SET007 Axioms: SET007+389.ax
%------------------------------------------------------------------------------
% File : SET007+389 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Decomposition of the States of SCM
% 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 : ami_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 121 ( 21 unt; 0 def)
% Number of atoms : 618 ( 102 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 592 ( 95 ~; 4 |; 204 &)
% ( 5 <=>; 284 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-3 aty)
% Number of functors : 77 ( 77 usr; 17 con; 0-4 aty)
% Number of variables : 284 ( 280 !; 4 ?)
% 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_ami_5,axiom,
( ~ v1_xboole_0(k2_ami_2)
& ~ v1_finset_1(k2_ami_2)
& v1_membered(k2_ami_2)
& v2_membered(k2_ami_2)
& v3_membered(k2_ami_2)
& v4_membered(k2_ami_2)
& v5_membered(k2_ami_2) ) ).
fof(fc2_ami_5,axiom,
( ~ v1_xboole_0(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
& ~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(fc3_ami_5,axiom,
! [A] :
( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( v4_ordinal2(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A))
& v1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A))
& v1_int_1(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A))
& v1_xcmplx_0(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)) ) ) ).
fof(rc1_ami_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> ? [C] :
( m1_ami_1(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_ami_5(C,A,B) ) ) ).
fof(rc2_ami_5,axiom,
? [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& v1_relat_1(A)
& v1_funct_1(A)
& v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3) ) ).
fof(t1_ami_5,axiom,
$true ).
fof(t2_ami_5,axiom,
$true ).
fof(t3_ami_5,axiom,
$true ).
fof(t4_ami_5,axiom,
$true ).
fof(t5_ami_5,axiom,
$true ).
fof(t6_ami_5,axiom,
$true ).
fof(t7_ami_5,axiom,
$true ).
fof(t8_ami_5,axiom,
$true ).
fof(t9_ami_5,axiom,
$true ).
fof(t10_ami_5,axiom,
$true ).
fof(t11_ami_5,axiom,
$true ).
fof(t12_ami_5,axiom,
$true ).
fof(t13_ami_5,axiom,
$true ).
fof(t14_ami_5,axiom,
$true ).
fof(t15_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A),B),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B))
& k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A),B),A) = k6_int_1(k2_ami_3(B,A),k2_ami_3(B,A))
& ! [C] :
( m1_ami_3(C)
=> ( C != A
=> k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A),B),C) = k2_ami_3(B,C) ) ) ) ) ) ).
fof(t16_ami_5,axiom,
! [A] :
( r2_hidden(A,k2_ami_2)
=> m1_ami_3(A) ) ).
fof(t17_ami_5,axiom,
$true ).
fof(t18_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k15_ami_3(B) ) ) ).
fof(t19_ami_5,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k16_ami_3(B) ) ) ).
fof(t20_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> A != k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ).
fof(t21_ami_5,axiom,
$true ).
fof(t22_ami_5,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_ami_3(B)
=> A != B ) ) ).
fof(t23_ami_5,axiom,
u1_struct_0(k1_ami_3) = k2_xboole_0(k2_xboole_0(k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)),k2_ami_2),k3_ami_2) ).
fof(t24_ami_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A)) ) ) ) ) ).
fof(t25_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_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)))
=> r2_hidden(k2_ami_1(A,B),k1_relat_1(C)) ) ) ) ).
fof(t26_ami_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B)
& ! [C] :
( m1_ami_3(C)
=> k2_ami_3(A,C) = k2_ami_3(B,C) )
& ! [C] :
( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,C) = k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,B,C) ) )
=> A = B ) ) ) ).
fof(t27_ami_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> r1_tarski(k2_ami_2,k1_relat_1(A)) ) ).
fof(t28_ami_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> r1_tarski(k3_ami_2,k1_relat_1(A)) ) ).
fof(t29_ami_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> k1_relat_1(k7_relat_1(A,k2_ami_2)) = k2_ami_2 ) ).
fof(t30_ami_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> k1_relat_1(k7_relat_1(A,k3_ami_2)) = k3_ami_2 ) ).
fof(t31_ami_5,axiom,
~ v1_finset_1(k2_ami_2) ).
fof(t32_ami_5,axiom,
~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ).
fof(t33_ami_5,axiom,
r1_subset_1(k2_ami_2,k3_ami_2) ).
fof(t34_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_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)))
=> k12_ami_3(A,B,k6_ami_1(A,B,C)) = k7_relat_1(C,k1_struct_0(B,k2_ami_1(A,B))) ) ) ) ).
fof(t35_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> k12_ami_3(A,B,C) = k1_tarski(k1_domain_1(u1_struct_0(B),u2_ami_1(A,B),k2_ami_1(A,B),C)) ) ) ) ).
fof(d1_ami_5,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_subset_1(C,u4_ami_1(A,B))
=> k1_ami_5(A,B,C) = k1_mcart_1(C) ) ) ).
fof(d2_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k2_ami_5(A) = A ) ).
fof(d3_ami_5,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k3_ami_2)
=> k3_ami_5(A) = A ) ).
fof(d4_ami_5,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k2_ami_2)
=> k4_ami_5(A) = A ) ).
fof(t36_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> r1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A),np__8) ) ).
fof(t37_ami_5,axiom,
k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = np__0 ).
fof(t38_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = np__1 ) ) ).
fof(t39_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = np__2 ) ) ).
fof(t40_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = np__3 ) ) ).
fof(t41_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = np__4 ) ) ).
fof(t42_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_ami_3(B)
=> k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = np__5 ) ) ).
fof(t43_ami_5,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = np__6 ) ).
fof(t44_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = np__7 ) ) ).
fof(t45_ami_5,axiom,
! [A] :
( m1_ami_3(A)
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = np__8 ) ) ).
fof(t46_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__0
=> A = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ) ).
fof(t47_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__1
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k3_ami_3(B,C) ) ) ) ) ).
fof(t48_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__2
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k4_ami_3(B,C) ) ) ) ) ).
fof(t49_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__3
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k5_ami_3(B,C) ) ) ) ) ).
fof(t50_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__4
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k6_ami_3(B,C) ) ) ) ) ).
fof(t51_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__5
& ! [B] :
( m1_ami_3(B)
=> ! [C] :
( m1_ami_3(C)
=> A != k7_ami_3(B,C) ) ) ) ) ).
fof(t52_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__6
& ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> A != k8_ami_3(B) ) ) ) ).
fof(t53_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__7
& ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m1_ami_3(C)
=> A != k9_ami_3(B,C) ) ) ) ) ).
fof(t54_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__8
& ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m1_ami_3(C)
=> A != k10_ami_3(B,C) ) ) ) ) ).
fof(t55_ami_5,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k11_ami_2(k2_ami_5(k8_ami_3(A))) = A ) ).
fof(t56_ami_5,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_ami_3(B)
=> ( k12_ami_2(k2_ami_5(k9_ami_3(A,B))) = A
& k13_ami_2(k2_ami_5(k9_ami_3(A,B))) = B ) ) ) ).
fof(t57_ami_5,axiom,
! [A] :
( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_ami_3(B)
=> ( k12_ami_2(k2_ami_5(k10_ami_3(A,B))) = A
& k13_ami_2(k2_ami_5(k10_ami_3(A,B))) = B ) ) ) ).
fof(t58_ami_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( k7_relat_1(A,k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) = k7_relat_1(B,k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3))))
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,A),k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,B),k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) ) ) ) ) ).
fof(t59_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),k3_ami_2) = k7_relat_1(B,k3_ami_2) ) ) ).
fof(t60_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ( ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
& r1_tarski(C,D) )
=> k13_ami_3(A,B,C) = k6_ami_1(A,B,D) ) ) ) ) ) ).
fof(d5_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r2_hidden(D,k1_relat_1(C))
=> k5_ami_5(A,B,C,D) = k1_funct_1(C,D) ) ) ) ) ) ).
fof(t61_ami_5,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C,D] :
( m1_ami_1(D,A,B)
=> ( r1_tarski(C,D)
=> m1_ami_1(C,A,B) ) ) ) ).
fof(d6_ami_5,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_ami_1(C,A,B)
=> k6_ami_5(A,B,C) = k7_relat_1(C,u2_ami_1(A,B)) ) ) ).
fof(d7_ami_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> k7_ami_5(A,B,C) = k7_relat_1(C,k4_xboole_0(u1_struct_0(B),k4_subset_1(u1_struct_0(B),k1_struct_0(B,k2_ami_1(A,B)),u2_ami_1(A,B)))) ) ) ).
fof(d8_ami_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( v1_ami_5(C,A,B)
<=> r1_xboole_0(k1_relat_1(C),k4_subset_1(u1_struct_0(B),k1_struct_0(B,k2_ami_1(A,B)),u2_ami_1(A,B))) ) ) ) ).
fof(t62_ami_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> r1_tarski(k7_ami_5(A,B,C),C) ) ) ).
fof(t63_ami_5,axiom,
! [A,B] :
( l1_ami_1(B,A)
=> ! [C] :
( m1_ami_1(C,A,B)
=> r1_tarski(k6_ami_5(A,B,C),C) ) ) ).
fof(t64_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v7_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ( r1_tarski(C,D)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r1_tarski(k6_ami_5(A,B,C),k11_ami_1(A,B,k10_ami_1(A,B,D),E)) ) ) ) ) ) ) ).
fof(t65_ami_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ~ r2_hidden(k2_ami_1(A,B),k1_relat_1(k7_ami_5(A,B,C))) ) ) ).
fof(t66_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ~ r2_hidden(k2_ami_1(A,B),k1_relat_1(k6_ami_5(A,B,C))) ) ) ) ).
fof(t67_ami_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> r1_xboole_0(k1_struct_0(B,k2_ami_1(A,B)),k1_relat_1(k7_ami_5(A,B,C))) ) ) ).
fof(t68_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> r1_xboole_0(k1_struct_0(B,k2_ami_1(A,B)),k1_relat_1(k6_ami_5(A,B,C))) ) ) ) ).
fof(t69_ami_5,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> r1_tarski(k1_relat_1(k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)),k2_ami_2) ) ).
fof(t70_ami_5,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> r1_tarski(k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)),k3_ami_2) ) ).
fof(t71_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( m1_ami_1(D,A,B)
=> r1_xboole_0(k1_relat_1(k7_ami_5(A,B,C)),k1_relat_1(k6_ami_5(A,B,D))) ) ) ) ) ).
fof(t72_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> k6_ami_5(A,B,C) = C ) ) ) ).
fof(t73_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( r2_hidden(D,k1_relat_1(C))
=> r2_hidden(D,k1_relat_1(k6_ami_5(A,B,C))) ) ) ) ) ) ).
fof(t74_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_ami_5(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( m1_ami_1(D,A,B)
=> ( r1_tarski(C,D)
<=> r1_tarski(C,k7_ami_5(A,B,D)) ) ) ) ) ) ).
fof(t75_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
=> C = k17_ami_1(A,B,k17_ami_1(A,B,k12_ami_3(A,B,k13_ami_3(A,B,C)),k6_ami_5(A,B,C)),k7_ami_5(A,B,C)) ) ) ) ) ).
fof(d9_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
=> ( v2_ami_5(C,A,B)
<=> ! [D] :
( m1_ami_1(D,A,B)
=> ( r2_hidden(D,k1_relat_1(C))
=> ( v1_ami_5(D,A,B)
& ! [E] :
( m1_ami_1(E,A,B)
=> ( E = k1_funct_1(C,D)
=> v1_ami_5(E,A,B) ) ) ) ) ) ) ) ) ) ).
fof(t76_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ~ ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
& v1_ami_3(C,A,B) ) ) ) ) ).
fof(t77_ami_5,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(C,k1_tarski(k4_numbers),k1_ami_3) )
=> k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,B,C)) = k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),C) ) ) ) ).
fof(t78_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
=> r1_tarski(k12_ami_3(A,B,k13_ami_3(A,B,C)),C) ) ) ) ) ).
fof(t79_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_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)))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> k6_ami_1(A,B,k8_ami_5(A,B,C,k12_ami_3(A,B,D))) = D ) ) ) ) ).
fof(t80_ami_5,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [B] :
( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [C] :
( m1_ami_3(C)
=> k2_ami_3(A,C) = k2_ami_3(k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,A,k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,B)),C) ) ) ) ).
fof(t81_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ! [E] :
( m1_struct_0(E,B,u2_ami_1(A,B))
=> k13_ami_1(A,B,C,E) = k13_ami_1(A,B,k8_ami_5(A,B,C,k12_ami_3(A,B,D)),E) ) ) ) ) ) ).
fof(t82_ami_5,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_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)))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
=> ! [E] : m1_subset_1(k1_funct_4(C,k7_relat_1(D,E)),k4_card_3(u5_ami_1(A,B))) ) ) ) ) ).
fof(t83_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ( k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) != k1_xboole_0
=> r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A)) ) ) ).
fof(t84_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A)) ) ).
fof(t85_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A))
=> r2_hidden(k13_ami_3(k1_tarski(k4_numbers),k1_ami_3,A),k1_relat_1(A)) ) ) ).
fof(t86_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( r1_tarski(A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),C)),k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A))) ) ) ) ) ).
fof(t87_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( E = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D))
& E = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D)) ) ) ) ) ) ) ) ) ).
fof(t88_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_ami_3(E)
=> ! [F] :
( m1_ami_3(F)
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
& G = k3_ami_3(E,F)
& r2_hidden(E,k1_relat_1(A)) )
=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F) ) ) ) ) ) ) ) ) ) ).
fof(t89_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_ami_3(E)
=> ! [F] :
( m1_ami_3(F)
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
& G = k4_ami_3(E,F)
& r2_hidden(E,k1_relat_1(A)) )
=> k2_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k2_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ).
fof(t90_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_ami_3(E)
=> ! [F] :
( m1_ami_3(F)
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
& G = k5_ami_3(E,F)
& r2_hidden(E,k1_relat_1(A)) )
=> k6_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k6_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ).
fof(t91_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_ami_3(E)
=> ! [F] :
( m1_ami_3(F)
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
& G = k6_ami_3(E,F)
& r2_hidden(E,k1_relat_1(A)) )
=> k3_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k3_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ).
fof(t92_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_ami_3(E)
=> ! [F] :
( m1_ami_3(F)
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
& G = k7_ami_3(E,F)
& r2_hidden(E,k1_relat_1(A)) )
=> ( E = F
| k5_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k5_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t93_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_ami_3(E)
=> ! [F] :
( m1_ami_3(F)
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
& G = k7_ami_3(E,F)
& r2_hidden(F,k1_relat_1(A)) )
=> ( E = F
| k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t94_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_ami_3(E)
=> ! [F] :
( m1_struct_0(F,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
& G = k9_ami_3(F,E) )
=> ( F = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)))
| ( k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E) = np__0
<=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E) = np__0 ) ) ) ) ) ) ) ) ) ) ) ).
fof(t95_ami_5,axiom,
! [A] :
( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
& ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
& m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
=> ( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_ami_3(E)
=> ! [F] :
( m1_struct_0(F,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ! [G] :
( m2_subset_1(G,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
& G = k10_ami_3(F,E) )
=> ( F = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)))
| ( ~ ( ~ r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),np__0)
& r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),np__0) )
& ~ ( ~ r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),np__0)
& r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),np__0) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t96_ami_5,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = k7_relat_1(A,k2_ami_2) ) ).
fof(t97_ami_5,axiom,
! [A] :
( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
=> ( v1_ami_5(A,k1_tarski(k4_numbers),k1_ami_3)
<=> r1_tarski(k1_relat_1(A),k2_ami_2) ) ) ).
fof(dt_k1_ami_5,axiom,
! [A,B,C] :
( ( l1_ami_1(B,A)
& m1_subset_1(C,u4_ami_1(A,B)) )
=> m1_subset_1(k1_ami_5(A,B,C),u3_ami_1(A,B)) ) ).
fof(dt_k2_ami_5,axiom,
! [A] :
( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
=> m1_subset_1(k2_ami_5(A),k4_ami_2) ) ).
fof(dt_k3_ami_5,axiom,
! [A] :
( m1_subset_1(A,k3_ami_2)
=> m1_struct_0(k3_ami_5(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ).
fof(dt_k4_ami_5,axiom,
! [A] :
( m1_subset_1(A,k2_ami_2)
=> m1_ami_3(k4_ami_5(A)) ) ).
fof(dt_k5_ami_5,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A)
& m1_ami_1(C,A,B)
& m1_subset_1(D,u2_ami_1(A,B)) )
=> m2_subset_1(k5_ami_5(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ).
fof(dt_k6_ami_5,axiom,
! [A,B,C] :
( ( l1_ami_1(B,A)
& m1_ami_1(C,A,B) )
=> ( v1_ami_3(k6_ami_5(A,B,C),A,B)
& m1_ami_1(k6_ami_5(A,B,C),A,B) ) ) ).
fof(dt_k7_ami_5,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_ami_1(B,A)
& m1_ami_1(C,A,B) )
=> m1_ami_1(k7_ami_5(A,B,C),A,B) ) ).
fof(dt_k8_ami_5,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
& m1_ami_1(D,A,B) )
=> m1_subset_1(k8_ami_5(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ).
fof(idempotence_k8_ami_5,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
& m1_ami_1(D,A,B) )
=> k8_ami_5(A,B,C,C) = C ) ).
fof(redefinition_k8_ami_5,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(A)
& ~ v2_ami_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
& m1_ami_1(D,A,B) )
=> k8_ami_5(A,B,C,D) = k1_funct_4(C,D) ) ).
%------------------------------------------------------------------------------