SET007 Axioms: SET007+801.ax
%------------------------------------------------------------------------------
% File : SET007+801 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : A Tree of Execution of a Macroinstruction
% 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 : amistd_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 64 ( 8 unt; 0 def)
% Number of atoms : 503 ( 38 equ)
% Maximal formula atoms : 27 ( 7 avg)
% Number of connectives : 526 ( 87 ~; 1 |; 310 &)
% ( 8 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 53 ( 51 usr; 1 prp; 0-4 aty)
% Number of functors : 55 ( 55 usr; 7 con; 0-5 aty)
% Number of variables : 153 ( 147 !; 6 ?)
% 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_amistd_3,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& m1_relset_1(B,A,k5_numbers) )
=> ( v1_ordinal1(k1_funct_1(B,C))
& v2_ordinal1(k1_funct_1(B,C))
& v3_ordinal1(k1_funct_1(B,C))
& v4_ordinal2(k1_funct_1(B,C))
& v1_card_1(k1_funct_1(B,C))
& v1_xreal_0(k1_funct_1(B,C))
& v1_xcmplx_0(k1_funct_1(B,C)) ) ) ).
fof(fc2_amistd_3,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_xboole_0(A) )
=> ( v1_relat_1(k7_relat_1(A,B))
& v1_ordinal1(k7_relat_1(A,B))
& v2_ordinal1(k7_relat_1(A,B))
& v3_ordinal1(k7_relat_1(A,B))
& v1_xboole_0(k7_relat_1(A,B))
& v4_ordinal2(k7_relat_1(A,B))
& v1_finset_1(k7_relat_1(A,B))
& v1_card_1(k7_relat_1(A,B))
& v1_xreal_0(k7_relat_1(A,B))
& ~ v2_xreal_0(k7_relat_1(A,B))
& ~ v3_xreal_0(k7_relat_1(A,B))
& v1_setfam_1(k7_relat_1(A,B))
& v1_xcmplx_0(k7_relat_1(A,B))
& v1_membered(k7_relat_1(A,B))
& v2_membered(k7_relat_1(A,B))
& v3_membered(k7_relat_1(A,B))
& v4_membered(k7_relat_1(A,B))
& v5_membered(k7_relat_1(A,B)) ) ) ).
fof(fc3_amistd_3,axiom,
! [A,B] :
( ~ v1_finset_1(A)
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& ~ v1_xboole_0(k2_funcop_1(A,B))
& ~ v1_finset_1(k2_funcop_1(A,B))
& v1_setfam_1(k2_funcop_1(A,B)) ) ) ).
fof(rc1_amistd_3,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& ~ v1_finset_1(A)
& v1_setfam_1(A) ) ).
fof(fc4_amistd_3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_finset_1(A) )
=> v1_finset_1(k3_relat_1(A)) ) ).
fof(fc5_amistd_3,axiom,
! [A] :
( ( v1_relat_1(A)
& ~ v1_finset_1(A) )
=> ( ~ v1_xboole_0(k3_relat_1(A))
& ~ v1_finset_1(k3_relat_1(A)) ) ) ).
fof(fc6_amistd_3,axiom,
( v1_relat_1(k1_wellord2(k1_xboole_0))
& v1_ordinal1(k1_wellord2(k1_xboole_0))
& v2_ordinal1(k1_wellord2(k1_xboole_0))
& v3_ordinal1(k1_wellord2(k1_xboole_0))
& v1_xboole_0(k1_wellord2(k1_xboole_0))
& v4_ordinal2(k1_wellord2(k1_xboole_0))
& v1_finset_1(k1_wellord2(k1_xboole_0))
& v1_card_1(k1_wellord2(k1_xboole_0))
& v1_xreal_0(k1_wellord2(k1_xboole_0))
& ~ v2_xreal_0(k1_wellord2(k1_xboole_0))
& ~ v3_xreal_0(k1_wellord2(k1_xboole_0))
& v1_setfam_1(k1_wellord2(k1_xboole_0))
& v1_xcmplx_0(k1_wellord2(k1_xboole_0))
& v1_membered(k1_wellord2(k1_xboole_0))
& v2_membered(k1_wellord2(k1_xboole_0))
& v3_membered(k1_wellord2(k1_xboole_0))
& v4_membered(k1_wellord2(k1_xboole_0))
& v5_membered(k1_wellord2(k1_xboole_0)) ) ).
fof(fc7_amistd_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v1_relat_1(k1_wellord2(A))
& ~ v1_xboole_0(k1_wellord2(A))
& v1_setfam_1(k1_wellord2(A)) ) ) ).
fof(fc8_amistd_3,axiom,
! [A] :
( v1_finset_1(A)
=> ( v1_relat_1(k1_wellord2(A))
& v1_finset_1(k1_wellord2(A))
& v1_setfam_1(k1_wellord2(A)) ) ) ).
fof(fc9_amistd_3,axiom,
! [A] :
( ~ v1_finset_1(A)
=> ( v1_relat_1(k1_wellord2(A))
& ~ v1_xboole_0(k1_wellord2(A))
& ~ v1_finset_1(k1_wellord2(A))
& v1_setfam_1(k1_wellord2(A)) ) ) ).
fof(fc10_amistd_3,axiom,
( v1_relat_1(k2_wellord2(k1_xboole_0))
& v1_ordinal1(k2_wellord2(k1_xboole_0))
& v2_ordinal1(k2_wellord2(k1_xboole_0))
& v3_ordinal1(k2_wellord2(k1_xboole_0))
& v1_xboole_0(k2_wellord2(k1_xboole_0))
& v4_ordinal2(k2_wellord2(k1_xboole_0))
& v1_finset_1(k2_wellord2(k1_xboole_0))
& v1_card_1(k2_wellord2(k1_xboole_0))
& v1_xreal_0(k2_wellord2(k1_xboole_0))
& ~ v2_xreal_0(k2_wellord2(k1_xboole_0))
& ~ v3_xreal_0(k2_wellord2(k1_xboole_0))
& v1_setfam_1(k2_wellord2(k1_xboole_0))
& v1_xcmplx_0(k2_wellord2(k1_xboole_0))
& v1_membered(k2_wellord2(k1_xboole_0))
& v2_membered(k2_wellord2(k1_xboole_0))
& v3_membered(k2_wellord2(k1_xboole_0))
& v4_membered(k2_wellord2(k1_xboole_0))
& v5_membered(k2_wellord2(k1_xboole_0)) ) ).
fof(fc11_amistd_3,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ( v1_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(B))),k1_wellord2(B)),C))
& v2_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(B))),k1_wellord2(B)),C))
& v3_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(B))),k1_wellord2(B)),C)) ) ) ).
fof(fc12_amistd_3,axiom,
! [A,B] :
( v5_membered(A)
=> ( v1_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
& v2_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
& v3_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
& v4_ordinal2(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
& v1_card_1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
& v1_xreal_0(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
& v1_xcmplx_0(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) ) ) ).
fof(fc13_amistd_3,axiom,
( ~ v1_xboole_0(k1_amistd_3)
& v1_trees_1(k1_amistd_3) ) ).
fof(fc14_amistd_3,axiom,
( ~ v1_xboole_0(k1_amistd_3)
& ~ v1_finset_1(k1_amistd_3)
& v1_trees_1(k1_amistd_3) ) ).
fof(fc15_amistd_3,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
=> ( v1_relat_1(k3_amistd_3(A,B,C))
& v1_ordinal1(k3_amistd_3(A,B,C))
& v2_ordinal1(k3_amistd_3(A,B,C))
& v3_ordinal1(k3_amistd_3(A,B,C))
& v1_xboole_0(k3_amistd_3(A,B,C))
& v4_ordinal2(k3_amistd_3(A,B,C))
& v1_finset_1(k3_amistd_3(A,B,C))
& v1_card_1(k3_amistd_3(A,B,C))
& v1_xreal_0(k3_amistd_3(A,B,C))
& ~ v2_xreal_0(k3_amistd_3(A,B,C))
& ~ v3_xreal_0(k3_amistd_3(A,B,C))
& v1_setfam_1(k3_amistd_3(A,B,C))
& v1_xcmplx_0(k3_amistd_3(A,B,C))
& v1_membered(k3_amistd_3(A,B,C))
& v2_membered(k3_amistd_3(A,B,C))
& v3_membered(k3_amistd_3(A,B,C))
& v4_membered(k3_amistd_3(A,B,C))
& v5_membered(k3_amistd_3(A,B,C)) ) ) ).
fof(fc16_amistd_3,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
=> ( ~ v1_xboole_0(k3_amistd_3(A,B,C))
& v1_membered(k3_amistd_3(A,B,C))
& v2_membered(k3_amistd_3(A,B,C))
& v3_membered(k3_amistd_3(A,B,C))
& v4_membered(k3_amistd_3(A,B,C))
& v5_membered(k3_amistd_3(A,B,C)) ) ) ).
fof(fc17_amistd_3,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
=> ( v1_relat_1(k4_amistd_3(A,B,C))
& v1_funct_1(k4_amistd_3(A,B,C))
& v2_funct_1(k4_amistd_3(A,B,C))
& v5_ordinal1(k4_amistd_3(A,B,C))
& v1_setfam_1(k4_amistd_3(A,B,C)) ) ) ).
fof(t1_amistd_3,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( ( k1_relat_1(C) = k1_tarski(A)
& k2_relat_1(C) = k1_tarski(B) )
=> C = k3_cqc_lang(A,B) ) ) ).
fof(t2_amistd_3,axiom,
! [A] : k3_relat_1(k1_tarski(k4_tarski(A,A))) = k1_tarski(A) ).
fof(t3_amistd_3,axiom,
! [A] :
( v1_relat_1(A)
=> ( v1_finset_1(k3_relat_1(A))
=> v1_finset_1(A) ) ) ).
fof(t4_amistd_3,axiom,
! [A] :
( v1_relat_1(A)
=> ( ( v1_finset_1(k1_relat_1(A))
& v1_finset_1(k2_relat_1(A)) )
=> v1_finset_1(A) ) ) ).
fof(t5_amistd_3,axiom,
! [A] : k1_wellord2(k1_tarski(A)) = k1_tarski(k4_tarski(A,A)) ).
fof(t6_amistd_3,axiom,
! [A] : r1_tarski(k1_wellord2(A),k2_zfmisc_1(A,A)) ).
fof(t7_amistd_3,axiom,
! [A] :
( v1_finset_1(k1_wellord2(A))
=> v1_finset_1(A) ) ).
fof(t8_amistd_3,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( ( r4_wellord1(A,B)
& v2_wellord1(A) )
=> v2_wellord1(B) ) ) ) ).
fof(t9_amistd_3,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( ( r4_wellord1(A,B)
& v1_finset_1(A) )
=> v1_finset_1(B) ) ) ) ).
fof(t10_amistd_3,axiom,
! [A,B] : r3_wellord1(k1_tarski(k4_tarski(A,A)),k1_tarski(k4_tarski(B,B)),k3_cqc_lang(A,B)) ).
fof(t11_amistd_3,axiom,
! [A,B] : r4_wellord1(k1_tarski(k4_tarski(A,A)),k1_tarski(k4_tarski(B,B))) ).
fof(t12_amistd_3,axiom,
! [A] :
( v3_ordinal1(A)
=> k2_wellord2(k1_wellord2(A)) = A ) ).
fof(t13_amistd_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( v1_finset_1(B)
=> ( r1_tarski(B,A)
=> k2_wellord2(k1_wellord2(B)) = k4_card_1(B) ) ) ) ).
fof(t14_amistd_3,axiom,
! [A,B] :
( v3_ordinal1(B)
=> ( r1_tarski(k1_tarski(A),B)
=> k2_wellord2(k1_wellord2(k1_tarski(A))) = np__1 ) ) ).
fof(t15_amistd_3,axiom,
! [A,B] :
( v3_ordinal1(B)
=> ( r1_tarski(k1_tarski(A),B)
=> k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(k1_tarski(A)))),k1_wellord2(k1_tarski(A))) = k3_cqc_lang(np__0,A) ) ) ).
fof(t16_amistd_3,axiom,
! [A,B] :
( v4_ordinal2(B)
=> ! [C] :
( v4_ordinal2(C)
=> ( k2_finseq_2(B,A) = k2_finseq_2(C,A)
=> B = C ) ) ) ).
fof(t17_amistd_3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_trees_1(B) )
=> ! [C] :
( m1_trees_1(C,B)
=> r2_hidden(k2_partfun1(k5_numbers,k5_numbers,C,k2_finseq_1(A)),B) ) ) ) ).
fof(t18_amistd_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_trees_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_trees_1(B) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_trees_2(A,C) = k2_trees_2(B,C) )
=> A = B ) ) ) ).
fof(t19_amistd_3,axiom,
r2_wellord2(k5_numbers,k1_amistd_3) ).
fof(t20_amistd_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_trees_2(k1_amistd_3,A) = k1_tarski(k2_finseq_2(A,np__0)) ) ).
fof(t21_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> r2_hidden(k2_amistd_3(A,B,C),k1_relat_1(C)) ) ) ) ).
fof(t22_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& m1_ami_1(C,A,B) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> ( r1_tarski(C,D)
=> r1_amistd_1(A,B,k2_amistd_3(A,B,D),k2_amistd_3(A,B,C)) ) ) ) ) ) ).
fof(t23_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_ami_3(D,A,B)
& m1_ami_1(D,A,B) )
=> ( r2_hidden(C,k1_relat_1(D))
=> r1_amistd_1(A,B,k2_amistd_3(A,B,D),C) ) ) ) ) ) ).
fof(t24_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_ami_3(C,A,B)
& v9_amistd_1(C,A,B)
& m1_ami_1(C,A,B) )
=> k2_amistd_3(A,B,C) = k5_amistd_1(A,B,np__0) ) ) ) ).
fof(t25_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u2_ami_1(A,B)))
=> ( r2_hidden(k7_amistd_1(A,B,C),k3_amistd_3(A,B,D))
<=> r2_hidden(C,D) ) ) ) ) ) ).
fof(t26_amistd_3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u2_ami_1(B,C)))
=> ( D = k1_struct_0(C,k5_amistd_1(B,C,A))
=> k3_amistd_3(B,C,D) = k1_tarski(A) ) ) ) ) ) ).
fof(t27_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
=> r2_wellord2(C,k3_amistd_3(A,B,C)) ) ) ) ).
fof(t28_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
=> r1_ordinal1(k1_card_1(C),k2_wellord2(k1_wellord2(k3_amistd_3(A,B,C)))) ) ) ) ).
fof(t29_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m2_subset_1(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))
=> ( ( v10_ami_1(B,A)
& v3_ami_1(D,A,B) )
=> k3_amistd_3(A,B,k1_amistd_1(A,B,C,D)) = k15_cqc_sim1(k5_numbers,k7_amistd_1(A,B,C)) ) ) ) ) ) ).
fof(t30_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m2_subset_1(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))
=> ( ( v10_ami_1(B,A)
& v5_amistd_1(D,A,B) )
=> k3_amistd_3(A,B,k1_amistd_1(A,B,C,D)) = k15_cqc_sim1(k5_numbers,k7_amistd_1(A,B,k9_amistd_1(A,B,C))) ) ) ) ) ) ).
fof(d4_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
=> ! [D] :
( m1_ordinal1(D,u2_ami_1(A,B))
=> ( D = k4_amistd_3(A,B,C)
<=> ( k1_relat_1(D) = k1_card_1(C)
& ! [E] :
( r2_hidden(E,k1_card_1(C))
=> k1_funct_1(D,E) = k5_amistd_1(A,B,k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(k3_amistd_3(A,B,C)))),k1_wellord2(k3_amistd_3(A,B,C))),E)) ) ) ) ) ) ) ) ).
fof(t31_amistd_3,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u2_ami_1(B,C)))
=> ( D = k1_struct_0(C,k5_amistd_1(B,C,A))
=> k4_amistd_3(B,C,D) = k3_cqc_lang(np__0,k5_amistd_1(B,C,A)) ) ) ) ) ) ).
fof(t32_amistd_3,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v10_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> k5_amistd_3(A,B,k7_amistd_2(A,B)) = k9_trees_2(u2_ami_1(A,B),k1_amistd_3,k5_amistd_1(A,B,np__0)) ) ) ).
fof(dt_k1_amistd_3,axiom,
$true ).
fof(dt_k2_amistd_3,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_ami_1(C,A,B) )
=> m1_struct_0(k2_amistd_3(A,B,C),B,u2_ami_1(A,B)) ) ).
fof(dt_k3_amistd_3,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
=> m1_subset_1(k3_amistd_3(A,B,C),k1_zfmisc_1(k5_numbers)) ) ).
fof(dt_k4_amistd_3,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
=> m1_ordinal1(k4_amistd_3(A,B,C),u2_ami_1(A,B)) ) ).
fof(dt_k5_amistd_3,axiom,
! [A,B,C] :
( ( v1_setfam_1(A)
& ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& v4_amistd_1(B,A)
& l1_ami_1(B,A)
& m1_ami_1(C,A,B) )
=> ( v1_funct_1(k5_amistd_3(A,B,C))
& v3_trees_2(k5_amistd_3(A,B,C))
& m3_trees_2(k5_amistd_3(A,B,C),u2_ami_1(A,B)) ) ) ).
fof(d1_amistd_3,axiom,
k1_amistd_3 = a_0_0_amistd_3 ).
fof(d2_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ( v1_ami_3(C,A,B)
=> ( v1_xboole_0(C)
| ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( D = k2_amistd_3(A,B,C)
<=> ? [E] :
( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(k5_numbers))
& E = a_3_0_amistd_3(A,B,C)
& D = k5_amistd_1(A,B,k10_cqc_sim1(E)) ) ) ) ) ) ) ) ) ).
fof(d3_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
=> k3_amistd_3(A,B,C) = a_3_1_amistd_3(A,B,C) ) ) ) ).
fof(d5_amistd_3,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)
& v4_amistd_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_ami_1(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v3_trees_2(D)
& m3_trees_2(D,u2_ami_1(A,B)) )
=> ( D = k5_amistd_3(A,B,C)
<=> ( k1_funct_1(D,k1_xboole_0) = k2_amistd_3(A,B,C)
& ! [E] :
( m1_trees_1(E,k1_relat_1(D))
=> ( k1_trees_2(k1_relat_1(D),E) = a_5_0_amistd_3(A,B,C,D,E)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k1_card_1(k1_amistd_1(A,B,k3_trees_2(u2_ami_1(A,B),D,E),k5_ami_5(A,B,C,k3_trees_2(u2_ami_1(A,B),D,E)))))
=> k1_funct_1(D,k8_finseq_1(k5_numbers,E,k12_finseq_1(k5_numbers,F))) = k1_funct_1(k4_amistd_3(A,B,k1_amistd_1(A,B,k3_trees_2(u2_ami_1(A,B),D,E),k5_ami_5(A,B,C,k3_trees_2(u2_ami_1(A,B),D,E)))),F) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_0_0_amistd_3,axiom,
! [A] :
( r2_hidden(A,a_0_0_amistd_3)
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k2_finseq_2(B,np__0) ) ) ).
fof(fraenkel_a_3_0_amistd_3,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(B)
& ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B)
& m1_ami_1(D,B,C) )
=> ( r2_hidden(A,a_3_0_amistd_3(B,C,D))
<=> ? [E] :
( m1_struct_0(E,C,u2_ami_1(B,C))
& A = k7_amistd_1(B,C,E)
& r2_hidden(E,k1_relat_1(D)) ) ) ) ).
fof(fraenkel_a_3_1_amistd_3,axiom,
! [A,B,C,D] :
( ( v1_setfam_1(B)
& ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B)
& m1_subset_1(D,k1_zfmisc_1(u2_ami_1(B,C))) )
=> ( r2_hidden(A,a_3_1_amistd_3(B,C,D))
<=> ? [E] :
( m1_struct_0(E,C,u2_ami_1(B,C))
& A = k7_amistd_1(B,C,E)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_5_0_amistd_3,axiom,
! [A,B,C,D,E,F] :
( ( v1_setfam_1(B)
& ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v8_ami_1(C,B)
& v4_amistd_1(C,B)
& l1_ami_1(C,B)
& m1_ami_1(D,B,C)
& v1_funct_1(E)
& v3_trees_2(E)
& m3_trees_2(E,u2_ami_1(B,C))
& m1_trees_1(F,k1_relat_1(E)) )
=> ( r2_hidden(A,a_5_0_amistd_3(B,C,D,E,F))
<=> ? [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
& A = k8_finseq_1(k5_numbers,F,k12_finseq_1(k5_numbers,G))
& r2_hidden(G,k1_card_1(k1_amistd_1(B,C,k3_trees_2(u2_ami_1(B,C),E,F),k5_ami_5(B,C,D,k3_trees_2(u2_ami_1(B,C),E,F))))) ) ) ) ).
%------------------------------------------------------------------------------