SET007 Axioms: SET007+472.ax
%------------------------------------------------------------------------------
% File : SET007+472 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Memory Handling for SCMFSA
% 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 : sf_mastr [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 101 ( 6 unt; 0 def)
% Number of atoms : 624 ( 195 equ)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 592 ( 69 ~; 24 |; 204 &)
% ( 17 <=>; 278 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 96 ( 96 usr; 19 con; 0-5 aty)
% Number of variables : 260 ( 237 !; 23 ?)
% 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_sf_mastr,axiom,
! [A,B] :
( v1_finset_1(A)
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B) )
=> ( v1_funct_1(C)
& v1_finset_1(C)
& v1_funct_2(C,A,B) ) ) ) ) ).
fof(fc1_sf_mastr,axiom,
! [A,B,C] :
( ( v1_finset_1(A)
& v1_funct_1(C)
& v1_funct_2(C,A,k5_finsub_1(B))
& m1_relset_1(C,A,k5_finsub_1(B)) )
=> v1_finset_1(k3_card_3(C)) ) ).
fof(fc2_sf_mastr,axiom,
~ v1_xboole_0(k2_scmfsa_2) ).
fof(fc3_sf_mastr,axiom,
~ v1_xboole_0(k3_scmfsa_2) ).
fof(fc4_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> v1_finset_1(k2_sf_mastr(A)) ) ).
fof(fc5_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> v1_finset_1(k4_sf_mastr(A)) ) ).
fof(fc6_sf_mastr,axiom,
v1_sf_mastr(k4_scmfsa_2(np__0)) ).
fof(rc1_sf_mastr,axiom,
? [A] :
( m1_scmfsa_2(A)
& ~ v1_sf_mastr(A) ) ).
fof(fc7_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ v1_sf_mastr(k6_sf_mastr(A)) ) ).
fof(t1_sf_mastr,axiom,
! [A,B,C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( k1_funct_1(D,A) = k1_funct_1(D,B)
=> k1_funct_1(D,C) = k1_funct_1(k5_relat_1(k2_funct_7(k6_relat_1(k1_relat_1(D)),A,B),D),C) ) ) ).
fof(t2_sf_mastr,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(A,k1_relat_1(C))
=> ( r2_hidden(B,k1_relat_1(C))
& k1_funct_1(C,A) = k1_funct_1(C,B) ) )
=> C = k5_relat_1(k2_funct_7(k6_relat_1(k1_relat_1(C)),A,B),C) ) ) ).
fof(t3_sf_mastr,axiom,
$true ).
fof(t4_sf_mastr,axiom,
$true ).
fof(t5_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ( k8_scmfsa_2(A,B) = k8_scmfsa_2(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t6_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ( k9_scmfsa_2(A,B) = k9_scmfsa_2(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t7_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ( k10_scmfsa_2(A,B) = k10_scmfsa_2(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t8_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ( k11_scmfsa_2(A,B) = k11_scmfsa_2(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t9_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ( k12_scmfsa_2(A,B) = k12_scmfsa_2(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t10_sf_mastr,axiom,
! [A] :
( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( k13_scmfsa_2(A) = k13_scmfsa_2(B)
=> A = B ) ) ) ).
fof(t11_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [D] :
( m1_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( k14_scmfsa_2(C,A) = k14_scmfsa_2(D,B)
=> ( A = B
& C = D ) ) ) ) ) ) ).
fof(t12_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [D] :
( m1_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( k15_scmfsa_2(C,A) = k15_scmfsa_2(D,B)
=> ( A = B
& C = D ) ) ) ) ) ) ).
fof(t13_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m2_scmfsa_2(E)
=> ! [F] :
( m2_scmfsa_2(F)
=> ( k16_scmfsa_2(A,B,E) = k16_scmfsa_2(C,D,F)
=> ( B = D
& A = C
& E = F ) ) ) ) ) ) ) ) ).
fof(t14_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m2_scmfsa_2(E)
=> ! [F] :
( m2_scmfsa_2(F)
=> ( k17_scmfsa_2(B,A,E) = k17_scmfsa_2(D,C,F)
=> ( A = C
& B = D
& E = F ) ) ) ) ) ) ) ) ).
fof(t15_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> ( k18_scmfsa_2(A,C) = k18_scmfsa_2(B,D)
=> ( A = B
& C = D ) ) ) ) ) ) ).
fof(t16_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> ( k19_scmfsa_2(A,C) = k19_scmfsa_2(B,D)
=> ( A = B
& C = D ) ) ) ) ) ) ).
fof(d1_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(k2_scmfsa_2))
=> ( ( r2_hidden(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k3_enumset1(np__1,np__2,np__3,np__4,np__5))
=> ( B = k1_sf_mastr(A)
<=> ? [C] :
( m1_scmfsa_2(C)
& ? [D] :
( m1_scmfsa_2(D)
& ~ ( A != k8_scmfsa_2(C,D)
& A != k9_scmfsa_2(C,D)
& A != k10_scmfsa_2(C,D)
& A != k11_scmfsa_2(C,D)
& A != k12_scmfsa_2(C,D) )
& B = k3_setwiseo(u1_struct_0(k1_scmfsa_2),C,D) ) ) ) )
& ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__7
| k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__8 )
=> ( B = k1_sf_mastr(A)
<=> ? [C] :
( m1_scmfsa_2(C)
& ? [D] :
( m1_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& ( A = k14_scmfsa_2(D,C)
| A = k15_scmfsa_2(D,C) )
& B = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),C) ) ) ) )
& ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__9
| k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__10 )
=> ( B = k1_sf_mastr(A)
<=> ? [C] :
( m1_scmfsa_2(C)
& ? [D] :
( m1_scmfsa_2(D)
& ? [E] :
( m2_scmfsa_2(E)
& ( A = k16_scmfsa_2(D,C,E)
| A = k17_scmfsa_2(D,C,E) )
& B = k3_setwiseo(u1_struct_0(k1_scmfsa_2),C,D) ) ) ) ) )
& ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__11
| k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__12 )
=> ( B = k1_sf_mastr(A)
<=> ? [C] :
( m1_scmfsa_2(C)
& ? [D] :
( m2_scmfsa_2(D)
& ( A = k18_scmfsa_2(C,D)
| A = k19_scmfsa_2(C,D) )
& B = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),C) ) ) ) )
& ~ ( ~ r2_hidden(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k3_enumset1(np__1,np__2,np__3,np__4,np__5))
& k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__7
& k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__8
& k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__9
& k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__10
& k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__11
& k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__12
& ~ ( B = k1_sf_mastr(A)
<=> B = k1_xboole_0 ) ) ) ) ) ).
fof(t17_sf_mastr,axiom,
k1_sf_mastr(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k1_xboole_0 ).
fof(t18_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ~ ( C != k8_scmfsa_2(A,B)
& C != k9_scmfsa_2(A,B)
& C != k10_scmfsa_2(A,B)
& C != k11_scmfsa_2(A,B)
& C != k12_scmfsa_2(A,B) )
=> k1_sf_mastr(C) = k3_setwiseo(u1_struct_0(k1_scmfsa_2),A,B) ) ) ) ) ).
fof(t19_sf_mastr,axiom,
! [A] :
( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k1_sf_mastr(k13_scmfsa_2(A)) = k1_xboole_0 ) ).
fof(t20_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ( C = k14_scmfsa_2(B,A)
| C = k15_scmfsa_2(B,A) )
=> k1_sf_mastr(C) = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),A) ) ) ) ) ).
fof(t21_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ( D = k16_scmfsa_2(A,B,C)
| D = k17_scmfsa_2(A,B,C) )
=> k1_sf_mastr(D) = k3_setwiseo(u1_struct_0(k1_scmfsa_2),B,A) ) ) ) ) ) ).
fof(t22_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ( C = k18_scmfsa_2(A,B)
| C = k19_scmfsa_2(A,B) )
=> k1_sf_mastr(C) = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),A) ) ) ) ) ).
fof(d2_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2))
=> ( B = k2_sf_mastr(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k2_scmfsa_2))
& m2_relset_1(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k2_scmfsa_2))
& ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k8_funct_2(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k2_scmfsa_2),C,D) = k1_sf_mastr(D) )
& B = k3_card_3(k5_relat_1(A,C)) ) ) ) ) ).
fof(t23_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r2_hidden(A,k2_relat_1(B))
=> r1_tarski(k1_sf_mastr(A),k2_sf_mastr(B)) ) ) ) ).
fof(t24_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> r1_tarski(k2_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)),k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k2_sf_mastr(A),k2_sf_mastr(B))) ) ) ).
fof(t25_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
=> k2_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k2_sf_mastr(A),k2_sf_mastr(B)) ) ) ) ).
fof(t26_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_sf_mastr(A) = k2_sf_mastr(k8_scmfsa_4(A,B)) ) ) ).
fof(t27_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_sf_mastr(A) = k1_sf_mastr(k4_scmfsa_4(A,B)) ) ) ).
fof(t28_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_sf_mastr(A) = k2_sf_mastr(k7_scmfsa_4(A,B)) ) ) ).
fof(t29_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_sf_mastr(A) = k2_sf_mastr(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B))) ) ) ).
fof(t30_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k2_sf_mastr(A) = k2_sf_mastr(k1_scmfsa6a(A)) ) ).
fof(t31_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k2_sf_mastr(k4_scmfsa6a(A,B)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k2_sf_mastr(A),k2_sf_mastr(B)) ) ) ).
fof(t32_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k2_sf_mastr(k2_scmfsa6a(A)) = k1_sf_mastr(A) ) ).
fof(t33_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k2_sf_mastr(k5_scmfsa6a(A,B)) = k2_xboole_0(k1_sf_mastr(A),k2_sf_mastr(B)) ) ) ).
fof(t34_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k2_sf_mastr(k6_scmfsa6a(B,A)) = k2_xboole_0(k2_sf_mastr(B),k1_sf_mastr(A)) ) ) ).
fof(t35_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k2_sf_mastr(k7_scmfsa6a(A,B)) = k5_setwiseo(k2_scmfsa_2,k1_sf_mastr(A),k1_sf_mastr(B)) ) ) ).
fof(d3_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m1_subset_1(B,k5_finsub_1(k3_scmfsa_2))
=> ( ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__9
| k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__10 )
=> ( B = k3_sf_mastr(A)
<=> ? [C] :
( m1_scmfsa_2(C)
& ? [D] :
( m1_scmfsa_2(D)
& ? [E] :
( m2_scmfsa_2(E)
& ( A = k16_scmfsa_2(D,C,E)
| A = k17_scmfsa_2(D,C,E) )
& B = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),E) ) ) ) ) )
& ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__11
| k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__12 )
=> ( B = k3_sf_mastr(A)
<=> ? [C] :
( m1_scmfsa_2(C)
& ? [D] :
( m2_scmfsa_2(D)
& ( A = k18_scmfsa_2(C,D)
| A = k19_scmfsa_2(C,D) )
& B = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),D) ) ) ) )
& ~ ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__9
& k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__10
& k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__11
& k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__12
& ~ ( B = k3_sf_mastr(A)
<=> B = k1_xboole_0 ) ) ) ) ) ).
fof(t36_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ~ ( D != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& D != k8_scmfsa_2(A,B)
& D != k9_scmfsa_2(A,B)
& D != k10_scmfsa_2(A,B)
& D != k11_scmfsa_2(A,B)
& D != k12_scmfsa_2(A,B)
& D != k13_scmfsa_2(C)
& D != k14_scmfsa_2(C,A)
& D != k15_scmfsa_2(C,A) )
=> k3_sf_mastr(D) = k1_xboole_0 ) ) ) ) ) ).
fof(t37_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ( D = k16_scmfsa_2(A,B,C)
| D = k17_scmfsa_2(A,B,C) )
=> k3_sf_mastr(D) = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),C) ) ) ) ) ) ).
fof(t38_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ( C = k18_scmfsa_2(A,B)
| C = k19_scmfsa_2(A,B) )
=> k3_sf_mastr(C) = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),B) ) ) ) ) ).
fof(d4_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k3_scmfsa_2))
=> ( B = k4_sf_mastr(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k3_scmfsa_2))
& m2_relset_1(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k3_scmfsa_2))
& ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k8_funct_2(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k3_scmfsa_2),C,D) = k3_sf_mastr(D) )
& B = k3_card_3(k5_relat_1(A,C)) ) ) ) ) ).
fof(t39_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r2_hidden(A,k2_relat_1(B))
=> r1_tarski(k3_sf_mastr(A),k4_sf_mastr(B)) ) ) ) ).
fof(t40_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> r1_tarski(k4_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)),k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(A),k4_sf_mastr(B))) ) ) ).
fof(t41_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
=> k4_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(A),k4_sf_mastr(B)) ) ) ) ).
fof(t42_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k4_sf_mastr(A) = k4_sf_mastr(k8_scmfsa_4(A,B)) ) ) ).
fof(t43_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k3_sf_mastr(A) = k3_sf_mastr(k4_scmfsa_4(A,B)) ) ) ).
fof(t44_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k4_sf_mastr(A) = k4_sf_mastr(k7_scmfsa_4(A,B)) ) ) ).
fof(t45_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k4_sf_mastr(A) = k4_sf_mastr(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B))) ) ) ).
fof(t46_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k4_sf_mastr(A) = k4_sf_mastr(k1_scmfsa6a(A)) ) ).
fof(t47_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k4_sf_mastr(k4_scmfsa6a(A,B)) = k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(A),k4_sf_mastr(B)) ) ) ).
fof(t48_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k4_sf_mastr(k2_scmfsa6a(A)) = k3_sf_mastr(A) ) ).
fof(t49_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k4_sf_mastr(k5_scmfsa6a(A,B)) = k2_xboole_0(k3_sf_mastr(A),k4_sf_mastr(B)) ) ) ).
fof(t50_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k4_sf_mastr(k6_scmfsa6a(B,A)) = k2_xboole_0(k4_sf_mastr(B),k3_sf_mastr(A)) ) ) ).
fof(t51_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k4_sf_mastr(k7_scmfsa6a(A,B)) = k5_setwiseo(k3_scmfsa_2,k3_sf_mastr(A),k3_sf_mastr(B)) ) ) ).
fof(d5_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ( v1_sf_mastr(A)
<=> A = k4_scmfsa_2(np__0) ) ) ).
fof(t52_sf_mastr,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> ~ r2_hidden(k5_sf_mastr(A),A) ) ).
fof(t53_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2)) )
=> ( k5_sf_mastr(C) = k4_scmfsa_2(A)
=> ( r2_hidden(k4_scmfsa_2(B),C)
| r1_xreal_0(A,B) ) ) ) ) ) ).
fof(d7_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m1_scmfsa_2(B)
=> ( B = k6_sf_mastr(A)
<=> ? [C] :
( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2))
& C = k2_xboole_0(k2_sf_mastr(A),k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),k4_scmfsa_2(np__0)))
& B = k5_sf_mastr(C) ) ) ) ) ).
fof(t54_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ r2_hidden(k6_sf_mastr(A),k2_sf_mastr(A)) ) ).
fof(t55_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ~ ( ~ r2_hidden(k8_scmfsa_2(A,B),k2_relat_1(C))
& ~ r2_hidden(k9_scmfsa_2(A,B),k2_relat_1(C))
& ~ r2_hidden(k10_scmfsa_2(A,B),k2_relat_1(C))
& ~ r2_hidden(k11_scmfsa_2(A,B),k2_relat_1(C))
& ~ r2_hidden(k12_scmfsa_2(A,B),k2_relat_1(C)) )
=> ( k6_sf_mastr(C) != A
& k6_sf_mastr(C) != B ) ) ) ) ) ).
fof(t56_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ ( ( r2_hidden(k14_scmfsa_2(B,A),k2_relat_1(C))
| r2_hidden(k15_scmfsa_2(B,A),k2_relat_1(C)) )
& k6_sf_mastr(C) = A ) ) ) ) ).
fof(t57_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( r2_hidden(k16_scmfsa_2(A,B,C),k2_relat_1(D))
| r2_hidden(k17_scmfsa_2(A,B,C),k2_relat_1(D)) )
=> ( k6_sf_mastr(D) != B
& k6_sf_mastr(D) != A ) ) ) ) ) ) ).
fof(t58_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ ( ( r2_hidden(k18_scmfsa_2(A,B),k2_relat_1(C))
| r2_hidden(k19_scmfsa_2(A,B),k2_relat_1(C)) )
& k6_sf_mastr(C) = A ) ) ) ) ).
fof(t59_sf_mastr,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) )
=> ~ r2_hidden(k7_sf_mastr(A),A) ) ).
fof(t60_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k3_scmfsa_2)) )
=> ( k7_sf_mastr(C) = k6_scmfsa_2(A)
=> ( r2_hidden(k6_scmfsa_2(B),C)
| r1_xreal_0(A,B) ) ) ) ) ) ).
fof(d9_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_scmfsa_2(B)
=> ( B = k8_sf_mastr(A)
<=> ? [C] :
( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(k3_scmfsa_2))
& C = k4_sf_mastr(A)
& B = k7_sf_mastr(C) ) ) ) ) ).
fof(t61_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ r2_hidden(k8_sf_mastr(A),k4_sf_mastr(A)) ) ).
fof(t62_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ ( ( r2_hidden(k16_scmfsa_2(A,B,C),k2_relat_1(D))
| r2_hidden(k17_scmfsa_2(A,B,C),k2_relat_1(D)) )
& k8_sf_mastr(D) = C ) ) ) ) ) ).
fof(t63_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ ( ( r2_hidden(k18_scmfsa_2(A,B),k2_relat_1(C))
| r2_hidden(k19_scmfsa_2(A,B),k2_relat_1(C)) )
& k8_sf_mastr(C) = B ) ) ) ) ).
fof(t64_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xboole_0(k1_relat_1(A),k1_relat_1(k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(B)))) ) ) ).
fof(t65_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k1_relat_1(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(B))))) ) ) ).
fof(t66_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(B))),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k5_scmfsa_2(B) ) ) ).
fof(t67_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(B))),C)
=> k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C) = k5_scmfsa_2(B) ) ) ) ) ).
fof(t68_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ~ r2_hidden(A,k1_sf_mastr(B))
=> k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,C),A) = k20_scmfsa_2(C,A) ) ) ) ) ).
fof(t69_sf_mastr,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(C,E)
=> r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),E)),k1_relat_1(B)) ) ) )
=> ( r2_hidden(A,k2_sf_mastr(B))
| k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),C),A) = k20_scmfsa_2(D,A) ) ) ) ) ) ) ).
fof(t70_sf_mastr,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ~ r2_hidden(A,k3_sf_mastr(B))
=> k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,C),A) = k21_scmfsa_2(C,A) ) ) ) ) ).
fof(t71_sf_mastr,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(C,E)
=> r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),E)),k1_relat_1(B)) ) ) )
=> ( r2_hidden(A,k4_sf_mastr(B))
| k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),C),A) = k21_scmfsa_2(D,A) ) ) ) ) ) ) ).
fof(t72_sf_mastr,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( k7_relat_1(B,k1_sf_mastr(A)) = k7_relat_1(C,k1_sf_mastr(A))
& k7_relat_1(B,k3_sf_mastr(A)) = k7_relat_1(C,k3_sf_mastr(A))
& k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C) )
=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C))
& k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),k1_sf_mastr(A)) = k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C),k1_sf_mastr(A))
& k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),k3_sf_mastr(A)) = k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C),k3_sf_mastr(A)) ) ) ) ) ) ).
fof(t73_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),C)
& r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),D)
& k7_relat_1(C,k2_sf_mastr(A)) = k7_relat_1(D,k2_sf_mastr(A))
& k7_relat_1(C,k4_sf_mastr(A)) = k7_relat_1(D,k4_sf_mastr(A))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,E)
=> r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C),E)),k1_relat_1(A)) ) ) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,E)
=> r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),E)),k1_relat_1(A)) ) )
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,B)
=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C),E)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),E))
& ! [F] :
( m1_scmfsa_2(F)
=> ( r2_hidden(F,k2_sf_mastr(A))
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C),E),F) = k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),E),F) ) )
& ! [F] :
( m2_scmfsa_2(F)
=> ( r2_hidden(F,k4_sf_mastr(A))
=> k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C),E),F) = k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D),E),F) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_sf_mastr,axiom,
! [A] :
( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> m1_subset_1(k1_sf_mastr(A),k5_finsub_1(k2_scmfsa_2)) ) ).
fof(dt_k2_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> m1_subset_1(k2_sf_mastr(A),k1_zfmisc_1(k2_scmfsa_2)) ) ).
fof(dt_k3_sf_mastr,axiom,
! [A] :
( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> m1_subset_1(k3_sf_mastr(A),k5_finsub_1(k3_scmfsa_2)) ) ).
fof(dt_k4_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> m1_subset_1(k4_sf_mastr(A),k1_zfmisc_1(k3_scmfsa_2)) ) ).
fof(dt_k5_sf_mastr,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> m1_scmfsa_2(k5_sf_mastr(A)) ) ).
fof(dt_k6_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> m1_scmfsa_2(k6_sf_mastr(A)) ) ).
fof(dt_k7_sf_mastr,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) )
=> m2_scmfsa_2(k7_sf_mastr(A)) ) ).
fof(dt_k8_sf_mastr,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> m2_scmfsa_2(k8_sf_mastr(A)) ) ).
fof(d6_sf_mastr,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> ! [B] :
( m1_scmfsa_2(B)
=> ( B = k5_sf_mastr(A)
<=> ? [C] :
( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k5_numbers))
& B = k4_scmfsa_2(k10_cqc_sim1(C))
& C = a_1_0_sf_mastr(A) ) ) ) ) ).
fof(d8_sf_mastr,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) )
=> ! [B] :
( m2_scmfsa_2(B)
=> ( B = k7_sf_mastr(A)
<=> ? [C] :
( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k5_numbers))
& B = k6_scmfsa_2(k10_cqc_sim1(C))
& C = a_1_1_sf_mastr(A) ) ) ) ) ).
fof(fraenkel_a_1_0_sf_mastr,axiom,
! [A,B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) )
=> ( r2_hidden(A,a_1_0_sf_mastr(B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = C
& ~ r2_hidden(k4_scmfsa_2(C),B) ) ) ) ).
fof(fraenkel_a_1_1_sf_mastr,axiom,
! [A,B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(k3_scmfsa_2)) )
=> ( r2_hidden(A,a_1_1_sf_mastr(B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = C
& ~ r2_hidden(k6_scmfsa_2(C),B) ) ) ) ).
%------------------------------------------------------------------------------