SET007 Axioms: SET007+608.ax
%------------------------------------------------------------------------------
% File : SET007+608 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Computation of Two Consecutive Program Blocks for SCMPDS
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : scmpds_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 86 ( 1 unt; 0 def)
% Number of atoms : 598 ( 50 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 526 ( 14 ~; 3 |; 334 &)
% ( 6 <=>; 169 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-3 aty)
% Number of functors : 69 ( 69 usr; 10 con; 0-4 aty)
% Number of variables : 208 ( 206 !; 2 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_scmpds_5,axiom,
? [A] :
( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& v4_scmpds_4(A)
& v1_scmpds_5(A)
& v2_scmpds_5(A) ) ).
fof(fc1_scmpds_5,axiom,
! [A] :
( m1_scmpds_2(A)
=> v1_scmpds_5(k5_scmpds_2(A)) ) ).
fof(fc2_scmpds_5,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> ( v4_scmpds_4(k6_scmpds_2(A,B))
& v1_scmpds_5(k6_scmpds_2(A,B)) ) ) ).
fof(fc3_scmpds_5,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> v1_scmpds_5(k7_scmpds_2(A,B)) ) ).
fof(fc4_scmpds_5,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> v1_scmpds_5(k8_scmpds_2(A,B,C)) ) ).
fof(fc5_scmpds_5,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> v1_scmpds_5(k9_scmpds_2(A,B,C)) ) ).
fof(fc6_scmpds_5,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> v1_scmpds_5(k10_scmpds_2(A,B,C)) ) ).
fof(fc7_scmpds_5,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> ( v4_scmpds_4(k11_scmpds_2(A,B,C))
& v1_scmpds_5(k11_scmpds_2(A,B,C)) ) ) ).
fof(fc8_scmpds_5,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> ( v4_scmpds_4(k12_scmpds_2(A,B,C))
& v1_scmpds_5(k12_scmpds_2(A,B,C)) ) ) ).
fof(fc9_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k13_scmpds_2(A,B,C,D))
& v1_scmpds_5(k13_scmpds_2(A,B,C,D)) ) ) ).
fof(fc10_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k14_scmpds_2(A,B,C,D))
& v1_scmpds_5(k14_scmpds_2(A,B,C,D)) ) ) ).
fof(fc11_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k15_scmpds_2(A,B,C,D))
& v1_scmpds_5(k15_scmpds_2(A,B,C,D)) ) ) ).
fof(fc12_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k16_scmpds_2(A,B,C,D))
& v1_scmpds_5(k16_scmpds_2(A,B,C,D)) ) ) ).
fof(fc13_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k17_scmpds_2(A,B,C,D))
& v1_scmpds_5(k17_scmpds_2(A,B,C,D)) ) ) ).
fof(fc14_scmpds_5,axiom,
( v3_ami_1(k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_tarski(k4_numbers),k1_scmpds_2)
& v2_scmpds_5(k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ).
fof(fc15_scmpds_5,axiom,
! [A] :
( ( v2_scmpds_5(A)
& m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( ~ v1_xboole_0(k1_scmpds_4(A))
& v1_relat_1(k1_scmpds_4(A))
& v1_funct_1(k1_scmpds_4(A))
& v1_finset_1(k1_scmpds_4(A))
& v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_4(A))
& v1_scmpds_4(k1_scmpds_4(A))
& v2_scmpds_4(k1_scmpds_4(A)) ) ) ).
fof(fc16_scmpds_5,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> ( v4_scmpds_4(k6_scmpds_2(A,B))
& v1_scmpds_5(k6_scmpds_2(A,B))
& v2_scmpds_5(k6_scmpds_2(A,B)) ) ) ).
fof(fc17_scmpds_5,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> ( v4_scmpds_4(k11_scmpds_2(A,B,C))
& v1_scmpds_5(k11_scmpds_2(A,B,C))
& v2_scmpds_5(k11_scmpds_2(A,B,C)) ) ) ).
fof(fc18_scmpds_5,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> ( v4_scmpds_4(k12_scmpds_2(A,B,C))
& v1_scmpds_5(k12_scmpds_2(A,B,C))
& v2_scmpds_5(k12_scmpds_2(A,B,C)) ) ) ).
fof(fc19_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k13_scmpds_2(A,B,C,D))
& v1_scmpds_5(k13_scmpds_2(A,B,C,D))
& v2_scmpds_5(k13_scmpds_2(A,B,C,D)) ) ) ).
fof(fc20_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k14_scmpds_2(A,B,C,D))
& v1_scmpds_5(k14_scmpds_2(A,B,C,D))
& v2_scmpds_5(k14_scmpds_2(A,B,C,D)) ) ) ).
fof(fc21_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k15_scmpds_2(A,B,C,D))
& v1_scmpds_5(k15_scmpds_2(A,B,C,D))
& v2_scmpds_5(k15_scmpds_2(A,B,C,D)) ) ) ).
fof(fc22_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k16_scmpds_2(A,B,C,D))
& v1_scmpds_5(k16_scmpds_2(A,B,C,D))
& v2_scmpds_5(k16_scmpds_2(A,B,C,D)) ) ) ).
fof(fc23_scmpds_5,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v4_scmpds_4(k17_scmpds_2(A,B,C,D))
& v1_scmpds_5(k17_scmpds_2(A,B,C,D))
& v2_scmpds_5(k17_scmpds_2(A,B,C,D)) ) ) ).
fof(rc2_scmpds_5,axiom,
? [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v1_scmpds_4(A)
& v2_scmpds_4(A)
& v3_scmpds_4(A)
& v3_scmpds_5(A) ) ).
fof(fc24_scmpds_5,axiom,
! [A,B] :
( ( 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) )
=> ( v1_relat_1(k3_scmpds_4(A,B))
& v1_funct_1(k3_scmpds_4(A,B))
& v1_finset_1(k3_scmpds_4(A,B))
& v1_ami_3(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_4(A,B))
& v3_scmpds_5(k3_scmpds_4(A,B)) ) ) ).
fof(fc25_scmpds_5,axiom,
! [A] :
( ( v1_scmpds_5(A)
& m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( ~ v1_xboole_0(k1_scmpds_4(A))
& v1_relat_1(k1_scmpds_4(A))
& v1_funct_1(k1_scmpds_4(A))
& v1_finset_1(k1_scmpds_4(A))
& v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k1_scmpds_4(A))
& v3_scmpds_5(k1_scmpds_4(A)) ) ) ).
fof(fc26_scmpds_5,axiom,
! [A,B] :
( ( v1_scmpds_5(A)
& m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v3_scmpds_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_relat_1(k4_scmpds_4(A,B))
& v1_funct_1(k4_scmpds_4(A,B))
& v1_finset_1(k4_scmpds_4(A,B))
& v1_ami_3(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k4_scmpds_4(A,B))
& v3_scmpds_5(k4_scmpds_4(A,B)) ) ) ).
fof(fc27_scmpds_5,axiom,
! [A,B] :
( ( 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_scmpds_5(B)
& m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( v1_relat_1(k5_scmpds_4(A,B))
& v1_funct_1(k5_scmpds_4(A,B))
& v1_finset_1(k5_scmpds_4(A,B))
& v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k5_scmpds_4(A,B))
& v3_scmpds_5(k5_scmpds_4(A,B)) ) ) ).
fof(fc28_scmpds_5,axiom,
! [A,B] :
( ( v1_scmpds_5(A)
& m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& v1_scmpds_5(B)
& m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( v1_relat_1(k6_scmpds_4(A,B))
& v1_funct_1(k6_scmpds_4(A,B))
& v1_finset_1(k6_scmpds_4(A,B))
& v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k6_scmpds_4(A,B))
& v3_scmpds_5(k6_scmpds_4(A,B)) ) ) ).
fof(fc29_scmpds_5,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_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) )
=> ( v1_relat_1(k3_scmpds_4(A,B))
& v1_funct_1(k3_scmpds_4(A,B))
& v1_finset_1(k3_scmpds_4(A,B))
& v1_ami_3(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k3_scmpds_4(A,B))
& v1_scmpds_4(k3_scmpds_4(A,B))
& v2_scmpds_4(k3_scmpds_4(A,B)) ) ) ).
fof(fc30_scmpds_5,axiom,
! [A,B] :
( ( v2_scmpds_5(A)
& m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v2_scmpds_4(B)
& v3_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( v1_relat_1(k4_scmpds_4(A,B))
& v1_funct_1(k4_scmpds_4(A,B))
& v1_finset_1(k4_scmpds_4(A,B))
& v1_ami_3(k4_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k4_scmpds_4(A,B))
& v1_scmpds_4(k4_scmpds_4(A,B))
& v2_scmpds_4(k4_scmpds_4(A,B)) ) ) ).
fof(fc31_scmpds_5,axiom,
! [A,B] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& v2_scmpds_4(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v4_scmpds_4(B)
& v2_scmpds_5(B)
& m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( v1_relat_1(k5_scmpds_4(A,B))
& v1_funct_1(k5_scmpds_4(A,B))
& v1_finset_1(k5_scmpds_4(A,B))
& v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k5_scmpds_4(A,B))
& v1_scmpds_4(k5_scmpds_4(A,B))
& v2_scmpds_4(k5_scmpds_4(A,B)) ) ) ).
fof(fc32_scmpds_5,axiom,
! [A,B] :
( ( v2_scmpds_5(A)
& m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
& v4_scmpds_4(B)
& v2_scmpds_5(B)
& m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( v1_relat_1(k6_scmpds_4(A,B))
& v1_funct_1(k6_scmpds_4(A,B))
& v1_finset_1(k6_scmpds_4(A,B))
& v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(k6_scmpds_4(A,B))
& v1_scmpds_4(k6_scmpds_4(A,B))
& v2_scmpds_4(k6_scmpds_4(A,B)) ) ) ).
fof(t1_scmpds_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ( C = k9_ami_1(A,B,C)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k11_ami_1(A,B,k10_ami_1(A,B,C),D) = C ) ) ) ) ) ).
fof(t2_scmpds_5,axiom,
! [A,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(A,k1_relat_1(k1_scmpds_4(B)))
<=> A = k2_scmpds_3(np__0) ) ) ).
fof(t3_scmpds_5,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(k8_scmpds_4(B)))
=> ( k1_funct_1(k8_scmpds_4(B),A) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)
| r2_hidden(A,k1_relat_1(B)) ) ) ) ) ).
fof(t4_scmpds_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( k1_relat_1(k1_scmpds_4(A)) = k1_struct_0(k1_scmpds_2,k2_scmpds_3(np__0))
& k1_funct_1(k1_scmpds_4(A),k2_scmpds_3(np__0)) = A ) ) ).
fof(t5_scmpds_5,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))
=> r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k1_scmpds_4(A))) ) ).
fof(t6_scmpds_5,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))
=> k4_card_1(k1_scmpds_4(A)) = np__1 ) ).
fof(t7_scmpds_5,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) )
=> k4_card_1(k8_scmpds_4(A)) = k1_nat_1(k4_card_1(A),np__1) ) ).
fof(t8_scmpds_5,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))
=> k4_card_1(k8_scmpds_4(k1_scmpds_4(A))) = np__2 ) ).
fof(t9_scmpds_5,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))
=> ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k8_scmpds_4(k1_scmpds_4(A))))
& r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k8_scmpds_4(k1_scmpds_4(A)))) ) ) ).
fof(t10_scmpds_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( k1_funct_1(k8_scmpds_4(k1_scmpds_4(A)),k2_scmpds_3(np__0)) = A
& k1_funct_1(k8_scmpds_4(k1_scmpds_4(A)),k2_scmpds_3(np__1)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t11_scmpds_5,axiom,
! [A,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(A,k1_relat_1(k8_scmpds_4(k1_scmpds_4(B))))
<=> ( A = k2_scmpds_3(np__0)
| A = k2_scmpds_3(np__1) ) ) ) ).
fof(t12_scmpds_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k1_relat_1(k8_scmpds_4(k1_scmpds_4(A))) = k2_struct_0(k1_scmpds_2,k2_scmpds_3(np__0),k2_scmpds_3(np__1)) ) ).
fof(t13_scmpds_5,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))
=> ( r2_hidden(k2_scmpds_3(np__0),k1_relat_1(k2_scmpds_4(k8_scmpds_4(k1_scmpds_4(A)))))
& r2_hidden(k2_scmpds_3(np__1),k1_relat_1(k2_scmpds_4(k8_scmpds_4(k1_scmpds_4(A)))))
& k1_funct_1(k2_scmpds_4(k8_scmpds_4(k1_scmpds_4(A))),k2_scmpds_3(np__0)) = A
& k1_funct_1(k2_scmpds_4(k8_scmpds_4(k1_scmpds_4(A))),k2_scmpds_3(np__1)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t14_scmpds_5,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) )
=> k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))) = k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_4(A,k3_scmpds_4(B,k5_scmpds_3)),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))) ) ) ).
fof(t15_scmpds_5,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(k2_scmpds_4(A),k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B)))) ) ) ).
fof(t16_scmpds_5,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> r1_tarski(k1_relat_1(k8_scmpds_4(A)),k1_relat_1(k8_scmpds_4(k3_scmpds_4(A,B)))) ) ) ).
fof(t17_scmpds_5,axiom,
! [A] :
( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(A)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_4(k8_scmpds_4(A)),k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B)))) = k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))) ) ) ).
fof(t18_scmpds_5,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) )
=> ( r1_tarski(k2_scmpds_4(B),A)
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(np__0) ) ) ) ).
fof(t19_scmpds_5,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)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> k2_scmpds_2(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(C)),A) = k2_scmpds_2(B,A) ) ) ) ).
fof(t20_scmpds_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& v2_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( 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(t21_scmpds_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(C)
& v2_scmpds_4(C)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( ( 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(t22_scmpds_5,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,k9_scmpds_4(B,A)) = k6_ami_1(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))))) ) ) ).
fof(t23_scmpds_5,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] :
( ( 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(k2_scmpds_4(k8_scmpds_4(B)),A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
=> 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k3_scmpds_4(B,C))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ) ).
fof(t24_scmpds_5,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] :
( ( 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(k2_scmpds_4(k8_scmpds_4(B)),A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
=> 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(B,C))))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ) ).
fof(d1_scmpds_5,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))
=> ( v1_scmpds_5(A)
<=> A != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(d2_scmpds_5,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))
=> ( v2_scmpds_5(A)
<=> v2_scmpds_4(k1_scmpds_4(A)) ) ) ).
fof(t25_scmpds_5,axiom,
! [A] :
( v1_int_1(A)
=> ( A != np__0
=> v1_scmpds_5(k4_scmpds_2(A)) ) ) ).
fof(t26_scmpds_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__1
& v2_scmpds_5(A) ) ) ).
fof(d3_scmpds_5,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> ( v3_scmpds_5(A)
<=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ~ ( r2_hidden(B,k1_relat_1(A))
& k1_funct_1(A,B) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ).
fof(t27_scmpds_5,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_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( r1_tarski(k2_scmpds_4(k8_scmpds_4(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,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(B)))))) = k2_scmpds_3(k4_card_1(B)) ) ) ) ).
fof(t28_scmpds_5,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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ~ 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(t29_scmpds_5,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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_tarski(k2_scmpds_4(B),A)
& r1_xreal_0(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))))) )
=> r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),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)))),C),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ).
fof(t30_scmpds_5,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_5(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( r1_tarski(k2_scmpds_4(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,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(B)))))) = k2_scmpds_3(k4_card_1(B)) ) ) ) ).
fof(t31_scmpds_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(B)
& v2_scmpds_4(B)
& m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ~ ( r1_tarski(k2_scmpds_4(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,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(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,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(B)))))) != k2_scmpds_3(k4_card_1(B)) ) ) ) ).
fof(t32_scmpds_5,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_5(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(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)
& 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),C)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ).
fof(t33_scmpds_5,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] :
( ( 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_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(t34_scmpds_5,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] :
( ( 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_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,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(B,C))))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ).
fof(t35_scmpds_5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [E] :
( ( v1_ami_3(E,k1_tarski(k4_numbers),k1_scmpds_2)
& v1_scmpds_3(E)
& v2_scmpds_4(E)
& v3_scmpds_4(E)
& m1_ami_1(E,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ( 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,D,k2_scmpds_4(k8_scmpds_4(E)))),A)
=> k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),B)))) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C)),B))) ) ) ) ) ) ) ).
fof(t36_scmpds_5,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_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)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_tarski(k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(B,C))),A)
=> r1_funct_7(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,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)))),D),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,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,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)))),D)),k4_card_1(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(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)))),D)),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) ).
fof(t37_scmpds_5,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_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)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_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(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(t38_scmpds_5,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_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)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
=> 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(t39_scmpds_5,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)
& v2_scmpds_4(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)
& v2_scmpds_4(D)
& v3_scmpds_4(D)
& m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
=> 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(d4_scmpds_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> k1_scmpds_5(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(np__0))) ) ).
fof(t40_scmpds_5,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))
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k1_scmpds_5(B)) = k2_scmpds_3(np__0)
& k2_scmpds_2(k1_scmpds_5(B),A) = k2_scmpds_2(B,A)
& k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k1_scmpds_5(B),C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,C) ) ) ) ) ).
fof(t41_scmpds_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
<=> k7_relat_1(A,k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) = k7_relat_1(B,k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) ) ) ) ).
fof(t42_scmpds_5,axiom,
$true ).
fof(t43_scmpds_5,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)))
=> ( k7_relat_1(B,k2_ami_2) = k7_relat_1(C,k2_ami_2)
=> ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = np__3
| 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(t44_scmpds_5,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] :
( ( v4_scmpds_4(C)
& m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
=> ( k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
=> k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,A),k2_ami_2) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,B),k2_ami_2) ) ) ) ) ).
fof(t45_scmpds_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [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)) )
=> k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k1_scmpds_5(A)) = k9_scmpds_4(k1_scmpds_4(B),A) ) ) ).
fof(t46_scmpds_5,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)
& v2_scmpds_4(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)) )
=> 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(t47_scmpds_5,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_scmpds_5(C)
& v2_scmpds_5(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] :
( ( 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)) )
=> k2_scmpds_2(k9_scmpds_4(k6_scmpds_4(C,D),B),A) = k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k1_scmpds_5(B))),A) ) ) ) ) ).
fof(dt_k1_scmpds_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> m1_subset_1(k1_scmpds_5(A),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ).
%------------------------------------------------------------------------------