SET007 Axioms: SET007+167.ax
%------------------------------------------------------------------------------
% File : SET007+167 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Theory of Rearrangement
% 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 : rearran1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 51 ( 0 unt; 0 def)
% Number of atoms : 617 ( 87 equ)
% Maximal formula atoms : 20 ( 12 avg)
% Number of connectives : 653 ( 87 ~; 3 |; 336 &)
% ( 6 <=>; 221 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 12 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 0 prp; 1-4 aty)
% Number of functors : 39 ( 39 usr; 5 con; 0-4 aty)
% Number of variables : 199 ( 196 !; 3 ?)
% 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_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ? [B] :
( m1_finseq_1(B,k1_zfmisc_1(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v1_rearran1(B)
& v2_rearran1(B)
& v3_rearran1(B,k1_zfmisc_1(A)) ) ) ).
fof(d1_rearran1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_rearran1(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A)) )
=> ! [C] :
( v1_finset_1(C)
=> ( C = k1_funct_1(A,B)
=> k4_card_1(C) = B ) ) ) ) ) ) ).
fof(d2_rearran1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v2_rearran1(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k5_real_1(k3_finseq_1(A),np__1)) )
=> r1_tarski(k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,np__1))) ) ) ) ) ).
fof(d3_rearran1,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ( v3_rearran1(B,A)
<=> ? [C] :
( v1_finset_1(C)
& C = k3_tarski(A)
& k3_finseq_1(B) = k4_card_1(C) ) ) ) ).
fof(t1_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m2_finseq_1(B,k1_zfmisc_1(A))
=> ( v3_rearran1(B,k1_zfmisc_1(A))
<=> k3_finseq_1(B) = k4_card_1(A) ) ) ) ).
fof(t2_rearran1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v2_rearran1(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(B,C)
& r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A)) )
=> r1_tarski(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ) ) ).
fof(t3_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( v1_rearran1(B)
& v3_rearran1(B,k1_zfmisc_1(A))
& m2_finseq_1(B,k1_zfmisc_1(A)) )
=> k1_funct_1(B,k3_finseq_1(B)) = A ) ) ).
fof(t4_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( v3_rearran1(B,k1_zfmisc_1(A))
& m2_finseq_1(B,k1_zfmisc_1(A)) )
=> k3_finseq_1(B) != np__0 ) ) ).
fof(t5_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( v1_rearran1(B)
& v2_rearran1(B)
& m2_finseq_1(B,k1_zfmisc_1(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(B))
& r2_hidden(D,k4_finseq_1(B))
& C != D
& k1_funct_1(B,C) = k1_funct_1(B,D) ) ) ) ) ) ).
fof(t6_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( v1_rearran1(B)
& v2_rearran1(B)
& m2_finseq_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k5_real_1(k3_finseq_1(B),np__1))
& k1_funct_1(B,C) = k1_funct_1(B,k1_nat_1(C,np__1)) ) ) ) ) ).
fof(t7_rearran1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_rearran1(C)
& m2_finseq_1(C,k1_zfmisc_1(B)) )
=> ~ ( r2_hidden(A,k4_finseq_1(C))
& k1_funct_1(C,A) = k1_xboole_0 ) ) ) ) ).
fof(t8_rearran1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_rearran1(C)
& m2_finseq_1(C,k1_zfmisc_1(B)) )
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k5_real_1(k3_finseq_1(C),np__1))
& k4_xboole_0(k1_funct_1(C,k1_nat_1(A,np__1)),k1_funct_1(C,A)) = k1_xboole_0 ) ) ) ) ).
fof(t9_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( v1_rearran1(B)
& v3_rearran1(B,k1_zfmisc_1(A))
& m2_finseq_1(B,k1_zfmisc_1(A)) )
=> ? [C] :
( m1_subset_1(C,A)
& k1_funct_1(B,np__1) = k1_tarski(C) ) ) ) ).
fof(t10_rearran1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_rearran1(C)
& v2_rearran1(C)
& m2_finseq_1(C,k1_zfmisc_1(B)) )
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k5_real_1(k3_finseq_1(C),np__1))
& ! [D] :
( m1_subset_1(D,B)
=> ~ ( k4_xboole_0(k1_funct_1(C,k1_nat_1(A,np__1)),k1_funct_1(C,A)) = k1_tarski(D)
& k1_funct_1(C,k1_nat_1(A,np__1)) = k2_xboole_0(k1_funct_1(C,A),k1_tarski(D))
& k4_xboole_0(k1_funct_1(C,k1_nat_1(A,np__1)),k1_tarski(D)) = k1_funct_1(C,A) ) ) ) ) ) ) ).
fof(d4_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( v1_rearran1(B)
& v2_rearran1(B)
& v3_rearran1(B,k1_zfmisc_1(A))
& m2_finseq_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_rearran1(C)
& v2_rearran1(C)
& v3_rearran1(C,k1_zfmisc_1(A))
& m2_finseq_1(C,k1_zfmisc_1(A)) )
=> ( C = k2_rearran1(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k5_real_1(k3_finseq_1(C),np__1)) )
=> k1_funct_1(C,D) = k4_xboole_0(A,k1_funct_1(B,k5_real_1(k3_finseq_1(B),D))) ) ) ) ) ) ) ).
fof(t11_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( v1_rearran1(B)
& v2_rearran1(B)
& v3_rearran1(B,k1_zfmisc_1(A))
& m2_finseq_1(B,k1_zfmisc_1(A)) )
=> k2_rearran1(A,k2_rearran1(A,B)) = B ) ) ).
fof(t12_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> k3_finseq_1(k2_rfinseq(k22_rfunct_3(A,C,A))) = k3_finseq_1(k16_rfunct_3(B,D)) ) ) ) ) ) ).
fof(d5_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_rearran1(C)
& v2_rearran1(C)
& v3_rearran1(C,k1_zfmisc_1(B))
& m2_finseq_1(C,k1_zfmisc_1(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k1_numbers) )
=> k3_rearran1(A,B,C,D) = k15_rfunct_3(B,k17_rfunct_3(B,k16_rfunct_3(B,C),k2_rfinseq(k22_rfunct_3(A,D,A)))) ) ) ) ) ).
fof(d6_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_rearran1(C)
& v2_rearran1(C)
& v3_rearran1(C,k1_zfmisc_1(B))
& m2_finseq_1(C,k1_zfmisc_1(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k1_numbers) )
=> k4_rearran1(A,B,C,D) = k15_rfunct_3(B,k17_rfunct_3(B,k16_rfunct_3(B,k2_rearran1(B,C)),k2_rfinseq(k22_rfunct_3(A,D,A)))) ) ) ) ) ).
fof(t13_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> k4_relset_1(B,k1_numbers,k3_rearran1(A,B,D,C)) = B ) ) ) ) ) ).
fof(t14_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(A))
& m2_finseq_1(E,k1_zfmisc_1(A)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(A) = k4_card_1(B) )
=> ( ( r2_hidden(C,k1_funct_1(E,np__1))
=> k18_rfunct_3(A,k17_rfunct_3(A,k16_rfunct_3(A,E),k2_rfinseq(k22_rfunct_3(B,D,B))),C) = k2_rfinseq(k22_rfunct_3(B,D,B)) )
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,F)
& r2_hidden(C,k4_xboole_0(k1_funct_1(E,k1_nat_1(F,np__1)),k1_funct_1(E,F))) )
=> ( r1_xreal_0(k3_finseq_1(E),F)
| k18_rfunct_3(A,k17_rfunct_3(A,k16_rfunct_3(A,E),k2_rfinseq(k22_rfunct_3(B,D,B))),C) = k8_finseq_1(k1_numbers,k4_finseqop(k1_numbers,F,np__0),k2_rfinseq(k1_rfinseq(k1_numbers,k22_rfunct_3(B,D,B),F))) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(A))
& m2_finseq_1(E,k1_zfmisc_1(A)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(A) = k4_card_1(B) )
=> ( ( r2_hidden(C,k1_funct_1(E,np__1))
=> k2_seq_1(A,k1_numbers,k3_rearran1(B,A,E,D),C) = k2_seq_1(k5_numbers,k1_numbers,k22_rfunct_3(B,D,B),np__1) )
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,F)
& r2_hidden(C,k4_xboole_0(k1_funct_1(E,k1_nat_1(F,np__1)),k1_funct_1(E,F))) )
=> ( r1_xreal_0(k3_finseq_1(E),F)
| k2_seq_1(A,k1_numbers,k3_rearran1(B,A,E,D),C) = k2_seq_1(k5_numbers,k1_numbers,k22_rfunct_3(B,D,B),k1_nat_1(F,np__1)) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> k5_relset_1(B,k1_numbers,k3_rearran1(A,B,D,C)) = k5_relset_1(k5_numbers,k1_numbers,k22_rfunct_3(A,C,A)) ) ) ) ) ) ).
fof(t17_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> r1_rfinseq(k3_rearran1(A,B,D,C),k22_rfunct_3(A,C,A)) ) ) ) ) ) ).
fof(t18_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> k22_rfunct_3(B,k3_rearran1(A,B,D,C),B) = k22_rfunct_3(A,C,A) ) ) ) ) ) ).
fof(t19_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> k24_rfunct_3(B,k3_rearran1(A,B,D,C),B) = k24_rfunct_3(A,C,A) ) ) ) ) ) ).
fof(t20_rearran1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(C) = k4_card_1(B) )
=> ( k22_rfunct_3(C,k21_rfunct_3(C,k3_rearran1(B,C,E,D),A),C) = k22_rfunct_3(B,k21_rfunct_3(B,D,A),B)
& k24_rfunct_3(C,k21_rfunct_3(C,k3_rearran1(B,C,E,D),A),C) = k24_rfunct_3(B,k21_rfunct_3(B,D,A),B) ) ) ) ) ) ) ) ).
fof(t21_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> k4_relset_1(B,k1_numbers,k4_rearran1(A,B,D,C)) = B ) ) ) ) ) ).
fof(t22_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(A))
& m2_finseq_1(E,k1_zfmisc_1(A)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(A) = k4_card_1(B) )
=> ( ( r2_hidden(C,k1_funct_1(k2_rearran1(A,E),np__1))
=> k2_seq_1(A,k1_numbers,k4_rearran1(B,A,E,D),C) = k2_seq_1(k5_numbers,k1_numbers,k22_rfunct_3(B,D,B),np__1) )
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,F)
& r2_hidden(C,k4_xboole_0(k1_funct_1(k2_rearran1(A,E),k1_nat_1(F,np__1)),k1_funct_1(k2_rearran1(A,E),F))) )
=> ( r1_xreal_0(k3_finseq_1(k2_rearran1(A,E)),F)
| k2_seq_1(A,k1_numbers,k4_rearran1(B,A,E,D),C) = k2_seq_1(k5_numbers,k1_numbers,k22_rfunct_3(B,D,B),k1_nat_1(F,np__1)) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> k5_relset_1(B,k1_numbers,k4_rearran1(A,B,D,C)) = k5_relset_1(k5_numbers,k1_numbers,k22_rfunct_3(A,C,A)) ) ) ) ) ) ).
fof(t24_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> r1_rfinseq(k4_rearran1(A,B,D,C),k22_rfunct_3(A,C,A)) ) ) ) ) ) ).
fof(t25_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> k22_rfunct_3(B,k4_rearran1(A,B,D,C),B) = k22_rfunct_3(A,C,A) ) ) ) ) ) ).
fof(t26_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> k24_rfunct_3(B,k4_rearran1(A,B,D,C),B) = k24_rfunct_3(A,C,A) ) ) ) ) ) ).
fof(t27_rearran1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(C) = k4_card_1(B) )
=> ( k22_rfunct_3(C,k21_rfunct_3(C,k4_rearran1(B,C,E,D),A),C) = k22_rfunct_3(B,k21_rfunct_3(B,D,A),B)
& k24_rfunct_3(C,k21_rfunct_3(C,k4_rearran1(B,C,E,D),A),C) = k24_rfunct_3(B,k21_rfunct_3(B,D,A),B) ) ) ) ) ) ) ) ).
fof(t28_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(B) = k4_card_1(A) )
=> ( r1_rfinseq(k4_rearran1(A,B,D,C),k3_rearran1(A,B,D,C))
& k22_rfunct_3(B,k4_rearran1(A,B,D,C),B) = k22_rfunct_3(B,k3_rearran1(A,B,D,C),B)
& k24_rfunct_3(B,k4_rearran1(A,B,D,C),B) = k24_rfunct_3(B,k3_rearran1(A,B,D,C),B) ) ) ) ) ) ) ).
fof(t29_rearran1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(C) = k4_card_1(B) )
=> ( r1_rfinseq(k19_rfunct_3(C,k21_rfunct_3(C,k3_rearran1(B,C,E,D),A)),k19_rfunct_3(B,k21_rfunct_3(B,D,A)))
& k22_rfunct_3(C,k19_rfunct_3(C,k21_rfunct_3(C,k3_rearran1(B,C,E,D),A)),C) = k22_rfunct_3(B,k19_rfunct_3(B,k21_rfunct_3(B,D,A)),B)
& k24_rfunct_3(C,k19_rfunct_3(C,k21_rfunct_3(C,k3_rearran1(B,C,E,D),A)),C) = k24_rfunct_3(B,k19_rfunct_3(B,k21_rfunct_3(B,D,A)),B) ) ) ) ) ) ) ) ).
fof(t30_rearran1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(C) = k4_card_1(B) )
=> ( r1_rfinseq(k20_rfunct_3(C,k21_rfunct_3(C,k3_rearran1(B,C,E,D),A)),k20_rfunct_3(B,k21_rfunct_3(B,D,A)))
& k22_rfunct_3(C,k20_rfunct_3(C,k21_rfunct_3(C,k3_rearran1(B,C,E,D),A)),C) = k22_rfunct_3(B,k20_rfunct_3(B,k21_rfunct_3(B,D,A)),B)
& k24_rfunct_3(C,k20_rfunct_3(C,k21_rfunct_3(C,k3_rearran1(B,C,E,D),A)),C) = k24_rfunct_3(B,k20_rfunct_3(B,k21_rfunct_3(B,D,A)),B) ) ) ) ) ) ) ) ).
fof(t31_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(A) = k4_card_1(B) )
=> ( k3_finseq_1(k22_rfunct_3(B,k3_rearran1(A,B,D,C),B)) = k4_card_1(B)
& r1_xreal_0(np__1,k3_finseq_1(k22_rfunct_3(B,k3_rearran1(A,B,D,C),B))) ) ) ) ) ) ) ).
fof(t32_rearran1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(B) = k4_card_1(C)
& r2_hidden(A,k4_finseq_1(E)) )
=> k16_finseq_1(k1_numbers,k22_rfunct_3(C,k3_rearran1(B,C,E,D),C),A) = k22_rfunct_3(C,k3_rearran1(B,C,E,D),k1_funct_1(E,A)) ) ) ) ) ) ) ).
fof(t33_rearran1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(B) = k4_card_1(C) )
=> k3_rearran1(B,C,E,k21_rfunct_3(B,D,A)) = k21_rfunct_3(C,k3_rearran1(B,C,E,D),A) ) ) ) ) ) ) ).
fof(t34_rearran1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(C) = k4_card_1(B) )
=> ( r1_rfinseq(k19_rfunct_3(C,k21_rfunct_3(C,k4_rearran1(B,C,E,D),A)),k19_rfunct_3(B,k21_rfunct_3(B,D,A)))
& k22_rfunct_3(C,k19_rfunct_3(C,k21_rfunct_3(C,k4_rearran1(B,C,E,D),A)),C) = k22_rfunct_3(B,k19_rfunct_3(B,k21_rfunct_3(B,D,A)),B)
& k24_rfunct_3(C,k19_rfunct_3(C,k21_rfunct_3(C,k4_rearran1(B,C,E,D),A)),C) = k24_rfunct_3(B,k19_rfunct_3(B,k21_rfunct_3(B,D,A)),B) ) ) ) ) ) ) ) ).
fof(t35_rearran1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(C) = k4_card_1(B) )
=> ( r1_rfinseq(k20_rfunct_3(C,k21_rfunct_3(C,k4_rearran1(B,C,E,D),A)),k20_rfunct_3(B,k21_rfunct_3(B,D,A)))
& k22_rfunct_3(C,k20_rfunct_3(C,k21_rfunct_3(C,k4_rearran1(B,C,E,D),A)),C) = k22_rfunct_3(B,k20_rfunct_3(B,k21_rfunct_3(B,D,A)),B)
& k24_rfunct_3(C,k20_rfunct_3(C,k21_rfunct_3(C,k4_rearran1(B,C,E,D),A)),C) = k24_rfunct_3(B,k20_rfunct_3(B,k21_rfunct_3(B,D,A)),B) ) ) ) ) ) ) ) ).
fof(t36_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(A) = k4_card_1(B) )
=> ( k3_finseq_1(k22_rfunct_3(B,k4_rearran1(A,B,D,C),B)) = k4_card_1(B)
& r1_xreal_0(np__1,k3_finseq_1(k22_rfunct_3(B,k4_rearran1(A,B,D,C),B))) ) ) ) ) ) ) ).
fof(t37_rearran1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(B) = k4_card_1(C)
& r2_hidden(A,k4_finseq_1(E)) )
=> k16_finseq_1(k1_numbers,k22_rfunct_3(C,k4_rearran1(B,C,E,D),C),A) = k22_rfunct_3(C,k4_rearran1(B,C,E,D),k1_funct_1(k2_rearran1(C,E),A)) ) ) ) ) ) ) ).
fof(t38_rearran1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k1_numbers) )
=> ! [E] :
( ( v1_rearran1(E)
& v2_rearran1(E)
& v3_rearran1(E,k1_zfmisc_1(C))
& m2_finseq_1(E,k1_zfmisc_1(C)) )
=> ( ( v1_partfun1(D,B,k1_numbers)
& k4_card_1(B) = k4_card_1(C) )
=> k4_rearran1(B,C,E,k21_rfunct_3(B,D,A)) = k21_rfunct_3(C,k4_rearran1(B,C,E,D),A) ) ) ) ) ) ) ).
fof(t39_rearran1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_rearran1(D)
& v2_rearran1(D)
& v3_rearran1(D,k1_zfmisc_1(B))
& m2_finseq_1(D,k1_zfmisc_1(B)) )
=> ( ( v1_partfun1(C,A,k1_numbers)
& k4_card_1(A) = k4_card_1(B) )
=> ( r1_rfinseq(k3_rearran1(A,B,D,C),C)
& r1_rfinseq(k4_rearran1(A,B,D,C),C)
& k5_relset_1(B,k1_numbers,k3_rearran1(A,B,D,C)) = k5_relset_1(A,k1_numbers,C)
& k5_relset_1(B,k1_numbers,k4_rearran1(A,B,D,C)) = k5_relset_1(A,k1_numbers,C) ) ) ) ) ) ) ).
fof(dt_k1_rearran1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v2_membered(B)
& v1_funct_1(C)
& m1_relset_1(C,A,B)
& m1_subset_1(D,k1_numbers) )
=> m2_rfunct_3(k1_rearran1(A,B,C,D),A,k1_numbers,k4_rfunct_3(A,k1_numbers)) ) ).
fof(redefinition_k1_rearran1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v2_membered(B)
& v1_funct_1(C)
& m1_relset_1(C,A,B)
& m1_subset_1(D,k1_numbers) )
=> k1_rearran1(A,B,C,D) = k12_seq_1(C,D) ) ).
fof(dt_k2_rearran1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v1_rearran1(B)
& v2_rearran1(B)
& v3_rearran1(B,k1_zfmisc_1(A))
& m1_finseq_1(B,k1_zfmisc_1(A)) )
=> ( v1_rearran1(k2_rearran1(A,B))
& v2_rearran1(k2_rearran1(A,B))
& v3_rearran1(k2_rearran1(A,B),k1_zfmisc_1(A))
& m2_finseq_1(k2_rearran1(A,B),k1_zfmisc_1(A)) ) ) ).
fof(dt_k3_rearran1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_rearran1(C)
& v2_rearran1(C)
& v3_rearran1(C,k1_zfmisc_1(B))
& m1_finseq_1(C,k1_zfmisc_1(B))
& v1_funct_1(D)
& m1_relset_1(D,A,k1_numbers) )
=> ( v1_funct_1(k3_rearran1(A,B,C,D))
& m2_relset_1(k3_rearran1(A,B,C,D),B,k1_numbers) ) ) ).
fof(dt_k4_rearran1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_rearran1(C)
& v2_rearran1(C)
& v3_rearran1(C,k1_zfmisc_1(B))
& m1_finseq_1(C,k1_zfmisc_1(B))
& v1_funct_1(D)
& m1_relset_1(D,A,k1_numbers) )
=> ( v1_funct_1(k4_rearran1(A,B,C,D))
& m2_relset_1(k4_rearran1(A,B,C,D),B,k1_numbers) ) ) ).
%------------------------------------------------------------------------------