SET007 Axioms: SET007+607.ax
%------------------------------------------------------------------------------
% File : SET007+607 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Construction and Shiftability of Program Blocks for SCMPDS
% 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 : scmpds_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 136 ( 5 unt; 0 def)
% Number of atoms : 819 ( 90 equ)
% Maximal formula atoms : 25 ( 6 avg)
% Number of connectives : 723 ( 40 ~; 3 |; 389 &)
% ( 8 <=>; 283 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 85 ( 85 usr; 14 con; 0-5 aty)
% Number of variables : 308 ( 303 !; 5 ?)
% 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_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( ~ v1_xboole_0(k1_scmpds_4(A))
& v1_relat_1(k1_scmpds_4(A))
& v1_funct_1(k1_scmpds_4(A))
& v1_finset_1(k1_scmpds_4(A))
& v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_4(A)) ) ) ).
fof(fc2_scmpds_4,axiom,
! [A] :
( ( v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
& v1_funct_1(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
& v1_finset_1(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
& v1_ami_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)) ) ) ).
fof(rc1_scmpds_4,axiom,
? [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A) ) ).
fof(fc3_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_relat_1(k2_scmpds_4(k8_scmpds_4(A)))
& v1_funct_1(k2_scmpds_4(k8_scmpds_4(A)))
& v1_finset_1(k2_scmpds_4(k8_scmpds_4(A)))
& v12_ami_1(k2_scmpds_4(k8_scmpds_4(A)),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(cc1_scmpds_4,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v1_scmpds_4(A) ) ) ) ).
fof(rc2_scmpds_4,axiom,
? [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v1_scmpds_4(A)
& v2_scmpds_4(A)
& v3_scmpds_4(A) ) ).
fof(rc3_scmpds_4,axiom,
? [A] :
( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& v4_scmpds_4(A) ) ).
fof(fc4_scmpds_4,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> v4_scmpds_4(k6_scmpds_2(A,B)) ) ).
fof(fc5_scmpds_4,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> v4_scmpds_4(k11_scmpds_2(A,B,C)) ) ).
fof(fc6_scmpds_4,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> v4_scmpds_4(k12_scmpds_2(A,B,C)) ) ).
fof(fc7_scmpds_4,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> v4_scmpds_4(k13_scmpds_2(A,B,C,D)) ) ).
fof(fc8_scmpds_4,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> v4_scmpds_4(k14_scmpds_2(A,B,C,D)) ) ).
fof(fc9_scmpds_4,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> v4_scmpds_4(k15_scmpds_2(A,B,C,D)) ) ).
fof(fc10_scmpds_4,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> v4_scmpds_4(k16_scmpds_2(A,B,C,D)) ) ).
fof(fc11_scmpds_4,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> v4_scmpds_4(k17_scmpds_2(A,B,C,D)) ) ).
fof(fc12_scmpds_4,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_relat_1(k3_scmpds_4(A,B))
& v1_funct_1(k3_scmpds_4(A,B))
& v1_finset_1(k3_scmpds_4(A,B))
& v1_ami_3(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_4(A,B))
& v3_scmpds_4(k3_scmpds_4(A,B)) ) ) ).
fof(fc13_scmpds_4,axiom,
! [A] :
( ( v4_scmpds_4(A)
& m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( ~ v1_xboole_0(k1_scmpds_4(A))
& v1_relat_1(k1_scmpds_4(A))
& v1_funct_1(k1_scmpds_4(A))
& v1_finset_1(k1_scmpds_4(A))
& v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_4(A))
& v3_scmpds_4(k1_scmpds_4(A)) ) ) ).
fof(fc14_scmpds_4,axiom,
! [A,B] :
( ( v4_scmpds_4(A)
& m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_relat_1(k4_scmpds_4(A,B))
& v1_funct_1(k4_scmpds_4(A,B))
& v1_finset_1(k4_scmpds_4(A,B))
& v1_ami_3(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k4_scmpds_4(A,B))
& v3_scmpds_4(k4_scmpds_4(A,B)) ) ) ).
fof(fc15_scmpds_4,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v4_scmpds_4(B)
& m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( v1_relat_1(k5_scmpds_4(A,B))
& v1_funct_1(k5_scmpds_4(A,B))
& v1_finset_1(k5_scmpds_4(A,B))
& v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k5_scmpds_4(A,B))
& v3_scmpds_4(k5_scmpds_4(A,B)) ) ) ).
fof(fc16_scmpds_4,axiom,
! [A,B] :
( ( v4_scmpds_4(A)
& m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& v4_scmpds_4(B)
& m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( v1_relat_1(k6_scmpds_4(A,B))
& v1_funct_1(k6_scmpds_4(A,B))
& v1_finset_1(k6_scmpds_4(A,B))
& v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k6_scmpds_4(A,B))
& v3_scmpds_4(k6_scmpds_4(A,B)) ) ) ).
fof(fc17_scmpds_4,axiom,
( ~ v1_xboole_0(k5_scmpds_3)
& v1_relat_1(k5_scmpds_3)
& v1_funct_1(k5_scmpds_3)
& v1_finset_1(k5_scmpds_3)
& v1_ami_3(k5_scmpds_3,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k5_scmpds_3)
& v1_scmpds_4(k5_scmpds_3)
& v2_scmpds_4(k5_scmpds_3)
& v3_scmpds_4(k5_scmpds_3) ) ).
fof(fc18_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_relat_1(k8_scmpds_4(A))
& v1_funct_1(k8_scmpds_4(A))
& v1_finset_1(k8_scmpds_4(A))
& v1_ami_3(k8_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k8_scmpds_4(A))
& v3_scmpds_4(k8_scmpds_4(A)) ) ) ).
fof(fc19_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k1_scmpds_4(k4_scmpds_2(A)))
& v1_relat_1(k1_scmpds_4(k4_scmpds_2(A)))
& v1_funct_1(k1_scmpds_4(k4_scmpds_2(A)))
& v1_finset_1(k1_scmpds_4(k4_scmpds_2(A)))
& v1_ami_3(k1_scmpds_4(k4_scmpds_2(A)),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_4(k4_scmpds_2(A)))
& v3_scmpds_4(k1_scmpds_4(k4_scmpds_2(A))) ) ) ).
fof(fc20_scmpds_4,axiom,
! [A,B,C] :
( ( v1_int_1(A)
& m1_scmpds_2(B)
& m1_subset_1(C,k5_numbers) )
=> ( ~ v1_xboole_0(k1_scmpds_4(k8_scmpds_2(B,A,C)))
& v1_relat_1(k1_scmpds_4(k8_scmpds_2(B,A,C)))
& v1_funct_1(k1_scmpds_4(k8_scmpds_2(B,A,C)))
& v1_finset_1(k1_scmpds_4(k8_scmpds_2(B,A,C)))
& v1_ami_3(k1_scmpds_4(k8_scmpds_2(B,A,C)),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_4(k8_scmpds_2(B,A,C)))
& v3_scmpds_4(k1_scmpds_4(k8_scmpds_2(B,A,C))) ) ) ).
fof(fc21_scmpds_4,axiom,
! [A,B,C] :
( ( v1_int_1(A)
& m1_scmpds_2(B)
& m1_subset_1(C,k5_numbers) )
=> ( ~ v1_xboole_0(k1_scmpds_4(k9_scmpds_2(B,A,C)))
& v1_relat_1(k1_scmpds_4(k9_scmpds_2(B,A,C)))
& v1_funct_1(k1_scmpds_4(k9_scmpds_2(B,A,C)))
& v1_finset_1(k1_scmpds_4(k9_scmpds_2(B,A,C)))
& v1_ami_3(k1_scmpds_4(k9_scmpds_2(B,A,C)),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_4(k9_scmpds_2(B,A,C)))
& v3_scmpds_4(k1_scmpds_4(k9_scmpds_2(B,A,C))) ) ) ).
fof(fc22_scmpds_4,axiom,
! [A,B,C] :
( ( v1_int_1(A)
& m1_scmpds_2(B)
& m1_subset_1(C,k5_numbers) )
=> ( ~ v1_xboole_0(k1_scmpds_4(k10_scmpds_2(B,A,C)))
& v1_relat_1(k1_scmpds_4(k10_scmpds_2(B,A,C)))
& v1_funct_1(k1_scmpds_4(k10_scmpds_2(B,A,C)))
& v1_finset_1(k1_scmpds_4(k10_scmpds_2(B,A,C)))
& v1_ami_3(k1_scmpds_4(k10_scmpds_2(B,A,C)),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_4(k10_scmpds_2(B,A,C)))
& v3_scmpds_4(k1_scmpds_4(k10_scmpds_2(B,A,C))) ) ) ).
fof(d1_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k1_scmpds_4(A) = k14_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0),A) ) ).
fof(t1_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k4_card_1(A),B)
<=> r2_hidden(k2_scmpds_3(B),k1_relat_1(A)) ) ) ) ).
fof(t2_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_xboole_0(k1_relat_1(A),k1_relat_1(k6_scmpds_3(B,k4_card_1(A)))) ) ) ).
fof(t3_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_card_1(k6_scmpds_3(B,A)) = k4_card_1(B) ) ) ).
fof(t4_scmpds_4,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> ! [B] :
( m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
=> k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B)) = k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B)) ) ) ).
fof(t5_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
=> ! [C] :
( m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2)
=> k6_scmpds_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,C)),A) = k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B),A),k6_scmpds_3(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C),A)) ) ) ) ).
fof(d2_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k2_scmpds_4(A) = k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))) ) ).
fof(t6_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( r2_hidden(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),k3_enumset1(np__0,np__1,np__4,np__5,np__6))
| k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)) ) ) ) ).
fof(t7_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_relat_1(k2_scmpds_4(A))) ) ).
fof(t8_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k13_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_4(A)) = k2_scmpds_3(np__0) ) ).
fof(t9_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_tarski(A,k2_scmpds_4(A)) ) ).
fof(t10_scmpds_4,axiom,
$true ).
fof(t11_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
& ! [C] :
( m1_scmpds_2(C)
=> k2_scmpds_2(A,C) = k2_scmpds_2(B,C) ) )
=> r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ).
fof(t12_scmpds_4,axiom,
$true ).
fof(t13_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( m1_scmpds_2(C)
=> k2_scmpds_2(A,C) = k2_scmpds_2(B,C) ) ) ) ) ).
fof(t14_scmpds_4,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [D] :
( v1_int_1(D)
=> ( r1_funct_7(B,C,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k2_scmpds_2(B,k3_scmpds_2(k2_scmpds_2(B,A),D)) = k2_scmpds_2(C,k3_scmpds_2(k2_scmpds_2(C,A),D)) ) ) ) ) ) ).
fof(t15_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( r1_funct_7(B,C,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> r1_funct_7(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ).
fof(t16_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k7_relat_1(k2_scmpds_4(A),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = A ) ).
fof(t17_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( A != B
& k3_scmpds_2(A,np__0) = k3_scmpds_2(B,np__0) ) ) ) ).
fof(t18_scmpds_4,axiom,
! [A] :
( m1_scmpds_2(A)
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k3_scmpds_2(B,np__0) ) ) ).
fof(t19_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> k1_relat_1(A) = k2_xboole_0(k2_xboole_0(k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k2_ami_2),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ).
fof(t20_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
~ ( r2_hidden(B,k1_relat_1(A))
& ~ m1_scmpds_2(B)
& B != k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)
& ~ m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ).
fof(t21_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,C) )
<=> k7_relat_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ).
fof(t22_scmpds_4,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ~ r2_hidden(A,k2_ami_2) ) ).
fof(t23_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ! [C] :
( m1_scmpds_2(C)
=> k2_scmpds_2(A,C) = k2_scmpds_2(B,C) )
<=> k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) ) ) ) ).
fof(t24_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) ) ) ) ).
fof(t25_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] : k7_relat_1(k1_funct_4(B,k7_relat_1(A,C)),C) = k7_relat_1(A,C) ) ) ).
fof(t26_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ).
fof(t27_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k1_relat_1(k2_scmpds_4(A)) = k2_xboole_0(k1_relat_1(A),k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ).
fof(t28_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
~ ( r2_hidden(B,k1_relat_1(k2_scmpds_4(A)))
& ~ r2_hidden(B,k1_relat_1(A))
& B != k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t29_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k1_funct_1(k2_scmpds_4(A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k2_scmpds_3(np__0) ) ).
fof(t30_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ~ r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_relat_1(A)) ) ).
fof(t31_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( m1_scmpds_2(B)
=> ~ r2_hidden(B,k1_relat_1(k2_scmpds_4(A))) ) ) ).
fof(t32_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( r2_hidden(C,k1_relat_1(B))
=> k1_funct_1(B,C) = k1_funct_1(k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(A))),C) ) ) ) ).
fof(t33_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> k1_funct_1(A,B) = k1_funct_1(k2_scmpds_4(A),B) ) ) ).
fof(t34_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( r1_tarski(k2_scmpds_4(B),C)
=> k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(A)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,A) ) ) ) ) ).
fof(t35_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( r1_tarski(k2_scmpds_4(B),C)
=> r1_tarski(k2_scmpds_4(A),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,A)) ) ) ) ) ).
fof(t36_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> r1_funct_7(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(A)),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(B)),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ).
fof(d3_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k3_scmpds_4(A,B) = k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,A,k6_scmpds_3(B,k4_card_1(A))) ) ) ).
fof(t37_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( r2_hidden(C,k1_relat_1(A))
=> k1_funct_1(k3_scmpds_4(A,B),C) = k1_funct_1(A,C) ) ) ) ) ).
fof(t38_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( r2_hidden(C,k1_relat_1(B))
=> k1_funct_1(k3_scmpds_4(A,B),k3_scmpds_3(C,k4_card_1(A))) = k1_funct_1(B,C) ) ) ) ) ).
fof(t39_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_tarski(k1_relat_1(A),k1_relat_1(k3_scmpds_4(A,B))) ) ) ).
fof(t40_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_tarski(A,k3_scmpds_4(A,B)) ) ) ).
fof(t41_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,A,k3_scmpds_4(A,B)) = k3_scmpds_4(A,B) ) ) ).
fof(t42_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_4(A),k3_scmpds_4(A,B)) = k2_scmpds_4(k3_scmpds_4(A,B)) ) ) ).
fof(d4_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_scmpds_4(A,B) = k3_scmpds_4(k1_scmpds_4(A),B) ) ) ).
fof(d5_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k5_scmpds_4(A,B) = k3_scmpds_4(A,k1_scmpds_4(B)) ) ) ).
fof(d6_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k6_scmpds_4(A,B) = k3_scmpds_4(k1_scmpds_4(A),k1_scmpds_4(B)) ) ) ).
fof(t43_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k6_scmpds_4(A,B) = k5_scmpds_4(k1_scmpds_4(A),B) ) ) ).
fof(t44_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k6_scmpds_4(A,B) = k4_scmpds_4(A,k1_scmpds_4(B)) ) ) ).
fof(t45_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_card_1(k3_scmpds_4(A,B)) = k1_nat_1(k4_card_1(A),k4_card_1(B)) ) ) ).
fof(t46_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k3_scmpds_4(k3_scmpds_4(A,B),C) = k3_scmpds_4(A,k3_scmpds_4(B,C)) ) ) ) ).
fof(t47_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k5_scmpds_4(k3_scmpds_4(B,C),A) = k3_scmpds_4(B,k5_scmpds_4(C,A)) ) ) ) ).
fof(t48_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k3_scmpds_4(k5_scmpds_4(B,A),C) = k3_scmpds_4(B,k4_scmpds_4(A,C)) ) ) ) ).
fof(t49_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k5_scmpds_4(k5_scmpds_4(C,A),B) = k3_scmpds_4(C,k6_scmpds_4(A,B)) ) ) ) ).
fof(t50_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k3_scmpds_4(k4_scmpds_4(A,B),C) = k4_scmpds_4(A,k3_scmpds_4(B,C)) ) ) ) ).
fof(t51_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k5_scmpds_4(k4_scmpds_4(A,C),B) = k4_scmpds_4(A,k5_scmpds_4(C,B)) ) ) ) ).
fof(t52_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k3_scmpds_4(k6_scmpds_4(A,B),C) = k4_scmpds_4(A,k4_scmpds_4(B,C)) ) ) ) ).
fof(t53_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k5_scmpds_4(k6_scmpds_4(A,B),C) = k4_scmpds_4(A,k6_scmpds_4(B,C)) ) ) ) ).
fof(t54_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_xboole_0(k1_relat_1(B),k1_relat_1(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(A)))) ) ) ).
fof(t55_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_tarski(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0)),k2_scmpds_4(A)) ) ).
fof(t56_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( r1_tarski(k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(A))),C)
=> r1_tarski(B,C) ) ) ) ) ).
fof(t57_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( r1_tarski(k2_scmpds_4(A),B)
=> r1_tarski(A,B) ) ) ) ).
fof(t58_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k7_relat_1(k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(A))),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = B ) ) ).
fof(t59_scmpds_4,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ~ r2_hidden(A,k1_relat_1(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B))) ) ) ).
fof(t60_scmpds_4,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ~ r2_hidden(A,k1_relat_1(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B))) ) ) ).
fof(t61_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ~ r2_hidden(B,k1_relat_1(k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C)))) ) ) ) ).
fof(t62_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))),A) ) ) ).
fof(d7_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k8_scmpds_4(A) = k3_scmpds_4(A,k5_scmpds_3) ) ).
fof(d8_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> k9_scmpds_4(A,B) = k1_funct_4(k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A)))),k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ) ).
fof(d9_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_scmpds_4(A)
<=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_tarski(k2_scmpds_4(k8_scmpds_4(A)),B)
=> r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),C)),k1_relat_1(k8_scmpds_4(A))) ) ) ) ) ) ).
fof(d10_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v2_scmpds_4(A)
<=> v12_ami_1(k2_scmpds_4(k8_scmpds_4(A)),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t63_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v2_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( r1_tarski(k2_scmpds_4(k8_scmpds_4(B)),A)
=> v9_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(t64_scmpds_4,axiom,
$true ).
fof(t65_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) != k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) ) ).
fof(t66_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ~ v9_ami_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k10_scmpds_4(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)),k4_scmpds_2(np__1),k4_scmpds_2(k4_xcmplx_0(np__1)))),k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(t67_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_funct_7(C,D,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& r1_tarski(B,C)
& r1_tarski(B,D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,E)
=> r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D),E)),k1_relat_1(B)) ) ) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,A)
=> r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),E),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D),E),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ) ) ).
fof(t68_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> r2_hidden(B,k1_relat_1(A)) ) ) ).
fof(t69_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [D] :
( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [E] :
( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k10_scmpds_4(B,C,D,E)) = k2_funct_7(k2_funct_7(A,B,D),C,E) ) ) ) ) ) ).
fof(t70_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k18_scmpds_2(k2_scmpds_3(A)) = k2_scmpds_3(k1_nat_1(A,np__1)) ) ).
fof(t71_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ~ ( ~ r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),k1_relat_1(A))
& r2_hidden(k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)),k1_relat_1(A)) ) ) ) ).
fof(t72_scmpds_4,axiom,
k1_relat_1(k5_scmpds_3) = k1_struct_0(k1_scmpds_2,k2_scmpds_3(np__0)) ).
fof(t73_scmpds_4,axiom,
( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k5_scmpds_3))
& k1_funct_1(k5_scmpds_3,k2_scmpds_3(np__0)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(t74_scmpds_4,axiom,
k4_card_1(k5_scmpds_3) = np__1 ).
fof(t75_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k8_scmpds_4(A))) ) ).
fof(t76_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( r2_hidden(C,k1_relat_1(A))
=> r2_hidden(k3_scmpds_3(C,B),k1_relat_1(k6_scmpds_3(A,B))) ) ) ) ) ).
fof(d11_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_scmpds_4(A,B)
<=> ( ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__0
& ! [C] :
( v1_int_1(C)
=> ~ ( A = k4_scmpds_2(C)
& r1_xreal_0(np__0,k2_xcmplx_0(B,C)) ) ) )
& ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__4
& ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ~ ( A = k8_scmpds_2(C,D,E)
& r1_xreal_0(np__0,k2_xcmplx_0(B,E)) ) ) ) ) )
& ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__5
& ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ~ ( A = k9_scmpds_2(C,D,E)
& r1_xreal_0(np__0,k2_xcmplx_0(B,E)) ) ) ) ) )
& ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__6
& ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ~ ( A = k10_scmpds_2(C,D,E)
& r1_xreal_0(np__0,k2_xcmplx_0(B,E)) ) ) ) ) ) ) ) ) ) ).
fof(t77_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_scmpds_4(A,B)
& r1_xreal_0(B,C) )
=> r1_scmpds_4(A,C) ) ) ) ) ).
fof(d12_scmpds_4,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> ( v3_scmpds_4(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( ( r2_hidden(k2_scmpds_3(B),k1_relat_1(A))
& C = k1_funct_1(A,k2_scmpds_3(B)) )
=> ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C) != np__1
& k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C) != np__3
& r1_scmpds_4(C,B) ) ) ) ) ) ) ).
fof(d13_scmpds_4,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( v4_scmpds_4(A)
<=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) != np__2
& r1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),np__6) ) ) ) ).
fof(t78_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( v1_int_1(B)
=> ( r1_xreal_0(np__0,k2_xcmplx_0(k4_card_1(A),B))
=> v3_scmpds_4(k5_scmpds_4(A,k4_scmpds_2(B))) ) ) ) ).
fof(t79_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ( r1_xreal_0(np__0,k2_xcmplx_0(k4_card_1(A),C))
=> v3_scmpds_4(k5_scmpds_4(A,k8_scmpds_2(D,B,C))) ) ) ) ) ) ).
fof(t80_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ( r1_xreal_0(np__0,k2_xcmplx_0(k4_card_1(A),C))
=> v3_scmpds_4(k5_scmpds_4(A,k9_scmpds_2(D,B,C))) ) ) ) ) ) ).
fof(t81_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ( r1_xreal_0(np__0,k2_xcmplx_0(k4_card_1(A),C))
=> v3_scmpds_4(k5_scmpds_4(A,k10_scmpds_2(D,B,C))) ) ) ) ) ) ).
fof(t82_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( v1_int_1(E)
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(D)
& r1_xreal_0(np__0,k2_xcmplx_0(D,E))
& k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) )
=> k3_scmpds_3(k19_scmpds_2(A,E),C) = k19_scmpds_2(B,E) ) ) ) ) ) ) ).
fof(t83_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(D)
& r1_scmpds_4(E,D)
& k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
& k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
=> ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,E) = np__1
| k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,E) = np__3
| ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,A)),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,B))
& k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,A),k2_ami_2) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,B),k2_ami_2) ) ) ) ) ) ) ) ) ).
fof(t84_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_tarski(k6_scmpds_3(k8_scmpds_4(C),D),B)
& k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) = k2_scmpds_3(D)
& k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E)),D) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E))
& k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E)) = k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E))
& k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E),k2_ami_2) ) ) ) ) ) ) ) ) ).
fof(s1_scmpds_4,axiom,
? [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
& k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = f3_s1_scmpds_4
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_3(B)) = f1_s1_scmpds_4(B)
& k2_scmpds_2(A,k3_scmpds_2(B,np__0)) = f2_s1_scmpds_4(B) ) ) ) ).
fof(dt_k1_scmpds_4,axiom,
! [A] :
( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_4(A))
& m1_ami_1(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k2_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> m1_ami_1(k2_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(dt_k3_scmpds_4,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_ami_3(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_4(A,B))
& m1_ami_1(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k4_scmpds_4,axiom,
! [A,B] :
( ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_ami_3(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k4_scmpds_4(A,B))
& m1_ami_1(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k5_scmpds_4,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k5_scmpds_4(A,B))
& m1_ami_1(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k6_scmpds_4,axiom,
! [A,B] :
( ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k6_scmpds_4(A,B))
& m1_ami_1(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k7_scmpds_4,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
& m1_scmpds_2(B)
& v1_int_1(C) )
=> m1_subset_1(k7_scmpds_4(A,B,C),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ).
fof(redefinition_k7_scmpds_4,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
& m1_scmpds_2(B)
& v1_int_1(C) )
=> k7_scmpds_4(A,B,C) = k2_funct_7(A,B,C) ) ).
fof(dt_k8_scmpds_4,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_ami_3(k8_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k8_scmpds_4(A))
& m1_ami_1(k8_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k9_scmpds_4,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) )
=> m1_subset_1(k9_scmpds_4(A,B),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ).
fof(dt_k10_scmpds_4,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m1_subset_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m1_subset_1(C,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m1_subset_1(D,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> m1_ami_1(k10_scmpds_4(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(redefinition_k10_scmpds_4,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m1_subset_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m1_subset_1(C,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m1_subset_1(D,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> k10_scmpds_4(A,B,C,D) = k4_funct_4(A,B,C,D) ) ).
%------------------------------------------------------------------------------