SET007 Axioms: SET007+458.ax
%------------------------------------------------------------------------------
% File : SET007+458 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Modifying Addresses of Instructions of 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 : scmfsa_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 60 ( 2 unt; 0 def)
% Number of atoms : 328 ( 63 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 281 ( 13 ~; 1 |; 104 &)
% ( 10 <=>; 153 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 24 ( 23 usr; 0 prp; 1-3 aty)
% Number of functors : 68 ( 68 usr; 10 con; 0-4 aty)
% Number of variables : 175 ( 168 !; 7 ?)
% 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_scmfsa_4,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C) ) ) ) ).
fof(rc1_scmfsa_4,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ? [C] :
( m1_ami_1(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_ami_3(C,A,B) ) ) ).
fof(fc1_scmfsa_4,axiom,
( ~ v1_xboole_0(k5_scmfsa_4)
& v1_relat_1(k5_scmfsa_4)
& v1_funct_1(k5_scmfsa_4)
& v1_finset_1(k5_scmfsa_4)
& v1_ami_3(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_scmfsa_4) ) ).
fof(rc2_scmfsa_4,axiom,
? [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A) ) ).
fof(fc2_scmfsa_4,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B) )
=> ( v1_relat_1(k5_relat_1(B,A))
& v1_funct_1(k5_relat_1(B,A))
& v1_finset_1(k5_relat_1(B,A)) ) ) ).
fof(t1_scmfsa_4,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> r1_tarski(k2_relat_1(C),u4_ami_1(A,B)) ) ) ) ).
fof(t2_scmfsa_4,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u4_ami_1(A,B),u4_ami_1(A,B))
& m2_relset_1(C,u4_ami_1(A,B),u4_ami_1(A,B)) )
=> ! [D] :
( ( v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> k1_relat_1(k5_relat_1(D,C)) = k1_relat_1(D) ) ) ) ) ).
fof(d1_scmfsa_4,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] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( C = k2_scmfsa_4(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k5_scmfsa_2(D)
& C = k5_scmfsa_2(k1_nat_1(D,B)) ) ) ) ) ) ).
fof(d2_scmfsa_4,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] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( C = k3_scmfsa_4(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k5_scmfsa_2(D)
& C = k5_scmfsa_2(k5_binarith(D,B)) ) ) ) ) ) ).
fof(t3_scmfsa_4,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] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_scmfsa_4(k2_scmfsa_4(A,B),C) = k2_scmfsa_4(A,k1_nat_1(B,C)) ) ) ) ).
fof(t4_scmfsa_4,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] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k3_scmfsa_4(k2_scmfsa_4(A,B),B) = A ) ) ).
fof(t5_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( C = B
=> k2_scmfsa_4(B,A) = k1_reloc(C,A) ) ) ) ) ).
fof(t6_scmfsa_4,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))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_scmfsa_4(A,C)) = k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_scmfsa_4(B,C))
<=> k12_ami_3(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,B) ) ) ) ) ).
fof(t7_scmfsa_4,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))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k12_ami_3(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,B)
=> k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa_4(A,C)) = k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa_4(B,C)) ) ) ) ) ).
fof(d3_scmfsa_4,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)
=> ! [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))
=> ( ( r2_hidden(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k1_enumset1(np__6,np__7,np__8))
=> ( C = k4_scmfsa_4(A,B)
<=> ? [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& D = A
& C = k3_reloc(D,B) ) ) )
& ( ~ r2_hidden(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k1_enumset1(np__6,np__7,np__8))
=> ( C = k4_scmfsa_4(A,B)
<=> C = A ) ) ) ) ) ) ).
fof(t8_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k4_scmfsa_4(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ).
fof(t9_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> k4_scmfsa_4(k8_scmfsa_2(B,C),A) = k8_scmfsa_2(B,C) ) ) ) ).
fof(t10_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> k4_scmfsa_4(k9_scmfsa_2(B,C),A) = k9_scmfsa_2(B,C) ) ) ) ).
fof(t11_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> k4_scmfsa_4(k10_scmfsa_2(B,C),A) = k10_scmfsa_2(B,C) ) ) ) ).
fof(t12_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> k4_scmfsa_4(k11_scmfsa_2(B,C),A) = k11_scmfsa_2(B,C) ) ) ) ).
fof(t13_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> k4_scmfsa_4(k12_scmfsa_2(B,C),A) = k12_scmfsa_2(B,C) ) ) ) ).
fof(t14_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k4_scmfsa_4(k13_scmfsa_2(B),A) = k13_scmfsa_2(k2_scmfsa_4(B,A)) ) ) ).
fof(t15_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [C] :
( m1_scmfsa_2(C)
=> k4_scmfsa_4(k14_scmfsa_2(B,C),A) = k14_scmfsa_2(k2_scmfsa_4(B,A),C) ) ) ) ).
fof(t16_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [C] :
( m1_scmfsa_2(C)
=> k4_scmfsa_4(k15_scmfsa_2(B,C),A) = k15_scmfsa_2(k2_scmfsa_4(B,A),C) ) ) ) ).
fof(t17_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> k4_scmfsa_4(k16_scmfsa_2(C,B,D),A) = k16_scmfsa_2(C,B,D) ) ) ) ) ).
fof(t18_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> k4_scmfsa_4(k17_scmfsa_2(C,B,D),A) = k17_scmfsa_2(C,B,D) ) ) ) ) ).
fof(t19_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> k4_scmfsa_4(k18_scmfsa_2(B,C),A) = k18_scmfsa_2(B,C) ) ) ) ).
fof(t20_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> k4_scmfsa_4(k19_scmfsa_2(B,C),A) = k19_scmfsa_2(B,C) ) ) ) ).
fof(t21_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( B = C
=> k4_scmfsa_4(B,A) = k3_reloc(C,A) ) ) ) ) ).
fof(t22_scmfsa_4,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_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_4(A,B)) = k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) ) ) ).
fof(d4_scmfsa_4,axiom,
! [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ( v1_scmfsa_4(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(k5_scmfsa_2(C),k1_relat_1(A))
=> ( r1_xreal_0(C,B)
| r2_hidden(k5_scmfsa_2(B),k1_relat_1(A)) ) ) ) ) ) ) ).
fof(d5_scmfsa_4,axiom,
k5_scmfsa_4 = k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ).
fof(t23_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [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))
=> k4_scmfsa_4(k4_scmfsa_4(C,A),B) = k4_scmfsa_4(C,k1_nat_1(A,B)) ) ) ) ).
fof(d6_scmfsa_4,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)
=> ! [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) )
=> ( C = k7_scmfsa_4(A,B)
<=> ( k1_relat_1(C) = k1_relat_1(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k5_scmfsa_2(D),k1_relat_1(A))
=> k1_funct_1(C,k5_scmfsa_2(D)) = k4_scmfsa_4(k5_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k5_scmfsa_2(D)),B) ) ) ) ) ) ) ) ).
fof(t24_scmfsa_4,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)
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( r2_hidden(C,k1_relat_1(A))
=> k1_funct_1(k7_scmfsa_4(A,B),C) = k4_scmfsa_4(k5_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C),B) ) ) ) ) ).
fof(t25_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> ! [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) )
=> k7_scmfsa_4(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,C),A) = k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k7_scmfsa_4(B,A),k7_scmfsa_4(C,A)) ) ) ) ).
fof(t26_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& m2_relset_1(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( C = k1_funct_4(k6_relat_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k3_cqc_lang(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),B))
=> ! [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) )
=> k7_scmfsa_4(k6_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,C),A) = k5_relat_1(k7_scmfsa_4(D,A),k1_funct_4(k6_relat_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k3_cqc_lang(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k4_scmfsa_4(B,A)))) ) ) ) ) ) ).
fof(t27_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [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) )
=> k7_scmfsa_4(k7_scmfsa_4(C,A),B) = k7_scmfsa_4(C,k1_nat_1(A,B)) ) ) ) ).
fof(t28_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_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,k4_scmfsa_4(k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B),A),k8_ami_5(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,k2_scmfsa_4(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B),A)))) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k9_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,k2_scmfsa_4(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k9_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)),A))) ) ) ).
fof(t29_scmfsa_4,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_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B) = k5_scmfsa_2(k1_nat_1(E,F))
=> k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k8_ami_5(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,k3_scmfsa_4(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B),F)))) = k8_ami_5(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,k4_scmfsa_4(A,F),B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa_4(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,k4_scmfsa_4(A,F),B)),F))) ) ) ) ) ) ) ) ).
fof(t30_scmfsa_4,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] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ( r2_hidden(A,k1_relat_1(C))
=> k1_funct_1(k8_scmfsa_4(C,B),k2_scmfsa_4(A,B)) = k1_funct_1(C,A) ) ) ) ) ).
fof(t32_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> k8_scmfsa_4(k8_scmfsa_4(C,A),B) = k8_scmfsa_4(C,k1_nat_1(A,B)) ) ) ) ).
fof(t33_scmfsa_4,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_funct_1(B)
& v1_funct_2(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& m2_relset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k8_scmfsa_4(k6_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),C) = k6_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_4(A,C),B) ) ) ) ).
fof(t34_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ! [C] :
( m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> k8_scmfsa_4(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,C),A) = k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_4(B,A),k8_scmfsa_4(C,A)) ) ) ) ).
fof(t35_scmfsa_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [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) )
=> k8_scmfsa_4(k7_scmfsa_4(C,A),B) = k7_scmfsa_4(k8_scmfsa_4(C,B),A) ) ) ) ).
fof(dt_k1_scmfsa_4,axiom,
! [A,B,C,D] :
( ( l1_ami_1(B,A)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> ( v1_ami_3(k1_scmfsa_4(A,B,C,D),A,B)
& m1_ami_1(k1_scmfsa_4(A,B,C,D),A,B) ) ) ).
fof(idempotence_k1_scmfsa_4,axiom,
! [A,B,C,D] :
( ( l1_ami_1(B,A)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> k1_scmfsa_4(A,B,C,C) = C ) ).
fof(redefinition_k1_scmfsa_4,axiom,
! [A,B,C,D] :
( ( l1_ami_1(B,A)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> k1_scmfsa_4(A,B,C,D) = k1_funct_4(C,D) ) ).
fof(dt_k2_scmfsa_4,axiom,
! [A,B] :
( ( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& m1_subset_1(B,k5_numbers) )
=> m1_struct_0(k2_scmfsa_4(A,B),k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ).
fof(dt_k3_scmfsa_4,axiom,
! [A,B] :
( ( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& m1_subset_1(B,k5_numbers) )
=> m1_struct_0(k3_scmfsa_4(A,B),k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ).
fof(dt_k4_scmfsa_4,axiom,
! [A,B] :
( ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k4_scmfsa_4(A,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)) ) ).
fof(dt_k5_scmfsa_4,axiom,
m1_ami_1(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ).
fof(dt_k6_scmfsa_4,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v1_funct_1(D)
& v1_funct_2(D,u4_ami_1(A,B),u4_ami_1(A,B))
& m1_relset_1(D,u4_ami_1(A,B),u4_ami_1(A,B)) )
=> ( v1_ami_3(k6_scmfsa_4(A,B,C,D),A,B)
& m1_ami_1(k6_scmfsa_4(A,B,C,D),A,B) ) ) ).
fof(redefinition_k6_scmfsa_4,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B)
& v1_funct_1(D)
& v1_funct_2(D,u4_ami_1(A,B),u4_ami_1(A,B))
& m1_relset_1(D,u4_ami_1(A,B),u4_ami_1(A,B)) )
=> k6_scmfsa_4(A,B,C,D) = k5_relat_1(C,D) ) ).
fof(dt_k7_scmfsa_4,axiom,
! [A,B] :
( ( 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(B,k5_numbers) )
=> ( v1_ami_3(k7_scmfsa_4(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(k7_scmfsa_4(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k8_scmfsa_4,axiom,
! [A,B] :
( ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_subset_1(B,k5_numbers) )
=> ( v1_ami_3(k8_scmfsa_4(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(k8_scmfsa_4(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(d7_scmfsa_4,axiom,
! [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] :
( ( 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) )
=> ( C = k8_scmfsa_4(A,B)
<=> ( k1_relat_1(C) = a_2_0_scmfsa_4(A,B)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k5_scmfsa_2(D),k1_relat_1(A))
=> k1_funct_1(C,k5_scmfsa_2(k1_nat_1(D,B))) = k1_funct_1(A,k5_scmfsa_2(D)) ) ) ) ) ) ) ) ).
fof(t31_scmfsa_4,axiom,
! [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_relat_1(k8_scmfsa_4(A,B)) = a_2_1_scmfsa_4(A,B) ) ) ).
fof(fraenkel_a_2_0_scmfsa_4,axiom,
! [A,B,C] :
( ( m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_0_scmfsa_4(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k5_scmfsa_2(k1_nat_1(D,C))
& r2_hidden(k5_scmfsa_2(D),k1_relat_1(B)) ) ) ) ).
fof(fraenkel_a_2_1_scmfsa_4,axiom,
! [A,B,C] :
( ( m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_1_scmfsa_4(B,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 = k2_scmfsa_4(D,C)
& r2_hidden(D,k1_relat_1(B)) ) ) ) ).
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