SET007 Axioms: SET007+609.ax
%------------------------------------------------------------------------------
% File : SET007+609 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Construction and Computation of Conditional Statements 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_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 182 ( 1 unt; 0 def)
% Number of atoms : 1729 ( 137 equ)
% Maximal formula atoms : 20 ( 9 avg)
% Number of connectives : 1567 ( 20 ~; 14 |; 880 &)
% ( 6 <=>; 647 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 10 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-3 aty)
% Number of functors : 64 ( 64 usr; 8 con; 0-4 aty)
% Number of variables : 634 ( 634 !; 0 ?)
% 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_6,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> v1_scmpds_5(k4_scmpds_2(k1_nat_1(A,np__1))) ) ).
fof(fc2_scmpds_6,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> v1_scmpds_5(k4_scmpds_2(k4_xcmplx_0(k1_nat_1(A,np__1)))) ) ).
fof(fc3_scmpds_6,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( v1_relat_1(k1_scmpds_6(k1_nat_1(A,np__1)))
& v1_funct_1(k1_scmpds_6(k1_nat_1(A,np__1)))
& v1_finset_1(k1_scmpds_6(k1_nat_1(A,np__1)))
& v1_ami_3(k1_scmpds_6(k1_nat_1(A,np__1)),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_6(k1_nat_1(A,np__1)))
& v3_scmpds_5(k1_scmpds_6(k1_nat_1(A,np__1))) ) ) ).
fof(fc4_scmpds_6,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( v1_relat_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))))
& v1_funct_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))))
& v1_finset_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))))
& v1_ami_3(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1))))
& v3_scmpds_5(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,np__1)))) ) ) ).
fof(fc5_scmpds_6,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(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)
& v2_scmpds_4(B)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(C)
& v1_int_1(D) )
=> ( v1_relat_1(k2_scmpds_6(C,D,A,B))
& v1_funct_1(k2_scmpds_6(C,D,A,B))
& v1_finset_1(k2_scmpds_6(C,D,A,B))
& v1_ami_3(k2_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k2_scmpds_6(C,D,A,B))
& v1_scmpds_4(k2_scmpds_6(C,D,A,B))
& v2_scmpds_4(k2_scmpds_6(C,D,A,B))
& v3_scmpds_4(k2_scmpds_6(C,D,A,B)) ) ) ).
fof(fc6_scmpds_6,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(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_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(C)
& v1_int_1(D) )
=> ( v1_relat_1(k2_scmpds_6(C,D,A,B))
& v1_funct_1(k2_scmpds_6(C,D,A,B))
& v1_finset_1(k2_scmpds_6(C,D,A,B))
& v1_ami_3(k2_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k2_scmpds_6(C,D,A,B))
& v3_scmpds_5(k2_scmpds_6(C,D,A,B)) ) ) ).
fof(fc7_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k5_scmpds_6(B,C,A))
& v1_funct_1(k5_scmpds_6(B,C,A))
& v1_finset_1(k5_scmpds_6(B,C,A))
& v1_ami_3(k5_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k5_scmpds_6(B,C,A))
& v1_scmpds_4(k5_scmpds_6(B,C,A))
& v2_scmpds_4(k5_scmpds_6(B,C,A))
& v3_scmpds_4(k5_scmpds_6(B,C,A)) ) ) ).
fof(fc8_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k5_scmpds_6(B,C,A))
& v1_funct_1(k5_scmpds_6(B,C,A))
& v1_finset_1(k5_scmpds_6(B,C,A))
& v1_ami_3(k5_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k5_scmpds_6(B,C,A))
& v3_scmpds_5(k5_scmpds_6(B,C,A)) ) ) ).
fof(fc9_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k6_scmpds_6(B,C,A))
& v1_funct_1(k6_scmpds_6(B,C,A))
& v1_finset_1(k6_scmpds_6(B,C,A))
& v1_ami_3(k6_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k6_scmpds_6(B,C,A))
& v1_scmpds_4(k6_scmpds_6(B,C,A))
& v2_scmpds_4(k6_scmpds_6(B,C,A))
& v3_scmpds_4(k6_scmpds_6(B,C,A)) ) ) ).
fof(fc10_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k6_scmpds_6(B,C,A))
& v1_funct_1(k6_scmpds_6(B,C,A))
& v1_finset_1(k6_scmpds_6(B,C,A))
& v1_ami_3(k6_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k6_scmpds_6(B,C,A))
& v3_scmpds_5(k6_scmpds_6(B,C,A)) ) ) ).
fof(fc11_scmpds_6,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(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)
& v2_scmpds_4(B)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(C)
& v1_int_1(D) )
=> ( v1_relat_1(k3_scmpds_6(C,D,A,B))
& v1_funct_1(k3_scmpds_6(C,D,A,B))
& v1_finset_1(k3_scmpds_6(C,D,A,B))
& v1_ami_3(k3_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_6(C,D,A,B))
& v1_scmpds_4(k3_scmpds_6(C,D,A,B))
& v2_scmpds_4(k3_scmpds_6(C,D,A,B))
& v3_scmpds_4(k3_scmpds_6(C,D,A,B)) ) ) ).
fof(fc12_scmpds_6,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(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_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(C)
& v1_int_1(D) )
=> ( v1_relat_1(k3_scmpds_6(C,D,A,B))
& v1_funct_1(k3_scmpds_6(C,D,A,B))
& v1_finset_1(k3_scmpds_6(C,D,A,B))
& v1_ami_3(k3_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_6(C,D,A,B))
& v3_scmpds_5(k3_scmpds_6(C,D,A,B)) ) ) ).
fof(fc13_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k7_scmpds_6(B,C,A))
& v1_funct_1(k7_scmpds_6(B,C,A))
& v1_finset_1(k7_scmpds_6(B,C,A))
& v1_ami_3(k7_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k7_scmpds_6(B,C,A))
& v1_scmpds_4(k7_scmpds_6(B,C,A))
& v2_scmpds_4(k7_scmpds_6(B,C,A))
& v3_scmpds_4(k7_scmpds_6(B,C,A)) ) ) ).
fof(fc14_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k7_scmpds_6(B,C,A))
& v1_funct_1(k7_scmpds_6(B,C,A))
& v1_finset_1(k7_scmpds_6(B,C,A))
& v1_ami_3(k7_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k7_scmpds_6(B,C,A))
& v3_scmpds_5(k7_scmpds_6(B,C,A)) ) ) ).
fof(fc15_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k8_scmpds_6(B,C,A))
& v1_funct_1(k8_scmpds_6(B,C,A))
& v1_finset_1(k8_scmpds_6(B,C,A))
& v1_ami_3(k8_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k8_scmpds_6(B,C,A))
& v1_scmpds_4(k8_scmpds_6(B,C,A))
& v2_scmpds_4(k8_scmpds_6(B,C,A))
& v3_scmpds_4(k8_scmpds_6(B,C,A)) ) ) ).
fof(fc16_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k8_scmpds_6(B,C,A))
& v1_funct_1(k8_scmpds_6(B,C,A))
& v1_finset_1(k8_scmpds_6(B,C,A))
& v1_ami_3(k8_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k8_scmpds_6(B,C,A))
& v3_scmpds_5(k8_scmpds_6(B,C,A)) ) ) ).
fof(fc17_scmpds_6,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(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)
& v2_scmpds_4(B)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(C)
& v1_int_1(D) )
=> ( v1_relat_1(k4_scmpds_6(C,D,A,B))
& v1_funct_1(k4_scmpds_6(C,D,A,B))
& v1_finset_1(k4_scmpds_6(C,D,A,B))
& v1_ami_3(k4_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k4_scmpds_6(C,D,A,B))
& v1_scmpds_4(k4_scmpds_6(C,D,A,B))
& v2_scmpds_4(k4_scmpds_6(C,D,A,B))
& v3_scmpds_4(k4_scmpds_6(C,D,A,B)) ) ) ).
fof(fc18_scmpds_6,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(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_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(C)
& v1_int_1(D) )
=> ( v1_relat_1(k4_scmpds_6(C,D,A,B))
& v1_funct_1(k4_scmpds_6(C,D,A,B))
& v1_finset_1(k4_scmpds_6(C,D,A,B))
& v1_ami_3(k4_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k4_scmpds_6(C,D,A,B))
& v3_scmpds_5(k4_scmpds_6(C,D,A,B)) ) ) ).
fof(fc19_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k9_scmpds_6(B,C,A))
& v1_funct_1(k9_scmpds_6(B,C,A))
& v1_finset_1(k9_scmpds_6(B,C,A))
& v1_ami_3(k9_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k9_scmpds_6(B,C,A))
& v1_scmpds_4(k9_scmpds_6(B,C,A))
& v2_scmpds_4(k9_scmpds_6(B,C,A))
& v3_scmpds_4(k9_scmpds_6(B,C,A)) ) ) ).
fof(fc20_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k9_scmpds_6(B,C,A))
& v1_funct_1(k9_scmpds_6(B,C,A))
& v1_finset_1(k9_scmpds_6(B,C,A))
& v1_ami_3(k9_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k9_scmpds_6(B,C,A))
& v3_scmpds_5(k9_scmpds_6(B,C,A)) ) ) ).
fof(fc21_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k10_scmpds_6(B,C,A))
& v1_funct_1(k10_scmpds_6(B,C,A))
& v1_finset_1(k10_scmpds_6(B,C,A))
& v1_ami_3(k10_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k10_scmpds_6(B,C,A))
& v1_scmpds_4(k10_scmpds_6(B,C,A))
& v2_scmpds_4(k10_scmpds_6(B,C,A))
& v3_scmpds_4(k10_scmpds_6(B,C,A)) ) ) ).
fof(fc22_scmpds_6,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C) )
=> ( v1_relat_1(k10_scmpds_6(B,C,A))
& v1_funct_1(k10_scmpds_6(B,C,A))
& v1_finset_1(k10_scmpds_6(B,C,A))
& v1_ami_3(k10_scmpds_6(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k10_scmpds_6(B,C,A))
& v3_scmpds_5(k10_scmpds_6(B,C,A)) ) ) ).
fof(t1_scmpds_6,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> k1_relat_1(k7_relat_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) = u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(t2_scmpds_6,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( v9_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),B)
=> 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),B)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ).
fof(t3_scmpds_6,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( v9_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),B)
=> 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),B)) = 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),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A))) ) ) ) ) ).
fof(t4_scmpds_6,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))
<=> ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = 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) ) ) ) ) ).
fof(t5_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k1_scmpds_5(A),k2_scmpds_4(B)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B)) ) ) ).
fof(t6_scmpds_6,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_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> r1_tarski(A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B))) ) ) ).
fof(t7_scmpds_6,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))
=> k7_relat_1(A,k2_ami_2) = k7_relat_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B)),k2_ami_2) ) ) ).
fof(t8_scmpds_6,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)
& 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))
=> k7_relat_1(A,k2_ami_2) = k7_relat_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C))),k2_ami_2) ) ) ) ).
fof(t9_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k7_relat_1(A,k2_ami_2) = k7_relat_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B)),k2_ami_2) ) ) ).
fof(t10_scmpds_6,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))
=> r1_xboole_0(k1_relat_1(k7_relat_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))),k1_relat_1(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B))) ) ) ).
fof(t11_scmpds_6,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)
& 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) )
=> ! [D] :
( m1_struct_0(D,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> r1_funct_7(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,D))),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,D))),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ).
fof(t12_scmpds_6,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)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
=> r1_funct_7(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C)),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(D)),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ).
fof(t13_scmpds_6,axiom,
$true ).
fof(t14_scmpds_6,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))
=> k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(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,C)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C)) ) ) ) ).
fof(t15_scmpds_6,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_card_1(k4_scmpds_4(A,B)) = k1_nat_1(k4_card_1(B),np__1) ) ) ).
fof(t16_scmpds_6,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) )
=> k1_funct_1(k4_scmpds_4(A,B),k2_scmpds_3(np__0)) = A ) ) ).
fof(t17_scmpds_6,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(k8_scmpds_4(A))) ) ).
fof(t18_scmpds_6,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_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) )
=> ( r2_hidden(A,k1_relat_1(B))
=> r2_hidden(A,k1_relat_1(k8_scmpds_4(B))) ) ) ) ).
fof(t19_scmpds_6,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_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) )
=> ( r2_hidden(A,k1_relat_1(B))
=> k1_funct_1(k8_scmpds_4(B),A) = k1_funct_1(B,A) ) ) ) ).
fof(t20_scmpds_6,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_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) )
=> ( r2_hidden(A,k1_relat_1(B))
=> k1_funct_1(k2_scmpds_4(k8_scmpds_4(B)),A) = k1_funct_1(B,A) ) ) ) ).
fof(t21_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B))) = k2_scmpds_3(np__0) ) ) ).
fof(t22_scmpds_6,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)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k8_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(k4_scmpds_4(A,C))))) = A ) ) ) ).
fof(t23_scmpds_6,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_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)
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(B)
=> k19_scmpds_2(A,C) = k2_scmpds_3(k1_nat_1(B,C)) ) ) ) ) ).
fof(t24_scmpds_6,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(k6_scmpds_3(k8_scmpds_4(B),k4_card_1(A)),k8_scmpds_4(k3_scmpds_4(A,B))) ) ) ).
fof(t25_scmpds_6,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(k4_card_1(A)),k1_relat_1(k8_scmpds_4(A)))
& k1_funct_1(k8_scmpds_4(A),k2_scmpds_3(k4_card_1(A))) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t26_scmpds_6,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)
& 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) )
=> ! [D] :
( m1_struct_0(D,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [E] :
( m1_struct_0(E,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),D) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,E)),D) ) ) ) ) ) ).
fof(t27_scmpds_6,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)
& 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))
=> ! [D] :
( m1_struct_0(D,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,D)),C) ) ) ) ) ).
fof(t28_scmpds_6,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_scmpds_5(B)
& v2_scmpds_5(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)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> k2_scmpds_2(k9_scmpds_4(k4_scmpds_4(B,C),A),D) = k2_scmpds_2(k9_scmpds_4(C,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k1_scmpds_5(A))),D) ) ) ) ) ).
fof(t29_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> k8_scmpds_2(A,B,C) != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(t30_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> k9_scmpds_2(A,B,C) != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(t31_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> k10_scmpds_2(A,B,C) != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(d1_scmpds_6,axiom,
! [A] :
( v1_int_1(A)
=> k1_scmpds_6(A) = k1_scmpds_4(k4_scmpds_2(A)) ) ).
fof(t32_scmpds_6,axiom,
! [A] :
( v1_int_1(A)
=> k4_card_1(k1_scmpds_6(A)) = np__1 ) ).
fof(t33_scmpds_6,axiom,
! [A] :
( v1_int_1(A)
=> ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k1_scmpds_6(A)))
& k1_funct_1(k1_scmpds_6(A),k2_scmpds_3(np__0)) = k4_scmpds_2(A) ) ) ).
fof(d2_scmpds_6,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_scmpds_6(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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A)))),C)),k1_relat_1(k8_scmpds_4(A))) ) ) ) ) ).
fof(d3_scmpds_6,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_scmpds_6(A,B)
<=> v9_ami_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A))),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(t34_scmpds_6,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)))
=> r1_scmpds_6(A,B) ) ) ) ).
fof(t35_scmpds_6,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)
<=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> r2_scmpds_6(A,B) ) ) ) ).
fof(t36_scmpds_6,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)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
& r1_scmpds_6(C,A) )
=> r1_scmpds_6(C,B) ) ) ) ) ).
fof(t37_scmpds_6,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)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
& r1_scmpds_6(C,A)
& r2_scmpds_6(C,A) )
=> ( r1_scmpds_6(C,B)
& r2_scmpds_6(C,B) ) ) ) ) ) ).
fof(t38_scmpds_6,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)
& 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) )
=> ( r1_scmpds_6(B,A)
<=> r1_scmpds_6(B,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C))) ) ) ) ) ).
fof(t39_scmpds_6,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_scmpds_6(A,C)
& r2_scmpds_6(A,C) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A)))))
=> 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A)))),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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))))),D)) ) )
& k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A)))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A))))),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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A))))),k2_ami_2) ) ) ) ) ) ).
fof(t40_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),C)
| 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),C)),k1_relat_1(B)) ) ) ) ) ) ).
fof(t41_scmpds_6,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)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_scmpds_6(A,C)
& r2_scmpds_6(A,C) )
=> ( r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A)))),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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A)))),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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))))),D)) ) ) ) ) ) ) ).
fof(t42_scmpds_6,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(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)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_scmpds_6(A,B)
& r2_scmpds_6(A,B)
& ~ r1_xreal_0(k2_scm_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)))),C)
& 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A)))),C)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ).
fof(t43_scmpds_6,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_5(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_scmpds_6(A,B)
& r2_scmpds_6(A,B) )
=> 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A)))),k2_scm_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)))))) = k2_scmpds_3(k4_card_1(A)) ) ) ) ).
fof(t44_scmpds_6,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_scmpds_6(A,C)
& r2_scmpds_6(A,C) )
=> ( r2_scmpds_6(k3_scmpds_4(k3_scmpds_4(A,k1_scmpds_6(k1_nat_1(k4_card_1(B),np__1))),B),C)
& r1_scmpds_6(k3_scmpds_4(k3_scmpds_4(A,k1_scmpds_6(k1_nat_1(k4_card_1(B),np__1))),B),C) ) ) ) ) ) ).
fof(t45_scmpds_6,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)
& 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)
& r1_scmpds_6(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(t46_scmpds_6,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)
& v3_scmpds_5(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) )
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k3_scmpds_4(k3_scmpds_4(B,k1_scmpds_6(k1_nat_1(k4_card_1(C),np__1))),C),A)) = k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__1)) ) ) ) ) ).
fof(t47_scmpds_6,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)
& v3_scmpds_5(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) )
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> k9_scmpds_4(k3_scmpds_4(k3_scmpds_4(B,k1_scmpds_6(k1_nat_1(k4_card_1(C),np__1))),C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__1)))) ) ) ) ) ).
fof(t48_scmpds_6,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)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A)) = k2_scmpds_3(k4_card_1(B)) ) ) ) ).
fof(d4_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k2_scmpds_6(A,B,C,D) = k3_scmpds_4(k3_scmpds_4(k4_scmpds_4(k8_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)),C),k1_scmpds_6(k1_nat_1(k4_card_1(D),np__1))),D) ) ) ) ) ).
fof(d5_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k3_scmpds_6(A,B,C,D) = k3_scmpds_4(k3_scmpds_4(k4_scmpds_4(k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)),C),k1_scmpds_6(k1_nat_1(k4_card_1(D),np__1))),D) ) ) ) ) ).
fof(d6_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_scmpds_6(A,B,C,D) = k3_scmpds_4(k3_scmpds_4(k4_scmpds_4(k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)),C),k1_scmpds_6(k1_nat_1(k4_card_1(D),np__1))),D) ) ) ) ) ).
fof(d7_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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_6(A,B,C) = k4_scmpds_4(k8_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)),C) ) ) ) ).
fof(d8_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k6_scmpds_6(A,B,C) = k3_scmpds_4(k6_scmpds_4(k8_scmpds_2(A,B,np__2),k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1))),C) ) ) ) ).
fof(d9_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k7_scmpds_6(A,B,C) = k4_scmpds_4(k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)),C) ) ) ) ).
fof(d10_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k8_scmpds_6(A,B,C) = k3_scmpds_4(k6_scmpds_4(k9_scmpds_2(A,B,np__2),k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1))),C) ) ) ) ).
fof(d11_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k9_scmpds_6(A,B,C) = k4_scmpds_4(k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)),C) ) ) ) ).
fof(d12_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k10_scmpds_6(A,B,C) = k3_scmpds_4(k6_scmpds_4(k10_scmpds_2(A,B,np__2),k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1))),C) ) ) ) ).
fof(t49_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_card_1(k2_scmpds_6(A,B,C,D)) = k1_nat_1(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__2) ) ) ) ) ).
fof(t50_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k2_scmpds_6(A,B,C,D)))
& r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k2_scmpds_6(A,B,C,D))) ) ) ) ) ) ).
fof(t51_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k1_funct_1(k2_scmpds_6(A,B,C,D),k2_scmpds_3(np__0)) = k8_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)) ) ) ) ) ).
fof(t52_scmpds_6,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)
& v3_scmpds_4(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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)) = np__0
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_scmpds_6(k2_scmpds_6(D,E,B,C),A)
& r2_scmpds_6(k2_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) ).
fof(t53_scmpds_6,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)
& 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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_scmpds_6(C,A)
& r2_scmpds_6(C,A) )
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)) = np__0
| ( r1_scmpds_6(k2_scmpds_6(D,E,B,C),A)
& r2_scmpds_6(k2_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) ) ).
fof(t54_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)) = np__0
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> k9_scmpds_4(k2_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) ).
fof(t55_scmpds_6,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)
& 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)
& v3_scmpds_4(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_scmpds_6(C,A)
& r2_scmpds_6(C,A) )
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)) = np__0
| k9_scmpds_4(k2_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) ) ).
fof(t56_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(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)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k2_scmpds_6(D,E,B,C),A)) = k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)) ) ) ) ) ) ).
fof(t57_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ! [F] :
( v1_int_1(F)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)) = np__0
=> k2_scmpds_2(k9_scmpds_4(k2_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(B,A),E) ) ) ) ) ) ) ) ).
fof(t58_scmpds_6,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)
& 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)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ! [F] :
( v1_int_1(F)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)) != np__0
=> k2_scmpds_2(k9_scmpds_4(k2_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(C,A),E) ) ) ) ) ) ) ) ).
fof(t59_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k4_card_1(k5_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__1) ) ) ) ).
fof(t60_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k5_scmpds_6(A,B,C))) ) ) ) ).
fof(t61_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k1_funct_1(k5_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k8_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)) ) ) ) ).
fof(t62_scmpds_6,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)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_scmpds_6(k5_scmpds_6(C,D,B),A)
& r2_scmpds_6(k5_scmpds_6(C,D,B),A) ) ) ) ) ) ) ).
fof(t63_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) != np__0
=> ( r1_scmpds_6(k5_scmpds_6(C,D,B),A)
& r2_scmpds_6(k5_scmpds_6(C,D,B),A) ) ) ) ) ) ) ).
fof(t64_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> k9_scmpds_4(k5_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) ).
fof(t65_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) != np__0
=> k9_scmpds_4(k5_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) ).
fof(t66_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k5_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)) ) ) ) ) ).
fof(t67_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)) = np__0
=> k2_scmpds_2(k9_scmpds_4(k5_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) ).
fof(t68_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)) != np__0
=> k2_scmpds_2(k9_scmpds_4(k5_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(t69_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k4_card_1(k6_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__2) ) ) ) ).
fof(t70_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k6_scmpds_6(A,B,C)))
& r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k6_scmpds_6(A,B,C))) ) ) ) ) ).
fof(t71_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ( k1_funct_1(k6_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k8_scmpds_2(A,B,np__2)
& k1_funct_1(k6_scmpds_6(A,B,C),k2_scmpds_3(np__1)) = k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1)) ) ) ) ) ).
fof(t72_scmpds_6,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)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
| ( r1_scmpds_6(k6_scmpds_6(C,D,B),A)
& r2_scmpds_6(k6_scmpds_6(C,D,B),A) ) ) ) ) ) ) ) ).
fof(t73_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
=> ( r1_scmpds_6(k6_scmpds_6(C,D,B),A)
& r2_scmpds_6(k6_scmpds_6(C,D,B),A) ) ) ) ) ) ) ).
fof(t74_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
| k9_scmpds_4(k6_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) ) ).
fof(t75_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)) = np__0
=> k9_scmpds_4(k6_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) ).
fof(t76_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k6_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)) ) ) ) ) ).
fof(t77_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)) != np__0
=> k2_scmpds_2(k9_scmpds_4(k6_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) ).
fof(t78_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)) = np__0
=> k2_scmpds_2(k9_scmpds_4(k6_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(t79_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_card_1(k3_scmpds_6(A,B,C,D)) = k1_nat_1(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__2) ) ) ) ) ).
fof(t80_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k3_scmpds_6(A,B,C,D)))
& r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k3_scmpds_6(A,B,C,D))) ) ) ) ) ) ).
fof(t81_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k1_funct_1(k3_scmpds_6(A,B,C,D),k2_scmpds_3(np__0)) = k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)) ) ) ) ) ).
fof(t82_scmpds_6,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)
& v3_scmpds_4(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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)),np__0)
| ( r1_scmpds_6(k3_scmpds_6(D,E,B,C),A)
& r2_scmpds_6(k3_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) ) ).
fof(t83_scmpds_6,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)
& 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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)),np__0)
& r1_scmpds_6(C,A)
& r2_scmpds_6(C,A) )
=> ( r1_scmpds_6(k3_scmpds_6(D,E,B,C),A)
& r2_scmpds_6(k3_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) ).
fof(t84_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)),np__0)
| k9_scmpds_4(k3_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) ) ).
fof(t85_scmpds_6,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)
& 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)
& v3_scmpds_4(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)),np__0)
& r1_scmpds_6(C,A)
& r2_scmpds_6(C,A) )
=> k9_scmpds_4(k3_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) ).
fof(t86_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(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)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k3_scmpds_6(D,E,B,C),A)) = k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)) ) ) ) ) ) ).
fof(t87_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ! [F] :
( v1_int_1(F)
=> ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)),np__0)
=> k2_scmpds_2(k9_scmpds_4(k3_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(B,A),E) ) ) ) ) ) ) ) ).
fof(t88_scmpds_6,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)
& 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)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ! [F] :
( v1_int_1(F)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)),np__0)
=> k2_scmpds_2(k9_scmpds_4(k3_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(C,A),E) ) ) ) ) ) ) ) ).
fof(t89_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k4_card_1(k7_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__1) ) ) ) ).
fof(t90_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k7_scmpds_6(A,B,C))) ) ) ) ).
fof(t91_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k1_funct_1(k7_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k9_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)) ) ) ) ).
fof(t92_scmpds_6,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)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| ( r1_scmpds_6(k7_scmpds_6(C,D,B),A)
& r2_scmpds_6(k7_scmpds_6(C,D,B),A) ) ) ) ) ) ) ) ).
fof(t93_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> ( r1_scmpds_6(k7_scmpds_6(C,D,B),A)
& r2_scmpds_6(k7_scmpds_6(C,D,B),A) ) ) ) ) ) ) ).
fof(t94_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| k9_scmpds_4(k7_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) ) ).
fof(t95_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> k9_scmpds_4(k7_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) ).
fof(t96_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k7_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)) ) ) ) ) ).
fof(t97_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
=> k2_scmpds_2(k9_scmpds_4(k7_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) ).
fof(t98_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
=> k2_scmpds_2(k9_scmpds_4(k7_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(t99_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k4_card_1(k8_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__2) ) ) ) ).
fof(t100_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k8_scmpds_6(A,B,C)))
& r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k8_scmpds_6(A,B,C))) ) ) ) ) ).
fof(t101_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ( k1_funct_1(k8_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k9_scmpds_2(A,B,np__2)
& k1_funct_1(k8_scmpds_6(A,B,C),k2_scmpds_3(np__1)) = k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1)) ) ) ) ) ).
fof(t102_scmpds_6,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)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_scmpds_6(k8_scmpds_6(C,D,B),A)
& r2_scmpds_6(k8_scmpds_6(C,D,B),A) ) ) ) ) ) ) ).
fof(t103_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> ( r1_scmpds_6(k8_scmpds_6(C,D,B),A)
& r2_scmpds_6(k8_scmpds_6(C,D,B),A) ) ) ) ) ) ) ).
fof(t104_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> k9_scmpds_4(k8_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) ).
fof(t105_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> k9_scmpds_4(k8_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) ).
fof(t106_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k8_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)) ) ) ) ) ).
fof(t107_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
=> k2_scmpds_2(k9_scmpds_4(k8_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) ).
fof(t108_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
=> k2_scmpds_2(k9_scmpds_4(k8_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(t109_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k4_card_1(k4_scmpds_6(A,B,C,D)) = k1_nat_1(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__2) ) ) ) ) ).
fof(t110_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k4_scmpds_6(A,B,C,D)))
& r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k4_scmpds_6(A,B,C,D))) ) ) ) ) ) ).
fof(t111_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ! [D] :
( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k1_funct_1(k4_scmpds_6(A,B,C,D),k2_scmpds_3(np__0)) = k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__2)) ) ) ) ) ).
fof(t112_scmpds_6,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)
& v3_scmpds_4(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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)))
| ( r1_scmpds_6(k4_scmpds_6(D,E,B,C),A)
& r2_scmpds_6(k4_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) ) ).
fof(t113_scmpds_6,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)
& 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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)))
& r1_scmpds_6(C,A)
& r2_scmpds_6(C,A) )
=> ( r1_scmpds_6(k4_scmpds_6(D,E,B,C),A)
& r2_scmpds_6(k4_scmpds_6(D,E,B,C),A) ) ) ) ) ) ) ) ).
fof(t114_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)))
| k9_scmpds_4(k4_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) ) ).
fof(t115_scmpds_6,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)
& 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)
& v3_scmpds_4(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),E)))
& r1_scmpds_6(C,A)
& r2_scmpds_6(C,A) )
=> k9_scmpds_4(k4_scmpds_6(D,E,B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)))) ) ) ) ) ) ) ).
fof(t116_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(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)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k4_scmpds_6(D,E,B,C),A)) = k2_scmpds_3(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__2)) ) ) ) ) ) ).
fof(t117_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ! [F] :
( v1_int_1(F)
=> ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)))
=> k2_scmpds_2(k9_scmpds_4(k4_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(B,A),E) ) ) ) ) ) ) ) ).
fof(t118_scmpds_6,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)
& 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)
& v2_scmpds_4(C)
& v3_scmpds_4(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ! [F] :
( v1_int_1(F)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),F)))
=> k2_scmpds_2(k9_scmpds_4(k4_scmpds_6(D,F,B,C),A),E) = k2_scmpds_2(k9_scmpds_4(C,A),E) ) ) ) ) ) ) ) ).
fof(t119_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k4_card_1(k9_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__1) ) ) ) ).
fof(t120_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k9_scmpds_6(A,B,C))) ) ) ) ).
fof(t121_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k1_funct_1(k9_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k10_scmpds_2(A,B,k1_nat_1(k4_card_1(C),np__1)) ) ) ) ).
fof(t122_scmpds_6,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)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| ( r1_scmpds_6(k9_scmpds_6(C,D,B),A)
& r2_scmpds_6(k9_scmpds_6(C,D,B),A) ) ) ) ) ) ) ) ).
fof(t123_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
=> ( r1_scmpds_6(k9_scmpds_6(C,D,B),A)
& r2_scmpds_6(k9_scmpds_6(C,D,B),A) ) ) ) ) ) ) ).
fof(t124_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| k9_scmpds_4(k9_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) ) ).
fof(t125_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
=> k9_scmpds_4(k9_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)))) ) ) ) ) ) ).
fof(t126_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k9_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__1)) ) ) ) ) ).
fof(t127_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
=> k2_scmpds_2(k9_scmpds_4(k9_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) ).
fof(t128_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
=> k2_scmpds_2(k9_scmpds_4(k9_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(t129_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> k4_card_1(k10_scmpds_6(A,B,C)) = k1_nat_1(k4_card_1(C),np__2) ) ) ) ).
fof(t130_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k10_scmpds_6(A,B,C)))
& r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k10_scmpds_6(A,B,C))) ) ) ) ) ).
fof(t131_scmpds_6,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [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) )
=> ( k1_funct_1(k10_scmpds_6(A,B,C),k2_scmpds_3(np__0)) = k10_scmpds_2(A,B,np__2)
& k1_funct_1(k10_scmpds_6(A,B,C),k2_scmpds_3(np__1)) = k4_scmpds_2(k1_nat_1(k4_card_1(C),np__1)) ) ) ) ) ).
fof(t132_scmpds_6,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)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_scmpds_6(k10_scmpds_6(C,D,B),A)
& r2_scmpds_6(k10_scmpds_6(C,D,B),A) ) ) ) ) ) ) ).
fof(t133_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
=> ( r1_scmpds_6(k10_scmpds_6(C,D,B),A)
& r2_scmpds_6(k10_scmpds_6(C,D,B),A) ) ) ) ) ) ) ).
fof(t134_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> k9_scmpds_4(k10_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(B,A),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) ).
fof(t135_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
=> k9_scmpds_4(k10_scmpds_6(C,D,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)))) ) ) ) ) ) ).
fof(t136_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k10_scmpds_6(C,D,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__2)) ) ) ) ) ).
fof(t137_scmpds_6,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)
& v3_scmpds_4(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
=> k2_scmpds_2(k9_scmpds_4(k10_scmpds_6(C,E,B),A),D) = k2_scmpds_2(k9_scmpds_4(B,A),D) ) ) ) ) ) ) ).
fof(t138_scmpds_6,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)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( v1_int_1(E)
=> ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
=> k2_scmpds_2(k9_scmpds_4(k10_scmpds_6(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(dt_k1_scmpds_6,axiom,
! [A] :
( v1_int_1(A)
=> ( v1_ami_3(k1_scmpds_6(A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_6(A))
& m1_ami_1(k1_scmpds_6(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k2_scmpds_6,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& 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)
& v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_ami_3(k2_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k2_scmpds_6(A,B,C,D))
& m1_ami_1(k2_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k3_scmpds_6,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& 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)
& v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_ami_3(k3_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_6(A,B,C,D))
& m1_ami_1(k3_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k4_scmpds_6,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& 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)
& v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_ami_3(k4_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k4_scmpds_6(A,B,C,D))
& m1_ami_1(k4_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k5_scmpds_6,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& 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) )
=> ( v1_ami_3(k5_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k5_scmpds_6(A,B,C))
& m1_ami_1(k5_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k6_scmpds_6,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& 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) )
=> ( v1_ami_3(k6_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k6_scmpds_6(A,B,C))
& m1_ami_1(k6_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k7_scmpds_6,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& 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) )
=> ( v1_ami_3(k7_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k7_scmpds_6(A,B,C))
& m1_ami_1(k7_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k8_scmpds_6,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& 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) )
=> ( v1_ami_3(k8_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k8_scmpds_6(A,B,C))
& m1_ami_1(k8_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k9_scmpds_6,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& 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) )
=> ( v1_ami_3(k9_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k9_scmpds_6(A,B,C))
& m1_ami_1(k9_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k10_scmpds_6,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& 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) )
=> ( v1_ami_3(k10_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k10_scmpds_6(A,B,C))
& m1_ami_1(k10_scmpds_6(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
%------------------------------------------------------------------------------