SET007 Axioms: SET007+668.ax
%------------------------------------------------------------------------------
% File : SET007+668 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Replace Function and Swap Function for Finite Sequences
% 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 : finseq_7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 42 ( 2 unt; 0 def)
% Number of atoms : 305 ( 51 equ)
% Maximal formula atoms : 19 ( 7 avg)
% Number of connectives : 303 ( 40 ~; 18 |; 63 &)
% ( 0 <=>; 182 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-4 aty)
% Number of variables : 168 ( 168 !; 0 ?)
% 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(t1_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( r1_xreal_0(D,C)
| B = k7_finseq_1(k7_finseq_1(k7_finseq_1(k7_finseq_1(k16_finseq_1(A,B,k5_binarith(C,np__1)),k9_finseq_1(k1_funct_1(B,C))),k16_finseq_1(A,k1_rfinseq(A,B,C),k5_binarith(k5_binarith(D,C),np__1))),k9_finseq_1(k1_funct_1(B,D))),k1_rfinseq(A,B,D)) ) ) ) ) ) ) ).
fof(t2_finseq_7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ( ( k3_finseq_1(C) = k3_finseq_1(D)
& r1_xreal_0(A,k3_finseq_1(k7_finseq_1(C,B))) )
=> ( r1_xreal_0(A,k3_finseq_1(C))
| k1_funct_1(k7_finseq_1(C,B),A) = k1_funct_1(k7_finseq_1(D,B),A) ) ) ) ) ) ) ).
fof(t3_finseq_7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(B)) )
=> k1_funct_1(B,A) = k1_funct_1(k7_finseq_1(C,B),k1_nat_1(k3_finseq_1(C),A)) ) ) ) ) ).
fof(t4_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(k1_rfinseq(A,B,D)))
=> k1_funct_1(k1_rfinseq(A,B,D),C) = k1_funct_1(B,k1_nat_1(D,C)) ) ) ) ) ) ).
fof(d1_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,A)
=> ( ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> k1_finseq_7(A,B,C,D) = k8_finseq_1(A,k8_finseq_1(A,k16_finseq_1(A,B,k5_binarith(C,np__1)),k12_finseq_1(A,D)),k1_rfinseq(A,B,C)) )
& ( ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> k1_finseq_7(A,B,C,D) = B ) ) ) ) ) ) ).
fof(t5_finseq_7,axiom,
$true ).
fof(t6_finseq_7,axiom,
$true ).
fof(t7_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k3_finseq_1(k1_finseq_7(A,B,D,C)) = k3_finseq_1(B) ) ) ) ) ).
fof(t8_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_tarski(k2_relat_1(k1_finseq_7(A,B,D,C)),k2_xboole_0(k2_relat_1(B),k1_tarski(C))) ) ) ) ) ).
fof(t9_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> r2_hidden(C,k2_relat_1(k1_finseq_7(A,B,D,C))) ) ) ) ) ) ).
fof(t10_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> k4_finseq_4(k5_numbers,A,k1_finseq_7(A,B,D,C),D) = C ) ) ) ) ) ).
fof(t11_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k6_xcmplx_0(k3_finseq_1(B),D))
=> ( r1_xreal_0(E,np__0)
| k1_funct_1(k1_finseq_7(A,B,D,C),k1_nat_1(D,E)) = k1_funct_1(k1_rfinseq(A,B,D),E) ) ) ) ) ) ) ) ) ).
fof(t12_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( D = E
| k4_finseq_4(k5_numbers,A,k1_finseq_7(A,B,E,C),D) = k4_finseq_4(k5_numbers,A,B,D) ) ) ) ) ) ) ) ).
fof(t13_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(F,k3_finseq_1(B)) )
=> ( r1_xreal_0(F,E)
| k1_finseq_7(A,k1_finseq_7(A,B,F,C),E,D) = k8_finseq_1(A,k8_finseq_1(A,k8_finseq_1(A,k8_finseq_1(A,k16_finseq_1(A,B,k5_binarith(E,np__1)),k12_finseq_1(A,D)),k16_finseq_1(A,k1_rfinseq(A,B,E),k5_binarith(k5_binarith(F,E),np__1))),k12_finseq_1(A,C)),k1_rfinseq(A,B,F)) ) ) ) ) ) ) ) ) ).
fof(t14_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> k1_finseq_7(A,k12_finseq_1(A,B),np__1,C) = k12_finseq_1(A,C) ) ) ) ).
fof(t15_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> k1_finseq_7(A,k2_finseq_4(A,B,C),np__1,D) = k2_finseq_4(A,D,C) ) ) ) ) ).
fof(t16_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> k1_finseq_7(A,k2_finseq_4(A,B,C),np__2,D) = k2_finseq_4(A,B,D) ) ) ) ) ).
fof(t17_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> k1_finseq_7(A,k3_finseq_4(A,B,C,D),np__1,E) = k3_finseq_4(A,E,C,D) ) ) ) ) ) ).
fof(t18_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> k1_finseq_7(A,k3_finseq_4(A,B,C,D),np__2,E) = k3_finseq_4(A,B,E,D) ) ) ) ) ) ).
fof(t19_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> k1_finseq_7(A,k3_finseq_4(A,B,C,D),np__3,E) = k3_finseq_4(A,B,C,E) ) ) ) ) ) ).
fof(d2_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> k2_finseq_7(A,B,C,D) = k1_finseq_7(A,k1_finseq_7(A,B,C,k4_finseq_4(k5_numbers,A,B,D)),D,k4_finseq_4(k5_numbers,A,B,C)) )
& ( ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> k2_finseq_7(A,B,C,D) = B ) ) ) ) ) ) ).
fof(t20_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k3_finseq_1(k2_finseq_7(A,B,C,D)) = k3_finseq_1(B) ) ) ) ) ).
fof(t21_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_finseq_7(A,B,C,C) = B ) ) ) ).
fof(t22_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_finseq_7(A,k2_finseq_7(A,B,C,D),D,C) = B ) ) ) ) ).
fof(t23_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_finseq_7(A,B,C,D) = k2_finseq_7(A,B,D,C) ) ) ) ) ).
fof(t24_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_relat_1(k2_finseq_7(A,B,C,D)) = k2_relat_1(B) ) ) ) ) ).
fof(t25_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> k2_finseq_7(A,k2_finseq_4(A,B,C),np__1,np__2) = k2_finseq_4(A,C,B) ) ) ) ).
fof(t26_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> k2_finseq_7(A,k3_finseq_4(A,B,C,D),np__1,np__2) = k3_finseq_4(A,C,B,D) ) ) ) ) ).
fof(t27_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> k2_finseq_7(A,k3_finseq_4(A,B,C,D),np__1,np__3) = k3_finseq_4(A,D,C,B) ) ) ) ) ).
fof(t28_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> k2_finseq_7(A,k3_finseq_4(A,B,C,D),np__2,np__3) = k3_finseq_4(A,B,D,C) ) ) ) ) ).
fof(t29_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( r1_xreal_0(D,C)
| k2_finseq_7(A,B,C,D) = k8_finseq_1(A,k8_finseq_1(A,k8_finseq_1(A,k8_finseq_1(A,k16_finseq_1(A,B,k5_binarith(C,np__1)),k12_finseq_1(A,k4_finseq_4(k5_numbers,A,B,D))),k16_finseq_1(A,k1_rfinseq(A,B,C),k5_binarith(k5_binarith(D,C),np__1))),k12_finseq_1(A,k4_finseq_4(k5_numbers,A,B,C))),k1_rfinseq(A,B,D)) ) ) ) ) ) ) ).
fof(t30_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> ( r1_xreal_0(C,np__1)
| k2_finseq_7(A,B,np__1,C) = k8_finseq_1(A,k8_finseq_1(A,k8_finseq_1(A,k12_finseq_1(A,k4_finseq_4(k5_numbers,A,B,C)),k16_finseq_1(A,k1_rfinseq(A,B,np__1),k5_binarith(C,np__2))),k12_finseq_1(A,k4_finseq_4(k5_numbers,A,B,np__1))),k1_rfinseq(A,B,C)) ) ) ) ) ) ).
fof(t31_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,C)
=> ( r1_xreal_0(k3_finseq_1(B),C)
| k2_finseq_7(A,B,C,k3_finseq_1(B)) = k8_finseq_1(A,k8_finseq_1(A,k8_finseq_1(A,k16_finseq_1(A,B,k5_binarith(C,np__1)),k12_finseq_1(A,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)))),k16_finseq_1(A,k1_rfinseq(A,B,C),k5_binarith(k5_binarith(k3_finseq_1(B),C),np__1))),k12_finseq_1(A,k4_finseq_4(k5_numbers,A,B,C))) ) ) ) ) ) ).
fof(t32_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( C = D
| E = D
| k4_finseq_4(k5_numbers,A,k2_finseq_7(A,B,C,E),D) = k4_finseq_4(k5_numbers,A,B,D) ) ) ) ) ) ) ) ).
fof(t33_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( k4_finseq_4(k5_numbers,A,k2_finseq_7(A,B,C,D),C) = k4_finseq_4(k5_numbers,A,B,D)
& k4_finseq_4(k5_numbers,A,k2_finseq_7(A,B,C,D),D) = k4_finseq_4(k5_numbers,A,B,C) ) ) ) ) ) ) ).
fof(t34_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(B)) )
=> k1_finseq_7(A,k2_finseq_7(A,B,D,E),D,C) = k2_finseq_7(A,k1_finseq_7(A,B,E,C),D,E) ) ) ) ) ) ) ).
fof(t35_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B))
& r1_xreal_0(np__1,F)
& r1_xreal_0(F,k3_finseq_1(B))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(B)) )
=> ( D = E
| F = E
| k2_finseq_7(A,k1_finseq_7(A,B,E,C),D,F) = k1_finseq_7(A,k2_finseq_7(A,B,D,F),E,C) ) ) ) ) ) ) ) ) ).
fof(t36_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( C = D
| E = D
| k2_finseq_7(A,k2_finseq_7(A,B,C,E),E,D) = k2_finseq_7(A,k2_finseq_7(A,B,C,D),C,E) ) ) ) ) ) ) ) ).
fof(t37_finseq_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(B))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B))
& r1_xreal_0(np__1,F)
& r1_xreal_0(F,k3_finseq_1(B)) )
=> ( C = D
| E = D
| F = C
| F = E
| k2_finseq_7(A,k2_finseq_7(A,B,C,E),D,F) = k2_finseq_7(A,k2_finseq_7(A,B,D,F),C,E) ) ) ) ) ) ) ) ) ).
fof(dt_k1_finseq_7,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,A) )
=> m2_finseq_1(k1_finseq_7(A,B,C,D),A) ) ).
fof(redefinition_k1_finseq_7,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,A) )
=> k1_finseq_7(A,B,C,D) = k2_funct_7(B,C,D) ) ).
fof(dt_k2_finseq_7,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> m2_finseq_1(k2_finseq_7(A,B,C,D),A) ) ).
%------------------------------------------------------------------------------