SET007 Axioms: SET007+478.ax
%------------------------------------------------------------------------------
% File : SET007+478 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Conditional Branch Macro Instructions of SCMFSA. Part I
% 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 : scmfsa8a [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 77 ( 3 unt; 0 def)
% Number of atoms : 506 ( 64 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 439 ( 10 ~; 0 |; 222 &)
% ( 4 <=>; 203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 31 ( 29 usr; 1 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 9 con; 0-4 aty)
% Number of variables : 167 ( 165 !; 2 ?)
% 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(fc1_scmfsa8a,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,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( v1_relat_1(k1_scmfsa8a(A,B))
& v1_funct_1(k1_scmfsa8a(A,B))
& v1_finset_1(k1_scmfsa8a(A,B))
& v1_ami_3(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v2_scmfsa7b(k1_scmfsa8a(A,B)) ) ) ).
fof(fc2_scmfsa8a,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_relat_1(k1_scmfsa6a(A))
& v1_funct_1(k1_scmfsa6a(A))
& v1_finset_1(k1_scmfsa6a(A))
& v1_ami_3(k1_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v2_scmfsa7b(k1_scmfsa6a(A)) ) ) ).
fof(fc3_scmfsa8a,axiom,
! [A,B] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa7b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_subset_1(B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( v1_relat_1(k1_scmfsa8a(A,B))
& v1_funct_1(k1_scmfsa8a(A,B))
& v1_finset_1(k1_scmfsa8a(A,B))
& v1_ami_3(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa7b(k1_scmfsa8a(A,B))
& v2_scmfsa7b(k1_scmfsa8a(A,B)) ) ) ).
fof(fc4_scmfsa8a,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v1_scmfsa7b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( v1_relat_1(k1_scmfsa6a(A))
& v1_funct_1(k1_scmfsa6a(A))
& v1_finset_1(k1_scmfsa6a(A))
& v1_ami_3(k1_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k1_scmfsa6a(A))
& v1_scmfsa7b(k1_scmfsa6a(A))
& v2_scmfsa7b(k1_scmfsa6a(A)) ) ) ).
fof(fc5_scmfsa8a,axiom,
! [A,B] :
( ( 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)
& m1_subset_1(B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( v1_relat_1(k1_scmfsa8a(A,B))
& v1_funct_1(k1_scmfsa8a(A,B))
& v1_finset_1(k1_scmfsa8a(A,B))
& v1_ami_3(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k1_scmfsa8a(A,B))
& v2_scmfsa7b(k1_scmfsa8a(A,B)) ) ) ).
fof(fc6_scmfsa8a,axiom,
! [A,B] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v1_scmfsa7b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& v1_scmfsa7b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( v1_relat_1(k4_scmfsa6a(A,B))
& v1_funct_1(k4_scmfsa6a(A,B))
& v1_finset_1(k4_scmfsa6a(A,B))
& v1_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k4_scmfsa6a(A,B))
& v1_scmfsa7b(k4_scmfsa6a(A,B)) ) ) ).
fof(rc1_scmfsa8a,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)
& v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v1_scmfsa8a(A) ) ).
fof(t1_scmfsa8a,axiom,
$true ).
fof(t2_scmfsa8a,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( r1_xboole_0(k1_relat_1(B),C)
=> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C) ) ) ) ).
fof(t3_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> k1_relat_1(k7_relat_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) = u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ).
fof(t4_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( v9_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_xreal_0(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),B)
=> k8_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),B)) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ).
fof(t5_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( v9_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_xreal_0(k2_scm_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,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),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,A),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A))) ) ) ) ) ).
fof(t6_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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)))
=> ( r1_funct_7(A,B,u2_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) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)
& k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ).
fof(t7_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,A)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)))) ) ) ).
fof(t8_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A),k3_scmfsa6a(B)) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)) ) ) ).
fof(t9_scmfsa8a,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] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> r1_tarski(A,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,B))) ) ) ).
fof(t10_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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))
=> k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k8_ami_5(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)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ).
fof(t11_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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,C))),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ).
fof(t12_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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))
=> r1_xboole_0(k1_relat_1(k7_relat_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))),k1_relat_1(k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B))) ) ) ).
fof(t13_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A),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)))) ) ) ).
fof(t14_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& m1_ami_1(C,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))
=> r1_funct_7(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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,D))),k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D))),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ) ) ) ).
fof(t15_scmfsa8a,axiom,
k1_relat_1(k5_scmfsa_4) = k1_struct_0(k1_scmfsa_2,k5_scmfsa_2(np__0)) ).
fof(t16_scmfsa8a,axiom,
( r2_hidden(k5_scmfsa_2(np__0),k1_relat_1(k5_scmfsa_4))
& k1_funct_1(k5_scmfsa_4,k5_scmfsa_2(np__0)) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ).
fof(t17_scmfsa8a,axiom,
k4_card_1(k5_scmfsa_4) = np__1 ).
fof(d1_scmfsa8a,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_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k1_scmfsa8a(A,B) = k5_relat_1(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),k13_scmfsa_2(B)))) ) ) ).
fof(t18_scmfsa8a,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) )
=> k1_scmfsa6a(A) = k1_scmfsa8a(A,k5_scmfsa_2(k4_card_1(A))) ) ).
fof(t19_scmfsa8a,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_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k1_relat_1(k1_scmfsa8a(A,B)) = k1_relat_1(A) ) ) ).
fof(t20_scmfsa8a,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_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k1_scmfsa8a(A,B) = k1_funct_4(A,k5_relat_1(A,k3_cqc_lang(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_scmfsa_2(B)))) ) ) ).
fof(t21_scmfsa8a,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_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> ( ( k1_funct_1(A,C) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> k1_funct_1(k1_scmfsa8a(A,B),C) = k13_scmfsa_2(B) )
& ( k1_funct_1(A,C) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> k1_funct_1(k1_scmfsa8a(A,B),C) = k1_funct_1(A,C) ) ) ) ) ) ).
fof(t22_scmfsa8a,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_scmfsa_2(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r3_scmfsa7b(A,B)
=> r3_scmfsa7b(k4_scmfsa_4(A,C),B) ) ) ) ) ).
fof(t23_scmfsa8a,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_scmfsa_2(C)
=> ( r4_scmfsa7b(A,C)
=> r4_scmfsa7b(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B)),C) ) ) ) ) ).
fof(t24_scmfsa8a,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa7b(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)
=> v1_scmfsa7b(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B))) ) ) ).
fof(t25_scmfsa8a,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) )
=> ! [C] :
( m1_scmfsa_2(C)
=> ( ( r4_scmfsa7b(A,C)
& r4_scmfsa7b(B,C) )
=> r4_scmfsa7b(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),C) ) ) ) ) ).
fof(t26_scmfsa8a,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa7b(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_scmfsa7b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> v1_scmfsa7b(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) ) ) ).
fof(t27_scmfsa8a,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_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)
=> ( r4_scmfsa7b(A,C)
=> r4_scmfsa7b(k1_scmfsa8a(A,B),C) ) ) ) ) ).
fof(d2_scmfsa8a,axiom,
! [A] :
( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k2_scmfsa8a(A) = k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0),k13_scmfsa_2(A)) ) ).
fof(d3_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( ( v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_scmfsa8a(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),C)) = k5_scmfsa_2(k4_card_1(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(C,D)
=> 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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)),k1_relat_1(B)) ) ) ) ) ) ) ).
fof(d4_scmfsa8a,axiom,
! [A] :
( ( v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( v1_scmfsa8a(A)
<=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> r1_scmfsa8a(B,A) ) ) ) ).
fof(d5_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( ( v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_scmfsa8a(A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( C = k3_scmfsa8a(A,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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),C)) = k5_scmfsa_2(k4_card_1(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ~ 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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)),k1_relat_1(B))
=> r1_xreal_0(C,D) ) ) ) ) ) ) ) ) ).
fof(t28_scmfsa8a,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) )
=> ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> k1_funct_1(k4_scmfsa6a(A,B),C) = k1_funct_1(k1_scmfsa6a(A),C) ) ) ) ).
fof(t29_scmfsa8a,axiom,
! [A] :
( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k4_card_1(k2_scmfsa8a(A)) = np__1 ) ).
fof(t30_scmfsa8a,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] :
( r2_hidden(B,k1_relat_1(A))
=> ( ( k1_funct_1(A,B) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> k1_funct_1(k1_scmfsa6a(A),B) = k13_scmfsa_2(k5_scmfsa_2(k4_card_1(A))) )
& ( k1_funct_1(A,B) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> k1_funct_1(k1_scmfsa6a(A),B) = k1_funct_1(A,B) ) ) ) ) ).
fof(t31_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( ( v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_scmfsa8a(A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k3_scmfsa8a(A,B),C)
=> ( 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),C)),k1_relat_1(B))
& k8_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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),C)) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ) ) ).
fof(t32_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_scmfsa8a(A,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k3_scmfsa8a(A,B))
=> r1_funct_7(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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),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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ) ) ) ) ) ).
fof(t33_scmfsa8a,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_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k4_card_1(k1_scmfsa8a(A,B)) = k4_card_1(A) ) ) ).
fof(t34_scmfsa8a,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_card_1(k1_scmfsa6a(A)) = k4_card_1(A) ) ).
fof(t35_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ( ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))))
=> ( r1_funct_7(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),C),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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& k8_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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C)) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ) ) ).
fof(t36_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ( ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> ( 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),np__1))) = k5_scmfsa_2(k4_card_1(B))
& k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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)))))),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ).
fof(t37_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ( ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> r1_scmfsa8a(A,k1_scmfsa6a(B)) ) ) ) ).
fof(t38_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ( ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> k3_scmfsa8a(A,k1_scmfsa6a(B)) = k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),np__1) ) ) ) ).
fof(t39_scmfsa8a,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_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( v2_scmfsa7b(A)
=> k1_scmfsa8a(A,B) = A ) ) ) ).
fof(t40_scmfsa8a,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) )
=> ( v2_scmfsa7b(A)
=> k1_scmfsa6a(A) = A ) ) ).
fof(t41_scmfsa8a,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_scmfsa6a(k1_scmfsa6a(A),B) = k4_scmfsa6a(A,B) ) ) ).
fof(t42_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))))
=> ( 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D))
& k8_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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D)) = k8_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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D)) ) ) )
& k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2))
& 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6a(B),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),np__1))) = 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,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))))),np__1))) ) ) ) ) ) ).
fof(t43_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k1_scmfsa6c(A)) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k4_scmfsa6a(B,C)))),D))
& k8_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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),D)) = k8_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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k4_scmfsa6a(B,C)))),D)) ) ) )
& k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k4_scmfsa6a(B,C)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2))
& 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1))) = 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k4_scmfsa6a(B,C)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1))) ) ) ) ) ) ).
fof(t44_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k1_scmfsa6c(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))))
=> ( r1_funct_7(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),C),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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),C),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& k8_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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),C)) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ) ) ).
fof(t45_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k1_scmfsa6c(A)) )
=> ( 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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1))) = k5_scmfsa_2(k4_card_1(B))
& k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)))),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(k1_scmfsa6a(B)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ).
fof(t46_scmfsa8a,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] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,B)
& r6_scmfsa7b(A,B) )
=> ( r5_scmfsa7b(k4_scmfsa6a(A,k5_scmfsa_4),B)
& r6_scmfsa7b(k4_scmfsa6a(A,k5_scmfsa_4),B) ) ) ) ) ).
fof(t47_scmfsa8a,axiom,
! [A] :
( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( r2_hidden(k5_scmfsa_2(np__0),k1_relat_1(k2_scmfsa8a(A)))
& k1_funct_1(k2_scmfsa8a(A),k5_scmfsa_2(np__0)) = k13_scmfsa_2(A) ) ) ).
fof(t48_scmfsa8a,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) )
=> ! [D] :
( r2_hidden(D,k1_relat_1(C))
=> m2_subset_1(k1_funct_1(C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ) ) ) ).
fof(t49_scmfsa8a,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,C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k1_relat_1(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,C))))
=> k1_funct_1(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,C)),B) = k1_funct_1(k1_scmfsa_5(A,C),B) ) ) ) ).
fof(t50_scmfsa8a,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)
=> k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(k1_scmfsa6a(A),B)) = k1_scmfsa8a(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B)),k5_scmfsa_2(k1_nat_1(k4_card_1(A),B))) ) ) ).
fof(t51_scmfsa8a,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) )
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k1_scmfsa8a(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),C) = k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa8a(A,C),k1_scmfsa8a(B,C)) ) ) ) ).
fof(t52_scmfsa8a,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) )
=> k1_scmfsa6a(k4_scmfsa6a(A,B)) = k4_scmfsa6a(A,k1_scmfsa6a(B)) ) ) ).
fof(t53_scmfsa8a,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] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,k1_scmfsa6c(B))
& r6_scmfsa7b(A,k1_scmfsa6c(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(k4_scmfsa6a(A,k5_scmfsa_4)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A))),np__1))) = k5_scmfsa_2(k4_card_1(A)) ) ) ) ).
fof(t54_scmfsa8a,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] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,k1_scmfsa6c(B))
& r6_scmfsa7b(A,k1_scmfsa6c(B)) )
=> k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A)))),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(k4_scmfsa6a(A,k5_scmfsa_4)))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A))),np__1)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ).
fof(t55_scmfsa8a,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] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,k1_scmfsa6c(B))
& r6_scmfsa7b(A,k1_scmfsa6c(B)) )
=> v9_ami_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(k4_scmfsa6a(A,k5_scmfsa_4))),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ).
fof(t56_scmfsa8a,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] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,k1_scmfsa6c(B))
& r6_scmfsa7b(A,k1_scmfsa6c(B)) )
=> k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(k4_scmfsa6a(A,k5_scmfsa_4)))) = k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k3_scmfsa6a(A))),np__1) ) ) ) ).
fof(t57_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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) )
=> ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k1_scmfsa6c(A)) )
=> k3_scmfsa6b(k4_scmfsa6a(B,k5_scmfsa_4),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k4_card_1(B)))) ) ) ) ).
fof(t58_scmfsa8a,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) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,C)
& r6_scmfsa7b(A,C) )
=> ( r5_scmfsa7b(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),C)
& r6_scmfsa7b(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),C) ) ) ) ) ) ).
fof(t59_scmfsa8a,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) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,C)
& r6_scmfsa7b(A,C) )
=> v9_ami_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ).
fof(t60_scmfsa8a,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) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,k1_scmfsa6c(C))
& r6_scmfsa7b(A,k1_scmfsa6c(C)) )
=> v9_ami_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4))),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ).
fof(t61_scmfsa8a,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) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,k1_scmfsa6c(C))
& r6_scmfsa7b(A,k1_scmfsa6c(C)) )
=> k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),C)) = k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),np__1)) ) ) ) ) ).
fof(t62_scmfsa8a,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) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,k1_scmfsa6c(C))
& r6_scmfsa7b(A,k1_scmfsa6c(C)) )
=> k3_scmfsa6b(k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(A,k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4),C) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(A,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),np__1)))) ) ) ) ) ).
fof(dt_k1_scmfsa8a,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,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( v1_ami_3(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(k1_scmfsa8a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k2_scmfsa8a,axiom,
! [A] :
( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( v1_ami_3(k2_scmfsa8a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa8a(A))
& v1_scmfsa7b(k2_scmfsa8a(A))
& v2_scmfsa7b(k2_scmfsa8a(A))
& m1_ami_1(k2_scmfsa8a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k3_scmfsa8a,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(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) )
=> m2_subset_1(k3_scmfsa8a(A,B),k1_numbers,k5_numbers) ) ).
%------------------------------------------------------------------------------