SET007 Axioms: SET007+693.ax
%------------------------------------------------------------------------------
% File : SET007+693 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Set of Primitive Recursive Functions
% 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 : comput_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 243 ( 20 unt; 0 def)
% Number of atoms : 1886 ( 149 equ)
% Maximal formula atoms : 40 ( 7 avg)
% Number of connectives : 1801 ( 158 ~; 1 |;1161 &)
% ( 35 <=>; 446 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-5 aty)
% Number of functors : 90 ( 90 usr; 23 con; 0-5 aty)
% Number of variables : 502 ( 460 !; 42 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_fraenkel(A)
& v1_comput_1(A) ) ).
fof(fc1_comput_1,axiom,
! [A] :
( ( v1_fraenkel(A)
& v1_comput_1(A) )
=> ( v1_relat_1(k3_tarski(A))
& v1_funct_1(k3_tarski(A)) ) ) ).
fof(rc2_comput_1,axiom,
! [A,B] :
? [C] :
( m1_rfunct_3(C,A,B)
& ~ v1_xboole_0(C)
& v1_comput_1(C) ) ).
fof(cc1_comput_1,axiom,
! [A,B,C] :
( m1_rfunct_3(C,A,B)
=> ( ~ v1_xboole_0(C)
=> ( ~ v1_xboole_0(C)
& v1_fraenkel(C) ) ) ) ).
fof(rc3_comput_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A) ) ).
fof(fc2_comput_1,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0)
& v1_funct_1(k1_xboole_0)
& v2_funct_1(k1_xboole_0)
& v1_finset_1(k1_xboole_0)
& v1_finseq_1(k1_xboole_0)
& v1_funcop_1(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0)
& v1_funct_7(k1_xboole_0)
& v4_comput_1(k1_xboole_0) ) ).
fof(fc3_comput_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( ~ v1_xboole_0(k2_funcop_1(k1_tarski(A),B))
& v1_relat_1(k2_funcop_1(k1_tarski(A),B))
& v1_funct_1(k2_funcop_1(k1_tarski(A),B))
& v4_comput_1(k2_funcop_1(k1_tarski(A),B)) ) ) ).
fof(rc4_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A) ) ).
fof(fc4_comput_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B) )
=> ( v1_relat_1(k5_relat_1(A,B))
& v1_funct_1(k5_relat_1(A,B))
& v4_comput_1(k5_relat_1(A,B)) ) ) ).
fof(rc5_comput_1,axiom,
! [A,B] :
? [C] :
( m1_relset_1(C,k3_finseq_2(A),B)
& v1_relat_1(C)
& v1_funct_1(C)
& v4_comput_1(C) ) ).
fof(rc6_comput_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ? [C] :
( m1_relset_1(C,k3_finseq_2(A),B)
& ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v4_comput_1(C) ) ) ).
fof(rc7_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_relset_1(B,k3_finseq_2(A),A)
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_unialg_1(B,A)
& v4_comput_1(B) ) ) ).
fof(rc8_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A) ) ).
fof(cc2_comput_1,axiom,
! [A] :
( m1_relset_1(A,k3_finseq_2(k5_numbers),k5_numbers)
=> ( v1_funct_1(A)
=> ( v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A) ) ) ) ).
fof(cc3_comput_1,axiom,
! [A] :
( m1_relset_1(A,k3_finseq_2(k5_numbers),k5_numbers)
=> ( ( v1_funct_1(A)
& v2_unialg_1(A,k5_numbers) )
=> ( v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A) ) ) ) ).
fof(fc5_comput_1,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0)
& v1_funct_1(k1_xboole_0)
& v2_funct_1(k1_xboole_0)
& v1_finset_1(k1_xboole_0)
& v1_finseq_1(k1_xboole_0)
& v1_funcop_1(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0)
& v1_funct_7(k1_xboole_0)
& v4_comput_1(k1_xboole_0)
& v5_comput_1(k1_xboole_0) ) ).
fof(rc9_comput_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v5_comput_1(A) ) ).
fof(rc10_comput_1,axiom,
! [A] :
? [B] :
( m1_finseq_1(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v5_comput_1(B) ) ).
fof(rc11_comput_1,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k3_finseq_2(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v5_comput_1(B) ) ).
fof(rc12_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k5_comput_1(A))
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_unialg_1(B,A)
& v4_comput_1(B) ) ) ).
fof(cc4_comput_1,axiom,
! [A,B] :
( m1_subset_1(B,k5_comput_1(A))
=> ( v1_relat_1(B)
& v1_funct_1(B)
& v4_comput_1(B) ) ) ).
fof(cc5_comput_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k5_comput_1(A))) )
=> ! [C] :
( m1_subset_1(C,B)
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v4_comput_1(C) ) ) ) ).
fof(fc6_comput_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k6_comput_1(A,B))
& v1_relat_1(k6_comput_1(A,B))
& v1_funct_1(k6_comput_1(A,B))
& v7_seqm_3(k6_comput_1(A,B))
& v2_comput_1(k6_comput_1(A,B))
& v3_comput_1(k6_comput_1(A,B))
& v4_comput_1(k6_comput_1(A,B)) ) ) ).
fof(fc7_comput_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k7_comput_1(A,B))
& v1_relat_1(k7_comput_1(A,B))
& v1_funct_1(k7_comput_1(A,B))
& v7_seqm_3(k7_comput_1(A,B))
& v2_comput_1(k7_comput_1(A,B))
& v3_comput_1(k7_comput_1(A,B))
& v4_comput_1(k7_comput_1(A,B)) ) ) ).
fof(fc8_comput_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k8_comput_1(A,B))
& v1_relat_1(k8_comput_1(A,B))
& v1_funct_1(k8_comput_1(A,B))
& v7_seqm_3(k8_comput_1(A,B))
& v2_comput_1(k8_comput_1(A,B))
& v3_comput_1(k8_comput_1(A,B))
& v4_comput_1(k8_comput_1(A,B)) ) ) ).
fof(fc9_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(k5_comput_1(A))
& v1_fraenkel(k5_comput_1(A)) ) ).
fof(fc10_comput_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v5_comput_1(B)
& m1_finseq_1(B,k5_comput_1(A)) )
=> ( v1_relat_1(k6_funct_6(B))
& v1_funct_1(k6_funct_6(B))
& v4_comput_1(k6_funct_6(B)) ) ) ).
fof(fc11_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_comput_1(A)
& v4_comput_1(A) )
=> ( ~ v1_xboole_0(k5_finseq_1(A))
& v1_relat_1(k5_finseq_1(A))
& v1_funct_1(k5_finseq_1(A))
& v1_finset_1(k5_finseq_1(A))
& v1_finseq_1(k5_finseq_1(A))
& v1_funcop_1(k5_finseq_1(A))
& v1_funct_7(k5_finseq_1(A))
& v5_comput_1(k5_finseq_1(A)) ) ) ).
fof(rc13_comput_1,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers)))
& ~ v1_xboole_0(A)
& v1_fraenkel(A)
& v8_comput_1(A) ) ).
fof(fc12_comput_1,axiom,
( ~ v1_xboole_0(k11_comput_1)
& v1_fraenkel(k11_comput_1)
& v8_comput_1(k11_comput_1) ) ).
fof(cc6_comput_1,axiom,
! [A] :
( m1_subset_1(A,k11_comput_1)
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A) ) ) ).
fof(cc7_comput_1,axiom,
! [A] :
( v9_comput_1(A)
=> ( v1_relat_1(A)
& v1_funct_1(A) ) ) ).
fof(cc8_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v9_comput_1(A) )
=> ( v1_relat_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A) ) ) ).
fof(cc9_comput_1,axiom,
! [A] :
( m1_subset_1(A,k11_comput_1)
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A)
& v9_comput_1(A) ) ) ).
fof(rc14_comput_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A)
& v9_comput_1(A) ) ).
fof(rc15_comput_1,axiom,
? [A] :
( m1_subset_1(A,k5_comput_1(k5_numbers))
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A)
& v9_comput_1(A) ) ).
fof(cc10_comput_1,axiom,
! [A] :
( m1_subset_1(A,k11_comput_1)
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_unialg_1(A,k5_numbers)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A)
& v9_comput_1(A) ) ) ).
fof(cc11_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_comput_1(k5_numbers))
=> ( v9_comput_1(A)
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_unialg_1(A,k5_numbers)
& v4_comput_1(A) ) ) ) ).
fof(cc12_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_comput_1(A)
& v9_comput_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_comput_1(A)
& v3_comput_1(A) ) ) ).
fof(rc16_comput_1,axiom,
? [A] :
( m1_subset_1(A,k11_comput_1)
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v2_unialg_1(A,k5_numbers)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v9_comput_1(A) ) ).
fof(cc13_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A)
& v11_comput_1(A) )
=> ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A) ) ) ).
fof(cc14_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A)
& v12_comput_1(A) )
=> ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A) ) ) ).
fof(cc15_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A)
& v13_comput_1(A) )
=> ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A) ) ) ).
fof(fc13_comput_1,axiom,
( ~ v1_xboole_0(k8_comput_1(np__1,np__1))
& v1_relat_1(k8_comput_1(np__1,np__1))
& v1_funct_1(k8_comput_1(np__1,np__1))
& v7_seqm_3(k8_comput_1(np__1,np__1))
& v2_comput_1(k8_comput_1(np__1,np__1))
& v3_comput_1(k8_comput_1(np__1,np__1))
& v4_comput_1(k8_comput_1(np__1,np__1))
& v9_comput_1(k8_comput_1(np__1,np__1)) ) ).
fof(fc14_comput_1,axiom,
( ~ v1_xboole_0(k8_comput_1(np__2,np__1))
& v1_relat_1(k8_comput_1(np__2,np__1))
& v1_funct_1(k8_comput_1(np__2,np__1))
& v7_seqm_3(k8_comput_1(np__2,np__1))
& v2_comput_1(k8_comput_1(np__2,np__1))
& v3_comput_1(k8_comput_1(np__2,np__1))
& v4_comput_1(k8_comput_1(np__2,np__1))
& v9_comput_1(k8_comput_1(np__2,np__1)) ) ).
fof(fc15_comput_1,axiom,
( ~ v1_xboole_0(k8_comput_1(np__2,np__2))
& v1_relat_1(k8_comput_1(np__2,np__2))
& v1_funct_1(k8_comput_1(np__2,np__2))
& v7_seqm_3(k8_comput_1(np__2,np__2))
& v2_comput_1(k8_comput_1(np__2,np__2))
& v3_comput_1(k8_comput_1(np__2,np__2))
& v4_comput_1(k8_comput_1(np__2,np__2))
& v9_comput_1(k8_comput_1(np__2,np__2)) ) ).
fof(fc16_comput_1,axiom,
( ~ v1_xboole_0(k7_comput_1(np__1,np__1))
& v1_relat_1(k7_comput_1(np__1,np__1))
& v1_funct_1(k7_comput_1(np__1,np__1))
& v7_seqm_3(k7_comput_1(np__1,np__1))
& v2_comput_1(k7_comput_1(np__1,np__1))
& v3_comput_1(k7_comput_1(np__1,np__1))
& v4_comput_1(k7_comput_1(np__1,np__1))
& v9_comput_1(k7_comput_1(np__1,np__1)) ) ).
fof(fc17_comput_1,axiom,
( ~ v1_xboole_0(k7_comput_1(np__3,np__3))
& v1_relat_1(k7_comput_1(np__3,np__3))
& v1_funct_1(k7_comput_1(np__3,np__3))
& v7_seqm_3(k7_comput_1(np__3,np__3))
& v2_comput_1(k7_comput_1(np__3,np__3))
& v3_comput_1(k7_comput_1(np__3,np__3))
& v4_comput_1(k7_comput_1(np__3,np__3))
& v9_comput_1(k7_comput_1(np__3,np__3)) ) ).
fof(fc18_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k6_comput_1(np__0,A))
& v1_relat_1(k6_comput_1(np__0,A))
& v1_funct_1(k6_comput_1(np__0,A))
& v7_seqm_3(k6_comput_1(np__0,A))
& v2_comput_1(k6_comput_1(np__0,A))
& v3_comput_1(k6_comput_1(np__0,A))
& v4_comput_1(k6_comput_1(np__0,A))
& v10_comput_1(k6_comput_1(np__0,A)) ) ) ).
fof(fc19_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k6_comput_1(np__1,A))
& v1_relat_1(k6_comput_1(np__1,A))
& v1_funct_1(k6_comput_1(np__1,A))
& v7_seqm_3(k6_comput_1(np__1,A))
& v2_comput_1(k6_comput_1(np__1,A))
& v3_comput_1(k6_comput_1(np__1,A))
& v4_comput_1(k6_comput_1(np__1,A))
& v11_comput_1(k6_comput_1(np__1,A)) ) ) ).
fof(fc20_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k6_comput_1(np__2,A))
& v1_relat_1(k6_comput_1(np__2,A))
& v1_funct_1(k6_comput_1(np__2,A))
& v7_seqm_3(k6_comput_1(np__2,A))
& v2_comput_1(k6_comput_1(np__2,A))
& v3_comput_1(k6_comput_1(np__2,A))
& v4_comput_1(k6_comput_1(np__2,A))
& v12_comput_1(k6_comput_1(np__2,A)) ) ) ).
fof(fc21_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k6_comput_1(np__3,A))
& v1_relat_1(k6_comput_1(np__3,A))
& v1_funct_1(k6_comput_1(np__3,A))
& v7_seqm_3(k6_comput_1(np__3,A))
& v2_comput_1(k6_comput_1(np__3,A))
& v3_comput_1(k6_comput_1(np__3,A))
& v4_comput_1(k6_comput_1(np__3,A))
& v13_comput_1(k6_comput_1(np__3,A)) ) ) ).
fof(fc22_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k8_comput_1(np__1,A))
& v1_relat_1(k8_comput_1(np__1,A))
& v1_funct_1(k8_comput_1(np__1,A))
& v7_seqm_3(k8_comput_1(np__1,A))
& v2_comput_1(k8_comput_1(np__1,A))
& v3_comput_1(k8_comput_1(np__1,A))
& v4_comput_1(k8_comput_1(np__1,A))
& v11_comput_1(k8_comput_1(np__1,A)) ) ) ).
fof(fc23_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k8_comput_1(np__2,A))
& v1_relat_1(k8_comput_1(np__2,A))
& v1_funct_1(k8_comput_1(np__2,A))
& v7_seqm_3(k8_comput_1(np__2,A))
& v2_comput_1(k8_comput_1(np__2,A))
& v3_comput_1(k8_comput_1(np__2,A))
& v4_comput_1(k8_comput_1(np__2,A))
& v12_comput_1(k8_comput_1(np__2,A)) ) ) ).
fof(fc24_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k8_comput_1(np__3,A))
& v1_relat_1(k8_comput_1(np__3,A))
& v1_funct_1(k8_comput_1(np__3,A))
& v7_seqm_3(k8_comput_1(np__3,A))
& v2_comput_1(k8_comput_1(np__3,A))
& v3_comput_1(k8_comput_1(np__3,A))
& v4_comput_1(k8_comput_1(np__3,A))
& v13_comput_1(k8_comput_1(np__3,A)) ) ) ).
fof(fc25_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k7_comput_1(np__1,A))
& v1_relat_1(k7_comput_1(np__1,A))
& v1_funct_1(k7_comput_1(np__1,A))
& v7_seqm_3(k7_comput_1(np__1,A))
& v2_comput_1(k7_comput_1(np__1,A))
& v3_comput_1(k7_comput_1(np__1,A))
& v4_comput_1(k7_comput_1(np__1,A))
& v11_comput_1(k7_comput_1(np__1,A)) ) ) ).
fof(fc26_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k7_comput_1(np__2,A))
& v1_relat_1(k7_comput_1(np__2,A))
& v1_funct_1(k7_comput_1(np__2,A))
& v7_seqm_3(k7_comput_1(np__2,A))
& v2_comput_1(k7_comput_1(np__2,A))
& v3_comput_1(k7_comput_1(np__2,A))
& v4_comput_1(k7_comput_1(np__2,A))
& v12_comput_1(k7_comput_1(np__2,A)) ) ) ).
fof(fc27_comput_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k7_comput_1(np__3,A))
& v1_relat_1(k7_comput_1(np__3,A))
& v1_funct_1(k7_comput_1(np__3,A))
& v7_seqm_3(k7_comput_1(np__3,A))
& v2_comput_1(k7_comput_1(np__3,A))
& v3_comput_1(k7_comput_1(np__3,A))
& v4_comput_1(k7_comput_1(np__3,A))
& v13_comput_1(k7_comput_1(np__3,A)) ) ) ).
fof(fc28_comput_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k6_comput_1(A,B))
& v1_relat_1(k6_comput_1(A,B))
& v1_funct_1(k6_comput_1(A,B))
& v7_seqm_3(k6_comput_1(A,B))
& v2_comput_1(k6_comput_1(A,B))
& v3_comput_1(k6_comput_1(A,B))
& v4_comput_1(k6_comput_1(A,B))
& v9_comput_1(k6_comput_1(A,B)) ) ) ).
fof(rc17_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v9_comput_1(A)
& v10_comput_1(A) ) ).
fof(rc18_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v9_comput_1(A)
& v11_comput_1(A) ) ).
fof(rc19_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v9_comput_1(A)
& v12_comput_1(A) ) ).
fof(rc20_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v9_comput_1(A)
& v13_comput_1(A) ) ).
fof(rc21_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v10_comput_1(A) ) ).
fof(rc22_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v11_comput_1(A) ) ).
fof(rc23_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v12_comput_1(A) ) ).
fof(rc24_comput_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v13_comput_1(A) ) ).
fof(fc29_comput_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v9_comput_1(A)
& v10_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v9_comput_1(B)
& v12_comput_1(B) )
=> ( ~ v1_xboole_0(k10_comput_1(A,B,np__1))
& v1_relat_1(k10_comput_1(A,B,np__1))
& v1_funct_1(k10_comput_1(A,B,np__1))
& v2_unialg_1(k10_comput_1(A,B,np__1),k5_numbers)
& v7_seqm_3(k10_comput_1(A,B,np__1))
& v2_comput_1(k10_comput_1(A,B,np__1))
& v3_comput_1(k10_comput_1(A,B,np__1))
& v4_comput_1(k10_comput_1(A,B,np__1))
& v9_comput_1(k10_comput_1(A,B,np__1))
& v11_comput_1(k10_comput_1(A,B,np__1)) ) ) ).
fof(fc30_comput_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v9_comput_1(A)
& v11_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v9_comput_1(B)
& v13_comput_1(B) )
=> ( ~ v1_xboole_0(k10_comput_1(A,B,np__1))
& v1_relat_1(k10_comput_1(A,B,np__1))
& v1_funct_1(k10_comput_1(A,B,np__1))
& v2_unialg_1(k10_comput_1(A,B,np__1),k5_numbers)
& v7_seqm_3(k10_comput_1(A,B,np__1))
& v2_comput_1(k10_comput_1(A,B,np__1))
& v3_comput_1(k10_comput_1(A,B,np__1))
& v4_comput_1(k10_comput_1(A,B,np__1))
& v9_comput_1(k10_comput_1(A,B,np__1))
& v12_comput_1(k10_comput_1(A,B,np__1)) ) ) ).
fof(fc31_comput_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v9_comput_1(A)
& v11_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v9_comput_1(B)
& v13_comput_1(B) )
=> ( ~ v1_xboole_0(k10_comput_1(A,B,np__2))
& v1_relat_1(k10_comput_1(A,B,np__2))
& v1_funct_1(k10_comput_1(A,B,np__2))
& v2_unialg_1(k10_comput_1(A,B,np__2),k5_numbers)
& v7_seqm_3(k10_comput_1(A,B,np__2))
& v2_comput_1(k10_comput_1(A,B,np__2))
& v3_comput_1(k10_comput_1(A,B,np__2))
& v4_comput_1(k10_comput_1(A,B,np__2))
& v9_comput_1(k10_comput_1(A,B,np__2))
& v12_comput_1(k10_comput_1(A,B,np__2)) ) ) ).
fof(fc32_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A) )
=> ( v1_relat_1(k16_comput_1(A))
& v1_funct_1(k16_comput_1(A))
& v7_seqm_3(k16_comput_1(A))
& v2_comput_1(k16_comput_1(A)) ) ) ).
fof(fc33_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A) )
=> ( v1_relat_1(k16_comput_1(A))
& v1_funct_1(k16_comput_1(A))
& v4_comput_1(k16_comput_1(A)) ) ) ).
fof(fc34_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A)
& v12_comput_1(A) )
=> ( ~ v1_xboole_0(k16_comput_1(A))
& v1_relat_1(k16_comput_1(A))
& v1_funct_1(k16_comput_1(A))
& v7_seqm_3(k16_comput_1(A))
& v2_comput_1(k16_comput_1(A))
& v3_comput_1(k16_comput_1(A))
& v4_comput_1(k16_comput_1(A))
& v13_comput_1(k16_comput_1(A)) ) ) ).
fof(fc35_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A)
& v9_comput_1(A)
& v12_comput_1(A) )
=> ( ~ v1_xboole_0(k16_comput_1(A))
& v1_relat_1(k16_comput_1(A))
& v1_funct_1(k16_comput_1(A))
& v7_seqm_3(k16_comput_1(A))
& v2_comput_1(k16_comput_1(A))
& v3_comput_1(k16_comput_1(A))
& v4_comput_1(k16_comput_1(A))
& v9_comput_1(k16_comput_1(A))
& v13_comput_1(k16_comput_1(A)) ) ) ).
fof(fc36_comput_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v4_comput_1(A)
& v9_comput_1(A)
& v12_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v4_comput_1(B)
& v9_comput_1(B)
& v12_comput_1(B) )
=> ( v1_relat_1(k10_finseq_1(A,B))
& v1_funct_1(k10_finseq_1(A,B))
& v1_finset_1(k10_finseq_1(A,B))
& v1_finseq_1(k10_finseq_1(A,B))
& v1_funcop_1(k10_finseq_1(A,B))
& v5_comput_1(k10_finseq_1(A,B)) ) ) ).
fof(fc37_comput_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v9_comput_1(A)
& v12_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v9_comput_1(B)
& v12_comput_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v9_comput_1(C)
& v12_comput_1(C) )
=> ( v1_relat_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v1_funct_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v7_seqm_3(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v2_comput_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v3_comput_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v4_comput_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v9_comput_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A)) ) ) ).
fof(fc38_comput_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v9_comput_1(A)
& v12_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v9_comput_1(B)
& v12_comput_1(B)
& v1_relat_1(C)
& v1_funct_1(C)
& v9_comput_1(C)
& v12_comput_1(C) )
=> ( ~ v1_xboole_0(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v1_relat_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v1_funct_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v7_seqm_3(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v2_comput_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v3_comput_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v4_comput_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v9_comput_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A))
& v12_comput_1(k5_relat_1(k6_funct_6(k10_finseq_1(B,C)),A)) ) ) ).
fof(fc39_comput_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v9_comput_1(A)
& v11_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v9_comput_1(B) )
=> ( v1_relat_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v1_funct_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v7_seqm_3(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v2_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v3_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v4_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v9_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A)) ) ) ).
fof(fc40_comput_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v9_comput_1(A)
& v11_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v9_comput_1(B)
& v12_comput_1(B) )
=> ( ~ v1_xboole_0(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v1_relat_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v1_funct_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v7_seqm_3(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v2_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v3_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v4_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v9_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A))
& v12_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(B)),A)) ) ) ).
fof(t1_comput_1,axiom,
$true ).
fof(t2_comput_1,axiom,
$true ).
fof(t3_comput_1,axiom,
! [A,B,C] :
( k2_funct_7(k10_finseq_1(A,B),np__1,C) = k10_finseq_1(C,B)
& k2_funct_7(k10_finseq_1(A,B),np__2,C) = k10_finseq_1(A,C) ) ).
fof(t4_comput_1,axiom,
$true ).
fof(t5_comput_1,axiom,
! [A,B,C,D,E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( k2_funct_7(E,A,B) = k2_funct_7(F,A,C)
=> k2_funct_7(E,A,D) = k2_funct_7(F,A,D) ) ) ) ).
fof(t6_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> k2_finseq_3(A,k2_funct_7(C,A,B)) = k2_finseq_3(A,C) ) ) ).
fof(t7_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ( k2_funct_7(C,A,B) = k2_funct_7(D,A,B)
=> k2_finseq_3(A,C) = k2_finseq_3(A,D) ) ) ) ) ).
fof(t8_comput_1,axiom,
! [A] : k4_finseq_2(np__0,A) = k1_tarski(k1_xboole_0) ).
fof(t9_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( A != np__0
=> k4_finseq_2(A,k1_xboole_0) = k1_xboole_0 ) ) ).
fof(t10_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( r2_hidden(k1_xboole_0,k2_relat_1(A))
=> k6_funct_6(A) = k1_xboole_0 ) ) ).
fof(t11_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( k2_relat_1(B) = A
=> k2_relat_1(k6_funct_6(k9_finseq_1(B))) = k4_finseq_2(np__1,A) ) ) ) ).
fof(t12_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_nat_1(B,np__1)) )
=> ! [D] :
( m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(B,np__1),C))
=> r2_hidden(k2_finseq_3(A,D),k4_finseq_2(B,C)) ) ) ) ) ) ).
fof(t13_comput_1,axiom,
! [A,B] :
( m1_finseq_2(B,A)
=> r1_tarski(B,k3_finseq_2(A)) ) ).
fof(d1_comput_1,axiom,
! [A] :
( v1_comput_1(A)
<=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> r1_partfun1(B,C) ) ) ) ) ).
fof(t14_comput_1,axiom,
! [A] :
( ( v1_fraenkel(A)
& v1_comput_1(A) )
<=> ( v1_relat_1(k3_tarski(A))
& v1_funct_1(k3_tarski(A)) ) ) ).
fof(t16_comput_1,axiom,
! [A] :
( ( v1_fraenkel(A)
& v1_comput_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(B,A)
=> ( r1_tarski(k1_relat_1(B),k1_relat_1(k3_tarski(A)))
& ! [C] :
( r2_hidden(C,k1_relat_1(B))
=> k1_funct_1(k3_tarski(A),C) = k1_funct_1(B,C) ) ) ) ) ) ).
fof(t18_comput_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(C)
& v1_comput_1(C)
& m1_rfunct_3(C,A,B) )
=> ( v1_funct_1(k3_tarski(C))
& m2_relset_1(k3_tarski(C),A,B) ) ) ).
fof(d2_comput_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( v2_comput_1(A)
<=> r1_tarski(k1_relat_1(A),k3_finseq_2(k5_numbers)) ) ) ).
fof(d3_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_comput_1(A) )
=> ( v3_comput_1(A)
<=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ( ( k3_finseq_1(B) = k3_finseq_1(C)
& r2_hidden(B,k1_relat_1(A)) )
=> r2_hidden(C,k1_relat_1(A)) ) ) ) ) ) ).
fof(d4_comput_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( v4_comput_1(A)
<=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A)) )
=> k3_finseq_1(B) = k3_finseq_1(C) ) ) ) ) ) ).
fof(t19_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(k1_relat_1(C),k4_finseq_2(A,B))
=> v4_comput_1(C) ) ) ) ) ).
fof(t20_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A) )
=> ( v1_funct_1(A)
& v2_unialg_1(A,k5_numbers)
& m2_relset_1(A,k3_finseq_2(k5_numbers),k5_numbers) ) ) ).
fof(d5_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v4_comput_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( ? [C] :
( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C)
& r2_hidden(C,k1_relat_1(A)) )
=> ( B = k3_comput_1(A)
<=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( r2_hidden(C,k1_relat_1(A))
=> B = k3_finseq_1(C) ) ) ) )
& ( ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ~ r2_hidden(C,k1_relat_1(A)) )
=> ( B = k3_comput_1(A)
<=> B = np__0 ) ) ) ) ) ).
fof(t21_comput_1,axiom,
k3_comput_1(k1_xboole_0) = np__0 ).
fof(t22_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v4_comput_1(A) )
=> ( k1_relat_1(A) = k1_tarski(k1_xboole_0)
=> k3_comput_1(A) = np__0 ) ) ).
fof(t23_comput_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v4_comput_1(C)
& m2_relset_1(C,k3_finseq_2(A),B) )
=> r1_tarski(k4_relset_1(k3_finseq_2(A),B,C),k4_finseq_2(k3_comput_1(C),A)) ) ).
fof(t24_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_comput_1(A)
& v4_comput_1(A) )
=> r1_tarski(k1_relat_1(A),k4_finseq_2(k3_comput_1(A),k5_numbers)) ) ).
fof(t25_comput_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v4_comput_1(B)
& m2_relset_1(B,k3_finseq_2(A),A) )
=> ( ( v2_unialg_1(B,A)
& ~ v1_xboole_0(B) )
<=> k4_relset_1(k3_finseq_2(A),A,B) = k4_finseq_2(k3_comput_1(B),A) ) ) ).
fof(t26_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A) )
=> ( ( v3_comput_1(A)
& ~ v1_xboole_0(A) )
<=> k1_relat_1(A) = k4_finseq_2(k3_comput_1(A),k5_numbers) ) ) ).
fof(t27_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(B)
& v4_comput_1(B)
& m2_relset_1(B,k3_finseq_2(A),A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_tarski(k4_relset_1(k3_finseq_2(A),A,B),k4_finseq_2(C,A))
=> k3_comput_1(B) = C ) ) ) ) ).
fof(t28_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v4_comput_1(B)
& m2_relset_1(B,k3_finseq_2(A),A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k4_relset_1(k3_finseq_2(A),A,B) = k4_finseq_2(C,A)
=> k3_comput_1(B) = C ) ) ) ) ).
fof(d6_comput_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( v5_comput_1(A)
<=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(B,k2_relat_1(A))
& r2_hidden(C,k2_relat_1(A)) )
=> ( ~ ( v1_xboole_0(B)
& ~ v1_xboole_0(C)
& k1_relat_1(C) != k1_tarski(k1_xboole_0) )
& ~ ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ~ ( r1_tarski(k1_relat_1(B),k4_finseq_2(D,E))
& r1_tarski(k1_relat_1(C),k4_finseq_2(D,E)) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v5_comput_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( ? [C] :
( v1_relat_1(C)
& v1_funct_1(C)
& v4_comput_1(C)
& r2_hidden(C,k2_relat_1(A)) )
=> ( B = k4_comput_1(A)
<=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v4_comput_1(C) )
=> ( r2_hidden(C,k2_relat_1(A))
=> B = k3_comput_1(C) ) ) ) )
& ( ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v4_comput_1(C) )
=> ~ r2_hidden(C,k2_relat_1(A)) )
=> ( B = k4_comput_1(A)
<=> B = np__0 ) ) ) ) ) ).
fof(t29_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v5_comput_1(A) )
=> ( k3_finseq_1(A) = np__0
=> k4_comput_1(A) = np__0 ) ) ).
fof(t30_comput_1,axiom,
! [A] : r2_hidden(k1_xboole_0,k5_comput_1(A)) ).
fof(t31_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A) )
=> m2_rfunct_3(A,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) ) ).
fof(t32_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A) )
=> ( v2_unialg_1(A,k5_numbers)
& m2_rfunct_3(A,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) ) ) ).
fof(t33_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( v1_relat_1(B)
=> ( ( r1_tarski(k2_relat_1(B),k5_comput_1(A))
& ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v4_comput_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v4_comput_1(D) )
=> ( ( r2_hidden(C,k2_relat_1(B))
& r2_hidden(D,k2_relat_1(B)) )
=> k3_comput_1(C) = k3_comput_1(D) ) ) ) )
=> v5_comput_1(B) ) ) ) ).
fof(d9_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k6_comput_1(A,B) = k2_pre_circ(k4_finseq_2(A,k5_numbers),B) ) ) ).
fof(t34_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k6_comput_1(A,B),k5_comput_1(k5_numbers)) ) ) ).
fof(t35_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k3_comput_1(k6_comput_1(A,B)) = A ) ) ).
fof(t36_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k5_numbers,k4_finseq_2(A,k5_numbers))
=> k1_funct_1(k6_comput_1(A,B),C) = B ) ) ) ).
fof(d10_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ( C = k7_comput_1(A,B)
<=> ( k1_relat_1(C) = k4_finseq_2(A,k5_numbers)
& ! [D] :
( m2_finseq_2(D,k5_numbers,k4_finseq_2(A,k5_numbers))
=> k1_funct_1(C,D) = k1_nat_1(k4_finseq_4(k5_numbers,k5_numbers,D,B),np__1) ) ) ) ) ) ) ).
fof(t37_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k7_comput_1(A,B),k5_comput_1(k5_numbers)) ) ) ).
fof(t38_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k3_comput_1(k7_comput_1(A,B)) = A ) ) ).
fof(d11_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k8_comput_1(A,B) = k3_pralg_3(k2_finseq_2(A,k5_numbers),B) ) ) ).
fof(t39_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k8_comput_1(A,B),k5_comput_1(k5_numbers)) ) ) ).
fof(t40_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k1_relat_1(k8_comput_1(A,B)) = k4_finseq_2(A,k5_numbers)
& ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,A) )
=> k2_relat_1(k8_comput_1(A,B)) = k5_numbers ) ) ) ) ).
fof(t41_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k3_comput_1(k8_comput_1(A,B)) = A ) ) ).
fof(t42_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k5_numbers,k4_finseq_2(A,k5_numbers))
=> k1_funct_1(k8_comput_1(A,B),C) = k2_comput_1(A,C,B) ) ) ) ).
fof(t43_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,k5_comput_1(C))
& m2_relset_1(D,B,k5_comput_1(C)) )
=> ~ ( v1_comput_1(k2_relat_1(D))
& ! [E] :
( m1_subset_1(E,B)
=> r1_tarski(k1_relat_1(k8_funct_2(B,k5_comput_1(C),D,E)),k4_finseq_2(A,C)) )
& ! [E] :
( m2_rfunct_3(E,k3_finseq_2(C),C,k5_comput_1(C))
=> ~ ( E = k3_card_3(D)
& r1_tarski(k4_relset_1(k3_finseq_2(C),C,E),k4_finseq_2(A,C)) ) ) ) ) ) ) ) ).
fof(t44_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k5_comput_1(A))
& m2_relset_1(B,k5_numbers,k5_comput_1(A)) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_tarski(k8_funct_2(k5_numbers,k5_comput_1(A),B,C),k8_funct_2(k5_numbers,k5_comput_1(A),B,k1_nat_1(C,np__1))) )
=> r2_hidden(k3_card_3(B),k5_comput_1(A)) ) ) ) ).
fof(t45_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v5_comput_1(B)
& m2_finseq_1(B,k5_comput_1(A)) )
=> r1_tarski(k1_relat_1(k6_funct_6(B)),k4_finseq_2(k4_comput_1(B),A)) ) ) ).
fof(t46_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_rfunct_3(B,k3_finseq_2(A),A,k5_comput_1(A))
=> ! [C] :
( ( v5_comput_1(C)
& m2_finseq_1(C,k5_comput_1(A)) )
=> ( r1_tarski(k1_relat_1(k5_relat_1(k6_funct_6(C),B)),k4_finseq_2(k4_comput_1(C),A))
& r1_tarski(k2_relat_1(k5_relat_1(k6_funct_6(C),B)),A)
& r2_hidden(k5_relat_1(k6_funct_6(C),B),k5_comput_1(A)) ) ) ) ) ).
fof(t47_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A) )
=> k4_comput_1(k9_finseq_1(A)) = k3_comput_1(A) ) ).
fof(t48_comput_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_rfunct_3(A,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_rfunct_3(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) )
=> ! [C] :
( ( v5_comput_1(C)
& m2_finseq_1(C,k5_comput_1(k5_numbers)) )
=> ( B = k5_relat_1(k6_funct_6(C),A)
=> k3_comput_1(B) = k4_comput_1(C) ) ) ) ) ).
fof(t49_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_unialg_1(B,A)
& m2_rfunct_3(B,k3_finseq_2(A),A,k5_comput_1(A)) )
=> ! [C] :
( ( v5_comput_1(C)
& m2_finseq_1(C,k5_comput_1(A)) )
=> ( ( k3_comput_1(B) = k3_finseq_1(C)
& ! [D] :
( m2_rfunct_3(D,k3_finseq_2(A),A,k5_comput_1(A))
=> ( r2_hidden(D,k2_relat_1(C))
=> ( v2_unialg_1(D,A)
& ~ v1_xboole_0(D) ) ) ) )
=> ( v1_xboole_0(C)
| ( ~ v1_xboole_0(k5_relat_1(k6_funct_6(C),B))
& v2_unialg_1(k5_relat_1(k6_funct_6(C),B),A)
& m2_rfunct_3(k5_relat_1(k6_funct_6(C),B),k3_finseq_2(A),A,k5_comput_1(A))
& k1_relat_1(k5_relat_1(k6_funct_6(C),B)) = k4_finseq_2(k4_comput_1(C),A) ) ) ) ) ) ) ).
fof(t50_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_unialg_1(B,A)
& m2_rfunct_3(B,k3_finseq_2(A),A,k5_comput_1(A)) )
=> ! [C] :
( ( v5_comput_1(C)
& m2_finseq_1(C,k5_comput_1(A)) )
=> ( ( k3_comput_1(B) = k3_finseq_1(C)
& ! [D] :
( m2_rfunct_3(D,k3_finseq_2(A),A,k5_comput_1(A))
=> ( r2_hidden(D,k2_relat_1(C))
=> v2_unialg_1(D,A) ) ) )
=> ( v2_unialg_1(k5_relat_1(k6_funct_6(C),B),A)
& m2_rfunct_3(k5_relat_1(k6_funct_6(C),B),k3_finseq_2(A),A,k5_comput_1(A)) ) ) ) ) ) ).
fof(t51_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_unialg_1(B,A)
& m2_rfunct_3(B,k3_finseq_2(A),A,k5_comput_1(A)) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_unialg_1(C,A)
& m2_rfunct_3(C,k3_finseq_2(A),A,k5_comput_1(A)) )
=> ( ( k3_comput_1(B) = np__0
& k3_comput_1(C) = np__0
& k1_funct_1(B,k1_xboole_0) = k1_funct_1(C,k1_xboole_0) )
=> B = C ) ) ) ) ).
fof(t52_comput_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v3_comput_1(A)
& v4_comput_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v3_comput_1(B)
& v4_comput_1(B) )
=> ( ( k3_comput_1(A) = np__0
& k3_comput_1(B) = np__0
& k1_funct_1(A,k1_xboole_0) = k1_funct_1(B,k1_xboole_0) )
=> A = B ) ) ) ).
fof(d12_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_comput_1(A,B,C,D)
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_tarski(k1_relat_1(A),k4_finseq_2(E,k5_numbers))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& k1_nat_1(k3_comput_1(B),np__1) = E
& k1_nat_1(E,np__1) = k3_comput_1(C)
& ! [F] :
( m2_finseq_1(F,k5_numbers)
=> ( k3_finseq_1(F) = E
=> ( ( r2_hidden(k3_funct_7(k5_numbers,F,D,np__0),k1_relat_1(A))
=> r2_hidden(k2_finseq_3(D,F),k1_relat_1(B)) )
& ( r2_hidden(k2_finseq_3(D,F),k1_relat_1(B))
=> r2_hidden(k3_funct_7(k5_numbers,F,D,np__0),k1_relat_1(A)) )
& ( r2_hidden(k3_funct_7(k5_numbers,F,D,np__0),k1_relat_1(A))
=> k1_funct_1(A,k3_funct_7(k5_numbers,F,D,np__0)) = k1_funct_1(B,k2_finseq_3(D,F)) )
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k3_funct_7(k5_numbers,F,D,k1_nat_1(G,np__1)),k1_relat_1(A))
=> ( r2_hidden(k3_funct_7(k5_numbers,F,D,G),k1_relat_1(A))
& r2_hidden(k7_finseq_1(k3_funct_7(k5_numbers,F,D,G),k9_finseq_1(k1_funct_1(A,k3_funct_7(k5_numbers,F,D,G)))),k1_relat_1(C)) ) )
& ( ( r2_hidden(k3_funct_7(k5_numbers,F,D,G),k1_relat_1(A))
& r2_hidden(k7_finseq_1(k3_funct_7(k5_numbers,F,D,G),k9_finseq_1(k1_funct_1(A,k3_funct_7(k5_numbers,F,D,G)))),k1_relat_1(C)) )
=> r2_hidden(k3_funct_7(k5_numbers,F,D,k1_nat_1(G,np__1)),k1_relat_1(A)) )
& ( r2_hidden(k3_funct_7(k5_numbers,F,D,k1_nat_1(G,np__1)),k1_relat_1(A))
=> k1_funct_1(A,k3_funct_7(k5_numbers,F,D,k1_nat_1(G,np__1))) = k1_funct_1(C,k7_finseq_1(k3_funct_7(k5_numbers,F,D,G),k9_finseq_1(k1_funct_1(A,k3_funct_7(k5_numbers,F,D,G))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d13_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ! [E] :
( m2_rfunct_3(E,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ( E = k9_comput_1(A,B,C,D)
<=> ? [F] :
( v1_funct_1(F)
& v1_funct_2(F,k5_numbers,k5_comput_1(k5_numbers))
& m2_relset_1(F,k5_numbers,k5_comput_1(k5_numbers))
& E = k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,k4_finseq_4(k5_numbers,k5_numbers,D,C))
& ( ( r2_hidden(C,k4_finseq_1(D))
& r2_hidden(k2_finseq_3(C,D),k1_relat_1(A)) )
=> k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,np__0) = k2_pre_circ(k1_tarski(k3_funct_7(k5_numbers,D,C,np__0)),k1_funct_1(A,k2_finseq_3(C,D))) )
& ( ~ ( r2_hidden(C,k4_finseq_1(D))
& r2_hidden(k2_finseq_3(C,D),k1_relat_1(A)) )
=> k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,np__0) = k1_xboole_0 )
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( ( r2_hidden(C,k4_finseq_1(D))
& r2_hidden(k3_funct_7(k5_numbers,D,C,G),k1_relat_1(k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,G)))
& r2_hidden(k7_finseq_1(k3_funct_7(k5_numbers,D,C,G),k9_finseq_1(k1_funct_1(k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,G),k3_funct_7(k5_numbers,D,C,G)))),k1_relat_1(B)) )
=> k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,k1_nat_1(G,np__1)) = k1_funct_4(k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,G),k2_pre_circ(k1_tarski(k3_funct_7(k5_numbers,D,C,k1_nat_1(G,np__1))),k1_funct_1(B,k7_finseq_1(k3_funct_7(k5_numbers,D,C,G),k9_finseq_1(k1_funct_1(k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,G),k3_funct_7(k5_numbers,D,C,G))))))) )
& ( ~ ( r2_hidden(C,k4_finseq_1(D))
& r2_hidden(k3_funct_7(k5_numbers,D,C,G),k1_relat_1(k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,G)))
& r2_hidden(k7_finseq_1(k3_funct_7(k5_numbers,D,C,G),k9_finseq_1(k1_funct_1(k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,G),k3_funct_7(k5_numbers,D,C,G)))),k1_relat_1(B)) )
=> k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,k1_nat_1(G,np__1)) = k8_funct_2(k5_numbers,k5_comput_1(k5_numbers),F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t53_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ! [E] :
( m2_finseq_1(E,k5_numbers)
=> ~ ( r2_hidden(E,k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k9_comput_1(B,C,A,D)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> E != k3_funct_7(k5_numbers,D,A,F) ) ) ) ) ) ) ) ).
fof(t54_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ~ r2_hidden(A,k4_finseq_1(D))
=> k9_comput_1(B,C,A,D) = k1_xboole_0 ) ) ) ) ) ).
fof(t55_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ! [E] :
( m2_finseq_1(E,k5_numbers)
=> r1_partfun1(k9_comput_1(B,C,A,D),k9_comput_1(B,C,A,E)) ) ) ) ) ) ).
fof(t56_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> r1_tarski(k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k9_comput_1(B,C,A,D)),k4_finseq_2(k1_nat_1(np__1,k3_comput_1(B)),k5_numbers)) ) ) ) ) ).
fof(t57_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( v1_xboole_0(B)
=> v1_xboole_0(k9_comput_1(B,C,A,D)) ) ) ) ) ) ).
fof(t58_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_finseq_2(D,k5_numbers,k4_finseq_2(k1_nat_1(k3_comput_1(B),np__1),k5_numbers))
=> ( ( v3_comput_1(B)
& v3_comput_1(C)
& k1_nat_1(k3_comput_1(B),np__2) = k3_comput_1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_nat_1(np__1,k3_comput_1(B))) )
=> r2_hidden(D,k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k9_comput_1(B,C,A,D))) ) ) ) ) ) ).
fof(d14_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_rfunct_3(D,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ( D = k10_comput_1(A,B,C)
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_2(k1_nat_1(k3_comput_1(A),np__1),k5_numbers),k5_comput_1(k5_numbers))
& m2_relset_1(E,k4_finseq_2(k1_nat_1(k3_comput_1(A),np__1),k5_numbers),k5_comput_1(k5_numbers))
& D = k3_card_3(E)
& ! [F] :
( m2_finseq_2(F,k5_numbers,k4_finseq_2(k1_nat_1(k3_comput_1(A),np__1),k5_numbers))
=> k8_funct_2(k4_finseq_2(k1_nat_1(k3_comput_1(A),np__1),k5_numbers),k5_comput_1(k5_numbers),E,F) = k9_comput_1(A,B,C,F) ) ) ) ) ) ) ) ).
fof(t59_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ( v1_xboole_0(B)
=> v1_xboole_0(k10_comput_1(B,C,A)) ) ) ) ) ).
fof(t60_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> r1_tarski(k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k10_comput_1(B,C,A)),k4_finseq_2(k1_nat_1(k3_comput_1(B),np__1),k5_numbers)) ) ) ) ).
fof(t61_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ( ( v3_comput_1(B)
& v3_comput_1(C)
& k1_nat_1(k3_comput_1(B),np__2) = k3_comput_1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_nat_1(np__1,k3_comput_1(B))) )
=> ( k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k10_comput_1(B,C,A)) = k4_finseq_2(k1_nat_1(k3_comput_1(B),np__1),k5_numbers)
& k3_comput_1(k10_comput_1(B,C,A)) = k1_nat_1(k3_comput_1(B),np__1) ) ) ) ) ) ).
fof(t62_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_finseq_2(D,k5_numbers,k4_finseq_2(k1_nat_1(k3_comput_1(B),np__1),k5_numbers))
=> ( r2_hidden(A,k4_finseq_1(D))
=> ( r2_hidden(k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(B),np__1),D,A,np__0),k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k10_comput_1(B,C,A)))
<=> r2_hidden(k2_finseq_3(A,D),k1_relat_1(B)) ) ) ) ) ) ) ).
fof(t63_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_finseq_2(D,k5_numbers,k4_finseq_2(k1_nat_1(k3_comput_1(B),np__1),k5_numbers))
=> ( ( r2_hidden(A,k4_finseq_1(D))
& r2_hidden(k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(B),np__1),D,A,np__0),k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k10_comput_1(B,C,A))) )
=> k1_funct_1(k10_comput_1(B,C,A),k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(B),np__1),D,A,np__0)) = k1_funct_1(B,k2_finseq_3(A,D)) ) ) ) ) ) ).
fof(t64_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_finseq_2(D,k5_numbers,k4_finseq_2(k1_nat_1(k3_comput_1(B),np__1),k5_numbers))
=> ( ( r2_hidden(A,k4_finseq_1(D))
& v3_comput_1(B) )
=> k1_funct_1(k10_comput_1(B,C,A),k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(B),np__1),D,A,np__0)) = k1_funct_1(B,k2_finseq_3(A,D)) ) ) ) ) ) ).
fof(t65_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_relat_1(D)
& v1_funct_1(D)
& v7_seqm_3(D)
& v2_comput_1(D)
& v4_comput_1(D) )
=> ! [E] :
( m2_finseq_2(E,k5_numbers,k4_finseq_2(k1_nat_1(k3_comput_1(C),np__1),k5_numbers))
=> ( r2_hidden(A,k4_finseq_1(E))
=> ( r2_hidden(k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,k1_nat_1(B,np__1)),k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k10_comput_1(C,D,A)))
<=> ( r2_hidden(k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,B),k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k10_comput_1(C,D,A)))
& r2_hidden(k7_finseq_1(k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,B),k9_finseq_1(k1_funct_1(k10_comput_1(C,D,A),k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,B)))),k1_relat_1(D)) ) ) ) ) ) ) ) ) ).
fof(t66_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_relat_1(D)
& v1_funct_1(D)
& v7_seqm_3(D)
& v2_comput_1(D)
& v4_comput_1(D) )
=> ! [E] :
( m2_finseq_2(E,k5_numbers,k4_finseq_2(k1_nat_1(k3_comput_1(C),np__1),k5_numbers))
=> ( ( r2_hidden(A,k4_finseq_1(E))
& r2_hidden(k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,k1_nat_1(B,np__1)),k4_relset_1(k3_finseq_2(k5_numbers),k5_numbers,k10_comput_1(C,D,A))) )
=> k1_funct_1(k10_comput_1(C,D,A),k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,k1_nat_1(B,np__1))) = k1_funct_1(D,k7_finseq_1(k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,B),k9_finseq_1(k1_funct_1(k10_comput_1(C,D,A),k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,B))))) ) ) ) ) ) ) ).
fof(t67_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_relat_1(D)
& v1_funct_1(D)
& v7_seqm_3(D)
& v2_comput_1(D)
& v4_comput_1(D) )
=> ! [E] :
( m2_finseq_2(E,k5_numbers,k4_finseq_2(k1_nat_1(k3_comput_1(C),np__1),k5_numbers))
=> ( ( v3_comput_1(C)
& v3_comput_1(D)
& k1_nat_1(k3_comput_1(C),np__2) = k3_comput_1(D)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_nat_1(np__1,k3_comput_1(C))) )
=> k1_funct_1(k10_comput_1(C,D,A),k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,k1_nat_1(B,np__1))) = k1_funct_1(D,k7_finseq_1(k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,B),k9_finseq_1(k1_funct_1(k10_comput_1(C,D,A),k1_comput_1(k5_numbers,k1_nat_1(k3_comput_1(C),np__1),E,A,B))))) ) ) ) ) ) ) ).
fof(t68_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ( ( k1_nat_1(k3_comput_1(B),np__2) = k3_comput_1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_nat_1(k3_comput_1(B),np__1)) )
=> r1_comput_1(k10_comput_1(B,C,A),B,C,A) ) ) ) ) ).
fof(t69_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_nat_1(k3_comput_1(B),np__1)) )
=> ! [D] :
( m2_rfunct_3(D,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ( r1_comput_1(D,B,C,A)
=> D = k10_comput_1(B,C,A) ) ) ) ) ) ) ).
fof(d15_comput_1,axiom,
! [A] :
( v6_comput_1(A)
<=> ! [B] :
( m2_rfunct_3(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ! [C] :
( ( v5_comput_1(C)
& m2_finseq_1(C,k5_comput_1(k5_numbers)) )
=> ( ( r2_hidden(B,A)
& k3_comput_1(B) = k3_finseq_1(C)
& r1_tarski(k2_relat_1(C),A) )
=> r2_hidden(k5_relat_1(k6_funct_6(C),B),A) ) ) ) ) ).
fof(d16_comput_1,axiom,
! [A] :
( v7_comput_1(A)
<=> ! [B] :
( m2_rfunct_3(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ! [C] :
( m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ! [D] :
( m2_rfunct_3(D,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_comput_1(B,C,D,E)
& r2_hidden(C,A)
& r2_hidden(D,A) )
=> r2_hidden(B,A) ) ) ) ) ) ) ).
fof(d17_comput_1,axiom,
! [A] :
( v8_comput_1(A)
<=> ( r2_hidden(k6_comput_1(np__0,np__0),A)
& r2_hidden(k7_comput_1(np__1,np__1),A)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,B) )
=> r2_hidden(k8_comput_1(B,C),A) ) ) )
& v6_comput_1(A)
& v7_comput_1(A) ) ) ).
fof(t70_comput_1,axiom,
v8_comput_1(k5_comput_1(k5_numbers)) ).
fof(t71_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ! [D] :
( m2_rfunct_3(D,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ( ( B = k1_xboole_0
& r1_comput_1(D,B,C,A) )
=> D = k1_xboole_0 ) ) ) ) ) ).
fof(t72_comput_1,axiom,
! [A] :
( m2_rfunct_3(A,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ! [B] :
( ( v2_unialg_1(B,k5_numbers)
& m2_rfunct_3(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) )
=> ! [C] :
( ( v2_unialg_1(C,k5_numbers)
& m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_comput_1(A,B,C,D)
=> ( v2_unialg_1(A,k5_numbers)
& ~ ( ~ v1_xboole_0(B)
& v1_xboole_0(A) ) ) ) ) ) ) ) ).
fof(t73_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v8_comput_1(C)
& m1_subset_1(C,k1_zfmisc_1(k5_comput_1(k5_numbers))) )
=> r2_hidden(k6_comput_1(A,B),C) ) ) ) ).
fof(t74_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v8_comput_1(C)
& m1_subset_1(C,k1_zfmisc_1(k5_comput_1(k5_numbers))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B) )
=> r2_hidden(k7_comput_1(B,A),C) ) ) ) ) ).
fof(t75_comput_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v8_comput_1(A)
& m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers))) )
=> r2_hidden(k1_xboole_0,A) ) ).
fof(t76_comput_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v8_comput_1(A)
& m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers))) )
=> ! [B] :
( m1_comput_1(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers),A)
=> ! [C] :
( ( v5_comput_1(C)
& m2_finseq_1(C,A) )
=> ( k3_comput_1(B) = k3_finseq_1(C)
=> r2_hidden(k5_relat_1(k6_funct_6(C),B),A) ) ) ) ) ).
fof(t77_comput_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v8_comput_1(A)
& m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers))) )
=> ! [B] :
( m1_comput_1(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers),A)
=> ! [C] :
( m1_comput_1(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers),A)
=> ( k1_nat_1(k3_comput_1(B),np__2) = k3_comput_1(C)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_nat_1(k3_comput_1(B),np__1)) )
=> r2_hidden(k10_comput_1(B,C,D),A) ) ) ) ) ) ) ).
fof(t78_comput_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers)))
=> ( v8_comput_1(A)
=> r1_tarski(k11_comput_1,A) ) ) ).
fof(d19_comput_1,axiom,
! [A] :
( v9_comput_1(A)
<=> r2_hidden(A,k11_comput_1) ) ).
fof(d23_comput_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_zfmisc_1(k5_comput_1(k5_numbers)))
& m2_relset_1(A,k5_numbers,k1_zfmisc_1(k5_comput_1(k5_numbers))) )
=> ( A = k15_comput_1
<=> ( k1_prob_1(k5_comput_1(k5_numbers),A,np__0) = k12_comput_1
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_prob_1(k5_comput_1(k5_numbers),A,k1_nat_1(B,np__1)) = k4_subset_1(k5_comput_1(k5_numbers),k13_comput_1(k1_prob_1(k5_comput_1(k5_numbers),A,B)),k14_comput_1(k1_prob_1(k5_comput_1(k5_numbers),A,B))) ) ) ) ) ).
fof(t79_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,B)
=> r1_tarski(k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,A),k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,B)) ) ) ) ).
fof(t80_comput_1,axiom,
v8_comput_1(k2_prob_1(k5_comput_1(k5_numbers),k15_comput_1)) ).
fof(t81_comput_1,axiom,
k11_comput_1 = k2_prob_1(k5_comput_1(k5_numbers),k15_comput_1) ).
fof(t82_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_rfunct_3(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
=> ( r2_hidden(B,k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,A))
=> v2_unialg_1(B,k5_numbers) ) ) ) ).
fof(d24_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v4_comput_1(A) )
=> ( v10_comput_1(A)
<=> k3_comput_1(A) = np__0 ) ) ).
fof(d25_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v4_comput_1(A) )
=> ( v11_comput_1(A)
<=> k3_comput_1(A) = np__1 ) ) ).
fof(d26_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v4_comput_1(A) )
=> ( v12_comput_1(A)
<=> k3_comput_1(A) = np__2 ) ) ).
fof(d27_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v4_comput_1(A) )
=> ( v13_comput_1(A)
<=> k3_comput_1(A) = np__3 ) ) ).
fof(t83_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v3_comput_1(B)
& v4_comput_1(B)
& v11_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> k1_funct_1(k10_comput_1(B,C,np__2),k2_finseq_4(k5_numbers,A,np__0)) = k1_funct_1(B,k13_binarith(k5_numbers,A)) ) ) ) ).
fof(t84_comput_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ( ( v3_comput_1(A)
& k3_comput_1(A) = np__0 )
=> k1_funct_1(k10_comput_1(A,B,np__1),k13_binarith(k5_numbers,np__0)) = k1_funct_1(A,k1_xboole_0) ) ) ) ).
fof(t85_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v3_comput_1(C)
& v4_comput_1(C)
& v11_comput_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v7_seqm_3(D)
& v2_comput_1(D)
& v3_comput_1(D)
& v4_comput_1(D)
& v13_comput_1(D) )
=> k1_funct_1(k10_comput_1(C,D,np__2),k2_finseq_4(k5_numbers,A,k1_nat_1(B,np__1))) = k1_funct_1(D,k11_finseq_1(A,B,k1_funct_1(k10_comput_1(C,D,np__2),k2_finseq_4(k5_numbers,A,B)))) ) ) ) ) ).
fof(t86_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v7_seqm_3(C)
& v2_comput_1(C)
& v4_comput_1(C) )
=> ( ( v3_comput_1(B)
& v3_comput_1(C)
& k3_comput_1(B) = np__0
& k3_comput_1(C) = np__2 )
=> k1_funct_1(k10_comput_1(B,C,np__1),k13_binarith(k5_numbers,k1_nat_1(A,np__1))) = k1_funct_1(C,k10_finseq_1(A,k1_funct_1(k10_comput_1(B,C,np__1),k13_binarith(k5_numbers,A)))) ) ) ) ) ).
fof(d28_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> k16_comput_1(A) = k5_relat_1(k6_funct_6(k10_finseq_1(k8_comput_1(np__3,np__1),k8_comput_1(np__3,np__3))),A) ) ).
fof(t87_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v7_seqm_3(D)
& v2_comput_1(D)
& v3_comput_1(D)
& v4_comput_1(D)
& v12_comput_1(D) )
=> k1_funct_1(k16_comput_1(D),k3_finseq_4(k5_numbers,A,B,C)) = k1_funct_1(D,k2_finseq_4(k5_numbers,A,C)) ) ) ) ) ).
fof(t88_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v9_comput_1(A)
& v12_comput_1(A) )
=> r2_hidden(k16_comput_1(A),k11_comput_1) ) ).
fof(d29_comput_1,axiom,
k17_comput_1 = k10_comput_1(k8_comput_1(np__1,np__1),k7_comput_1(np__3,np__3),np__2) ).
fof(t89_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(k17_comput_1,k2_finseq_4(k5_numbers,A,B)) = k1_nat_1(A,B) ) ) ).
fof(d30_comput_1,axiom,
k18_comput_1 = k10_comput_1(k6_comput_1(np__1,np__0),k16_comput_1(k17_comput_1),np__2) ).
fof(t90_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(k18_comput_1,k2_finseq_4(k5_numbers,A,B)) = k2_nat_1(A,B) ) ) ).
fof(d31_comput_1,axiom,
k19_comput_1 = k10_comput_1(k6_comput_1(np__0,np__1),k5_relat_1(k6_funct_6(k10_finseq_1(k5_relat_1(k6_funct_6(k9_finseq_1(k8_comput_1(np__2,np__1))),k7_comput_1(np__1,np__1)),k8_comput_1(np__2,np__2))),k18_comput_1),np__1) ).
fof(t91_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_funct_1(k19_comput_1,k13_binarith(k5_numbers,A)) = k11_newton(A) ) ).
fof(d32_comput_1,axiom,
k20_comput_1 = k10_comput_1(k6_comput_1(np__1,np__1),k16_comput_1(k18_comput_1),np__2) ).
fof(t92_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(k20_comput_1,k2_finseq_4(k5_numbers,A,B)) = k1_card_4(A,B) ) ) ).
fof(d33_comput_1,axiom,
k21_comput_1 = k10_comput_1(k6_comput_1(np__0,np__0),k8_comput_1(np__2,np__1),np__1) ).
fof(t93_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k1_funct_1(k21_comput_1,k13_binarith(k5_numbers,np__0)) = np__0
& k1_funct_1(k21_comput_1,k13_binarith(k5_numbers,k1_nat_1(A,np__1))) = A ) ) ).
fof(d34_comput_1,axiom,
k22_comput_1 = k10_comput_1(k8_comput_1(np__1,np__1),k16_comput_1(k5_relat_1(k6_funct_6(k9_finseq_1(k8_comput_1(np__2,np__2))),k21_comput_1)),np__2) ).
fof(t94_comput_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(k22_comput_1,k2_finseq_4(k5_numbers,A,B)) = k5_binarith(A,B) ) ) ).
fof(s1_comput_1,axiom,
( ( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_funct_1(f1_s1_comput_1,k13_binarith(k5_numbers,A)) = f3_s1_comput_1(A) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(f2_s1_comput_1,k2_finseq_4(k5_numbers,A,B)) = f4_s1_comput_1(A,B) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(k5_relat_1(k6_funct_6(k9_finseq_1(f2_s1_comput_1)),f1_s1_comput_1),k2_finseq_4(k5_numbers,A,B)) = f3_s1_comput_1(f4_s1_comput_1(A,B)) ) ) ) ).
fof(s2_comput_1,axiom,
( ( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(f1_s2_comput_1,k2_finseq_4(k5_numbers,A,B)) = f4_s2_comput_1(A,B) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(f2_s2_comput_1,k2_finseq_4(k5_numbers,A,B)) = f5_s2_comput_1(A,B) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(f3_s2_comput_1,k2_finseq_4(k5_numbers,A,B)) = f6_s2_comput_1(A,B) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_funct_1(k5_relat_1(k6_funct_6(k10_finseq_1(f2_s2_comput_1,f3_s2_comput_1)),f1_s2_comput_1),k2_finseq_4(k5_numbers,A,B)) = f4_s2_comput_1(f5_s2_comput_1(A,B),f6_s2_comput_1(A,B)) ) ) ) ).
fof(dt_m1_comput_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_rfunct_3(C,A,B)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(C)) )
=> ! [E] :
( m1_comput_1(E,A,B,C,D)
=> m2_rfunct_3(E,A,B,C) ) ) ).
fof(existence_m1_comput_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_rfunct_3(C,A,B)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(C)) )
=> ? [E] : m1_comput_1(E,A,B,C,D) ) ).
fof(redefinition_m1_comput_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_rfunct_3(C,A,B)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(C)) )
=> ! [E] :
( m1_comput_1(E,A,B,C,D)
<=> m1_subset_1(E,D) ) ) ).
fof(dt_k1_comput_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k4_finseq_2(B,A))
& m1_subset_1(D,k5_numbers)
& m1_subset_1(E,A) )
=> m2_finseq_2(k1_comput_1(A,B,C,D,E),A,k4_finseq_2(B,A)) ) ).
fof(redefinition_k1_comput_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k4_finseq_2(B,A))
& m1_subset_1(D,k5_numbers)
& m1_subset_1(E,A) )
=> k1_comput_1(A,B,C,D,E) = k2_funct_7(C,D,E) ) ).
fof(dt_k2_comput_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k4_finseq_2(A,k5_numbers))
& m1_subset_1(C,k5_numbers) )
=> m2_subset_1(k2_comput_1(A,B,C),k1_numbers,k5_numbers) ) ).
fof(redefinition_k2_comput_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k4_finseq_2(A,k5_numbers))
& m1_subset_1(C,k5_numbers) )
=> k2_comput_1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k3_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v4_comput_1(A) )
=> m2_subset_1(k3_comput_1(A),k1_numbers,k5_numbers) ) ).
fof(dt_k4_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v5_comput_1(A) )
=> m2_subset_1(k4_comput_1(A),k1_numbers,k5_numbers) ) ).
fof(dt_k5_comput_1,axiom,
! [A] :
( ~ v1_xboole_0(k5_comput_1(A))
& m1_rfunct_3(k5_comput_1(A),k3_finseq_2(A),A) ) ).
fof(dt_k6_comput_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k6_comput_1(A,B))
& v1_funct_1(k6_comput_1(A,B))
& v7_seqm_3(k6_comput_1(A,B))
& v2_comput_1(k6_comput_1(A,B))
& v4_comput_1(k6_comput_1(A,B)) ) ) ).
fof(dt_k7_comput_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k7_comput_1(A,B))
& v1_funct_1(k7_comput_1(A,B))
& v7_seqm_3(k7_comput_1(A,B))
& v2_comput_1(k7_comput_1(A,B))
& v4_comput_1(k7_comput_1(A,B)) ) ) ).
fof(dt_k8_comput_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k8_comput_1(A,B))
& v1_funct_1(k8_comput_1(A,B))
& v7_seqm_3(k8_comput_1(A,B))
& v2_comput_1(k8_comput_1(A,B))
& v4_comput_1(k8_comput_1(A,B)) ) ) ).
fof(dt_k9_comput_1,axiom,
! [A,B,C,D] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B)
& m1_subset_1(C,k5_numbers)
& m1_finseq_1(D,k5_numbers) )
=> m2_rfunct_3(k9_comput_1(A,B,C,D),k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) ) ).
fof(dt_k10_comput_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& v2_comput_1(A)
& v4_comput_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v7_seqm_3(B)
& v2_comput_1(B)
& v4_comput_1(B)
& m1_subset_1(C,k5_numbers) )
=> m2_rfunct_3(k10_comput_1(A,B,C),k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) ) ).
fof(dt_k11_comput_1,axiom,
m1_subset_1(k11_comput_1,k1_zfmisc_1(k5_comput_1(k5_numbers))) ).
fof(dt_k12_comput_1,axiom,
m1_subset_1(k12_comput_1,k1_zfmisc_1(k5_comput_1(k5_numbers))) ).
fof(dt_k13_comput_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers)))
=> m1_subset_1(k13_comput_1(A),k1_zfmisc_1(k5_comput_1(k5_numbers))) ) ).
fof(dt_k14_comput_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers)))
=> m1_subset_1(k14_comput_1(A),k1_zfmisc_1(k5_comput_1(k5_numbers))) ) ).
fof(dt_k15_comput_1,axiom,
( v1_funct_1(k15_comput_1)
& v1_funct_2(k15_comput_1,k5_numbers,k1_zfmisc_1(k5_comput_1(k5_numbers)))
& m2_relset_1(k15_comput_1,k5_numbers,k1_zfmisc_1(k5_comput_1(k5_numbers))) ) ).
fof(dt_k16_comput_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_relat_1(k16_comput_1(A))
& v1_funct_1(k16_comput_1(A)) ) ) ).
fof(dt_k17_comput_1,axiom,
( v1_relat_1(k17_comput_1)
& v1_funct_1(k17_comput_1)
& v9_comput_1(k17_comput_1)
& v12_comput_1(k17_comput_1) ) ).
fof(dt_k18_comput_1,axiom,
( v1_relat_1(k18_comput_1)
& v1_funct_1(k18_comput_1)
& v9_comput_1(k18_comput_1)
& v12_comput_1(k18_comput_1) ) ).
fof(dt_k19_comput_1,axiom,
( v1_relat_1(k19_comput_1)
& v1_funct_1(k19_comput_1)
& v9_comput_1(k19_comput_1)
& v11_comput_1(k19_comput_1) ) ).
fof(dt_k20_comput_1,axiom,
( v1_relat_1(k20_comput_1)
& v1_funct_1(k20_comput_1)
& v9_comput_1(k20_comput_1)
& v12_comput_1(k20_comput_1) ) ).
fof(dt_k21_comput_1,axiom,
( v1_relat_1(k21_comput_1)
& v1_funct_1(k21_comput_1)
& v9_comput_1(k21_comput_1)
& v11_comput_1(k21_comput_1) ) ).
fof(dt_k22_comput_1,axiom,
( v1_relat_1(k22_comput_1)
& v1_funct_1(k22_comput_1)
& v9_comput_1(k22_comput_1)
& v12_comput_1(k22_comput_1) ) ).
fof(t15_comput_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_fraenkel(A)
& v1_comput_1(A) )
=> k1_relat_1(k3_tarski(A)) = k3_tarski(a_1_0_comput_1(A)) ) ).
fof(t17_comput_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_fraenkel(A)
& v1_comput_1(A) )
=> k2_relat_1(k3_tarski(A)) = k3_tarski(a_1_1_comput_1(A)) ) ).
fof(d8_comput_1,axiom,
! [A] : k5_comput_1(A) = a_1_2_comput_1(A) ).
fof(d18_comput_1,axiom,
k11_comput_1 = k1_setfam_1(a_0_0_comput_1) ).
fof(d20_comput_1,axiom,
k12_comput_1 = k2_xboole_0(k2_tarski(k6_comput_1(np__0,np__0),k7_comput_1(np__1,np__1)),a_0_1_comput_1) ).
fof(d21_comput_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers)))
=> k13_comput_1(A) = k2_xboole_0(A,a_1_3_comput_1(A)) ) ).
fof(d22_comput_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers)))
=> k14_comput_1(A) = k2_xboole_0(A,a_1_4_comput_1(A)) ) ).
fof(fraenkel_a_1_0_comput_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_fraenkel(B)
& v1_comput_1(B) )
=> ( r2_hidden(A,a_1_0_comput_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = k1_relat_1(C) ) ) ) ).
fof(fraenkel_a_1_1_comput_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_fraenkel(B)
& v1_comput_1(B) )
=> ( r2_hidden(A,a_1_1_comput_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = k2_relat_1(C) ) ) ) ).
fof(fraenkel_a_1_2_comput_1,axiom,
! [A,B] :
( r2_hidden(A,a_1_2_comput_1(B))
<=> ? [C] :
( m2_rfunct_3(C,k3_finseq_2(B),B,k4_rfunct_3(k3_finseq_2(B),B))
& A = C
& v4_comput_1(C) ) ) ).
fof(fraenkel_a_0_0_comput_1,axiom,
! [A] :
( r2_hidden(A,a_0_0_comput_1)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_comput_1(k5_numbers)))
& A = B
& v8_comput_1(B) ) ) ).
fof(fraenkel_a_0_1_comput_1,axiom,
! [A] :
( r2_hidden(A,a_0_1_comput_1)
<=> ? [B,C] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers)
& A = k8_comput_1(B,C)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,B) ) ) ).
fof(fraenkel_a_1_3_comput_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k5_comput_1(k5_numbers)))
=> ( r2_hidden(A,a_1_3_comput_1(B))
<=> ? [C] :
( m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
& A = C
& ? [D] :
( m2_rfunct_3(D,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
& ? [E] :
( m2_rfunct_3(E,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r2_hidden(D,B)
& r2_hidden(E,B)
& r1_comput_1(C,D,E,F) ) ) ) ) ) ) ).
fof(fraenkel_a_1_4_comput_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k5_comput_1(k5_numbers)))
=> ( r2_hidden(A,a_1_4_comput_1(B))
<=> ? [C,D] :
( m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers))
& v5_comput_1(D)
& m2_finseq_2(D,k5_comput_1(k5_numbers),k3_finseq_2(k5_comput_1(k5_numbers)))
& A = k5_relat_1(k6_funct_6(D),C)
& r2_hidden(C,B)
& k3_comput_1(C) = k3_finseq_1(D)
& r1_tarski(k2_relat_1(D),B) ) ) ) ).
%------------------------------------------------------------------------------