SET007 Axioms: SET007+604.ax
%------------------------------------------------------------------------------
% File : SET007+604 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : A Small Computer Model with Push-Down Stack
% 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 106 ( 16 unt; 0 def)
% Number of atoms : 590 ( 192 equ)
% Maximal formula atoms : 127 ( 5 avg)
% Number of connectives : 516 ( 32 ~; 0 |; 245 &)
% ( 23 <=>; 216 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 7 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 94 ( 94 usr; 30 con; 0-6 aty)
% Number of variables : 384 ( 272 !; 112 ?)
% 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_1,axiom,
! [A,B,C,D] :
( v1_relat_1(k1_scmpds_1(A,B,C,D))
& v1_funct_1(k1_scmpds_1(A,B,C,D)) ) ).
fof(fc2_scmpds_1,axiom,
! [A,B,C,D,E] :
( v1_relat_1(k2_scmpds_1(A,B,C,D,E))
& v1_funct_1(k2_scmpds_1(A,B,C,D,E)) ) ).
fof(fc3_scmpds_1,axiom,
! [A,B,C,D] :
( v1_relat_1(k1_scmpds_1(A,B,C,D))
& v1_funct_1(k1_scmpds_1(A,B,C,D))
& v1_finset_1(k1_scmpds_1(A,B,C,D))
& v1_finseq_1(k1_scmpds_1(A,B,C,D)) ) ).
fof(fc4_scmpds_1,axiom,
! [A,B,C,D,E] :
( v1_relat_1(k2_scmpds_1(A,B,C,D,E))
& v1_funct_1(k2_scmpds_1(A,B,C,D,E))
& v1_finset_1(k2_scmpds_1(A,B,C,D,E))
& v1_finseq_1(k2_scmpds_1(A,B,C,D,E)) ) ).
fof(fc5_scmpds_1,axiom,
( ~ v1_xboole_0(k5_scmpds_1)
& v1_relat_1(k5_scmpds_1) ) ).
fof(fc6_scmpds_1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1)))
& m1_relset_1(A,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1)))
& m1_subset_1(B,k5_scmpds_1) )
=> ( v1_relat_1(k1_funct_1(A,B))
& v1_funct_1(k1_funct_1(A,B)) ) ) ).
fof(d1_scmpds_1,axiom,
! [A,B,C,D] : k1_scmpds_1(A,B,C,D) = k7_finseq_1(k11_finseq_1(A,B,C),k9_finseq_1(D)) ).
fof(d2_scmpds_1,axiom,
! [A,B,C,D,E] : k2_scmpds_1(A,B,C,D,E) = k7_finseq_1(k11_finseq_1(A,B,C),k10_finseq_1(D,E)) ).
fof(t1_scmpds_1,axiom,
! [A,B,C,D] :
( k1_scmpds_1(A,B,C,D) = k7_finseq_1(k11_finseq_1(A,B,C),k9_finseq_1(D))
& k1_scmpds_1(A,B,C,D) = k7_finseq_1(k10_finseq_1(A,B),k10_finseq_1(C,D))
& k1_scmpds_1(A,B,C,D) = k7_finseq_1(k9_finseq_1(A),k11_finseq_1(B,C,D))
& k1_scmpds_1(A,B,C,D) = k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)) ) ).
fof(t2_scmpds_1,axiom,
! [A,B,C,D,E] :
( k2_scmpds_1(A,B,C,D,E) = k7_finseq_1(k11_finseq_1(A,B,C),k10_finseq_1(D,E))
& k2_scmpds_1(A,B,C,D,E) = k7_finseq_1(k1_scmpds_1(A,B,C,D),k9_finseq_1(E))
& k2_scmpds_1(A,B,C,D,E) = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)),k9_finseq_1(D)),k9_finseq_1(E))
& k2_scmpds_1(A,B,C,D,E) = k7_finseq_1(k10_finseq_1(A,B),k11_finseq_1(C,D,E))
& k2_scmpds_1(A,B,C,D,E) = k7_finseq_1(k9_finseq_1(A),k1_scmpds_1(B,C,D,E)) ) ).
fof(t3_scmpds_1,axiom,
! [A,B,C,D,E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ( E = k1_scmpds_1(A,B,C,D)
<=> ( k3_finseq_1(E) = np__4
& k1_funct_1(E,np__1) = A
& k1_funct_1(E,np__2) = B
& k1_funct_1(E,np__3) = C
& k1_funct_1(E,np__4) = D ) ) ) ).
fof(t4_scmpds_1,axiom,
! [A,B,C,D] : k4_finseq_1(k1_scmpds_1(A,B,C,D)) = k2_finseq_1(np__4) ).
fof(t5_scmpds_1,axiom,
! [A,B,C,D,E,F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F) )
=> ( F = k2_scmpds_1(A,B,C,D,E)
<=> ( k3_finseq_1(F) = np__5
& k1_funct_1(F,np__1) = A
& k1_funct_1(F,np__2) = B
& k1_funct_1(F,np__3) = C
& k1_funct_1(F,np__4) = D
& k1_funct_1(F,np__5) = E ) ) ) ).
fof(t6_scmpds_1,axiom,
! [A,B,C,D,E] : k4_finseq_1(k2_scmpds_1(A,B,C,D,E)) = k2_finseq_1(np__5) ).
fof(t7_scmpds_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ( k4_finseq_4(k5_numbers,A,k3_scmpds_1(A,B,C,D,E),np__1) = B
& k4_finseq_4(k5_numbers,A,k3_scmpds_1(A,B,C,D,E),np__2) = C
& k4_finseq_4(k5_numbers,A,k3_scmpds_1(A,B,C,D,E),np__3) = D
& k4_finseq_4(k5_numbers,A,k3_scmpds_1(A,B,C,D,E),np__4) = E ) ) ) ) ) ) ).
fof(t8_scmpds_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ( k4_finseq_4(k5_numbers,A,k4_scmpds_1(A,B,C,D,E,F),np__1) = B
& k4_finseq_4(k5_numbers,A,k4_scmpds_1(A,B,C,D,E,F),np__2) = C
& k4_finseq_4(k5_numbers,A,k4_scmpds_1(A,B,C,D,E,F),np__3) = D
& k4_finseq_4(k5_numbers,A,k4_scmpds_1(A,B,C,D,E,F),np__4) = E
& k4_finseq_4(k5_numbers,A,k4_scmpds_1(A,B,C,D,E,F),np__5) = F ) ) ) ) ) ) ) ).
fof(t9_scmpds_1,axiom,
! [A] :
( v1_int_1(A)
=> r2_hidden(A,k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers)) ) ).
fof(t10_scmpds_1,axiom,
! [A] :
( v1_int_1(A)
=> r2_hidden(A,k2_xboole_0(k2_ami_2,k4_numbers)) ) ).
fof(t11_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k2_ami_2)
=> r2_hidden(A,k2_xboole_0(k2_ami_2,k4_numbers)) ) ).
fof(t12_scmpds_1,axiom,
$true ).
fof(t13_scmpds_1,axiom,
r2_hidden(k4_tarski(np__0,k12_finseq_1(k5_numbers,np__0)),k5_scmpds_1) ).
fof(t14_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ~ ( A != np__0
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> A != k1_nat_1(k2_nat_1(np__2,B),np__1) )
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> A != k1_nat_1(k2_nat_1(np__2,B),np__2) ) ) ) ).
fof(t15_scmpds_1,axiom,
$true ).
fof(t16_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__1) )
=> ( A != np__0
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> A != k1_nat_1(k2_nat_1(np__2,B),np__2) ) ) )
& ( ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__2) )
=> ( A != np__0
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> A != k1_nat_1(k2_nat_1(np__2,B),np__1) ) ) ) ) ) ).
fof(d4_scmpds_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)))
& m2_relset_1(A,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2))) )
=> ( A = k6_scmpds_1
<=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)),A,np__0) = k3_ami_2
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)),A,k1_nat_1(k2_nat_1(np__2,B),np__1)) = k4_numbers
& k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)),A,k1_nat_1(k2_nat_1(np__2,B),np__2)) = k5_scmpds_1 ) ) ) ) ) ).
fof(t17_scmpds_1,axiom,
( k3_ami_2 != k5_scmpds_1
& k5_scmpds_1 != k4_numbers ) ).
fof(t18_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)),k6_scmpds_1,A) = k3_ami_2
<=> A = np__0 ) ) ).
fof(t19_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)),k6_scmpds_1,A) = k4_numbers
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__1) ) ) ) ).
fof(t20_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)),k6_scmpds_1,A) = k5_scmpds_1
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__2) ) ) ) ).
fof(t21_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k2_ami_2)
=> k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)),k6_scmpds_1,A) = k4_numbers ) ).
fof(t22_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k3_ami_2)
=> k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)),k6_scmpds_1,A) = k5_scmpds_1 ) ).
fof(t23_scmpds_1,axiom,
k5_card_3(np__0,k4_card_3(k6_scmpds_1)) = k3_ami_2 ).
fof(t24_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k2_ami_2)
=> k5_card_3(A,k4_card_3(k6_scmpds_1)) = k4_numbers ) ).
fof(t25_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k3_ami_2)
=> k5_card_3(A,k4_card_3(k6_scmpds_1)) = k5_scmpds_1 ) ).
fof(d5_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> k7_scmpds_1(A) = k1_funct_1(A,np__0) ) ).
fof(d6_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> k8_scmpds_1(A,B) = k1_funct_4(A,k3_cqc_lang(np__0,B)) ) ) ).
fof(t26_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> k1_funct_1(k8_scmpds_1(A,B),np__0) = B ) ) ).
fof(t27_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> k1_funct_1(k8_scmpds_1(A,B),C) = k1_funct_1(A,C) ) ) ) ).
fof(t28_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
=> k1_funct_1(k8_scmpds_1(A,B),C) = k1_funct_1(A,C) ) ) ) ).
fof(d7_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> k9_scmpds_1(A,B,C) = k1_funct_4(A,k3_cqc_lang(B,C)) ) ) ) ).
fof(t29_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> k1_funct_1(k9_scmpds_1(A,B,C),np__0) = k1_funct_1(A,np__0) ) ) ) ).
fof(t30_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> k1_funct_1(k9_scmpds_1(A,B,C),B) = C ) ) ) ).
fof(t31_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> ( D != B
=> k1_funct_1(k9_scmpds_1(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ) ).
fof(t32_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k3_ami_2)
=> k1_funct_1(k9_scmpds_1(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ).
fof(d8_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> k11_scmpds_1(A,B,C) = k1_nat_1(k2_nat_1(np__2,k1_int_2(k2_xcmplx_0(k10_scmpds_1(A,B),C))),np__1) ) ) ) ).
fof(d9_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( v1_int_1(B)
=> k12_scmpds_1(A,B) = k1_nat_1(k1_int_2(k2_xcmplx_0(k6_xcmplx_0(k7_scmpds_1(A),np__2),k3_xcmplx_0(np__2,B))),np__2) ) ) ).
fof(d10_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(C,k12_finseq_1(k2_ami_2,B)) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ( B = k14_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_ami_2)
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_ami_2,C,np__1) ) ) ) ) ) ).
fof(t33_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_gr_cy_1(np__14))
=> ! [B] :
( m1_subset_1(B,k5_scmpds_1)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ( B = k4_tarski(A,k12_finseq_1(k2_ami_2,C))
=> k14_scmpds_1(B) = C ) ) ) ) ).
fof(d11_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( v1_int_1(B)
& ? [C] :
( m2_subset_1(C,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(C,k9_finseq_1(B)) ) )
=> ! [B] :
( v1_int_1(B)
=> ( B = k15_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k4_numbers)
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k4_numbers,C,np__1) ) ) ) ) ) ).
fof(t34_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_gr_cy_1(np__14))
=> ! [B] :
( m1_subset_1(B,k5_scmpds_1)
=> ! [C] :
( v1_int_1(C)
=> ( B = k4_tarski(A,k9_finseq_1(C))
=> k15_scmpds_1(B) = C ) ) ) ) ).
fof(d12_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( v1_int_1(C)
& ? [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(D,k13_scmpds_1(B,C)) ) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ( B = k16_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_xboole_0(k2_ami_2,k4_numbers))
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_xboole_0(k2_ami_2,k4_numbers),C,np__1) ) ) ) ) ) ).
fof(d13_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( v1_int_1(C)
& ? [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(D,k13_scmpds_1(B,C)) ) ) )
=> ! [B] :
( v1_int_1(B)
=> ( B = k17_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_xboole_0(k2_ami_2,k4_numbers))
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_xboole_0(k2_ami_2,k4_numbers),C,np__2) ) ) ) ) ) ).
fof(t35_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_gr_cy_1(np__14))
=> ! [B] :
( m1_subset_1(B,k5_scmpds_1)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( v1_int_1(D)
=> ( B = k4_tarski(A,k13_scmpds_1(C,D))
=> ( k16_scmpds_1(B) = C
& k17_scmpds_1(B) = D ) ) ) ) ) ) ).
fof(d14_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( v1_int_1(C)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( m2_subset_1(E,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(E,k11_finseq_1(B,C,D)) ) ) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ( B = k18_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_xboole_0(k2_ami_2,k4_numbers))
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_xboole_0(k2_ami_2,k4_numbers),C,np__1) ) ) ) ) ) ).
fof(d15_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( v1_int_1(C)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( m2_subset_1(E,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(E,k11_finseq_1(B,C,D)) ) ) ) )
=> ! [B] :
( v1_int_1(B)
=> ( B = k19_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_xboole_0(k2_ami_2,k4_numbers))
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_xboole_0(k2_ami_2,k4_numbers),C,np__2) ) ) ) ) ) ).
fof(d16_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( v1_int_1(C)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( m2_subset_1(E,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(E,k11_finseq_1(B,C,D)) ) ) ) )
=> ! [B] :
( v1_int_1(B)
=> ( B = k20_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_xboole_0(k2_ami_2,k4_numbers))
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_xboole_0(k2_ami_2,k4_numbers),C,np__3) ) ) ) ) ) ).
fof(t36_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_gr_cy_1(np__14))
=> ! [B] :
( m1_subset_1(B,k5_scmpds_1)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ( B = k4_tarski(A,k11_finseq_1(C,D,E))
=> ( k18_scmpds_1(B) = C
& k19_scmpds_1(B) = D
& k20_scmpds_1(B) = E ) ) ) ) ) ) ) ).
fof(d17_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( v1_int_1(E)
& ? [F] :
( m2_subset_1(F,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(F,k1_scmpds_1(B,C,D,E)) ) ) ) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ( B = k21_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_xboole_0(k2_ami_2,k4_numbers))
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_xboole_0(k2_ami_2,k4_numbers),C,np__1) ) ) ) ) ) ).
fof(d18_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( v1_int_1(E)
& ? [F] :
( m2_subset_1(F,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(F,k1_scmpds_1(B,C,D,E)) ) ) ) ) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ( B = k22_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_xboole_0(k2_ami_2,k4_numbers))
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_xboole_0(k2_ami_2,k4_numbers),C,np__2) ) ) ) ) ) ).
fof(d19_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( v1_int_1(E)
& ? [F] :
( m2_subset_1(F,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(F,k1_scmpds_1(B,C,D,E)) ) ) ) ) )
=> ! [B] :
( v1_int_1(B)
=> ( B = k23_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_xboole_0(k2_ami_2,k4_numbers))
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_xboole_0(k2_ami_2,k4_numbers),C,np__3) ) ) ) ) ) ).
fof(d20_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ( ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( v1_int_1(E)
& ? [F] :
( m2_subset_1(F,k5_numbers,k1_gr_cy_1(np__14))
& A = k4_tarski(F,k1_scmpds_1(B,C,D,E)) ) ) ) ) )
=> ! [B] :
( v1_int_1(B)
=> ( B = k24_scmpds_1(A)
<=> ? [C] :
( m2_finseq_1(C,k2_xboole_0(k2_ami_2,k4_numbers))
& C = k2_mcart_1(A)
& B = k4_finseq_4(k5_numbers,k2_xboole_0(k2_ami_2,k4_numbers),C,np__4) ) ) ) ) ) ).
fof(t37_scmpds_1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_gr_cy_1(np__14))
=> ! [B] :
( m1_subset_1(B,k5_scmpds_1)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> ( B = k4_tarski(A,k1_scmpds_1(C,D,E,F))
=> ( k21_scmpds_1(B) = C
& k22_scmpds_1(B) = D
& k23_scmpds_1(B) = E
& k24_scmpds_1(B) = F ) ) ) ) ) ) ) ) ).
fof(d21_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> k25_scmpds_1(A,B) = k1_nat_1(k2_nat_1(np__2,k3_nat_1(k1_int_2(k10_scmpds_1(A,B)),np__2)),np__4) ) ) ).
fof(d22_scmpds_1,axiom,
k26_scmpds_1 = np__0 ).
fof(d23_scmpds_1,axiom,
k27_scmpds_1 = np__1 ).
fof(d24_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> ! [B] :
( m1_subset_1(B,k4_card_3(k6_scmpds_1))
=> ( ( ? [C] :
( v1_int_1(C)
& A = k4_tarski(np__0,k9_finseq_1(C)) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(B,k12_scmpds_1(B,k15_scmpds_1(A))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& A = k4_tarski(np__2,k13_scmpds_1(C,D)) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k16_scmpds_1(A),k17_scmpds_1(A)),k15_ami_2(k7_scmpds_1(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& A = k4_tarski(np__3,k13_scmpds_1(C,D)) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k16_scmpds_1(A),k17_scmpds_1(A)),k7_scmpds_1(B)),k15_ami_2(k7_scmpds_1(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& A = k4_tarski(np__1,k12_finseq_1(k2_ami_2,C)) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k14_scmpds_1(A),k10_scmpds_1(B,k11_scmpds_1(B,k14_scmpds_1(A),k26_scmpds_1))),k25_scmpds_1(B,k11_scmpds_1(B,k14_scmpds_1(A),k27_scmpds_1))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( v1_int_1(E)
& A = k4_tarski(np__4,k11_finseq_1(C,D,E)) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(B,k2_cqc_lang(k3_ami_2,k10_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A))),np__0,k15_ami_2(k7_scmpds_1(B)),k12_scmpds_1(B,k20_scmpds_1(A)))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( v1_int_1(E)
& A = k4_tarski(np__5,k11_finseq_1(C,D,E)) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(B,k14_ami_2(k3_ami_2,k10_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A))),np__0,k15_ami_2(k7_scmpds_1(B)),k12_scmpds_1(B,k20_scmpds_1(A)))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( v1_int_1(E)
& A = k4_tarski(np__6,k11_finseq_1(C,D,E)) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(B,k14_ami_2(k3_ami_2,np__0,k10_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A))),k15_ami_2(k7_scmpds_1(B)),k12_scmpds_1(B,k20_scmpds_1(A)))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( v1_int_1(E)
& A = k4_tarski(np__7,k11_finseq_1(C,D,E)) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A)),k20_scmpds_1(A)),k15_ami_2(k7_scmpds_1(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( v1_int_1(D)
& ? [E] :
( v1_int_1(E)
& A = k4_tarski(np__8,k11_finseq_1(C,D,E)) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A)),k2_xcmplx_0(k10_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A))),k20_scmpds_1(A))),k15_ami_2(k7_scmpds_1(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& ? [E] :
( v1_int_1(E)
& ? [F] :
( v1_int_1(F)
& A = k4_tarski(np__9,k1_scmpds_1(C,D,E,F)) ) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k2_xcmplx_0(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k15_ami_2(k7_scmpds_1(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& ? [E] :
( v1_int_1(E)
& ? [F] :
( v1_int_1(F)
& A = k4_tarski(np__10,k1_scmpds_1(C,D,E,F)) ) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k6_xcmplx_0(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k15_ami_2(k7_scmpds_1(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& ? [E] :
( v1_int_1(E)
& ? [F] :
( v1_int_1(F)
& A = k4_tarski(np__11,k1_scmpds_1(C,D,E,F)) ) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k3_xcmplx_0(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k15_ami_2(k7_scmpds_1(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& ? [E] :
( v1_int_1(E)
& ? [F] :
( v1_int_1(F)
& A = k4_tarski(np__13,k1_scmpds_1(C,D,E,F)) ) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A)))),k15_ami_2(k7_scmpds_1(B))) )
& ( ? [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
& ? [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
& ? [E] :
( v1_int_1(E)
& ? [F] :
( v1_int_1(F)
& A = k4_tarski(np__12,k1_scmpds_1(C,D,E,F)) ) ) ) )
=> k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k5_int_1(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A)),k6_int_1(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k15_ami_2(k7_scmpds_1(B))) )
& ( ( ! [C] :
( v1_int_1(C)
=> A != k4_tarski(np__0,k9_finseq_1(C)) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( v1_int_1(D)
=> A != k4_tarski(np__2,k13_scmpds_1(C,D)) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( v1_int_1(D)
=> A != k4_tarski(np__3,k13_scmpds_1(C,D)) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> A != k4_tarski(np__1,k12_finseq_1(k2_ami_2,C)) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k4_tarski(np__4,k11_finseq_1(C,D,E)) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k4_tarski(np__5,k11_finseq_1(C,D,E)) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k4_tarski(np__6,k11_finseq_1(C,D,E)) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k4_tarski(np__7,k11_finseq_1(C,D,E)) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k4_tarski(np__8,k11_finseq_1(C,D,E)) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> A != k4_tarski(np__9,k1_scmpds_1(C,D,E,F)) ) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> A != k4_tarski(np__10,k1_scmpds_1(C,D,E,F)) ) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> A != k4_tarski(np__11,k1_scmpds_1(C,D,E,F)) ) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> A != k4_tarski(np__13,k1_scmpds_1(C,D,E,F)) ) ) ) )
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k2_ami_2)
=> ! [E] :
( v1_int_1(E)
=> ! [F] :
( v1_int_1(F)
=> A != k4_tarski(np__12,k1_scmpds_1(C,D,E,F)) ) ) ) ) )
=> k28_scmpds_1(A,B) = B ) ) ) ) ).
fof(d25_scmpds_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1)))
& m2_relset_1(A,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1))) )
=> ( A = k29_scmpds_1
<=> ! [B] :
( m1_subset_1(B,k5_scmpds_1)
=> ! [C] :
( m1_subset_1(C,k4_card_3(k6_scmpds_1))
=> k8_funct_2(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1),k1_cat_2(k5_scmpds_1,k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1),k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1)),A,B),C) = k28_scmpds_1(B,C) ) ) ) ) ).
fof(dt_k1_scmpds_1,axiom,
$true ).
fof(dt_k2_scmpds_1,axiom,
$true ).
fof(dt_k3_scmpds_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A) )
=> m2_finseq_1(k3_scmpds_1(A,B,C,D,E),A) ) ).
fof(redefinition_k3_scmpds_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A) )
=> k3_scmpds_1(A,B,C,D,E) = k1_scmpds_1(B,C,D,E) ) ).
fof(dt_k4_scmpds_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A) )
=> m2_finseq_1(k4_scmpds_1(A,B,C,D,E,F),A) ) ).
fof(redefinition_k4_scmpds_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A)
& m1_subset_1(E,A)
& m1_subset_1(F,A) )
=> k4_scmpds_1(A,B,C,D,E,F) = k2_scmpds_1(B,C,D,E,F) ) ).
fof(dt_k5_scmpds_1,axiom,
m1_subset_1(k5_scmpds_1,k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(np__14),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))))) ).
fof(dt_k6_scmpds_1,axiom,
( v1_funct_1(k6_scmpds_1)
& v1_funct_2(k6_scmpds_1,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2)))
& m2_relset_1(k6_scmpds_1,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2))) ) ).
fof(dt_k7_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmpds_1))
=> m2_subset_1(k7_scmpds_1(A),k5_numbers,k3_ami_2) ) ).
fof(dt_k8_scmpds_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmpds_1))
& m1_subset_1(B,k3_ami_2) )
=> m1_subset_1(k8_scmpds_1(A,B),k4_card_3(k6_scmpds_1)) ) ).
fof(dt_k9_scmpds_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(k6_scmpds_1))
& m1_subset_1(B,k2_ami_2)
& v1_int_1(C) )
=> m1_subset_1(k9_scmpds_1(A,B,C),k4_card_3(k6_scmpds_1)) ) ).
fof(dt_k10_scmpds_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmpds_1))
& m1_subset_1(B,k2_ami_2) )
=> v1_int_1(k10_scmpds_1(A,B)) ) ).
fof(redefinition_k10_scmpds_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmpds_1))
& m1_subset_1(B,k2_ami_2) )
=> k10_scmpds_1(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k11_scmpds_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(k6_scmpds_1))
& m1_subset_1(B,k2_ami_2)
& v1_int_1(C) )
=> m2_subset_1(k11_scmpds_1(A,B,C),k5_numbers,k2_ami_2) ) ).
fof(dt_k12_scmpds_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmpds_1))
& v1_int_1(B) )
=> m2_subset_1(k12_scmpds_1(A,B),k5_numbers,k3_ami_2) ) ).
fof(dt_k13_scmpds_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_ami_2)
& v1_int_1(B) )
=> m2_finseq_1(k13_scmpds_1(A,B),k2_xboole_0(k2_ami_2,k4_numbers)) ) ).
fof(redefinition_k13_scmpds_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_ami_2)
& v1_int_1(B) )
=> k13_scmpds_1(A,B) = k10_finseq_1(A,B) ) ).
fof(dt_k14_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> m2_subset_1(k14_scmpds_1(A),k5_numbers,k2_ami_2) ) ).
fof(dt_k15_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> v1_int_1(k15_scmpds_1(A)) ) ).
fof(dt_k16_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> m2_subset_1(k16_scmpds_1(A),k5_numbers,k2_ami_2) ) ).
fof(dt_k17_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> v1_int_1(k17_scmpds_1(A)) ) ).
fof(dt_k18_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> m2_subset_1(k18_scmpds_1(A),k5_numbers,k2_ami_2) ) ).
fof(dt_k19_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> v1_int_1(k19_scmpds_1(A)) ) ).
fof(dt_k20_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> v1_int_1(k20_scmpds_1(A)) ) ).
fof(dt_k21_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> m2_subset_1(k21_scmpds_1(A),k5_numbers,k2_ami_2) ) ).
fof(dt_k22_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> m2_subset_1(k22_scmpds_1(A),k5_numbers,k2_ami_2) ) ).
fof(dt_k23_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> v1_int_1(k23_scmpds_1(A)) ) ).
fof(dt_k24_scmpds_1,axiom,
! [A] :
( m1_subset_1(A,k5_scmpds_1)
=> v1_int_1(k24_scmpds_1(A)) ) ).
fof(dt_k25_scmpds_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmpds_1))
& m1_subset_1(B,k2_ami_2) )
=> m2_subset_1(k25_scmpds_1(A,B),k5_numbers,k3_ami_2) ) ).
fof(dt_k26_scmpds_1,axiom,
m2_subset_1(k26_scmpds_1,k1_numbers,k5_numbers) ).
fof(dt_k27_scmpds_1,axiom,
m2_subset_1(k27_scmpds_1,k1_numbers,k5_numbers) ).
fof(dt_k28_scmpds_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_scmpds_1)
& m1_subset_1(B,k4_card_3(k6_scmpds_1)) )
=> m1_subset_1(k28_scmpds_1(A,B),k4_card_3(k6_scmpds_1)) ) ).
fof(dt_k29_scmpds_1,axiom,
( v1_funct_1(k29_scmpds_1)
& v1_funct_2(k29_scmpds_1,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1)))
& m2_relset_1(k29_scmpds_1,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1))) ) ).
fof(d3_scmpds_1,axiom,
k5_scmpds_1 = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_xboole_0(a_0_0_scmpds_1,a_0_1_scmpds_1),a_0_2_scmpds_1),a_0_3_scmpds_1),a_0_4_scmpds_1) ).
fof(fraenkel_a_0_0_scmpds_1,axiom,
! [A] :
( r2_hidden(A,a_0_0_scmpds_1)
<=> ? [B] :
( m1_subset_1(B,k4_numbers)
& A = k4_tarski(np__0,k12_finseq_1(k4_numbers,B)) ) ) ).
fof(fraenkel_a_0_1_scmpds_1,axiom,
! [A] :
( r2_hidden(A,a_0_1_scmpds_1)
<=> ? [B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
& A = k4_tarski(np__1,k12_finseq_1(k2_ami_2,B)) ) ) ).
fof(fraenkel_a_0_2_scmpds_1,axiom,
! [A] :
( r2_hidden(A,a_0_2_scmpds_1)
<=> ? [B,C,D] :
( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__14))
& m2_subset_1(C,k5_numbers,k2_ami_2)
& m1_subset_1(D,k4_numbers)
& A = k4_tarski(B,k10_finseq_1(C,D))
& r2_hidden(B,k2_tarski(np__2,np__3)) ) ) ).
fof(fraenkel_a_0_3_scmpds_1,axiom,
! [A] :
( r2_hidden(A,a_0_3_scmpds_1)
<=> ? [B,C,D,E] :
( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__14))
& m2_subset_1(C,k5_numbers,k2_ami_2)
& m1_subset_1(D,k4_numbers)
& m1_subset_1(E,k4_numbers)
& A = k4_tarski(B,k11_finseq_1(C,D,E))
& r2_hidden(B,k3_enumset1(np__4,np__5,np__6,np__7,np__8)) ) ) ).
fof(fraenkel_a_0_4_scmpds_1,axiom,
! [A] :
( r2_hidden(A,a_0_4_scmpds_1)
<=> ? [B,C,D,E,F] :
( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__14))
& m2_subset_1(C,k5_numbers,k2_ami_2)
& m2_subset_1(D,k5_numbers,k2_ami_2)
& m1_subset_1(E,k4_numbers)
& m1_subset_1(F,k4_numbers)
& A = k4_tarski(B,k1_scmpds_1(C,D,E,F))
& r2_hidden(B,k3_enumset1(np__9,np__10,np__11,np__12,np__13)) ) ) ).
%------------------------------------------------------------------------------