SET007 Axioms: SET007+337.ax
%------------------------------------------------------------------------------
% File : SET007+337 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Reper Algebras
% 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 : midsp_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 80 ( 3 unt; 0 def)
% Number of atoms : 667 ( 104 equ)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 647 ( 60 ~; 0 |; 221 &)
% ( 21 <=>; 345 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 12 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-3 aty)
% Number of functors : 43 ( 43 usr; 6 con; 0-6 aty)
% Number of variables : 382 ( 375 !; 7 ?)
% 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_midsp_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] :
( l1_midsp_3(B,A)
& v1_midsp_3(B,A) ) ) ).
fof(fc1_midsp_3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m1_relset_1(C,k2_zfmisc_1(B,B),B)
& v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(A,B),B)
& m1_relset_1(D,k4_finseq_2(A,B),B) )
=> ( ~ v3_struct_0(g1_midsp_3(A,B,C,D))
& v1_midsp_3(g1_midsp_3(A,B,C,D),A) ) ) ).
fof(rc2_midsp_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] :
( l1_midsp_3(B,A)
& ~ v3_struct_0(B) ) ) ).
fof(rc3_midsp_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] :
( l1_midsp_3(B,k1_nat_1(A,np__2))
& ~ v3_struct_0(B)
& v2_midsp_1(B) ) ) ).
fof(t1_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m2_finseq_1(D,C)
=> ~ ( k3_finseq_1(D) = k1_nat_1(k1_nat_1(A,np__1),B)
& ! [E] :
( m2_finseq_1(E,C)
=> ! [F] :
( m2_finseq_1(F,C)
=> ! [G] :
( m1_subset_1(G,C)
=> ~ ( k3_finseq_1(E) = A
& k3_finseq_1(F) = B
& D = k8_finseq_1(C,k8_finseq_1(C,E,k12_finseq_1(C,G)),F) ) ) ) ) ) ) ) ) ) ).
fof(t2_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(A,k2_finseq_1(B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( B = k1_nat_1(k1_nat_1(C,np__1),D)
& A = k1_nat_1(C,np__1) ) ) ) ) ) ) ).
fof(t3_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m2_finseq_1(D,B)
=> ! [E] :
( m2_finseq_1(E,B)
=> ! [F] :
( m2_finseq_1(F,B)
=> ( ( D = k8_finseq_1(B,k8_finseq_1(B,E,k12_finseq_1(B,C)),F)
& A = k1_nat_1(k3_finseq_1(E),np__1) )
=> ( ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,G)
& r1_xreal_0(G,k3_finseq_1(E)) )
=> k1_funct_1(D,G) = k1_funct_1(E,G) ) )
& k1_funct_1(D,A) = C
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(k1_nat_1(A,np__1),G)
& r1_xreal_0(G,k3_finseq_1(D)) )
=> k1_funct_1(D,G) = k1_funct_1(F,k6_xcmplx_0(G,A)) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(A,B)
& A != k1_nat_1(B,np__1)
& ~ r1_xreal_0(k1_nat_1(B,np__2),A) ) ) ) ).
fof(t5_midsp_3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(A,k4_xboole_0(k2_finseq_1(B),k1_tarski(C)))
& C = k1_nat_1(D,np__1)
& ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,D) )
& ~ ( r1_xreal_0(k1_nat_1(C,np__1),A)
& r1_xreal_0(A,B) ) ) ) ) ) ) ).
fof(d1_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( m2_finseq_2(E,C,k4_finseq_2(A,C))
=> ( r2_hidden(B,k2_finseq_1(A))
=> ! [F] :
( m2_finseq_2(F,C,k4_finseq_2(A,C))
=> ( F = k1_midsp_3(A,B,C,D,E)
<=> ( k1_funct_1(F,B) = D
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r2_hidden(G,k4_xboole_0(k4_finseq_1(E),k1_tarski(B)))
=> k1_funct_1(F,G) = k1_funct_1(E,G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> k4_midsp_3(A,B,C,D) = k1_funct_1(u1_midsp_3(k1_nat_1(A,np__2),B),k3_midsp_3(A,B,np__1,k1_nat_1(A,np__1),k2_midsp_3(A,B,C),D)) ) ) ) ) ).
fof(d3_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(A,np__2)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ( F = k5_midsp_3(A,B,C,D,E)
<=> ! [G] :
( ~ v1_xboole_0(G)
=> ! [H] :
( m2_finseq_2(H,G,k4_finseq_2(k1_nat_1(A,np__1),G))
=> ! [I] :
( m1_subset_1(I,G)
=> ( ( G = u1_struct_0(C)
& H = E
& I = D )
=> F = k1_midsp_3(k1_nat_1(A,np__1),B,G,I,H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_midsp_3,axiom,
$true ).
fof(t7_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(B,np__2)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(B,np__1),u1_struct_0(C)))
=> ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))
=> ( k1_funct_1(k5_midsp_3(B,A,C,D,E),A) = D
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k4_xboole_0(k4_finseq_1(E),k1_tarski(A)))
=> k1_funct_1(k5_midsp_3(B,A,C,D,E),F) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ) ).
fof(d4_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( m1_midsp_3(B,A)
<=> ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_nat_1(A,np__1)) ) ) ) ) ).
fof(t8_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( m1_midsp_3(A,B)
<=> r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1))) ) ) ) ).
fof(t9_midsp_3,axiom,
$true ).
fof(t10_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,B)
=> m1_midsp_3(k1_nat_1(A,np__1),B) ) ) ) ).
fof(t11_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ( ! [E] :
( m1_midsp_3(E,A)
=> k1_funct_1(C,E) = k1_funct_1(D,E) )
=> C = D ) ) ) ) ) ).
fof(t12_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(A,np__2)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ( ! [F] :
( m1_midsp_3(F,A)
=> ( F = B
=> k1_funct_1(k5_midsp_3(A,B,C,D,E),F) = D ) )
& ! [F] :
( m1_midsp_3(F,A)
=> ! [G] :
( m1_midsp_3(G,A)
=> ( F != G
=> k1_funct_1(k5_midsp_3(A,G,C,D,E),F) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ) ).
fof(d5_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ( v2_midsp_3(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ( ! [G] :
( m1_midsp_3(G,A)
=> k4_midsp_1(B,C,k6_midsp_3(A,u1_struct_0(B),F,G)) = k4_midsp_1(B,D,k6_midsp_3(A,u1_struct_0(B),E,G)) )
=> k4_midsp_1(B,C,k4_midsp_3(A,B,D,F)) = k4_midsp_1(B,D,k4_midsp_3(A,B,C,E)) ) ) ) ) ) ) ) ) ).
fof(d6_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(A,np__2)) )
=> ( r1_midsp_3(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> k4_midsp_3(A,C,D,k5_midsp_3(A,B,C,D,E)) = D ) ) ) ) ) ) ).
fof(d7_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(A,np__2)) )
=> ( r2_midsp_3(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ( k1_funct_1(F,B) = E
=> k4_midsp_3(A,C,D,k5_midsp_3(A,B,C,k4_midsp_1(C,D,E),F)) = k4_midsp_1(C,D,k4_midsp_3(A,C,D,F)) ) ) ) ) ) ) ) ) ).
fof(t13_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( m1_midsp_3(C,A)
=> ( r2_midsp_3(A,C,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ! [G] :
( m2_finseq_2(G,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ( G = k5_midsp_3(A,C,B,E,F)
=> k4_midsp_3(A,B,D,k5_midsp_3(A,C,B,k4_midsp_1(B,D,E),F)) = k4_midsp_1(B,D,k4_midsp_3(A,B,D,G)) ) ) ) ) ) ) ) ) ) ).
fof(d8_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(A,np__2)) )
=> ( r3_midsp_3(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m2_finseq_2(G,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ( k1_funct_1(G,B) = E
=> k4_midsp_3(A,C,D,k5_midsp_3(A,B,C,k4_midsp_1(C,E,F),G)) = k4_midsp_1(C,k4_midsp_3(A,C,D,G),k4_midsp_3(A,C,D,k5_midsp_3(A,B,C,F,G))) ) ) ) ) ) ) ) ) ) ).
fof(d9_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(A,np__2)) )
=> ( r4_midsp_3(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ( k1_funct_1(E,B) = F
=> k4_midsp_3(A,C,D,k5_midsp_3(A,k1_nat_1(B,np__1),C,F,E)) = D ) ) ) ) ) ) ) ) ).
fof(d10_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( ( v3_midsp_2(C,B)
& l1_midsp_2(C,B) )
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(u1_midsp_2(B,C)))
=> ! [G] :
( m2_finseq_2(G,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
=> ( G = k7_midsp_3(A,B,C,D,E,F)
<=> ! [H] :
( ~ v1_xboole_0(H)
=> ! [I] :
( m2_finseq_2(I,H,k4_finseq_2(k1_nat_1(A,np__1),H))
=> ! [J] :
( m1_subset_1(J,H)
=> ( ( H = u1_struct_0(u1_midsp_2(B,C))
& I = D
& J = F )
=> G = k1_midsp_3(k1_nat_1(A,np__1),E,H,J,I) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(B,np__2)) )
=> ! [D] :
( ( v3_midsp_2(D,C)
& l1_midsp_2(D,C) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(u1_midsp_2(C,D)))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(B,np__1),u1_struct_0(u1_midsp_2(C,D))))
=> ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))
=> ( k1_funct_1(k7_midsp_3(B,C,D,F,A,E),A) = E
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r2_hidden(G,k4_xboole_0(k4_finseq_1(F),k1_tarski(A)))
=> k1_funct_1(k7_midsp_3(B,C,D,F,A,E),G) = k1_funct_1(F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(A,np__2)) )
=> ! [D] :
( ( v3_midsp_2(D,C)
& l1_midsp_2(D,C) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(u1_midsp_2(C,D)))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
=> ( ! [G] :
( m1_midsp_3(G,A)
=> ( G = B
=> k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),k7_midsp_3(A,C,D,F,B,E),G) = E ) )
& ! [G] :
( m1_midsp_3(G,A)
=> ! [H] :
( m1_midsp_3(H,A)
=> ( G != H
=> k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),k7_midsp_3(A,C,D,F,H,E),G) = k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( ( v3_midsp_2(C,B)
& l1_midsp_2(C,B) )
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
=> ( ! [F] :
( m1_midsp_3(F,A)
=> k6_midsp_3(A,u1_struct_0(u1_midsp_2(B,C)),D,F) = k6_midsp_3(A,u1_struct_0(u1_midsp_2(B,C)),E,F) )
=> D = E ) ) ) ) ) ) ).
fof(d11_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( ( v3_midsp_2(C,B)
& l1_midsp_2(C,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ( F = k8_midsp_3(A,B,C,D,E)
<=> ! [G] :
( m1_midsp_3(G,A)
=> k6_midsp_3(A,u1_struct_0(B),F,G) = k10_midsp_2(B,C,D,k6_midsp_3(A,u1_struct_0(u1_midsp_2(B,C)),E,G)) ) ) ) ) ) ) ) ) ).
fof(d12_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( ( v3_midsp_2(C,B)
& l1_midsp_2(C,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
=> ( F = k9_midsp_3(A,B,C,D,E)
<=> ! [G] :
( m1_midsp_3(G,A)
=> k6_midsp_3(A,u1_struct_0(u1_midsp_2(B,C)),F,G) = k9_midsp_2(B,C,D,k6_midsp_3(A,u1_struct_0(B),E,G)) ) ) ) ) ) ) ) ) ).
fof(t17_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ! [E] :
( ( v3_midsp_2(E,B)
& l1_midsp_2(E,B) )
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,E)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,E))))
=> ( k9_midsp_3(A,B,E,C,D) = F
<=> k8_midsp_3(A,B,E,C,F) = D ) ) ) ) ) ) ) ).
fof(t18_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( ( v3_midsp_2(D,B)
& l1_midsp_2(D,B) )
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,D))))
=> k9_midsp_3(A,B,D,C,k8_midsp_3(A,B,D,C,E)) = E ) ) ) ) ) ).
fof(t19_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ! [E] :
( ( v3_midsp_2(E,B)
& l1_midsp_2(E,B) )
=> k8_midsp_3(A,B,E,C,k9_midsp_3(A,B,E,C,D)) = D ) ) ) ) ) ).
fof(d13_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( ( v3_midsp_2(C,B)
& l1_midsp_2(C,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
=> k10_midsp_3(A,B,C,D,E) = k9_midsp_2(B,C,D,k4_midsp_3(A,B,D,k8_midsp_3(A,B,C,D,E))) ) ) ) ) ) ).
fof(t20_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ! [F] :
( ( v3_midsp_2(F,B)
& l1_midsp_2(F,B) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(u1_midsp_2(B,F)))
=> ! [H] :
( m2_finseq_2(H,u1_struct_0(u1_midsp_2(B,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,F))))
=> ( ( k9_midsp_3(A,B,F,C,E) = H
& k9_midsp_2(B,F,C,D) = G )
=> ( k4_midsp_3(A,B,C,E) = D
<=> k10_midsp_3(A,B,F,C,H) = G ) ) ) ) ) ) ) ) ) ) ).
fof(t21_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ! [C] :
( ( v3_midsp_2(C,B)
& l1_midsp_2(C,B) )
=> ( v2_midsp_3(B,A)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
=> k10_midsp_3(A,B,C,D,F) = k10_midsp_3(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(t22_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> r2_hidden(np__1,k2_finseq_1(k1_nat_1(A,np__1))) ) ).
fof(t23_midsp_3,axiom,
$true ).
fof(t24_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> m1_midsp_3(np__1,A) ) ).
fof(d14_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) )
=> ( m2_midsp_3(B,A)
<=> v2_midsp_3(B,A) ) ) ) ).
fof(t25_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_midsp_3(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( ( v3_midsp_2(E,B)
& l1_midsp_2(E,B) )
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,E)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,E))))
=> k10_midsp_3(A,B,E,C,F) = k10_midsp_3(A,B,E,D,F) ) ) ) ) ) ) ).
fof(d15_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_midsp_3(B,A)
=> ! [C] :
( ( v3_midsp_2(C,B)
& l1_midsp_2(C,B) )
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(u1_midsp_2(B,C)))
=> ( E = k11_midsp_3(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> E = k10_midsp_3(A,B,C,F,D) ) ) ) ) ) ) ) ).
fof(t26_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_midsp_3(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ! [F] :
( ( v3_midsp_2(F,B)
& l1_midsp_2(F,B) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(u1_midsp_2(B,F)))
=> ! [H] :
( m2_finseq_2(H,u1_struct_0(u1_midsp_2(B,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,F))))
=> ( ( k9_midsp_3(A,B,F,C,E) = H
& k9_midsp_2(B,F,C,D) = G
& k11_midsp_3(A,B,F,H) = G )
=> k4_midsp_3(A,B,C,E) = D ) ) ) ) ) ) ) ) ) ).
fof(t27_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_midsp_3(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B)))
=> ! [F] :
( ( v3_midsp_2(F,B)
& l1_midsp_2(F,B) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(u1_midsp_2(B,F)))
=> ! [H] :
( m2_finseq_2(H,u1_struct_0(u1_midsp_2(B,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,F))))
=> ( ( k8_midsp_3(A,B,F,C,H) = E
& k10_midsp_2(B,F,C,G) = D
& k4_midsp_3(A,B,C,E) = D )
=> k11_midsp_3(A,B,F,H) = G ) ) ) ) ) ) ) ) ) ).
fof(t28_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> ! [C] :
( m2_midsp_3(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ! [G] :
( ( v3_midsp_2(G,C)
& l1_midsp_2(G,C) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(u1_midsp_2(C,G)))
=> ! [I] :
( m2_finseq_2(I,u1_struct_0(u1_midsp_2(C,G)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,G))))
=> ( ( k9_midsp_3(A,C,G,D,F) = I
& k9_midsp_2(C,G,D,E) = H )
=> k9_midsp_3(A,C,G,D,k5_midsp_3(A,B,C,E,F)) = k7_midsp_3(A,C,G,I,B,H) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> ! [C] :
( m2_midsp_3(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ! [G] :
( ( v3_midsp_2(G,C)
& l1_midsp_2(G,C) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(u1_midsp_2(C,G)))
=> ! [I] :
( m2_finseq_2(I,u1_struct_0(u1_midsp_2(C,G)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,G))))
=> ( ( k8_midsp_3(A,C,G,D,I) = F
& k10_midsp_2(C,G,D,H) = E )
=> k8_midsp_3(A,C,G,D,k7_midsp_3(A,C,G,I,B,H)) = k5_midsp_3(A,B,C,E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t30_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> ! [C] :
( m2_midsp_3(C,A)
=> ! [D] :
( ( v3_midsp_2(D,C)
& l1_midsp_2(D,C) )
=> ( r1_midsp_3(A,B,C)
<=> ! [E] :
( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
=> k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,B,k11_midsp_2(C,D))) = k11_midsp_2(C,D) ) ) ) ) ) ) ).
fof(t31_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> ! [C] :
( m2_midsp_3(C,A)
=> ! [D] :
( ( v3_midsp_2(D,C)
& l1_midsp_2(D,C) )
=> ( r2_midsp_3(A,B,C)
<=> ! [E] :
( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
=> k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,B,k1_midsp_2(u1_midsp_2(C,D),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),E,B)))) = k1_midsp_2(u1_midsp_2(C,D),k11_midsp_3(A,C,D,E)) ) ) ) ) ) ) ).
fof(t32_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> ! [C] :
( m2_midsp_3(C,A)
=> ( ( r1_midsp_3(A,B,C)
& r3_midsp_3(A,B,C) )
=> r2_midsp_3(A,B,C) ) ) ) ) ).
fof(t33_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> ! [C] :
( m2_midsp_3(C,A)
=> ! [D] :
( ( v3_midsp_2(D,C)
& l1_midsp_2(D,C) )
=> ( r1_midsp_3(A,B,C)
=> ( r3_midsp_3(A,B,C)
<=> ! [E] :
( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(u1_midsp_2(C,D)))
=> k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,B,k2_rlvect_1(u1_midsp_2(C,D),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),E,B),F))) = k2_rlvect_1(u1_midsp_2(C,D),k11_midsp_3(A,C,D,E),k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,B,F))) ) ) ) ) ) ) ) ) ).
fof(t34_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> ! [C] :
( m2_midsp_3(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ! [F] :
( ( v3_midsp_2(F,C)
& l1_midsp_2(F,C) )
=> ! [G] :
( m2_finseq_2(G,u1_struct_0(u1_midsp_2(C,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,F))))
=> ( ( k9_midsp_3(A,C,F,D,E) = G
& r1_xreal_0(B,A) )
=> k9_midsp_3(A,C,F,D,k5_midsp_3(A,k1_nat_1(B,np__1),C,k6_midsp_3(A,u1_struct_0(C),E,B),E)) = k7_midsp_3(A,C,F,G,k1_nat_1(B,np__1),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,F)),G,B)) ) ) ) ) ) ) ) ) ).
fof(t35_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> ! [C] :
( m2_midsp_3(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C)))
=> ! [F] :
( ( v3_midsp_2(F,C)
& l1_midsp_2(F,C) )
=> ! [G] :
( m2_finseq_2(G,u1_struct_0(u1_midsp_2(C,F)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,F))))
=> ( ( k8_midsp_3(A,C,F,D,G) = E
& r1_xreal_0(B,A) )
=> k8_midsp_3(A,C,F,D,k7_midsp_3(A,C,F,G,k1_nat_1(B,np__1),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,F)),G,B))) = k5_midsp_3(A,k1_nat_1(B,np__1),C,k6_midsp_3(A,u1_struct_0(C),E,B),E) ) ) ) ) ) ) ) ) ).
fof(t36_midsp_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> ! [C] :
( m2_midsp_3(C,A)
=> ! [D] :
( ( v3_midsp_2(D,C)
& l1_midsp_2(D,C) )
=> ( r1_xreal_0(B,A)
=> ( r4_midsp_3(A,B,C)
<=> ! [E] :
( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(C,D))))
=> k11_midsp_3(A,C,D,k7_midsp_3(A,C,D,E,k1_nat_1(B,np__1),k6_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),E,B))) = k11_midsp_2(C,D) ) ) ) ) ) ) ) ).
fof(s1_midsp_3,axiom,
? [A] :
( m2_finseq_1(A,f2_s1_midsp_3)
& k3_finseq_1(A) = k1_nat_1(f1_s1_midsp_3,np__1)
& ! [B] :
( m1_midsp_3(B,f1_s1_midsp_3)
=> k1_funct_1(A,B) = f3_s1_midsp_3(B) ) ) ).
fof(dt_m1_midsp_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ! [B] :
( m1_midsp_3(B,A)
=> m2_subset_1(B,k1_numbers,k5_numbers) ) ) ).
fof(existence_m1_midsp_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] : m1_midsp_3(B,A) ) ).
fof(dt_m2_midsp_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ! [B] :
( m2_midsp_3(B,A)
=> ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2)) ) ) ) ).
fof(existence_m2_midsp_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] : m2_midsp_3(B,A) ) ).
fof(dt_l1_midsp_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ! [B] :
( l1_midsp_3(B,A)
=> l1_midsp_1(B) ) ) ).
fof(existence_l1_midsp_3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] : l1_midsp_3(B,A) ) ).
fof(abstractness_v1_midsp_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& l1_midsp_3(B,A) )
=> ( v1_midsp_3(B,A)
=> B = g1_midsp_3(A,u1_struct_0(B),u1_midsp_1(B),u1_midsp_3(A,B)) ) ) ).
fof(dt_k1_midsp_3,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& ~ v1_xboole_0(C)
& m1_subset_1(D,C)
& m1_subset_1(E,k4_finseq_2(A,C)) )
=> m2_finseq_2(k1_midsp_3(A,B,C,D,E),C,k4_finseq_2(A,C)) ) ).
fof(dt_k2_midsp_3,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2))
& m1_subset_1(C,u1_struct_0(B)) )
=> m2_finseq_2(k2_midsp_3(A,B,C),u1_struct_0(B),k4_finseq_2(np__1,u1_struct_0(B))) ) ).
fof(redefinition_k2_midsp_3,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2))
& m1_subset_1(C,u1_struct_0(B)) )
=> k2_midsp_3(A,B,C) = k5_finseq_1(C) ) ).
fof(dt_k3_midsp_3,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(A,k5_numbers)
& ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2))
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers)
& m1_subset_1(E,k4_finseq_2(C,u1_struct_0(B)))
& m1_subset_1(F,k4_finseq_2(D,u1_struct_0(B))) )
=> m2_finseq_2(k3_midsp_3(A,B,C,D,E,F),u1_struct_0(B),k4_finseq_2(k1_nat_1(C,D),u1_struct_0(B))) ) ).
fof(redefinition_k3_midsp_3,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(A,k5_numbers)
& ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2))
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers)
& m1_subset_1(E,k4_finseq_2(C,u1_struct_0(B)))
& m1_subset_1(F,k4_finseq_2(D,u1_struct_0(B))) )
=> k3_midsp_3(A,B,C,D,E,F) = k7_finseq_1(E,F) ) ).
fof(dt_k4_midsp_3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2))
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B))) )
=> m1_subset_1(k4_midsp_3(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k5_midsp_3,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& ~ v3_struct_0(C)
& v2_midsp_1(C)
& l1_midsp_3(C,k1_nat_1(A,np__2))
& m1_subset_1(D,u1_struct_0(C))
& m1_subset_1(E,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C))) )
=> m2_finseq_2(k5_midsp_3(A,B,C,D,E),u1_struct_0(C),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(C))) ) ).
fof(dt_k6_midsp_3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& m1_subset_1(C,k4_finseq_2(k1_nat_1(A,np__1),B))
& m1_midsp_3(D,A) )
=> m1_subset_1(k6_midsp_3(A,B,C,D),B) ) ).
fof(redefinition_k6_midsp_3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& m1_subset_1(C,k4_finseq_2(k1_nat_1(A,np__1),B))
& m1_midsp_3(D,A) )
=> k6_midsp_3(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k7_midsp_3,axiom,
! [A,B,C,D,E,F] :
( ( m1_subset_1(A,k5_numbers)
& ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2))
& v3_midsp_2(C,B)
& l1_midsp_2(C,B)
& m1_subset_1(D,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C))))
& m1_subset_1(E,k5_numbers)
& m1_subset_1(F,u1_struct_0(u1_midsp_2(B,C))) )
=> m2_finseq_2(k7_midsp_3(A,B,C,D,E,F),u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) ) ).
fof(dt_k8_midsp_3,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2))
& v3_midsp_2(C,B)
& l1_midsp_2(C,B)
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) )
=> m2_finseq_2(k8_midsp_3(A,B,C,D,E),u1_struct_0(B),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B))) ) ).
fof(dt_k9_midsp_3,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2))
& v3_midsp_2(C,B)
& l1_midsp_2(C,B)
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(B))) )
=> m2_finseq_2(k9_midsp_3(A,B,C,D,E),u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) ) ).
fof(dt_k10_midsp_3,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_3(B,k1_nat_1(A,np__2))
& v3_midsp_2(C,B)
& l1_midsp_2(C,B)
& m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) )
=> m1_subset_1(k10_midsp_3(A,B,C,D,E),u1_struct_0(u1_midsp_2(B,C))) ) ).
fof(dt_k11_midsp_3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m2_midsp_3(B,A)
& v3_midsp_2(C,B)
& l1_midsp_2(C,B)
& m1_subset_1(D,k4_finseq_2(k1_nat_1(A,np__1),u1_struct_0(u1_midsp_2(B,C)))) )
=> m1_subset_1(k11_midsp_3(A,B,C,D),u1_struct_0(u1_midsp_2(B,C))) ) ).
fof(dt_u1_midsp_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& l1_midsp_3(B,A) )
=> ( v1_funct_1(u1_midsp_3(A,B))
& v1_funct_2(u1_midsp_3(A,B),k4_finseq_2(A,u1_struct_0(B)),u1_struct_0(B))
& m2_relset_1(u1_midsp_3(A,B),k4_finseq_2(A,u1_struct_0(B)),u1_struct_0(B)) ) ) ).
fof(dt_g1_midsp_3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m1_relset_1(C,k2_zfmisc_1(B,B),B)
& v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(A,B),B)
& m1_relset_1(D,k4_finseq_2(A,B),B) )
=> ( v1_midsp_3(g1_midsp_3(A,B,C,D),A)
& l1_midsp_3(g1_midsp_3(A,B,C,D),A) ) ) ).
fof(free_g1_midsp_3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m1_relset_1(C,k2_zfmisc_1(B,B),B)
& v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(A,B),B)
& m1_relset_1(D,k4_finseq_2(A,B),B) )
=> ! [E,F,G,H] :
( g1_midsp_3(A,B,C,D) = g1_midsp_3(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
%------------------------------------------------------------------------------