SET007 Axioms: SET007+606.ax
%------------------------------------------------------------------------------
% File : SET007+606 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Computation and Program Shift in the SCMPDS Computer
% 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_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 60 ( 5 unt; 0 def)
% Number of atoms : 374 ( 85 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 358 ( 44 ~; 4 |; 121 &)
% ( 9 <=>; 180 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 78 ( 78 usr; 22 con; 0-4 aty)
% Number of variables : 170 ( 163 !; 7 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_scmpds_3,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)
& v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(fc1_scmpds_3,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) ) ).
fof(rc2_scmpds_3,axiom,
? [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_xboole_0(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) ) ).
fof(t1_scmpds_3,axiom,
! [A] :
( v4_ordinal2(A)
=> ~ ( r1_xreal_0(A,np__13)
& A != np__0
& A != np__1
& A != np__2
& A != np__3
& A != np__4
& A != np__5
& A != np__6
& A != np__7
& A != np__8
& A != np__9
& A != np__10
& A != np__11
& A != np__12
& A != np__13 ) ) ).
fof(t2_scmpds_3,axiom,
! [A] :
( v1_int_1(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)))
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C)
=> k19_scmpds_2(B,A) = k19_scmpds_2(C,A) ) ) ) ) ).
fof(t3_scmpds_3,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [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)))
=> ( k7_relat_1(C,k2_ami_2) = k7_relat_1(D,k2_ami_2)
=> k2_scmpds_2(C,k3_scmpds_2(k2_scmpds_2(C,B),A)) = k2_scmpds_2(D,k3_scmpds_2(k2_scmpds_2(D,B),A)) ) ) ) ) ) ).
fof(t4_scmpds_3,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)))
=> ( k7_relat_1(B,k2_ami_2) = k7_relat_1(C,k2_ami_2)
=> k2_scmpds_2(B,A) = k2_scmpds_2(C,A) ) ) ) ) ).
fof(t5_scmpds_3,axiom,
u1_struct_0(k1_scmpds_2) = 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(t6_scmpds_3,axiom,
~ r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k2_ami_2) ).
fof(t7_scmpds_3,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)))
=> ( k7_relat_1(A,k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) = k7_relat_1(B,k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_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))
=> k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,A),k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,B),k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) ) ) ) ) ).
fof(t8_scmpds_3,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)))
=> k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k3_ami_2) = k7_relat_1(B,k3_ami_2) ) ) ).
fof(t9_scmpds_3,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> k7_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = k7_relat_1(A,k2_ami_2) ) ).
fof(t10_scmpds_3,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> ( v1_ami_5(A,k1_tarski(k4_numbers),k1_scmpds_2)
<=> r1_tarski(k1_relat_1(A),k2_ami_2) ) ) ).
fof(t11_scmpds_3,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> r1_tarski(k1_relat_1(k7_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)),k2_ami_2) ) ).
fof(t12_scmpds_3,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> r1_tarski(k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ).
fof(t13_scmpds_3,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] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,C)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),C) ) ) ) ).
fof(t14_scmpds_3,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_scmpds_2(C)
=> k2_scmpds_2(A,C) = k2_scmpds_2(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B)),C) ) ) ) ).
fof(t15_scmpds_3,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)))
=> m1_subset_1(k1_funct_4(A,k7_relat_1(B,k2_ami_2)),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ) ).
fof(t16_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( k7_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) != k1_xboole_0
=> r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_relat_1(A)) ) ) ).
fof(t17_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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(t18_scmpds_3,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_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ~ ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
& C != D
& E = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)
& r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,C)))
& r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,D)))
& k19_scmpds_2(A,C) = k19_scmpds_2(B,D) ) ) ) ) ) ) ).
fof(t19_scmpds_3,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)
=> ~ ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
& C != D
& k19_scmpds_2(A,C) = k19_scmpds_2(B,D) ) ) ) ) ) ).
fof(t20_scmpds_3,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) = k19_scmpds_2(A,np__1) ) ).
fof(t21_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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))
=> r2_hidden(k13_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,A),k1_relat_1(A)) ) ) ).
fof(t22_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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(A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> 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(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))) ) ) ) ) ).
fof(t23_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( 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),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,C),D))
& 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),D)) = 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,C),D)) ) ) ) ) ) ) ).
fof(t24_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> ! [G] :
( m1_scmpds_2(G)
=> ! [H] :
( m1_scmpds_2(H)
=> ( ( 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),D)) = k17_scmpds_2(G,H,E,F)
& r2_hidden(G,k1_relat_1(A))
& r2_hidden(k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E),k1_relat_1(A)) )
=> k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),H),F)) = k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),H),F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> ! [G] :
( m1_scmpds_2(G)
=> ! [H] :
( m1_scmpds_2(H)
=> ( ( 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),D)) = k13_scmpds_2(G,H,E,F)
& r2_hidden(G,k1_relat_1(A))
& r2_hidden(k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E),k1_relat_1(A)) )
=> k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),H),F)) = k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),H),F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> ! [G] :
( m1_scmpds_2(G)
=> ! [H] :
( m1_scmpds_2(H)
=> ( ( 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),D)) = k14_scmpds_2(G,H,E,F)
& r2_hidden(G,k1_relat_1(A))
& r2_hidden(k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E),k1_relat_1(A)) )
=> k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),H),F)) = k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),H),F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> ! [G] :
( m1_scmpds_2(G)
=> ! [H] :
( m1_scmpds_2(H)
=> ( ( 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),D)) = k15_scmpds_2(G,H,E,F)
& r2_hidden(G,k1_relat_1(A))
& r2_hidden(k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E),k1_relat_1(A)) )
=> k3_xcmplx_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E)),k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),H),F))) = k3_xcmplx_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),G),E)),k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),H),F))) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_scmpds_2(F)
=> ! [G] :
( v1_int_1(G)
=> ! [H] :
( v1_int_1(H)
=> ( ( 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),D)) = k8_scmpds_2(F,G,H)
& E = 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),D))
& r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,H))) )
=> ( H = np__1
| ( k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G)) = np__0
<=> k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G)) = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_scmpds_2(F)
=> ! [G] :
( v1_int_1(G)
=> ! [H] :
( v1_int_1(H)
=> ( ( 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),D)) = k9_scmpds_2(F,G,H)
& E = 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),D))
& r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,H))) )
=> ( H = np__1
| ( ~ ( ~ r1_xreal_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G)),np__0)
& r1_xreal_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G)),np__0) )
& ~ ( ~ r1_xreal_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G)),np__0)
& r1_xreal_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G)),np__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t30_scmpds_3,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& 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)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_scmpds_2(F)
=> ! [G] :
( v1_int_1(G)
=> ! [H] :
( v1_int_1(H)
=> ( ( 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),D)) = k10_scmpds_2(F,G,H)
& E = 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),D))
& r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,H))) )
=> ( H = np__1
| ( ~ ( ~ r1_xreal_0(np__0,k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G)))
& r1_xreal_0(np__0,k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G))) )
& ~ ( ~ r1_xreal_0(np__0,k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G)))
& r1_xreal_0(np__0,k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_scmpds_3,axiom,
$true ).
fof(d2_scmpds_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_scmpds_3(A) = k16_ami_3(A) ) ).
fof(t31_scmpds_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( A != B
& k2_scmpds_3(A) = k2_scmpds_3(B) ) ) ) ).
fof(t32_scmpds_3,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k2_scmpds_3(B) ) ) ).
fof(d3_scmpds_3,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(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))
=> ( C = k3_scmpds_3(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k2_scmpds_3(D)
& C = k2_scmpds_3(k1_nat_1(D,B)) ) ) ) ) ) ).
fof(d4_scmpds_3,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(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))
=> ( C = k4_scmpds_3(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k2_scmpds_3(D)
& C = k2_scmpds_3(k5_binarith(D,B)) ) ) ) ) ) ).
fof(t33_scmpds_3,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_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)
=> k3_scmpds_3(k3_scmpds_3(A,B),C) = k3_scmpds_3(A,k1_nat_1(B,C)) ) ) ) ).
fof(t34_scmpds_3,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k4_scmpds_3(k3_scmpds_3(A,B),B) = A ) ) ).
fof(t35_scmpds_3,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))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(A,C)) = k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(B,C))
<=> k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,A) = k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B) ) ) ) ) ).
fof(t36_scmpds_3,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))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,A) = k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B)
=> k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_3(A,C)) = k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_3(B,C)) ) ) ) ) ).
fof(d5_scmpds_3,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> ( v1_scmpds_3(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(k2_scmpds_3(C),k1_relat_1(A))
=> ( r1_xreal_0(C,B)
| r2_hidden(k2_scmpds_3(B),k1_relat_1(A)) ) ) ) ) ) ) ).
fof(d6_scmpds_3,axiom,
k5_scmpds_3 = k14_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0),k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ).
fof(t37_scmpds_3,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( r2_hidden(A,k1_relat_1(C))
=> k1_funct_1(k6_scmpds_3(C,B),k3_scmpds_3(A,B)) = k1_funct_1(C,A) ) ) ) ) ).
fof(t39_scmpds_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k6_scmpds_3(k6_scmpds_3(C,A),B) = k6_scmpds_3(C,k1_nat_1(A,B)) ) ) ) ).
fof(t40_scmpds_3,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] :
( ( v1_funct_1(B)
& v1_funct_2(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m2_relset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k6_scmpds_3(k6_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,A,B),C) = k6_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_3(A,C),B) ) ) ) ).
fof(t41_scmpds_3,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) )
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k6_scmpds_3(k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,B,C),A) = k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_3(B,A),k6_scmpds_3(C,A)) ) ) ) ).
fof(dt_k1_scmpds_3,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> m1_ami_1(k1_scmpds_3(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(redefinition_k1_scmpds_3,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> k1_scmpds_3(A,B) = k3_cqc_lang(A,B) ) ).
fof(dt_k2_scmpds_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_struct_0(k2_scmpds_3(A),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ).
fof(dt_k3_scmpds_3,axiom,
! [A,B] :
( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m1_subset_1(B,k5_numbers) )
=> m1_struct_0(k3_scmpds_3(A,B),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ).
fof(dt_k4_scmpds_3,axiom,
! [A,B] :
( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& m1_subset_1(B,k5_numbers) )
=> m1_struct_0(k4_scmpds_3(A,B),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ).
fof(dt_k5_scmpds_3,axiom,
m1_ami_1(k5_scmpds_3,k1_tarski(k4_numbers),k1_scmpds_2) ).
fof(dt_k6_scmpds_3,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_subset_1(B,k5_numbers) )
=> ( v1_ami_3(k6_scmpds_3(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(k6_scmpds_3(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(d7_scmpds_3,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] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( C = k6_scmpds_3(A,B)
<=> ( k1_relat_1(C) = a_2_0_scmpds_3(A,B)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k2_scmpds_3(D),k1_relat_1(A))
=> k1_funct_1(C,k2_scmpds_3(k1_nat_1(D,B))) = k1_funct_1(A,k2_scmpds_3(D)) ) ) ) ) ) ) ) ).
fof(t38_scmpds_3,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)
=> k1_relat_1(k6_scmpds_3(A,B)) = a_2_1_scmpds_3(A,B) ) ) ).
fof(fraenkel_a_2_0_scmpds_3,axiom,
! [A,B,C] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_0_scmpds_3(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k2_scmpds_3(k1_nat_1(D,C))
& r2_hidden(k2_scmpds_3(D),k1_relat_1(B)) ) ) ) ).
fof(fraenkel_a_2_1_scmpds_3,axiom,
! [A,B,C] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_1_scmpds_3(B,C))
<=> ? [D] :
( m1_struct_0(D,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& A = k3_scmpds_3(D,C)
& r2_hidden(D,k1_relat_1(B)) ) ) ) ).
%------------------------------------------------------------------------------