SET007 Axioms: SET007+105.ax
%------------------------------------------------------------------------------
% File : SET007+105 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Properties of Real 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 : rfunct_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 94 ( 7 unt; 0 def)
% Number of atoms : 622 ( 43 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 534 ( 6 ~; 9 |; 269 &)
% ( 14 <=>; 236 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-4 aty)
% Number of functors : 49 ( 49 usr; 4 con; 0-6 aty)
% Number of variables : 237 ( 236 !; 1 ?)
% 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_rfunct_2,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v2_funct_1(B) )
=> ( v1_relat_1(k7_relat_1(B,A))
& v1_funct_1(k7_relat_1(B,A))
& v2_funct_1(k7_relat_1(B,A)) ) ) ).
fof(t1_rfunct_2,axiom,
$true ).
fof(t2_rfunct_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] : k5_relat_1(k7_relat_1(A,C),k7_relat_1(B,k9_relat_1(A,C))) = k7_relat_1(k5_relat_1(A,B),C) ) ) ).
fof(t3_rfunct_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D] : k5_relat_1(k7_relat_1(A,C),k7_relat_1(B,D)) = k7_relat_1(k5_relat_1(A,B),k3_xboole_0(C,k10_relat_1(A,D))) ) ) ).
fof(t4_rfunct_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( r1_tarski(C,k1_relat_1(k5_relat_1(A,B)))
<=> ( r1_tarski(C,k1_relat_1(A))
& r1_tarski(k9_relat_1(A,C),k1_relat_1(B)) ) ) ) ) ).
fof(t5_rfunct_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] : k9_relat_1(k7_relat_1(A,B),B) = k9_relat_1(A,B) ) ).
fof(t6_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( A = k10_seq_1(B,C)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,D) = k5_real_1(k2_seq_1(k5_numbers,k1_numbers,B,D),k2_seq_1(k5_numbers,k1_numbers,C,D)) ) ) ) ) ) ).
fof(t7_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_tarski(k1_rfunct_2(k1_seqm_3(A,B)),k1_rfunct_2(A)) ) ) ).
fof(t8_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,C))
=> r2_hidden(k2_seq_1(k5_numbers,k1_numbers,A,B),k4_relset_1(k1_numbers,k1_numbers,C)) ) ) ) ) ).
fof(t9_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( r2_hidden(A,k1_rfunct_2(B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = k2_seq_1(k5_numbers,k1_numbers,B,C) ) ) ) ).
fof(t10_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k2_seq_1(k5_numbers,k1_numbers,A,B),k1_rfunct_2(A)) ) ) ).
fof(t11_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( m1_seqm_3(A,B)
=> r1_tarski(k1_rfunct_2(A),k1_rfunct_2(B)) ) ) ) ).
fof(t12_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ( m1_seqm_3(A,B)
& v2_relat_1(B) )
=> v2_relat_1(A) ) ) ) ).
fof(t13_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( k3_seqm_3(C,k9_seq_1(A,B)) = k9_seq_1(k3_seqm_3(C,A),k3_seqm_3(C,B))
& k3_seqm_3(C,k10_seq_1(A,B)) = k10_seq_1(k3_seqm_3(C,A),k3_seqm_3(C,B))
& k3_seqm_3(C,k11_seq_1(A,B)) = k11_seq_1(k3_seqm_3(C,A),k3_seqm_3(C,B)) ) ) ) ) ).
fof(t14_rfunct_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k3_seqm_3(C,k14_seq_1(B,A)) = k14_seq_1(k3_seqm_3(C,B),A) ) ) ) ).
fof(t15_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( k3_seqm_3(B,k17_seq_1(A)) = k17_seq_1(k3_seqm_3(B,A))
& k3_seqm_3(B,k22_seq_1(A)) = k22_seq_1(k3_seqm_3(B,A)) ) ) ) ).
fof(t16_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> k18_seq_1(k3_seqm_3(B,A)) = k3_seqm_3(B,k18_seq_1(A)) ) ) ).
fof(t17_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> k3_seqm_3(C,k19_seq_1(A,B)) = k19_seq_1(k3_seqm_3(C,A),k3_seqm_3(C,B)) ) ) ) ).
fof(t18_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( v4_seq_2(A)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,B),np__0) ) )
=> r1_xreal_0(k2_seq_2(A),np__0) ) ) ).
fof(t19_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r2_hidden(k2_seq_1(k5_numbers,k1_numbers,B,C),A) )
=> r1_tarski(k1_rfunct_2(B),A) ) ) ).
fof(d1_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(B),k4_relset_1(k1_numbers,k1_numbers,A))
=> k2_rfunct_2(A,B) = k5_relat_1(B,A) ) ) ) ).
fof(t20_rfunct_2,axiom,
$true ).
fof(t21_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,C))
=> k2_seq_1(k5_numbers,k1_numbers,k2_rfunct_2(C,A),B) = k2_seq_1(k1_numbers,k1_numbers,C,k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t22_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,C))
=> k1_seqm_3(k2_rfunct_2(C,A),B) = k2_rfunct_2(C,k1_seqm_3(A,B)) ) ) ) ) ).
fof(t23_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k5_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_relset_1(k1_numbers,k1_numbers,C)))
=> ( k2_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,B,C),A) = k9_seq_1(k2_rfunct_2(B,A),k2_rfunct_2(C,A))
& k2_rfunct_2(k7_seq_1(k1_numbers,k1_numbers,B,C),A) = k10_seq_1(k2_rfunct_2(B,A),k2_rfunct_2(C,A))
& k2_rfunct_2(k8_seq_1(k1_numbers,k1_numbers,B,C),A) = k11_seq_1(k2_rfunct_2(B,A),k2_rfunct_2(C,A)) ) ) ) ) ) ).
fof(t24_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,B))
=> k2_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,B,C),A) = k14_seq_1(k2_rfunct_2(B,A),C) ) ) ) ) ).
fof(t25_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,B))
=> ( k22_seq_1(k2_rfunct_2(B,A)) = k2_rfunct_2(k21_seq_1(k1_numbers,k1_numbers,B),A)
& k17_seq_1(k2_rfunct_2(B,A)) = k2_rfunct_2(k16_seq_1(k1_numbers,k1_numbers,B),A) ) ) ) ) ).
fof(t26_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B)))
=> v2_relat_1(k2_rfunct_2(B,A)) ) ) ) ).
fof(t27_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B)))
=> k2_rfunct_2(k4_rfunct_1(k1_numbers,k1_numbers,B),A) = k18_seq_1(k2_rfunct_2(B,A)) ) ) ) ).
fof(t28_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,C))
=> k3_seqm_3(B,k2_rfunct_2(C,A)) = k2_rfunct_2(C,k3_seqm_3(B,A)) ) ) ) ) ).
fof(t29_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,C))
& m1_seqm_3(B,A) )
=> m1_seqm_3(k2_rfunct_2(C,B),k2_rfunct_2(C,A)) ) ) ) ) ).
fof(t30_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( v1_partfun1(C,k1_numbers,k1_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,k2_rfunct_2(C,A),B) = k2_seq_1(k1_numbers,k1_numbers,C,k2_seq_1(k5_numbers,k1_numbers,A,B)) ) ) ) ) ).
fof(t31_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( v1_partfun1(C,k1_numbers,k1_numbers)
=> k2_rfunct_2(C,k1_seqm_3(A,B)) = k1_seqm_3(k2_rfunct_2(C,A),B) ) ) ) ) ).
fof(t32_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( v1_partfun1(B,k1_numbers,k1_numbers)
& v1_partfun1(C,k1_numbers,k1_numbers) )
=> ( k2_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,B,C),A) = k9_seq_1(k2_rfunct_2(B,A),k2_rfunct_2(C,A))
& k2_rfunct_2(k7_seq_1(k1_numbers,k1_numbers,B,C),A) = k10_seq_1(k2_rfunct_2(B,A),k2_rfunct_2(C,A))
& k2_rfunct_2(k8_seq_1(k1_numbers,k1_numbers,B,C),A) = k11_seq_1(k2_rfunct_2(B,A),k2_rfunct_2(C,A)) ) ) ) ) ) ).
fof(t33_rfunct_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( v1_partfun1(C,k1_numbers,k1_numbers)
=> k2_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,C,A),B) = k14_seq_1(k2_rfunct_2(C,B),A) ) ) ) ) ).
fof(t34_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(B),k4_relset_1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,A)))
=> k2_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,C,A),B) = k2_rfunct_2(C,B) ) ) ) ).
fof(t35_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,D,A)))
=> ( ( ~ r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,D,B)))
& ~ r1_tarski(A,B) )
| k2_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,D,A),C) = k2_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,D,B),C) ) ) ) ) ).
fof(t36_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(B),k4_relset_1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,A)))
=> k22_seq_1(k2_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,C,A),B)) = k2_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,k21_seq_1(k1_numbers,k1_numbers,C),A),B) ) ) ) ).
fof(t37_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(k1_rfunct_2(B),k4_relset_1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,A)))
& k11_relset_1(k1_numbers,k1_numbers,C,k1_seq_4(np__0)) = k1_xboole_0 )
=> k2_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,C),A),B) = k18_seq_1(k2_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,C,A),B)) ) ) ) ).
fof(t38_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,B))
=> k10_relset_1(k1_numbers,k1_numbers,B,k1_rfunct_2(A)) = k1_rfunct_2(k2_rfunct_2(B,A)) ) ) ) ).
fof(t39_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,B)))
=> k2_rfunct_2(B,k2_rfunct_2(C,A)) = k2_rfunct_2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,B),A) ) ) ) ) ).
fof(t40_rfunct_2,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v2_funct_1(B) )
=> k2_funct_1(k7_relat_1(B,A)) = k7_relat_1(k2_funct_1(B),k9_relat_1(B,A)) ) ).
fof(t41_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ( ( v3_seq_4(k5_relset_1(k1_numbers,k1_numbers,A))
& k4_seq_4(k5_relset_1(k1_numbers,k1_numbers,A)) = k5_seq_4(k5_relset_1(k1_numbers,k1_numbers,A)) )
=> r1_partfun2(k1_numbers,k1_numbers,A,k4_relset_1(k1_numbers,k1_numbers,A)) ) ) ).
fof(t42_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k4_relset_1(k1_numbers,k1_numbers,B))
& v3_seq_4(k10_relset_1(k1_numbers,k1_numbers,B,A))
& k4_seq_4(k10_relset_1(k1_numbers,k1_numbers,B,A)) = k5_seq_4(k10_relset_1(k1_numbers,k1_numbers,B,A)) )
=> r1_partfun2(k1_numbers,k1_numbers,B,A) ) ) ).
fof(d2_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( r1_rfunct_2(A,B)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( r2_hidden(C,k3_xboole_0(B,k4_relset_1(k1_numbers,k1_numbers,A)))
& r2_hidden(D,k3_xboole_0(B,k4_relset_1(k1_numbers,k1_numbers,A)))
& ~ r1_xreal_0(D,C)
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,A,C)) ) ) ) ) ) ).
fof(d3_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( r2_rfunct_2(A,B)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( r2_hidden(C,k3_xboole_0(B,k4_relset_1(k1_numbers,k1_numbers,A)))
& r2_hidden(D,k3_xboole_0(B,k4_relset_1(k1_numbers,k1_numbers,A)))
& ~ r1_xreal_0(D,C)
& r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,C),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) ) ) ) ) ).
fof(d4_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( r3_rfunct_2(A,B)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( r2_hidden(C,k3_xboole_0(B,k4_relset_1(k1_numbers,k1_numbers,A)))
& r2_hidden(D,k3_xboole_0(B,k4_relset_1(k1_numbers,k1_numbers,A))) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,C),k2_seq_1(k1_numbers,k1_numbers,A,D)) ) ) ) ) ) ) ).
fof(d5_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( r4_rfunct_2(A,B)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( r2_hidden(C,k3_xboole_0(B,k4_relset_1(k1_numbers,k1_numbers,A)))
& r2_hidden(D,k3_xboole_0(B,k4_relset_1(k1_numbers,k1_numbers,A))) )
=> ( r1_xreal_0(D,C)
| r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,A,D),k2_seq_1(k1_numbers,k1_numbers,A,C)) ) ) ) ) ) ) ).
fof(d6_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( r5_rfunct_2(A,B)
<=> ( r3_rfunct_2(A,B)
| r4_rfunct_2(A,B) ) ) ) ).
fof(t43_rfunct_2,axiom,
$true ).
fof(t44_rfunct_2,axiom,
$true ).
fof(t45_rfunct_2,axiom,
$true ).
fof(t46_rfunct_2,axiom,
$true ).
fof(t47_rfunct_2,axiom,
$true ).
fof(t48_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r3_rfunct_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( r2_hidden(C,k3_xboole_0(A,k4_relset_1(k1_numbers,k1_numbers,B)))
& r2_hidden(D,k3_xboole_0(A,k4_relset_1(k1_numbers,k1_numbers,B)))
& r1_xreal_0(C,D) )
=> r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,C),k2_seq_1(k1_numbers,k1_numbers,B,D)) ) ) ) ) ) ).
fof(t49_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r4_rfunct_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( r2_hidden(C,k3_xboole_0(A,k4_relset_1(k1_numbers,k1_numbers,B)))
& r2_hidden(D,k3_xboole_0(A,k4_relset_1(k1_numbers,k1_numbers,B)))
& r1_xreal_0(C,D) )
=> r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),k2_seq_1(k1_numbers,k1_numbers,B,C)) ) ) ) ) ) ).
fof(t50_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_rfunct_2(B,A)
<=> r1_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,B,A),A) ) ) ).
fof(t51_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r2_rfunct_2(B,A)
<=> r2_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,B,A),A) ) ) ).
fof(t52_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r3_rfunct_2(B,A)
<=> r3_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,B,A),A) ) ) ).
fof(t53_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r4_rfunct_2(B,A)
<=> r4_rfunct_2(k2_partfun1(k1_numbers,k1_numbers,B,A),A) ) ) ).
fof(t54_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_xboole_0(A,k4_relset_1(k1_numbers,k1_numbers,B))
=> ( r1_rfunct_2(B,A)
& r2_rfunct_2(B,A)
& r3_rfunct_2(B,A)
& r4_rfunct_2(B,A)
& r5_rfunct_2(B,A) ) ) ) ).
fof(t55_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_rfunct_2(B,A)
=> r3_rfunct_2(B,A) ) ) ).
fof(t56_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r2_rfunct_2(B,A)
=> r4_rfunct_2(B,A) ) ) ).
fof(t57_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_partfun2(k1_numbers,k1_numbers,B,A)
=> r3_rfunct_2(B,A) ) ) ).
fof(t58_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_partfun2(k1_numbers,k1_numbers,B,A)
=> r4_rfunct_2(B,A) ) ) ).
fof(t59_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r3_rfunct_2(C,A)
& r4_rfunct_2(C,B) )
=> r1_partfun2(k1_numbers,k1_numbers,C,k3_xboole_0(A,B)) ) ) ).
fof(t60_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,B)
& r1_rfunct_2(C,B) )
=> r1_rfunct_2(C,A) ) ) ).
fof(t61_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,B)
& r2_rfunct_2(C,B) )
=> r2_rfunct_2(C,A) ) ) ).
fof(t62_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,B)
& r3_rfunct_2(C,B) )
=> r3_rfunct_2(C,A) ) ) ).
fof(t63_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,B)
& r4_rfunct_2(C,B) )
=> r4_rfunct_2(C,A) ) ) ).
fof(t64_rfunct_2,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_rfunct_2(C,A)
=> ( r1_xreal_0(B,np__0)
| r1_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,C,B),A) ) )
& ( B = np__0
=> r1_partfun2(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,C,B),A) )
& ( r1_rfunct_2(C,A)
=> ( r1_xreal_0(np__0,B)
| r2_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,C,B),A) ) ) ) ) ) ).
fof(t65_rfunct_2,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r2_rfunct_2(C,A)
=> ( r1_xreal_0(B,np__0)
| r2_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,C,B),A) ) )
& ( r2_rfunct_2(C,A)
=> ( r1_xreal_0(np__0,B)
| r1_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,C,B),A) ) ) ) ) ) ).
fof(t66_rfunct_2,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( ( r3_rfunct_2(C,A)
& r1_xreal_0(np__0,B) )
=> r3_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,C,B),A) )
& ( ( r3_rfunct_2(C,A)
& r1_xreal_0(B,np__0) )
=> r4_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,C,B),A) ) ) ) ) ).
fof(t67_rfunct_2,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( ( r4_rfunct_2(C,A)
& r1_xreal_0(np__0,B) )
=> r4_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,C,B),A) )
& ( ( r4_rfunct_2(C,A)
& r1_xreal_0(B,np__0) )
=> r3_rfunct_2(k13_seq_1(k1_numbers,k1_numbers,C,B),A) ) ) ) ) ).
fof(t68_rfunct_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,k1_numbers,k1_numbers) )
=> ( r2_hidden(C,k3_xboole_0(k3_xboole_0(A,B),k4_relset_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,D,E))))
=> ( r2_hidden(C,k3_xboole_0(A,k4_relset_1(k1_numbers,k1_numbers,D)))
& r2_hidden(C,k3_xboole_0(B,k4_relset_1(k1_numbers,k1_numbers,E))) ) ) ) ) ) ).
fof(t69_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( ( r1_rfunct_2(C,A)
& r1_rfunct_2(D,B) )
=> r1_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) )
& ( ( r2_rfunct_2(C,A)
& r2_rfunct_2(D,B) )
=> r2_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) )
& ( ( r3_rfunct_2(C,A)
& r3_rfunct_2(D,B) )
=> r3_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) )
& ( ( r4_rfunct_2(C,A)
& r4_rfunct_2(D,B) )
=> r4_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) ) ) ) ) ).
fof(t70_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( ( r1_rfunct_2(C,A)
& r1_partfun2(k1_numbers,k1_numbers,D,B) )
=> r1_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) )
& ( ( r2_rfunct_2(C,A)
& r1_partfun2(k1_numbers,k1_numbers,D,B) )
=> r2_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) ) ) ) ) ).
fof(t71_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r1_rfunct_2(C,A)
& r3_rfunct_2(D,B) )
=> r1_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) ) ) ) ).
fof(t72_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r4_rfunct_2(C,A)
& r1_partfun2(k1_numbers,k1_numbers,D,B) )
=> r4_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) ) ) ) ).
fof(t73_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r2_rfunct_2(C,A)
& r4_rfunct_2(D,B) )
=> r2_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) ) ) ) ).
fof(t74_rfunct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r3_rfunct_2(C,A)
& r1_partfun2(k1_numbers,k1_numbers,D,B) )
=> r3_rfunct_2(k6_seq_1(k1_numbers,k1_numbers,C,D),k3_xboole_0(A,B)) ) ) ) ).
fof(t75_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> r1_rfunct_2(B,k1_tarski(A)) ) ).
fof(t76_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> r2_rfunct_2(B,k1_tarski(A)) ) ).
fof(t77_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> r3_rfunct_2(B,k1_tarski(A)) ) ).
fof(t78_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> r4_rfunct_2(B,k1_tarski(A)) ) ).
fof(t79_rfunct_2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> r1_rfunct_2(k1_partfun2(k1_numbers,A),A) ) ).
fof(t80_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r1_rfunct_2(B,A)
=> r2_rfunct_2(k16_seq_1(k1_numbers,k1_numbers,B),A) ) ) ).
fof(t81_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( r3_rfunct_2(B,A)
=> r4_rfunct_2(k16_seq_1(k1_numbers,k1_numbers,B),A) ) ) ).
fof(t82_rfunct_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_rfunct_2(C,k1_rcomp_1(A,B))
| r2_rfunct_2(C,k1_rcomp_1(A,B)) )
=> v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,B))) ) ) ) ) ).
fof(t83_rfunct_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v2_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r1_rfunct_2(C,k1_rcomp_1(A,B))
=> r1_rfunct_2(k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,B))),k10_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,B))) ) ) ) ) ).
fof(t84_rfunct_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v2_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( r2_rfunct_2(C,k1_rcomp_1(A,B))
=> r2_rfunct_2(k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,B))),k10_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,B))) ) ) ) ) ).
fof(dt_k1_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> m1_subset_1(k1_rfunct_2(A),k1_zfmisc_1(k1_numbers)) ) ).
fof(redefinition_k1_rfunct_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m1_relset_1(A,k5_numbers,k1_numbers) )
=> k1_rfunct_2(A) = k2_relat_1(A) ) ).
fof(dt_k2_rfunct_2,axiom,
! [A,B] :
( ( v1_funct_1(A)
& m1_relset_1(A,k1_numbers,k1_numbers)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m1_relset_1(B,k5_numbers,k1_numbers) )
=> ( v1_funct_1(k2_rfunct_2(A,B))
& v1_funct_2(k2_rfunct_2(A,B),k5_numbers,k1_numbers)
& m2_relset_1(k2_rfunct_2(A,B),k5_numbers,k1_numbers) ) ) ).
%------------------------------------------------------------------------------