& ! [B] :
( r2_hidden(B,k4_xboole_0(f3_s2_stirl2_1,f1_s2_stirl2_1))
=> k1_funct_1(A,B) = f6_s2_stirl2_1(B) ) ) ) ).
fof(s5_stirl2_1,axiom,
( ( p1_s5_stirl2_1(k4_afinsq_1(f1_s5_stirl2_1))
& ! [A] :
( ( v1_finset_1(A)
& m1_ordinal1(A,f1_s5_stirl2_1) )
=> ! [B] :
( m1_subset_1(B,f1_s5_stirl2_1)
=> ( p1_s5_stirl2_1(A)
=> p1_s5_stirl2_1(k5_afinsq_1(f1_s5_stirl2_1,A,k9_afinsq_1(f1_s5_stirl2_1,B))) ) ) ) )
=> ! [A] :
( ( v1_finset_1(A)
& m1_ordinal1(A,f1_s5_stirl2_1) )
=> p1_s5_stirl2_1(A) ) ) ).
fof(s6_stirl2_1,axiom,
( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(A,f2_s6_stirl2_1)
& ! [B] :
( m1_subset_1(B,f1_s6_stirl2_1)
=> ~ p1_s6_stirl2_1(A,B) ) ) )
=> ? [A] :
( v1_finset_1(A)
& m1_ordinal1(A,f1_s6_stirl2_1)
& k2_afinsq_1(A) = f2_s6_stirl2_1
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,f2_s6_stirl2_1)
=> p1_s6_stirl2_1(B,k1_funct_1(A,B)) ) ) ) ) ).
fof(s7_stirl2_1,axiom,
( ( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r2_hidden(A,k2_afinsq_1(f2_s7_stirl2_1))
=> v1_finset_1(k1_funct_1(f2_s7_stirl2_1,A)) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r2_hidden(A,k2_afinsq_1(f2_s7_stirl2_1))
& r2_hidden(B,k2_afinsq_1(f2_s7_stirl2_1)) )
=> ( A = B
| r1_xboole_0(k1_funct_1(f2_s7_stirl2_1,A),k1_funct_1(f2_s7_stirl2_1,B)) ) ) ) ) )
=> ? [A] :
( v1_finset_1(A)
& m1_ordinal1(A,k5_numbers)
& k2_afinsq_1(A) = k2_afinsq_1(f2_s7_stirl2_1)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k2_afinsq_1(A))
=> k11_stirl2_1(A,B) = k1_card_1(k1_funct_1(f2_s7_stirl2_1,B)) ) )
& k1_card_1(k3_tarski(k2_relat_1(f2_s7_stirl2_1))) = k10_stirl2_1(A) ) ) ).
fof(s9_stirl2_1,axiom,
( ( p1_s9_stirl2_1(k1_xboole_0)
& ! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( ! [B] :
( ( r2_hidden(B,k2_relat_1(A))
& p2_s9_stirl2_1(B,A) )
=> p1_s9_stirl2_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k10_relat_1(A,k1_tarski(B))))) )
=> p1_s9_stirl2_1(A) ) ) )
=> ! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_finset_1(k2_relat_1(A))
=> p1_s9_stirl2_1(A) ) ) ) ).
fof(dt_k1_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_subset_1(k1_stirl2_1(A),k1_zfmisc_1(k5_numbers)) ) ).
fof(redefinition_k1_stirl2_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> k1_stirl2_1(A) = k1_tarski(A) ) ).
fof(dt_k2_stirl2_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k2_stirl2_1(A,B),k1_zfmisc_1(k5_numbers)) ) ).
fof(commutativity_k2_stirl2_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> k2_stirl2_1(A,B) = k2_stirl2_1(B,A) ) ).
fof(redefinition_k2_stirl2_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> k2_stirl2_1(A,B) = k2_tarski(A,B) ) ).
fof(dt_k3_stirl2_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> ( ~ v1_xboole_0(k3_stirl2_1(A,B,C))
& m1_subset_1(k3_stirl2_1(A,B,C),k1_zfmisc_1(k5_numbers)) ) ) ).
fof(redefinition_k3_stirl2_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> k3_stirl2_1(A,B,C) = k1_enumset1(A,B,C) ) ).
fof(dt_k4_stirl2_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k4_stirl2_1(A,B,C,D),k1_zfmisc_1(k5_numbers)) ) ).
fof(redefinition_k4_stirl2_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> k4_stirl2_1(A,B,C,D) = k10_relat_1(C,D) ) ).
fof(dt_k5_stirl2_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(B,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k5_stirl2_1(A,B,C,D),B) ) ).
fof(redefinition_k5_stirl2_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(B,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> k5_stirl2_1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k6_stirl2_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k6_stirl2_1(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k7_stirl2_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(B)
& m1_ordinal1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A) )
=> m1_subset_1(k7_stirl2_1(A,B,C),A) ) ).
fof(dt_k8_stirl2_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A) )
=> ( v1_finset_1(k8_stirl2_1(A,B,C))
& m1_ordinal1(k8_stirl2_1(A,B,C),A) ) ) ).
fof(redefinition_k8_stirl2_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A) )
=> k8_stirl2_1(A,B,C) = k7_afinsq_1(B,C) ) ).
fof(dt_k9_stirl2_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) )
=> ( v1_finset_1(k9_stirl2_1(A,B,C,D))
& m1_ordinal1(k9_stirl2_1(A,B,C,D),A) ) ) ).
fof(redefinition_k9_stirl2_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) )
=> k9_stirl2_1(A,B,C,D) = k8_afinsq_1(B,C,D) ) ).
fof(dt_k10_stirl2_1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_ordinal1(A,k5_numbers) )
=> m2_subset_1(k10_stirl2_1(A),k1_numbers,k5_numbers) ) ).
fof(dt_k11_stirl2_1,axiom,
! [A,B] :
( ( v1_finset_1(A)
& m1_ordinal1(A,k5_numbers) )
=> m2_subset_1(k11_stirl2_1(A,B),k1_numbers,k5_numbers) ) ).
fof(redefinition_k11_stirl2_1,axiom,
! [A,B] :
( ( v1_finset_1(A)
& m1_ordinal1(A,k5_numbers) )
=> k11_stirl2_1(A,B) = k1_funct_1(A,B) ) ).
fof(t24_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> v1_finset_1(a_2_0_stirl2_1(A,B)) ) ) ).
fof(t25_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> m2_subset_1(k1_card_1(a_2_0_stirl2_1(A,B)),k1_numbers,k5_numbers) ) ) ).
fof(d2_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k6_stirl2_1(A,B) = k1_card_1(a_2_0_stirl2_1(A,B)) ) ) ).
fof(t42_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_card_1(a_2_1_stirl2_1(A,B)) = k1_card_1(a_2_0_stirl2_1(A,B)) ) ) ).
fof(t43_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,C)
=> k1_card_1(a_3_0_stirl2_1(A,B,C)) = k1_card_1(a_2_2_stirl2_1(A,B)) ) ) ) ) ).
fof(t55_stirl2_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k24_binop_2(A,k6_stirl2_1(B,A)) = k1_card_1(a_2_3_stirl2_1(A,B)) ) ) ).
fof(s1_stirl2_1,axiom,
v1_finset_1(a_0_0_stirl2_1) ).
fof(s3_stirl2_1,axiom,
( ( ! [A] :
( r2_hidden(A,k4_xboole_0(f3_s3_stirl2_1,f1_s3_stirl2_1))
=> r2_hidden(f5_s3_stirl2_1(A),f4_s3_stirl2_1) )
& r1_tarski(f1_s3_stirl2_1,f3_s3_stirl2_1)
& r1_tarski(f2_s3_stirl2_1,f4_s3_stirl2_1)
& ( v1_xboole_0(f2_s3_stirl2_1)
=> v1_xboole_0(f1_s3_stirl2_1) )
& ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,f3_s3_stirl2_1,f4_s3_stirl2_1)
& m2_relset_1(A,f3_s3_stirl2_1,f4_s3_stirl2_1) )
=> ( ! [B] :
( r2_hidden(B,k4_xboole_0(f3_s3_stirl2_1,f1_s3_stirl2_1))
=> f5_s3_stirl2_1(B) = k1_funct_1(A,B) )
=> ( p1_s3_stirl2_1(A,f3_s3_stirl2_1,f4_s3_stirl2_1)
<=> p1_s3_stirl2_1(k2_partfun1(f3_s3_stirl2_1,f4_s3_stirl2_1,A,f1_s3_stirl2_1),f1_s3_stirl2_1,f2_s3_stirl2_1) ) ) ) )
=> k1_card_1(a_0_1_stirl2_1) = k1_card_1(a_0_2_stirl2_1) ) ).
fof(s4_stirl2_1,axiom,
( ( ( v1_xboole_0(f2_s4_stirl2_1)
=> v1_xboole_0(f1_s4_stirl2_1) )
& ~ r2_hidden(f3_s4_stirl2_1,f1_s4_stirl2_1)
& ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
& m2_relset_1(A,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1))) )
=> ( k1_funct_1(A,f3_s4_stirl2_1) = f4_s4_stirl2_1
=> ( p1_s4_stirl2_1(A,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
<=> p1_s4_stirl2_1(k2_partfun1(k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)),A,f1_s4_stirl2_1),f1_s4_stirl2_1,f2_s4_stirl2_1) ) ) ) )
=> k1_card_1(a_0_3_stirl2_1) = k1_card_1(a_0_4_stirl2_1) ) ).
fof(s8_stirl2_1,axiom,
( ( v2_funct_2(f4_s8_stirl2_1,k4_card_1(f2_s8_stirl2_1),f2_s8_stirl2_1)
& v2_funct_1(f4_s8_stirl2_1)
& ~ v1_xboole_0(f2_s8_stirl2_1)
& r2_hidden(f3_s8_stirl2_1,f1_s8_stirl2_1) )
=> ? [A] :
( v1_finset_1(A)
& m1_ordinal1(A,k5_numbers)
& k2_afinsq_1(A) = k4_card_1(f2_s8_stirl2_1)
& k1_card_1(a_0_5_stirl2_1) = k10_stirl2_1(A)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k2_afinsq_1(A))
=> k11_stirl2_1(A,B) = k1_card_1(a_1_0_stirl2_1(B)) ) ) ) ) ).
fof(fraenkel_a_2_0_stirl2_1,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_0_stirl2_1(B,C))
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,B,C)
& m2_relset_1(D,B,C)
& A = D
& v2_funct_2(D,B,C)
& v1_stirl2_1(D,B,C) ) ) ) ).
fof(fraenkel_a_2_1_stirl2_1,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_1_stirl2_1(B,C))
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k23_binop_2(B,np__1),k23_binop_2(C,np__1))
& m2_relset_1(D,k23_binop_2(B,np__1),k23_binop_2(C,np__1))
& A = D
& v2_funct_2(D,k23_binop_2(B,np__1),k23_binop_2(C,np__1))
& v1_stirl2_1(D,k23_binop_2(B,np__1),k23_binop_2(C,np__1))
& k4_stirl2_1(k23_binop_2(B,np__1),k23_binop_2(C,np__1),D,k2_setwiseo(k23_binop_2(C,np__1),k5_stirl2_1(k23_binop_2(B,np__1),k23_binop_2(C,np__1),D,B))) = k1_stirl2_1(B) ) ) ) ).
fof(fraenkel_a_3_0_stirl2_1,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_3_0_stirl2_1(B,C,D))
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k23_binop_2(C,np__1),B)
& m2_relset_1(E,k23_binop_2(C,np__1),B)
& A = E
& v2_funct_2(E,k23_binop_2(C,np__1),B)
& v1_stirl2_1(E,k23_binop_2(C,np__1),B)
& k4_stirl2_1(k23_binop_2(C,np__1),B,E,k1_tarski(k5_stirl2_1(k23_binop_2(C,np__1),B,E,C))) != k1_stirl2_1(C)
& k5_stirl2_1(k23_binop_2(C,np__1),B,E,C) = D ) ) ) ).
fof(fraenkel_a_2_2_stirl2_1,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_2_stirl2_1(B,C))
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,C,B)
& m2_relset_1(D,C,B)
& A = D
& v2_funct_2(D,C,B)
& v1_stirl2_1(D,C,B) ) ) ) ).
fof(fraenkel_a_2_3_stirl2_1,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_3_stirl2_1(B,C))
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k23_binop_2(C,np__1),B)
& m2_relset_1(D,k23_binop_2(C,np__1),B)
& A = D
& v2_funct_2(D,k23_binop_2(C,np__1),B)
& v1_stirl2_1(D,k23_binop_2(C,np__1),B)
& k4_stirl2_1(k23_binop_2(C,np__1),B,D,k1_tarski(k5_stirl2_1(k23_binop_2(C,np__1),B,D,C))) != k1_stirl2_1(C) ) ) ) ).
fof(fraenkel_a_0_0_stirl2_1,axiom,
! [A] :
( r2_hidden(A,a_0_0_stirl2_1)
<=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,f1_s1_stirl2_1,f2_s1_stirl2_1)
& m2_relset_1(B,f1_s1_stirl2_1,f2_s1_stirl2_1)
& A = B
& p1_s1_stirl2_1(B) ) ) ).
fof(fraenkel_a_0_1_stirl2_1,axiom,
! [A] :
( r2_hidden(A,a_0_1_stirl2_1)
<=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,f1_s3_stirl2_1,f2_s3_stirl2_1)
& m2_relset_1(B,f1_s3_stirl2_1,f2_s3_stirl2_1)
& A = B
& p1_s3_stirl2_1(B,f1_s3_stirl2_1,f2_s3_stirl2_1) ) ) ).
fof(fraenkel_a_0_2_stirl2_1,axiom,
! [A] :
( r2_hidden(A,a_0_2_stirl2_1)
<=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,f3_s3_stirl2_1,f4_s3_stirl2_1)
& m2_relset_1(B,f3_s3_stirl2_1,f4_s3_stirl2_1)
& A = B
& p1_s3_stirl2_1(B,f3_s3_stirl2_1,f4_s3_stirl2_1)
& r1_tarski(k5_relset_1(f3_s3_stirl2_1,f4_s3_stirl2_1,k2_partfun1(f3_s3_stirl2_1,f4_s3_stirl2_1,B,f1_s3_stirl2_1)),f2_s3_stirl2_1)
& ! [C] :
( r2_hidden(C,k4_xboole_0(f3_s3_stirl2_1,f1_s3_stirl2_1))
=> k1_funct_1(B,C) = f5_s3_stirl2_1(C) ) ) ) ).
fof(fraenkel_a_0_3_stirl2_1,axiom,
! [A] :
( r2_hidden(A,a_0_3_stirl2_1)
<=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,f1_s4_stirl2_1,f2_s4_stirl2_1)
& m2_relset_1(B,f1_s4_stirl2_1,f2_s4_stirl2_1)
& A = B
& p1_s4_stirl2_1(B,f1_s4_stirl2_1,f2_s4_stirl2_1) ) ) ).
fof(fraenkel_a_0_4_stirl2_1,axiom,
! [A] :
( r2_hidden(A,a_0_4_stirl2_1)
<=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
& m2_relset_1(B,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
& A = B
& p1_s4_stirl2_1(B,k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)))
& r1_tarski(k5_relset_1(k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)),k2_partfun1(k2_xboole_0(f1_s4_stirl2_1,k1_tarski(f3_s4_stirl2_1)),k2_xboole_0(f2_s4_stirl2_1,k1_tarski(f4_s4_stirl2_1)),B,f1_s4_stirl2_1)),f2_s4_stirl2_1)
& k1_funct_1(B,f3_s4_stirl2_1) = f4_s4_stirl2_1 ) ) ).
fof(fraenkel_a_0_5_stirl2_1,axiom,
! [A] :
( r2_hidden(A,a_0_5_stirl2_1)
<=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,f1_s8_stirl2_1,f2_s8_stirl2_1)
& m2_relset_1(B,f1_s8_stirl2_1,f2_s8_stirl2_1)
& A = B
& p1_s8_stirl2_1(B) ) ) ).
fof(fraenkel_a_1_0_stirl2_1,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(A,a_1_0_stirl2_1(B))
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,f1_s8_stirl2_1,f2_s8_stirl2_1)
& m2_relset_1(C,f1_s8_stirl2_1,f2_s8_stirl2_1)
& A = C
& p1_s8_stirl2_1(C)
& k1_funct_1(C,f3_s8_stirl2_1) = k1_funct_1(f4_s8_stirl2_1,B) ) ) ) ).
%------------------------------------------------------------------------------