SET007 Axioms: SET007+605.ax
%------------------------------------------------------------------------------
% File : SET007+605 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The SCMPDS Computer and the Basic Semantics of its Instructions
% 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 146 ( 15 unt; 0 def)
% Number of atoms : 684 ( 172 equ)
% Maximal formula atoms : 57 ( 4 avg)
% Number of connectives : 632 ( 94 ~; 0 |; 135 &)
% ( 5 <=>; 398 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 31 ( 29 usr; 1 prp; 0-3 aty)
% Number of functors : 91 ( 91 usr; 26 con; 0-8 aty)
% Number of variables : 415 ( 407 !; 8 ?)
% 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_2,axiom,
( ~ v3_struct_0(k1_scmpds_2)
& v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ) ).
fof(fc2_scmpds_2,axiom,
( ~ v3_struct_0(k1_scmpds_2)
& v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ) ).
fof(fc3_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( v4_ordinal2(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
& v1_xcmplx_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
& v1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
& ~ v3_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))
& v1_int_1(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)) ) ) ).
fof(fc4_scmpds_2,axiom,
( ~ v3_struct_0(k1_scmpds_2)
& v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ) ).
fof(fc5_scmpds_2,axiom,
( ~ v3_struct_0(k1_scmpds_2)
& v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ) ).
fof(d1_scmpds_2,axiom,
k1_scmpds_2 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,np__0,k3_ami_2,k1_gr_cy_1(np__14),k5_scmpds_1,k6_scmpds_1,k29_scmpds_1) ).
fof(t1_scmpds_2,axiom,
! [A] :
( ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__2) )
<=> r2_hidden(A,k3_ami_2) ) ).
fof(t2_scmpds_2,axiom,
v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ).
fof(t3_scmpds_2,axiom,
v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ).
fof(t4_scmpds_2,axiom,
( u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != k4_numbers
& u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != k4_numbers
& u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(t5_scmpds_2,axiom,
k5_numbers = k2_xboole_0(k2_xboole_0(k1_tarski(np__0),k2_ami_2),k3_ami_2) ).
fof(t6_scmpds_2,axiom,
k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) = np__0 ).
fof(t7_scmpds_2,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(k6_scmpds_1))
=> ( B = A
=> k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k7_scmpds_1(B) ) ) ) ).
fof(d2_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_scmpds_2))
=> ( m1_scmpds_2(A)
<=> r2_hidden(A,k2_ami_2) ) ) ).
fof(t8_scmpds_2,axiom,
$true ).
fof(t9_scmpds_2,axiom,
! [A] :
( r2_hidden(A,k2_ami_2)
=> m1_scmpds_2(A) ) ).
fof(t10_scmpds_2,axiom,
r1_subset_1(k2_ami_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ).
fof(t11_scmpds_2,axiom,
~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ).
fof(t12_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> m1_ami_3(A) ) ).
fof(t13_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> k3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k4_numbers ) ).
fof(t14_scmpds_2,axiom,
! [A] :
( r2_hidden(A,k3_ami_2)
=> m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ).
fof(t15_scmpds_2,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))
=> r1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),np__13) ) ).
fof(d3_scmpds_2,axiom,
$true ).
fof(d4_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> k3_scmpds_2(A,B) = k1_nat_1(k2_nat_1(np__2,k1_int_2(k2_xcmplx_0(A,B))),np__1) ) ) ).
fof(t16_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> r2_hidden(k4_tarski(np__0,k9_finseq_1(A)),k5_scmpds_1) ) ).
fof(t17_scmpds_2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k2_ami_2)
=> r2_hidden(k4_tarski(np__1,k12_finseq_1(k2_ami_2,A)),k5_scmpds_1) ) ).
fof(t18_scmpds_2,axiom,
! [A,B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> ( r2_hidden(A,k2_tarski(np__2,np__3))
=> r2_hidden(k4_tarski(A,k13_scmpds_1(B,C)),k5_scmpds_1) ) ) ) ).
fof(t19_scmpds_2,axiom,
! [A,B] :
( m2_subset_1(B,k5_numbers,k2_ami_2)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> ( r2_hidden(A,k3_enumset1(np__4,np__5,np__6,np__7,np__8))
=> r2_hidden(k4_tarski(A,k11_finseq_1(B,C,D)),k5_scmpds_1) ) ) ) ) ).
fof(t20_scmpds_2,axiom,
! [A,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)
=> ( r2_hidden(A,k3_enumset1(np__9,np__10,np__11,np__12,np__13))
=> r2_hidden(k4_tarski(A,k1_scmpds_1(B,C,D,E)),k5_scmpds_1) ) ) ) ) ) ).
fof(d5_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> k4_scmpds_2(A) = k4_tarski(np__0,k9_finseq_1(A)) ) ).
fof(d6_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> k5_scmpds_2(A) = k4_tarski(np__1,k12_finseq_1(u1_struct_0(k1_scmpds_2),A)) ) ).
fof(d7_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> k6_scmpds_2(A,B) = k4_tarski(np__2,k10_finseq_1(A,B)) ) ) ).
fof(d8_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> k7_scmpds_2(A,B) = k4_tarski(np__3,k10_finseq_1(A,B)) ) ) ).
fof(d9_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> k8_scmpds_2(A,B,C) = k4_tarski(np__4,k11_finseq_1(A,B,C)) ) ) ) ).
fof(d10_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> k9_scmpds_2(A,B,C) = k4_tarski(np__5,k11_finseq_1(A,B,C)) ) ) ) ).
fof(d11_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> k10_scmpds_2(A,B,C) = k4_tarski(np__6,k11_finseq_1(A,B,C)) ) ) ) ).
fof(d12_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> k11_scmpds_2(A,B,C) = k4_tarski(np__7,k11_finseq_1(A,B,C)) ) ) ) ).
fof(d13_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> k12_scmpds_2(A,B,C) = k4_tarski(np__8,k11_finseq_1(A,B,C)) ) ) ) ).
fof(d14_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k13_scmpds_2(A,B,C,D) = k4_tarski(np__9,k1_scmpds_1(A,B,C,D)) ) ) ) ) ).
fof(d15_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k14_scmpds_2(A,B,C,D) = k4_tarski(np__10,k1_scmpds_1(A,B,C,D)) ) ) ) ) ).
fof(d16_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k15_scmpds_2(A,B,C,D) = k4_tarski(np__11,k1_scmpds_1(A,B,C,D)) ) ) ) ) ).
fof(d17_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k16_scmpds_2(A,B,C,D) = k4_tarski(np__12,k1_scmpds_1(A,B,C,D)) ) ) ) ) ).
fof(d18_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k17_scmpds_2(A,B,C,D) = k4_tarski(np__13,k1_scmpds_1(A,B,C,D)) ) ) ) ) ).
fof(t21_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)) = np__0 ) ).
fof(t22_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A)) = np__1 ) ).
fof(t23_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( m1_scmpds_2(B)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(B,A)) = np__2 ) ) ).
fof(t24_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( m1_scmpds_2(B)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(B,A)) = np__3 ) ) ).
fof(t25_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(C,A,B)) = np__4 ) ) ) ).
fof(t26_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(C,A,B)) = np__5 ) ) ) ).
fof(t27_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(C,A,B)) = np__6 ) ) ) ).
fof(t28_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(C,A,B)) = np__7 ) ) ) ).
fof(t29_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(C,A,B)) = np__8 ) ) ) ).
fof(t30_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(C,D,A,B)) = np__9 ) ) ) ) ).
fof(t31_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(C,D,A,B)) = np__10 ) ) ) ) ).
fof(t32_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(C,D,A,B)) = np__11 ) ) ) ) ).
fof(t33_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(C,D,A,B)) = np__12 ) ) ) ) ).
fof(t34_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(C,D,A,B)) = np__13 ) ) ) ) ).
fof(t35_scmpds_2,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__0
& ! [B] :
( v1_int_1(B)
=> A != k4_scmpds_2(B) ) ) ) ).
fof(t36_scmpds_2,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
& ! [B] :
( m1_scmpds_2(B)
=> A != k5_scmpds_2(B) ) ) ) ).
fof(t37_scmpds_2,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__2
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> A != k6_scmpds_2(B,C) ) ) ) ) ).
fof(t38_scmpds_2,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__3
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> A != k7_scmpds_2(B,C) ) ) ) ) ).
fof(t39_scmpds_2,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__4
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> A != k8_scmpds_2(B,C,D) ) ) ) ) ) ).
fof(t40_scmpds_2,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__5
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> A != k9_scmpds_2(B,C,D) ) ) ) ) ) ).
fof(t41_scmpds_2,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__6
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> A != k10_scmpds_2(B,C,D) ) ) ) ) ) ).
fof(t42_scmpds_2,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__7
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> A != k11_scmpds_2(B,C,D) ) ) ) ) ) ).
fof(t43_scmpds_2,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__8
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> A != k12_scmpds_2(B,C,D) ) ) ) ) ) ).
fof(t44_scmpds_2,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__9
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k13_scmpds_2(B,C,D,E) ) ) ) ) ) ) ).
fof(t45_scmpds_2,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__10
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k14_scmpds_2(B,C,D,E) ) ) ) ) ) ) ).
fof(t46_scmpds_2,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__11
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k15_scmpds_2(B,C,D,E) ) ) ) ) ) ) ).
fof(t47_scmpds_2,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__12
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k16_scmpds_2(B,C,D,E) ) ) ) ) ) ) ).
fof(t48_scmpds_2,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__13
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k17_scmpds_2(B,C,D,E) ) ) ) ) ) ) ).
fof(t49_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_scmpds_2(B)
=> r2_hidden(B,k1_relat_1(A)) ) ) ).
fof(t50_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> r1_tarski(k2_ami_2,k1_relat_1(A)) ) ).
fof(t51_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> k1_relat_1(k7_relat_1(A,k2_ami_2)) = k2_ami_2 ) ).
fof(t52_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> A != k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(t53_scmpds_2,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m1_scmpds_2(B)
=> A != B ) ) ).
fof(t54_scmpds_2,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)
& ! [C] :
( m1_scmpds_2(C)
=> k2_scmpds_2(A,C) = k2_scmpds_2(B,C) )
& ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,C) ) )
=> A = B ) ) ) ).
fof(d19_scmpds_2,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( B = k18_scmpds_2(A)
<=> ? [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
& C = A
& B = k15_ami_2(C) ) ) ) ) ).
fof(t55_scmpds_2,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m2_subset_1(B,k5_numbers,k3_ami_2)
=> ( B = A
=> k15_ami_2(B) = k18_scmpds_2(A) ) ) ) ).
fof(t56_scmpds_2,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))
=> ! [C] :
( m1_subset_1(C,k5_scmpds_1)
=> ( C = B
=> ! [D] :
( m1_subset_1(D,k4_card_3(k6_scmpds_1))
=> ( D = A
=> k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A) = k28_scmpds_1(C,D) ) ) ) ) ) ) ).
fof(t57_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(C,B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(C,B),A),C) = B
& ! [D] :
( m1_scmpds_2(D)
=> ( D != C
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(C,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(t58_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(D,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = C
& ! [E] :
( m1_scmpds_2(E)
=> ( E != k3_scmpds_2(k2_scmpds_2(A,D),B)
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) ) ).
fof(t59_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C))
& ! [F] :
( m1_scmpds_2(F)
=> ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(D,E,B,C),A),F) = k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) ).
fof(t60_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(D,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k2_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),C)
& ! [E] :
( m1_scmpds_2(E)
=> ( E != k3_scmpds_2(k2_scmpds_2(A,D),B)
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) ) ).
fof(t61_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k2_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C)))
& ! [F] :
( m1_scmpds_2(F)
=> ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(D,E,B,C),A),F) = k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) ).
fof(t62_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k6_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C)))
& ! [F] :
( m1_scmpds_2(F)
=> ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(D,E,B,C),A),F) = k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) ).
fof(t63_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k3_xcmplx_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C)))
& ! [F] :
( m1_scmpds_2(F)
=> ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(D,E,B,C),A),F) = k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) ).
fof(t64_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(D,E,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& ( k3_scmpds_2(k2_scmpds_2(A,D),B) != k3_scmpds_2(k2_scmpds_2(A,E),C)
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,D),B)) = k5_int_1(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C))) )
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(D,E,B,C),A),k3_scmpds_2(k2_scmpds_2(A,E),C)) = k6_int_1(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,E),C)))
& ! [F] :
( m1_scmpds_2(F)
=> ~ ( F != k3_scmpds_2(k2_scmpds_2(A,D),B)
& F != k3_scmpds_2(k2_scmpds_2(A,E),C)
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(D,E,B,C),A),F) != k2_scmpds_2(A,F) ) ) ) ) ) ) ) ) ).
fof(t65_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(C,C,B,B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(C,C,B,B),A),k3_scmpds_2(k2_scmpds_2(A,C),B)) = k6_int_1(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),B)),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),B)))
& ! [D] :
( m1_scmpds_2(D)
=> ( D != k3_scmpds_2(k2_scmpds_2(A,C),B)
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(C,C,B,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(d20_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( C = k19_scmpds_2(A,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& D = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)
& C = k1_nat_1(k1_int_2(k2_xcmplx_0(k6_xcmplx_0(D,np__2),k3_xcmplx_0(np__2,B))),np__2) ) ) ) ) ) ).
fof(t66_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k19_scmpds_2(A,B)
& ! [C] :
( m1_scmpds_2(C)
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(B),A),C) = k2_scmpds_2(A,C) ) ) ) ) ).
fof(t67_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ( ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)) != np__0
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k19_scmpds_2(A,C) )
& ( k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)) = np__0
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) )
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) ).
fof(t68_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ( ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),np__0)
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k19_scmpds_2(A,C) )
& ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)),np__0)
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) )
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) ).
fof(t69_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ! [E] :
( m1_scmpds_2(E)
=> ( ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)))
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k19_scmpds_2(A,C) )
& ( ~ r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,D),B)))
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(D,B,C),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) )
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(D,B,C),A),E) = k2_scmpds_2(A,E) ) ) ) ) ) ) ).
fof(t70_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( m1_scmpds_2(B)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k1_nat_1(k2_nat_1(np__2,k3_nat_1(k1_int_2(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,B),k27_scmpds_1))),np__2)),np__4)
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(B),A),B) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,B),k26_scmpds_1))
& ! [C] :
( m1_scmpds_2(C)
=> ( B != C
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(B),A),C) = k2_scmpds_2(A,C) ) ) ) ) ) ).
fof(t71_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(C,B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A))
& k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(C,B),A),k3_scmpds_2(k2_scmpds_2(A,C),B)) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)
& ! [D] :
( m1_scmpds_2(D)
=> ( k3_scmpds_2(k2_scmpds_2(A,C),B) != D
=> k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(C,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ).
fof(t72_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k2_ami_2,k4_numbers)
& m2_relset_1(B,k2_ami_2,k4_numbers)
& ! [C] :
( m2_subset_1(C,k5_numbers,k2_ami_2)
=> k8_funct_2(k2_ami_2,k4_numbers,B,C) = A ) ) ) ).
fof(t73_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ? [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
& ! [C] :
( m1_scmpds_2(C)
=> k2_scmpds_2(B,C) = A ) ) ) ).
fof(t74_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_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)))
& k1_funct_1(C,np__0) = B
& ! [D] :
( m1_scmpds_2(D)
=> k2_scmpds_2(C,D) = A ) ) ) ) ).
fof(t75_scmpds_2,axiom,
v3_ami_1(k4_scmpds_2(np__0),k1_tarski(k4_numbers),k1_scmpds_2) ).
fof(t76_scmpds_2,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)))
& k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)) )
& v3_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t77_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ~ v3_ami_1(k6_scmpds_2(B,A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t78_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ~ v3_ami_1(k11_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(t79_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ~ v3_ami_1(k17_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ).
fof(t80_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ~ v3_ami_1(k12_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(t81_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ~ v3_ami_1(k13_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ).
fof(t82_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ~ v3_ami_1(k14_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ).
fof(t83_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ~ v3_ami_1(k15_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ).
fof(t84_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( m1_scmpds_2(D)
=> ~ v3_ami_1(k16_scmpds_2(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ).
fof(t85_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ~ ( A != np__0
& v3_ami_1(k4_scmpds_2(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t86_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ~ v3_ami_1(k8_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(t87_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ~ v3_ami_1(k9_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(t88_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ~ v3_ami_1(k10_scmpds_2(C,A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ).
fof(t89_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> ~ v3_ami_1(k5_scmpds_2(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(t90_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ~ v3_ami_1(k7_scmpds_2(B,A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t91_scmpds_2,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
<=> ~ ( ! [B] :
( v1_int_1(B)
=> A != k4_scmpds_2(B) )
& ! [B] :
( m1_scmpds_2(B)
=> A != k5_scmpds_2(B) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> A != k7_scmpds_2(B,C) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> A != k6_scmpds_2(B,C) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> A != k11_scmpds_2(B,C,D) ) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> A != k8_scmpds_2(B,C,D) ) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> A != k9_scmpds_2(B,C,D) ) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> A != k10_scmpds_2(B,C,D) ) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k12_scmpds_2(B,D,E) ) ) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k13_scmpds_2(B,C,D,E) ) ) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k14_scmpds_2(B,C,D,E) ) ) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k15_scmpds_2(B,C,D,E) ) ) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k16_scmpds_2(B,C,D,E) ) ) ) )
& ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_scmpds_2(C)
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> A != k17_scmpds_2(B,C,D,E) ) ) ) ) ) ) ).
fof(t92_scmpds_2,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))
=> ( v3_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
=> A = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(t93_scmpds_2,axiom,
k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) = k4_scmpds_2(np__0) ).
fof(t94_scmpds_2,axiom,
$true ).
fof(t95_scmpds_2,axiom,
$true ).
fof(t96_scmpds_2,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))
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A),C) = k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C) ) ) ) ).
fof(t97_scmpds_2,axiom,
v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ).
fof(t98_scmpds_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != k15_ami_3(A)
& k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) != k16_ami_3(A) ) ) ).
fof(t99_scmpds_2,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))
=> ( A = k4_scmpds_2(np__0)
=> v3_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) ) ).
fof(dt_m1_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) ).
fof(existence_m1_scmpds_2,axiom,
? [A] : m1_scmpds_2(A) ).
fof(dt_k1_scmpds_2,axiom,
( v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& l1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ) ).
fof(dt_k2_scmpds_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
& m1_scmpds_2(B) )
=> v1_int_1(k2_scmpds_2(A,B)) ) ).
fof(redefinition_k2_scmpds_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
& m1_scmpds_2(B) )
=> k2_scmpds_2(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k3_scmpds_2,axiom,
! [A,B] :
( ( v1_int_1(A)
& v1_int_1(B) )
=> m1_scmpds_2(k3_scmpds_2(A,B)) ) ).
fof(dt_k4_scmpds_2,axiom,
! [A] :
( v1_int_1(A)
=> m2_subset_1(k4_scmpds_2(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)) ) ).
fof(dt_k5_scmpds_2,axiom,
! [A] :
( m1_scmpds_2(A)
=> m2_subset_1(k5_scmpds_2(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)) ) ).
fof(dt_k6_scmpds_2,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> m2_subset_1(k6_scmpds_2(A,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)) ) ).
fof(dt_k7_scmpds_2,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> m2_subset_1(k7_scmpds_2(A,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)) ) ).
fof(dt_k8_scmpds_2,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> m2_subset_1(k8_scmpds_2(A,B,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)) ) ).
fof(dt_k9_scmpds_2,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> m2_subset_1(k9_scmpds_2(A,B,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)) ) ).
fof(dt_k10_scmpds_2,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> m2_subset_1(k10_scmpds_2(A,B,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)) ) ).
fof(dt_k11_scmpds_2,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> m2_subset_1(k11_scmpds_2(A,B,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)) ) ).
fof(dt_k12_scmpds_2,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> m2_subset_1(k12_scmpds_2(A,B,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)) ) ).
fof(dt_k13_scmpds_2,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> m2_subset_1(k13_scmpds_2(A,B,C,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)) ) ).
fof(dt_k14_scmpds_2,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> m2_subset_1(k14_scmpds_2(A,B,C,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)) ) ).
fof(dt_k15_scmpds_2,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> m2_subset_1(k15_scmpds_2(A,B,C,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)) ) ).
fof(dt_k16_scmpds_2,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> m2_subset_1(k16_scmpds_2(A,B,C,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)) ) ).
fof(dt_k17_scmpds_2,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> m2_subset_1(k17_scmpds_2(A,B,C,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)) ) ).
fof(dt_k18_scmpds_2,axiom,
! [A] :
( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> m1_struct_0(k18_scmpds_2(A),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ).
fof(dt_k19_scmpds_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
& v1_int_1(B) )
=> m1_struct_0(k19_scmpds_2(A,B),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ).
%------------------------------------------------------------------------------