SET007 Axioms: SET007+634.ax
%------------------------------------------------------------------------------
% File : SET007+634 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Construction and Computation of for-loop Programs 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_7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 87 ( 1 unt; 0 def)
% Number of atoms : 855 ( 119 equ)
% Maximal formula atoms : 28 ( 9 avg)
% Number of connectives : 784 ( 16 ~; 39 |; 359 &)
% ( 3 <=>; 367 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-3 aty)
% Number of functors : 80 ( 80 usr; 13 con; 0-5 aty)
% Number of variables : 326 ( 326 !; 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_7,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_relat_1(k2_scmpds_4(A))
& v1_funct_1(k2_scmpds_4(A))
& v1_finset_1(k2_scmpds_4(A))
& v1_scmpds_3(k2_scmpds_4(A)) ) ) ).
fof(fc2_scmpds_7,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k1_scmpds_7(B,C,D,A))
& v1_funct_1(k1_scmpds_7(B,C,D,A))
& v1_finset_1(k1_scmpds_7(B,C,D,A))
& v1_ami_3(k1_scmpds_7(B,C,D,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_7(B,C,D,A))
& v3_scmpds_4(k1_scmpds_7(B,C,D,A)) ) ) ).
fof(fc3_scmpds_7,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)
& m1_scmpds_2(B)
& v1_int_1(C)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k1_scmpds_7(B,C,D,A))
& v1_funct_1(k1_scmpds_7(B,C,D,A))
& v1_finset_1(k1_scmpds_7(B,C,D,A))
& v1_ami_3(k1_scmpds_7(B,C,D,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_7(B,C,D,A))
& v3_scmpds_5(k1_scmpds_7(B,C,D,A)) ) ) ).
fof(fc4_scmpds_7,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v3_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_scmpds_2(B)
& v1_int_1(C)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k2_scmpds_7(B,C,D,A))
& v1_funct_1(k2_scmpds_7(B,C,D,A))
& v1_finset_1(k2_scmpds_7(B,C,D,A))
& v1_ami_3(k2_scmpds_7(B,C,D,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k2_scmpds_7(B,C,D,A))
& v3_scmpds_4(k2_scmpds_7(B,C,D,A)) ) ) ).
fof(fc5_scmpds_7,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)
& m1_scmpds_2(B)
& v1_int_1(C)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k2_scmpds_7(B,C,D,A))
& v1_funct_1(k2_scmpds_7(B,C,D,A))
& v1_finset_1(k2_scmpds_7(B,C,D,A))
& v1_ami_3(k2_scmpds_7(B,C,D,A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k2_scmpds_7(B,C,D,A))
& v3_scmpds_5(k2_scmpds_7(B,C,D,A)) ) ) ).
fof(t1_scmpds_7,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,k6_xcmplx_0(C,B)) = k2_scmpds_3(C) ) ) ) ) ).
fof(t2_scmpds_7,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> ! [B] :
( m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
=> ( r1_tarski(A,B)
=> r1_tarski(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B)) ) ) ) ).
fof(t3_scmpds_7,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_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_tarski(A,B)
=> r1_tarski(k6_scmpds_3(A,C),k6_scmpds_3(B,C)) ) ) ) ) ).
fof(t4_scmpds_7,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(np__0)
=> k1_scmpds_5(A) = A ) ) ).
fof(t5_scmpds_7,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,A) = k2_scmpds_3(np__0)
=> k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,B) ) ) ) ).
fof(t6_scmpds_7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_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),A),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ).
fof(t7_scmpds_7,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
& k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
& k7_relat_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> A = B ) ) ) ).
fof(t8_scmpds_7,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(k2_scmpds_4(B))) ) ) ) ).
fof(t9_scmpds_7,axiom,
! [A,B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [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(A,k1_relat_1(D))
=> k1_funct_1(D,A) = k1_funct_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C))),A) ) ) ) ) ).
fof(t10_scmpds_7,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] :
( ( 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(B,k1_relat_1(C))
=> k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C)),B) = k1_funct_1(C,B) ) ) ) ) ).
fof(t11_scmpds_7,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_struct_0(C,k1_scmpds_2,u2_ami_1(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_2(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C))),A) = k2_scmpds_2(B,A) ) ) ) ) ).
fof(t12_scmpds_7,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))
=> k1_funct_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_1(k1_tarski(k4_numbers),k1_scmpds_2)) = B ) ) ).
fof(t13_scmpds_7,axiom,
$true ).
fof(t14_scmpds_7,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k1_funct_1(k5_scmpds_4(k5_scmpds_4(C,A),B),k2_scmpds_3(k4_card_1(C))) = A ) ) ) ).
fof(t15_scmpds_7,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [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) )
=> k5_scmpds_4(k5_scmpds_4(k4_scmpds_4(A,D),B),C) = k4_scmpds_4(A,k5_scmpds_4(k5_scmpds_4(D,B),C)) ) ) ) ) ).
fof(t16_scmpds_7,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_tarski(k6_scmpds_3(A,k4_card_1(B)),k3_scmpds_4(k3_scmpds_4(B,A),C)) ) ) ) ).
fof(t17_scmpds_7,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_tarski(A,k8_scmpds_4(k3_scmpds_4(A,B))) ) ) ).
fof(t18_scmpds_7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_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) )
=> ( r2_hidden(B,k1_relat_1(C))
=> k1_funct_1(k6_scmpds_3(k8_scmpds_4(C),A),k3_scmpds_3(B,A)) = k1_funct_1(k6_scmpds_3(C,A),k3_scmpds_3(B,A)) ) ) ) ) ).
fof(t19_scmpds_7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ~ r1_xreal_0(k4_card_1(B),np__0)
=> k1_funct_1(k6_scmpds_3(k8_scmpds_4(B),A),k2_scmpds_3(A)) = k1_funct_1(k6_scmpds_3(B,A),k2_scmpds_3(A)) ) ) ) ).
fof(t20_scmpds_7,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( r2_hidden(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B),k2_enumset1(np__0,np__4,np__5,np__6))
=> k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A),k2_ami_2) = k7_relat_1(A,k2_ami_2) ) ) ) ).
fof(t21_scmpds_7,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(k1_funct_4(A,k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))),k2_ami_2) = k7_relat_1(A,k2_ami_2) ) ) ).
fof(t22_scmpds_7,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))
=> k2_relat_1(k1_scmpds_4(A)) = k1_tarski(A) ) ).
fof(t23_scmpds_7,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C)
& k7_relat_1(B,k2_ami_2) = k7_relat_1(C,k2_ami_2) )
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B)) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C))
& k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k2_ami_2) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C),k2_ami_2) ) ) ) ) ) ).
fof(t24_scmpds_7,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) )
=> ( ( r1_scmpds_6(C,A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
& k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
=> ! [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,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,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,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,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,A),D),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),D),k2_ami_2) ) ) ) ) ) ) ).
fof(t25_scmpds_7,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) )
=> ( ( r1_scmpds_6(C,A)
& k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_funct_7(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(C)))),D),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(C)))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& 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,A,k2_scmpds_4(k8_scmpds_4(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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(C)))),D)) ) ) ) ) ) ) ).
fof(t26_scmpds_7,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) )
=> ( ( r1_scmpds_6(C,A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
& r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& 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),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)) ) ) ) ) ) ) ).
fof(t27_scmpds_7,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) )
=> ( ( r1_scmpds_6(C,A)
& r2_scmpds_6(C,A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
& k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
=> k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,B) ) ) ) ) ).
fof(t28_scmpds_7,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) )
=> ( ( r1_scmpds_6(C,A)
& r2_scmpds_6(C,A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
& r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
& r1_funct_7(k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ).
fof(t29_scmpds_7,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) )
=> ( ( r1_scmpds_6(C,A)
& r2_scmpds_6(C,A)
& k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
=> ( 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(C)))) = 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(C))))
& r1_funct_7(k12_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(C)))),k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(C)))),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ).
fof(t30_scmpds_7,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) )
=> ( ( r1_scmpds_6(C,A)
& r2_scmpds_6(C,A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
& r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B) )
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
| r1_funct_7(k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ).
fof(t31_scmpds_7,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)
=> ( r2_scmpds_6(B,A)
=> k2_scmpds_2(k9_scmpds_4(B,A),C) = k2_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)))),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) ) ) ) ) ).
fof(t32_scmpds_7,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v2_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [C] :
( m1_scmpds_2(C)
=> k2_scmpds_2(k9_scmpds_4(B,A),C) = k2_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)))),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) ) ) ) ).
fof(t33_scmpds_7,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_tarski(k2_scmpds_4(k8_scmpds_4(B)),A)
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> ( r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),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,A),C)),k1_relat_1(B)) ) ) ) ) ) ).
fof(t34_scmpds_7,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)
& r2_scmpds_6(C,A) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_tarski(k6_scmpds_3(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) )
=> ( r1_xreal_0(k4_card_1(C),np__0)
| ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E)
=> ( 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(t35_scmpds_7,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_tarski(k2_scmpds_4(k8_scmpds_4(B)),A)
& r2_scmpds_6(B,A)
& ~ r1_xreal_0(k4_card_1(B),np__0)
& r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),np__0) ) ) ) ).
fof(t36_scmpds_7,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)
& v3_scmpds_5(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)
& r2_scmpds_6(C,A) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_tarski(k6_scmpds_3(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) )
=> ( r1_xreal_0(k4_card_1(C),np__0)
| ( 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),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A))) = k2_scmpds_3(k1_nat_1(k4_card_1(C),D))
& k7_relat_1(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)),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),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A)),k2_ami_2) ) ) ) ) ) ) ) ) ).
fof(t37_scmpds_7,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)
=> ( 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(B))),C)) = k2_scmpds_3(np__0)
=> k8_ami_5(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(B))),C),k2_scmpds_4(B)) = 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(B))),C) ) ) ) ) ).
fof(t38_scmpds_7,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A)
& r1_xreal_0(D,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))))) )
=> r1_funct_7(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)))),D),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,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_4(B,C),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ).
fof(t39_scmpds_7,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_tarski(B,C)
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A)
& r1_xreal_0(D,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))))) )
=> r1_funct_7(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(C))),D),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)))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ).
fof(t40_scmpds_7,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] :
( 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,A,k2_scmpds_4(k8_scmpds_4(B)))))
& r1_tarski(B,C)
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A) )
=> 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(C))),D)),k1_relat_1(k8_scmpds_4(B))) ) ) ) ) ) ).
fof(t41_scmpds_7,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_tarski(B,C)
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,A)
& 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,A,k2_scmpds_4(C))),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)))))) != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)
& 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(C))),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)))))) != k2_scmpds_3(k4_card_1(B)) ) ) ) ) ).
fof(t42_scmpds_7,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) )
=> ( ( r2_scmpds_6(B,A)
& r1_scmpds_6(C,k9_scmpds_4(B,A))
& r2_scmpds_6(C,k9_scmpds_4(B,A)) )
=> ( r1_scmpds_6(C,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)))),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))))))
& r2_scmpds_6(C,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)))),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)))))) ) ) ) ) ) ).
fof(t43_scmpds_7,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) )
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A)
& r1_scmpds_6(C,k9_scmpds_4(B,A))
& r2_scmpds_6(C,k9_scmpds_4(B,A)) )
=> ( r1_scmpds_6(k3_scmpds_4(B,C),A)
& r2_scmpds_6(k3_scmpds_4(B,C),A) ) ) ) ) ) ).
fof(t44_scmpds_7,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_tarski(B,C)
& r1_scmpds_6(B,A)
& r2_scmpds_6(B,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,A,k2_scmpds_4(C))),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)))))) = k2_scmpds_3(k4_card_1(B)) ) ) ) ) ).
fof(t45_scmpds_7,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)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( 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(t46_scmpds_7,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(k3_scmpds_4(A,B))))),D)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ) ).
fof(t47_scmpds_7,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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A)
& r1_scmpds_6(C,k9_scmpds_4(B,A))
& r2_scmpds_6(C,k9_scmpds_4(B,A)) )
=> 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(k3_scmpds_4(B,C))))) = k1_nat_1(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)))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k12_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)))),k2_scmpds_4(k8_scmpds_4(C))))) ) ) ) ) ).
fof(t48_scmpds_7,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)
& v3_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( r1_scmpds_6(B,A)
& r2_scmpds_6(B,A)
& r1_scmpds_6(C,k9_scmpds_4(B,A))
& r2_scmpds_6(C,k9_scmpds_4(B,A)) )
=> k9_scmpds_4(k3_scmpds_4(B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,k9_scmpds_4(B,A)),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,k9_scmpds_4(B,A))),k4_card_1(B)))) ) ) ) ) ).
fof(t49_scmpds_7,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] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& v3_scmpds_5(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)
& v3_scmpds_4(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( r1_scmpds_6(C,B)
& r2_scmpds_6(C,B)
& r1_scmpds_6(D,k9_scmpds_4(C,B))
& r2_scmpds_6(D,k9_scmpds_4(C,B)) )
=> k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(C,D),B),A) = k2_scmpds_2(k9_scmpds_4(D,k9_scmpds_4(C,B)),A) ) ) ) ) ) ).
fof(t50_scmpds_7,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] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& v3_scmpds_5(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( ( v4_scmpds_4(D)
& v2_scmpds_5(D)
& m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( ( r1_scmpds_6(C,B)
& r2_scmpds_6(C,B) )
=> k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(C,D),B),A) = k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D,k9_scmpds_4(C,B)),A) ) ) ) ) ) ).
fof(d1_scmpds_7,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [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_scmpds_7(A,B,C,D) = k5_scmpds_4(k5_scmpds_4(k4_scmpds_4(k10_scmpds_2(A,B,k1_nat_1(k4_card_1(D),np__3)),D),k12_scmpds_2(A,B,C)),k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(D),np__2)))) ) ) ) ) ).
fof(t51_scmpds_7,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [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(k1_scmpds_7(A,B,C,D)) = k1_nat_1(k4_card_1(D),np__3) ) ) ) ) ).
fof(t52_scmpds_7,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_ami_3(E,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(E)
& m1_ami_1(E,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ~ r1_xreal_0(k1_nat_1(k4_card_1(E),np__3),D)
<=> r2_hidden(k2_scmpds_3(D),k1_relat_1(k1_scmpds_7(A,B,C,E))) ) ) ) ) ) ) ).
fof(t53_scmpds_7,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [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(k1_scmpds_7(A,B,C,D),k2_scmpds_3(np__0)) = k10_scmpds_2(A,B,k1_nat_1(k4_card_1(D),np__3))
& k1_funct_1(k1_scmpds_7(A,B,C,D),k2_scmpds_3(k1_nat_1(k4_card_1(D),np__1))) = k12_scmpds_2(A,B,C)
& k1_funct_1(k1_scmpds_7(A,B,C,D),k2_scmpds_3(k1_nat_1(k4_card_1(D),np__2))) = k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(D),np__2))) ) ) ) ) ) ).
fof(t54_scmpds_7,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
=> ( r1_scmpds_6(k1_scmpds_7(C,D,E,B),A)
& r2_scmpds_6(k1_scmpds_7(C,D,E,B),A) ) ) ) ) ) ) ) ).
fof(t55_scmpds_7,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)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
=> k9_scmpds_4(k1_scmpds_7(C,E,F,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__3)))) ) ) ) ) ) ) ) ).
fof(t56_scmpds_7,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k1_scmpds_7(C,D,E,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__3)) ) ) ) ) ) ) ).
fof(t57_scmpds_7,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)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
=> k2_scmpds_2(k9_scmpds_4(k1_scmpds_7(C,E,F,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ) ).
fof(t58_scmpds_7,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
& k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
=> ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
& k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D)) = k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))
& r1_scmpds_6(B,G)
& r2_scmpds_6(B,G)
& ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| r2_hidden(k3_scmpds_2(k2_scmpds_2(A,C),D),F)
| r1_xreal_0(E,np__0)
| r1_xreal_0(k4_card_1(B),np__0)
| C = k3_scmpds_2(k2_scmpds_2(A,C),D)
| ( r1_scmpds_6(k1_scmpds_7(C,D,E,B),A)
& r2_scmpds_6(k1_scmpds_7(C,D,E,B),A) ) ) ) ) ) ) ) ) ).
fof(t59_scmpds_7,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
& k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
=> ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
& k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D)) = k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))
& r1_scmpds_6(B,G)
& r2_scmpds_6(B,G)
& ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) )
=> ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
| r2_hidden(k3_scmpds_2(k2_scmpds_2(A,C),D),F)
| r1_xreal_0(E,np__0)
| r1_xreal_0(k4_card_1(B),np__0)
| C = k3_scmpds_2(k2_scmpds_2(A,C),D)
| k9_scmpds_4(k1_scmpds_7(C,D,E,B),A) = k9_scmpds_4(k1_scmpds_7(C,D,E,B),k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,D,E)),A)) ) ) ) ) ) ) ) ).
fof(d2_scmpds_7,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [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_7(A,B,C,D) = k5_scmpds_4(k5_scmpds_4(k4_scmpds_4(k9_scmpds_2(A,B,k1_nat_1(k4_card_1(D),np__3)),D),k12_scmpds_2(A,B,k4_xcmplx_0(C))),k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(D),np__2)))) ) ) ) ) ).
fof(t60_scmpds_7,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [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_7(A,B,C,D)) = k1_nat_1(k4_card_1(D),np__3) ) ) ) ) ).
fof(t61_scmpds_7,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_ami_3(E,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(E)
& m1_ami_1(E,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ~ r1_xreal_0(k1_nat_1(k4_card_1(E),np__3),D)
<=> r2_hidden(k2_scmpds_3(D),k1_relat_1(k2_scmpds_7(A,B,C,E))) ) ) ) ) ) ) ).
fof(t62_scmpds_7,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [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_7(A,B,C,D),k2_scmpds_3(np__0)) = k9_scmpds_2(A,B,k1_nat_1(k4_card_1(D),np__3))
& k1_funct_1(k2_scmpds_7(A,B,C,D),k2_scmpds_3(k1_nat_1(k4_card_1(D),np__1))) = k12_scmpds_2(A,B,k4_xcmplx_0(C))
& k1_funct_1(k2_scmpds_7(A,B,C,D),k2_scmpds_3(k1_nat_1(k4_card_1(D),np__2))) = k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(D),np__2))) ) ) ) ) ) ).
fof(t63_scmpds_7,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> ( r1_scmpds_6(k2_scmpds_7(C,D,E,B),A)
& r2_scmpds_6(k2_scmpds_7(C,D,E,B),A) ) ) ) ) ) ) ) ).
fof(t64_scmpds_7,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)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
=> k9_scmpds_4(k2_scmpds_7(C,E,F,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__3)))) ) ) ) ) ) ) ) ).
fof(t65_scmpds_7,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k2_scmpds_7(C,D,E,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__3)) ) ) ) ) ) ) ).
fof(t66_scmpds_7,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)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
=> k2_scmpds_2(k9_scmpds_4(k2_scmpds_7(C,E,F,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ) ).
fof(t67_scmpds_7,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
& k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
=> ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
& k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D)) = k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))
& r1_scmpds_6(B,G)
& r2_scmpds_6(B,G)
& ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| r2_hidden(k3_scmpds_2(k2_scmpds_2(A,C),D),F)
| r1_xreal_0(E,np__0)
| r1_xreal_0(k4_card_1(B),np__0)
| C = k3_scmpds_2(k2_scmpds_2(A,C),D)
| ( r1_scmpds_6(k2_scmpds_7(C,D,E,B),A)
& r2_scmpds_6(k2_scmpds_7(C,D,E,B),A) ) ) ) ) ) ) ) ) ).
fof(t68_scmpds_7,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)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ! [G] :
( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
& k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
=> ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
& k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D)) = k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))
& r1_scmpds_6(B,G)
& r2_scmpds_6(B,G)
& ! [H] :
( m1_scmpds_2(H)
=> ( r2_hidden(H,F)
=> k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) )
=> ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
| r2_hidden(k3_scmpds_2(k2_scmpds_2(A,C),D),F)
| r1_xreal_0(E,np__0)
| r1_xreal_0(k4_card_1(B),np__0)
| C = k3_scmpds_2(k2_scmpds_2(A,C),D)
| k9_scmpds_4(k2_scmpds_7(C,D,E,B),A) = k9_scmpds_4(k2_scmpds_7(C,D,E,B),k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,D,k4_xcmplx_0(E))),A)) ) ) ) ) ) ) ) ).
fof(d3_scmpds_7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_scmpds_7(A) = k3_scmpds_4(k5_scmpds_4(k6_scmpds_4(k6_scmpds_2(k2_scmp_gcd,np__0),k11_scmpds_2(k2_scmp_gcd,np__2,A)),k11_scmpds_2(k2_scmp_gcd,np__3,np__0)),k2_scmpds_7(k2_scmp_gcd,np__2,np__1,k1_scmpds_4(k12_scmpds_2(k2_scmp_gcd,np__3,np__1)))) ) ).
fof(t69_scmpds_7,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( k2_scmpds_2(A,k2_scmp_gcd) = np__0
=> ( r1_scmpds_6(k2_scmpds_7(k2_scmp_gcd,np__2,np__1,k1_scmpds_4(k12_scmpds_2(k2_scmp_gcd,np__3,np__1))),A)
& r2_scmpds_6(k2_scmpds_7(k2_scmp_gcd,np__2,np__1,k1_scmpds_4(k12_scmpds_2(k2_scmp_gcd,np__3,np__1))),A) ) ) ) ).
fof(t70_scmpds_7,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)
=> ( ( k2_scmpds_2(A,k2_scmp_gcd) = np__0
& k2_scmpds_2(A,k1_scmp_gcd(np__2)) = B
& k2_scmpds_2(A,k1_scmp_gcd(np__3)) = np__0 )
=> k2_scmpds_2(k9_scmpds_4(k2_scmpds_7(k2_scmp_gcd,np__2,np__1,k1_scmpds_4(k12_scmpds_2(k2_scmp_gcd,np__3,np__1))),A),k1_scmp_gcd(np__3)) = B ) ) ) ).
fof(t71_scmpds_7,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)
=> k2_scmpds_2(k9_scmpds_4(k3_scmpds_7(B),A),k1_scmp_gcd(np__3)) = B ) ) ).
fof(d4_scmpds_7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k4_scmpds_7(A,B,C,D,E) = k3_scmpds_4(k6_scmpds_4(k11_scmpds_2(k1_scmp_gcd(A),C,np__0),k6_scmpds_2(k1_scmp_gcd(D),E)),k2_scmpds_7(k1_scmp_gcd(A),B,np__1,k6_scmpds_4(k13_scmpds_2(k1_scmp_gcd(A),k1_scmp_gcd(E),C,np__0),k12_scmpds_2(k1_scmp_gcd(D),np__0,np__1)))) ) ) ) ) ) ).
fof(t72_scmpds_7,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)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( k2_scmpds_2(A,k1_scmp_gcd(E)) = F
=> ( r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(B)),B)
| r1_xreal_0(D,C)
| r1_xreal_0(E,k2_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(B)),D))
| r1_xreal_0(F,E)
| r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(F)),F)
| ( r1_scmpds_6(k2_scmpds_7(k1_scmp_gcd(B),C,np__1,k6_scmpds_4(k13_scmpds_2(k1_scmp_gcd(B),k1_scmp_gcd(F),D,np__0),k12_scmpds_2(k1_scmp_gcd(E),np__0,np__1))),A)
& r2_scmpds_6(k2_scmpds_7(k1_scmp_gcd(B),C,np__1,k6_scmpds_4(k13_scmpds_2(k1_scmp_gcd(B),k1_scmp_gcd(F),D,np__0),k12_scmpds_2(k1_scmp_gcd(E),np__0,np__1))),A) ) ) ) ) ) ) ) ) ) ).
fof(t73_scmpds_7,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)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m1_trees_4(G,k1_numbers,k5_numbers)
=> ( ( k2_scmpds_2(A,k1_scmp_gcd(E)) = F
& k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),D)) = np__0
& k3_finseq_1(G) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),C))
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k3_finseq_1(G),H)
=> k3_wsierp_1(G,k1_nat_1(H,np__1)) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(F)),H)) ) ) )
=> ( r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(B)),B)
| r1_xreal_0(D,C)
| r1_xreal_0(E,k2_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(B)),D))
| r1_xreal_0(F,E)
| r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(F)),F)
| k2_scmpds_2(k9_scmpds_4(k2_scmpds_7(k1_scmp_gcd(B),C,np__1,k6_scmpds_4(k13_scmpds_2(k1_scmp_gcd(B),k1_scmp_gcd(F),D,np__0),k12_scmpds_2(k1_scmp_gcd(E),np__0,np__1))),A),k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),D)) = k9_wsierp_1(G) ) ) ) ) ) ) ) ) ) ).
fof(t74_scmpds_7,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)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m1_trees_4(G,k1_numbers,k5_numbers)
=> ( ( k3_finseq_1(G) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),C))
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k3_finseq_1(G),H)
=> k3_wsierp_1(G,k1_nat_1(H,np__1)) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(F)),H)) ) ) )
=> ( r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(B)),B)
| r1_xreal_0(D,C)
| r1_xreal_0(E,k2_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(B)),D))
| r1_xreal_0(F,E)
| r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(F)),F)
| k2_scmpds_2(k9_scmpds_4(k4_scmpds_7(B,C,D,E,F),A),k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),D)) = k9_wsierp_1(G) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_scmpds_7,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& m1_subset_1(C,k5_numbers)
& 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(k1_scmpds_7(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_7(A,B,C,D))
& m1_ami_1(k1_scmpds_7(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k2_scmpds_7,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& m1_subset_1(C,k5_numbers)
& 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_7(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k2_scmpds_7(A,B,C,D))
& m1_ami_1(k2_scmpds_7(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k3_scmpds_7,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( v1_ami_3(k3_scmpds_7(A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_7(A))
& m1_ami_1(k3_scmpds_7(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_k4_scmpds_7,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers)
& m1_subset_1(E,k5_numbers) )
=> ( v1_ami_3(k4_scmpds_7(A,B,C,D,E),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k4_scmpds_7(A,B,C,D,E))
& m1_ami_1(k4_scmpds_7(A,B,C,D,E),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
%------------------------------------------------------------------------------