SET007 Axioms: SET007+465.ax
%------------------------------------------------------------------------------
% File : SET007+465 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Multi Instructions Defined by Sequence 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_7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 54 ( 13 unt; 0 def)
% Number of atoms : 253 ( 71 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 220 ( 21 ~; 3 |; 66 &)
% ( 11 <=>; 119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 60 ( 60 usr; 11 con; 0-4 aty)
% Number of variables : 113 ( 106 !; 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_7,axiom,
! [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A) ) ) ).
fof(fc1_scmfsa_7,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_relat_1(k2_funct_7(A,B,C))
& v1_funct_1(k2_funct_7(A,B,C))
& v1_finset_1(k2_funct_7(A,B,C))
& v1_finseq_1(k2_funct_7(A,B,C)) ) ) ).
fof(t1_scmfsa_7,axiom,
! [A] :
( v4_ordinal2(A)
=> k1_int_2(A) = A ) ).
fof(t2_scmfsa_7,axiom,
$true ).
fof(t3_scmfsa_7,axiom,
$true ).
fof(t4_scmfsa_7,axiom,
$true ).
fof(t5_scmfsa_7,axiom,
$true ).
fof(t6_scmfsa_7,axiom,
$true ).
fof(t7_scmfsa_7,axiom,
$true ).
fof(t8_scmfsa_7,axiom,
$true ).
fof(t9_scmfsa_7,axiom,
$true ).
fof(t10_scmfsa_7,axiom,
$true ).
fof(t11_scmfsa_7,axiom,
$true ).
fof(t12_scmfsa_7,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( A != k1_xboole_0
=> r2_hidden(k3_finseq_1(A),k5_finsop_1(A)) ) ) ).
fof(t13_scmfsa_7,axiom,
! [A] : k15_dtconstr(A,k6_finseq_1(k13_finseq_1(A))) = k6_finseq_1(A) ).
fof(t14_scmfsa_7,axiom,
! [A,B] :
( m2_finseq_1(B,k13_finseq_1(A))
=> ! [C] :
( m2_finseq_1(C,k13_finseq_1(A))
=> k15_dtconstr(A,k8_finseq_1(k13_finseq_1(A),B,C)) = k8_finseq_1(A,k15_dtconstr(A,B),k15_dtconstr(A,C)) ) ) ).
fof(t15_scmfsa_7,axiom,
! [A,B] :
( m1_subset_1(B,k13_finseq_1(A))
=> ! [C] :
( m1_subset_1(C,k13_finseq_1(A))
=> k15_dtconstr(A,k2_finseq_4(k13_finseq_1(A),B,C)) = k7_finseq_1(B,C) ) ) ).
fof(t16_scmfsa_7,axiom,
! [A,B] :
( m1_subset_1(B,k13_finseq_1(A))
=> ! [C] :
( m1_subset_1(C,k13_finseq_1(A))
=> ! [D] :
( m1_subset_1(D,k13_finseq_1(A))
=> k15_dtconstr(A,k3_finseq_4(k13_finseq_1(A),B,C,D)) = k7_finseq_1(k7_finseq_1(B,C),D) ) ) ) ).
fof(t17_scmfsa_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ~ ( r1_tarski(B,C)
& ! [D] :
( m2_finseq_1(D,A)
=> k8_finseq_1(A,B,D) != C ) ) ) ) ) ).
fof(t18_scmfsa_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_tarski(B,C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> k1_funct_1(C,D) = k1_funct_1(B,D) ) ) ) ) ) ).
fof(t19_scmfsa_7,axiom,
! [A,B] :
( m2_finseq_1(B,k13_finseq_1(A))
=> ! [C] :
( m2_finseq_1(C,k13_finseq_1(A))
=> ( r1_tarski(B,C)
=> r1_tarski(k15_dtconstr(A,B),k15_dtconstr(A,C)) ) ) ) ).
fof(t20_scmfsa_7,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> k7_relat_1(A,k2_finseq_1(np__0)) = k1_xboole_0 ) ).
fof(t21_scmfsa_7,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> k7_relat_1(A,k2_finseq_1(np__0)) = k7_relat_1(B,k2_finseq_1(np__0)) ) ) ).
fof(t22_scmfsa_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> m2_finseq_1(k12_finseq_1(A,B),A) ) ) ).
fof(t23_scmfsa_7,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> m2_finseq_1(k8_finseq_1(A,B,C),A) ) ) ).
fof(t24_scmfsa_7,axiom,
$true ).
fof(t25_scmfsa_7,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k4_card_1(k1_scmfsa_7(A)) = k3_finseq_1(A) ) ).
fof(t26_scmfsa_7,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(k5_scmfsa_2(B),k1_relat_1(k1_scmfsa_7(A)))
<=> r2_hidden(k1_nat_1(B,np__1),k5_finsop_1(A)) ) ) ) ).
fof(t27_scmfsa_7,axiom,
$true ).
fof(t28_scmfsa_7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,A)
<=> ( r1_xreal_0(np__1,k1_nat_1(A,np__1))
& r1_xreal_0(k1_nat_1(A,np__1),B) ) ) ) ) ).
fof(t29_scmfsa_7,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(k5_scmfsa_2(B),k1_relat_1(k1_scmfsa_7(A)))
<=> ~ r1_xreal_0(k3_finseq_1(A),B) ) ) ) ).
fof(t30_scmfsa_7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( r2_hidden(np__1,k5_finsop_1(A))
& r2_hidden(k5_scmfsa_2(np__0),k1_relat_1(k1_scmfsa_7(A))) ) ) ).
fof(t31_scmfsa_7,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m2_finseq_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> r1_tarski(k1_scmfsa_7(A),k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A,B))) ) ) ).
fof(t32_scmfsa_7,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m2_finseq_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( r1_tarski(A,B)
=> r1_tarski(k1_scmfsa_7(A),k1_scmfsa_7(B)) ) ) ) ).
fof(d2_scmfsa_7,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ( ( ~ r1_xreal_0(B,np__0)
=> ( C = k2_scmfsa_7(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& k1_nat_1(D,np__1) = B
& C = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k1_finsop_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D,k9_scmfsa_2(A,k4_scmfsa_2(np__0)))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ) )
& ( r1_xreal_0(B,np__0)
=> ( C = k2_scmfsa_7(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& k2_xcmplx_0(D,B) = np__1
& C = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k1_finsop_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D,k10_scmfsa_2(A,k4_scmfsa_2(np__0)))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ) ) ) ) ) ) ).
fof(d3_scmfsa_7,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_finseq_1(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ( ~ r1_xreal_0(B,np__0)
=> ( C = k3_scmfsa_7(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& k1_nat_1(D,np__1) = B
& C = k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k1_finsop_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D,k9_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) ) )
& ( r1_xreal_0(B,np__0)
=> ( C = k3_scmfsa_7(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& k2_xcmplx_0(D,B) = np__1
& C = k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k1_finsop_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D,k10_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) ) ) ) ) ) ) ).
fof(t33_scmfsa_7,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( v1_int_1(B)
=> k2_scmfsa_7(A,B) = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k3_scmfsa_7(A,B),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ) ).
fof(d4_scmfsa_7,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( m2_finseq_1(B,k4_numbers)
=> ! [C] :
( m2_finseq_1(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( C = k4_scmfsa_7(A,B)
<=> ? [D] :
( m2_finseq_1(D,k13_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
& k3_finseq_1(D) = k3_finseq_1(B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(B))
& ! [F] :
( v1_int_1(F)
=> ~ ( F = k1_funct_1(B,E)
& k1_funct_1(D,E) = k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k3_scmfsa_7(k4_scmfsa_2(np__1),E),k3_scmfsa_7(k4_scmfsa_2(np__2),F)),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k17_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__1),A))) ) ) ) )
& C = k15_dtconstr(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),D) ) ) ) ) ) ).
fof(d5_scmfsa_7,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( m2_finseq_1(B,k4_numbers)
=> k5_scmfsa_7(A,B) = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k3_scmfsa_7(k4_scmfsa_2(np__1),k3_finseq_1(B)),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k19_scmfsa_2(k4_scmfsa_2(np__1),A))),k4_scmfsa_7(A,B)),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ) ).
fof(t34_scmfsa_7,axiom,
! [A] :
( m1_scmfsa_2(A)
=> k2_scmfsa_7(A,np__1) = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ).
fof(t35_scmfsa_7,axiom,
! [A] :
( m1_scmfsa_2(A)
=> k2_scmfsa_7(A,np__0) = k1_scmfsa_7(k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k10_scmfsa_2(A,k4_scmfsa_2(np__0)))),k12_finseq_1(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ).
fof(t36_scmfsa_7,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k5_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k5_finsop_1(k3_scmfsa_7(C,D)))
=> k1_funct_1(k3_scmfsa_7(C,D),E) = k13_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k5_scmfsa_2(k5_binarith(k1_nat_1(B,E),np__1))) ) )
=> ( C = k4_scmfsa_2(np__0)
| ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k3_finseq_1(k3_scmfsa_7(C,D)))
=> ( 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,A),E)) = k5_scmfsa_2(k1_nat_1(B,E))
& ! [F] :
( m1_scmfsa_2(F)
=> ( F != C
=> 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,A),E),F) = k20_scmfsa_2(A,F) ) )
& ! [F] :
( m2_scmfsa_2(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,A),E),F) = k21_scmfsa_2(A,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,A),k3_finseq_1(k3_scmfsa_7(C,D))),C) = D ) ) ) ) ) ) ) ) ) ).
fof(t37_scmfsa_7,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k5_scmfsa_2(np__0)
& k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( v1_int_1(C)
=> ( r1_tarski(k1_scmfsa_7(k3_scmfsa_7(B,C)),A)
=> ( B = k4_scmfsa_2(np__0)
| ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k3_finseq_1(k3_scmfsa_7(B,C)))
=> ( 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,A),D)) = k5_scmfsa_2(D)
& ! [E] :
( m1_scmfsa_2(E)
=> ( E != 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,A),D),E) = k20_scmfsa_2(A,E) ) )
& ! [E] :
( m2_scmfsa_2(E)
=> 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,A),D),E) = k21_scmfsa_2(A,E) ) ) ) )
& 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,A),k3_finseq_1(k3_scmfsa_7(B,C))),B) = C ) ) ) ) ) ) ) ).
fof(t38_scmfsa_7,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k5_scmfsa_2(np__0)
& k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( v1_int_1(C)
=> ( r1_tarski(k2_scmfsa_7(B,C),A)
=> ( B = k4_scmfsa_2(np__0)
| ( v9_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& k20_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),B) = C
& ! [D] :
( m1_scmfsa_2(D)
=> ( D != B
=> k20_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D) = k20_scmfsa_2(A,D) ) )
& ! [D] :
( m2_scmfsa_2(D)
=> k21_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D) = k21_scmfsa_2(A,D) ) ) ) ) ) ) ) ) ).
fof(t39_scmfsa_7,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k5_scmfsa_2(np__0)
& k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> ( r1_tarski(k5_scmfsa_7(B,C),A)
=> ( v9_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& k21_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),B) = C
& ! [D] :
( m1_scmfsa_2(D)
=> ~ ( D != k4_scmfsa_2(np__1)
& D != k4_scmfsa_2(np__2)
& k20_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D) != k20_scmfsa_2(A,D) ) )
& ! [D] :
( m2_scmfsa_2(D)
=> ( D != B
=> k21_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D) = k21_scmfsa_2(A,D) ) ) ) ) ) ) ) ) ).
fof(dt_k1_scmfsa_7,axiom,
! [A] :
( m1_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> m1_ami_1(k1_scmfsa_7(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ).
fof(dt_k2_scmfsa_7,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& v1_int_1(B) )
=> m1_ami_1(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ).
fof(dt_k3_scmfsa_7,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& v1_int_1(B) )
=> m2_finseq_1(k3_scmfsa_7(A,B),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ).
fof(dt_k4_scmfsa_7,axiom,
! [A,B] :
( ( m2_scmfsa_2(A)
& m1_finseq_1(B,k4_numbers) )
=> m2_finseq_1(k4_scmfsa_7(A,B),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ).
fof(dt_k5_scmfsa_7,axiom,
! [A,B] :
( ( m2_scmfsa_2(A)
& m1_finseq_1(B,k4_numbers) )
=> m1_ami_1(k5_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ).
fof(d1_scmfsa_7,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ( B = k1_scmfsa_7(A)
<=> ( k1_relat_1(B) = a_1_0_scmfsa_7(A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(k5_scmfsa_2(C),k1_relat_1(B))
=> k1_funct_1(B,k5_scmfsa_2(C)) = k4_finseq_4(k5_numbers,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A,k1_nat_1(C,np__1)) ) ) ) ) ) ) ).
fof(s1_scmfsa_7,axiom,
( ( r1_tarski(f1_s1_scmfsa_7,f2_s1_scmfsa_7)
& ! [A] :
( m1_subset_1(A,f2_s1_scmfsa_7)
=> ! [B] :
( m1_subset_1(B,f2_s1_scmfsa_7)
=> ( ( r2_hidden(A,f1_s1_scmfsa_7)
& r2_hidden(B,f1_s1_scmfsa_7)
& f3_s1_scmfsa_7(A) = f3_s1_scmfsa_7(B) )
=> A = B ) ) ) )
=> r2_tarski(f1_s1_scmfsa_7,a_0_0_scmfsa_7) ) ).
fof(fraenkel_a_1_0_scmfsa_7,axiom,
! [A,B] :
( m2_finseq_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( r2_hidden(A,a_1_0_scmfsa_7(B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = k5_scmfsa_2(k5_binarith(C,np__1))
& r2_hidden(C,k5_finsop_1(B)) ) ) ) ).
fof(fraenkel_a_0_0_scmfsa_7,axiom,
! [A] :
( r2_hidden(A,a_0_0_scmfsa_7)
<=> ? [B] :
( m1_subset_1(B,f2_s1_scmfsa_7)
& A = f3_s1_scmfsa_7(B)
& r2_hidden(B,f1_s1_scmfsa_7) ) ) ).
%------------------------------------------------------------------------------