SET007 Axioms: SET007+302.ax
%------------------------------------------------------------------------------
% File : SET007+302 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Atlas of Midpoint Algebra
% 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 80 ( 6 unt; 0 def)
% Number of atoms : 818 ( 104 equ)
% Maximal formula atoms : 34 ( 10 avg)
% Number of connectives : 852 ( 114 ~; 0 |; 432 &)
% ( 19 <=>; 287 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 0 con; 1-6 aty)
% Number of variables : 292 ( 281 !; 11 ?)
% 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_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ( ~ v3_struct_0(k19_midsp_1(A))
& v1_rlvect_1(k19_midsp_1(A))
& v3_rlvect_1(k19_midsp_1(A))
& v4_rlvect_1(k19_midsp_1(A))
& v5_rlvect_1(k19_midsp_1(A))
& v6_rlvect_1(k19_midsp_1(A)) ) ) ).
fof(cc1_midsp_2,axiom,
! [A] :
( l1_rlvect_1(A)
=> ( ( ~ v3_struct_0(A)
& v1_midsp_2(A) )
=> ( ~ v3_struct_0(A)
& v13_vectsp_1(A) ) ) ) ).
fof(rc1_midsp_2,axiom,
? [A] :
( l1_rlvect_1(A)
& ~ v3_struct_0(A)
& v1_rlvect_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& v1_midsp_2(A) ) ).
fof(fc2_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ( ~ v3_struct_0(k19_midsp_1(A))
& v1_rlvect_1(k19_midsp_1(A))
& v3_rlvect_1(k19_midsp_1(A))
& v4_rlvect_1(k19_midsp_1(A))
& v5_rlvect_1(k19_midsp_1(A))
& v6_rlvect_1(k19_midsp_1(A))
& v13_vectsp_1(k19_midsp_1(A))
& v1_midsp_2(k19_midsp_1(A)) ) ) ).
fof(fc3_midsp_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ( ~ v3_struct_0(g1_midsp_1(A,B))
& v1_midsp_1(g1_midsp_1(A,B)) ) ) ).
fof(rc2_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A) )
=> ? [B] :
( l1_midsp_2(B,A)
& v2_midsp_2(B,A) ) ) ).
fof(rc3_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ? [B] :
( l1_midsp_2(B,A)
& v3_midsp_2(B,A) ) ) ).
fof(d1_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_midsp_2(A,B) = k2_rlvect_1(A,B,B) ) ) ).
fof(d2_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B)) )
=> ( r1_midsp_2(A,B,C)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( k1_midsp_1(A,D,E) = F
<=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,D,F) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,F,E) ) ) ) ) ) ) ) ) ).
fof(t1_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_midsp_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( r1_midsp_2(B,A,D)
=> k1_midsp_1(B,C,C) = C ) ) ) ) ) ).
fof(d3_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( r2_midsp_2(A,B,C)
<=> ( ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ? [F] :
( m1_subset_1(F,A)
& k2_binop_1(A,A,u1_struct_0(B),C,D,F) = E ) ) )
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ( k2_binop_1(A,A,u1_struct_0(B),C,D,E) = k2_binop_1(A,A,u1_struct_0(B),C,D,F)
=> E = F ) ) ) )
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> k2_rlvect_1(B,k2_binop_1(A,A,u1_struct_0(B),C,D,E),k2_binop_1(A,A,u1_struct_0(B),C,E,F)) = k2_binop_1(A,A,u1_struct_0(B),C,D,F) ) ) ) ) ) ) ) ) ).
fof(d4_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_midsp_2(A,B,C)
=> ! [F] :
( m1_subset_1(F,A)
=> ( F = k2_midsp_2(A,B,C,D,E)
<=> k2_binop_1(A,A,u1_struct_0(B),C,D,F) = E ) ) ) ) ) ) ) ) ).
fof(t2_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> k1_midsp_2(A,k1_rlvect_1(A)) = k1_rlvect_1(A) ) ).
fof(t3_midsp_2,axiom,
$true ).
fof(t4_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),u1_struct_0(C))
& m2_relset_1(D,k2_zfmisc_1(A,A),u1_struct_0(C)) )
=> ( r2_midsp_2(A,C,D)
=> k2_binop_1(A,A,u1_struct_0(C),D,B,B) = k1_rlvect_1(C) ) ) ) ) ) ).
fof(t5_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& l1_rlvect_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),u1_struct_0(D))
& m2_relset_1(E,k2_zfmisc_1(A,A),u1_struct_0(D)) )
=> ( ( r2_midsp_2(A,D,E)
& k2_binop_1(A,A,u1_struct_0(D),E,B,C) = k1_rlvect_1(D) )
=> B = C ) ) ) ) ) ) ).
fof(t6_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& l1_rlvect_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),u1_struct_0(D))
& m2_relset_1(E,k2_zfmisc_1(A,A),u1_struct_0(D)) )
=> ( r2_midsp_2(A,D,E)
=> k2_binop_1(A,A,u1_struct_0(D),E,B,C) = k5_rlvect_1(D,k2_binop_1(A,A,u1_struct_0(D),E,C,B)) ) ) ) ) ) ) ).
fof(t7_midsp_2,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)
=> ! [F] :
( ( ~ v3_struct_0(F)
& v4_rlvect_1(F)
& v5_rlvect_1(F)
& v6_rlvect_1(F)
& l1_rlvect_1(F) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(A,A),u1_struct_0(F))
& m2_relset_1(G,k2_zfmisc_1(A,A),u1_struct_0(F)) )
=> ( ( r2_midsp_2(A,F,G)
& k2_binop_1(A,A,u1_struct_0(F),G,B,C) = k2_binop_1(A,A,u1_struct_0(F),G,D,E) )
=> k2_binop_1(A,A,u1_struct_0(F),G,C,B) = k2_binop_1(A,A,u1_struct_0(F),G,E,D) ) ) ) ) ) ) ) ) ).
fof(t8_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( r2_midsp_2(A,B,C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ? [F] :
( m1_subset_1(F,A)
& k2_binop_1(A,A,u1_struct_0(B),C,F,D) = E ) ) ) ) ) ) ) ).
fof(t9_midsp_2,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] :
( ( ~ v3_struct_0(E)
& v4_rlvect_1(E)
& v5_rlvect_1(E)
& v6_rlvect_1(E)
& l1_rlvect_1(E) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),u1_struct_0(E))
& m2_relset_1(F,k2_zfmisc_1(A,A),u1_struct_0(E)) )
=> ( ( r2_midsp_2(A,E,F)
& k2_binop_1(A,A,u1_struct_0(E),F,B,C) = k2_binop_1(A,A,u1_struct_0(E),F,D,C) )
=> B = D ) ) ) ) ) ) ) ).
fof(t10_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& l1_rlvect_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D)) )
=> ( ( r2_midsp_2(u1_struct_0(A),D,E)
& r1_midsp_2(A,D,E) )
=> k1_midsp_1(A,B,C) = k1_midsp_1(A,C,B) ) ) ) ) ) ) ).
fof(t11_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& l1_rlvect_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D)) )
=> ~ ( r2_midsp_2(u1_struct_0(A),D,E)
& r1_midsp_2(A,D,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k1_midsp_1(A,F,B) != C ) ) ) ) ) ) ) ).
fof(t12_midsp_2,axiom,
$true ).
fof(t13_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k4_rlvect_1(A,k4_rlvect_1(A,B,C),k4_rlvect_1(A,D,E)) = k4_rlvect_1(A,k4_rlvect_1(A,B,D),k4_rlvect_1(A,C,E)) ) ) ) ) ) ).
fof(t14_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_midsp_2(A,k4_rlvect_1(A,B,C)) = k4_rlvect_1(A,k1_midsp_2(A,B),k1_midsp_2(A,C)) ) ) ) ).
fof(t15_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_midsp_2(A,k5_rlvect_1(A,B)) = k5_rlvect_1(A,k1_midsp_2(A,B)) ) ) ).
fof(t16_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B)) )
=> ( ( r2_midsp_2(u1_struct_0(A),B,C)
& r1_midsp_2(A,B,C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( k1_midsp_1(A,D,E) = k1_midsp_1(A,F,G)
<=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,D,G) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,F,E) ) ) ) ) ) ) ) ) ) ).
fof(t17_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( r2_midsp_2(A,B,C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,A)
=> ( ( k2_binop_1(A,A,u1_struct_0(B),C,D,E) = k2_binop_1(A,A,u1_struct_0(B),C,E,G)
& k2_binop_1(A,A,u1_struct_0(B),C,D,F) = k2_binop_1(A,A,u1_struct_0(B),C,F,H) )
=> k2_binop_1(A,A,u1_struct_0(B),C,G,H) = k1_midsp_2(B,k2_binop_1(A,A,u1_struct_0(B),C,E,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(k19_midsp_1(A)))
<=> m1_midsp_1(B,A) )
& k1_rlvect_1(k19_midsp_1(A)) = k10_midsp_1(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(k19_midsp_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k19_midsp_1(A)))
=> ! [D] :
( m1_midsp_1(D,A)
=> ! [E] :
( m1_midsp_1(E,A)
=> ( ( B = D
& C = E )
=> k4_rlvect_1(k19_midsp_1(A),B,C) = k11_midsp_1(A,D,E) ) ) ) ) ) ) ) ).
fof(d5_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ( v1_midsp_2(A)
<=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& k1_midsp_2(A,C) = B ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k1_midsp_2(A,B) = k1_rlvect_1(A)
=> B = k1_rlvect_1(A) ) ) ) ) ) ).
fof(t19_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B = k5_rlvect_1(A,B)
=> B = k1_rlvect_1(A) ) ) ) ).
fof(t20_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_midsp_2(A,B) = k1_midsp_2(A,C)
=> B = C ) ) ) ) ).
fof(d6_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_midsp_2(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k3_midsp_2(A,B)
<=> k1_midsp_2(A,C) = B ) ) ) ) ).
fof(t21_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_midsp_2(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k3_midsp_2(A,k1_rlvect_1(A)) = k1_rlvect_1(A)
& k3_midsp_2(A,k4_rlvect_1(A,B,C)) = k4_rlvect_1(A,k3_midsp_2(A,B),k3_midsp_2(A,C))
& ( k3_midsp_2(A,B) = k3_midsp_2(A,C)
=> B = C )
& k3_midsp_2(A,k1_midsp_2(A,B)) = B ) ) ) ) ).
fof(t22_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_midsp_2(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_midsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( ( r2_midsp_2(u1_struct_0(B),A,C)
& r1_midsp_2(B,A,C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> k1_midsp_1(B,k1_midsp_1(B,D,E),k1_midsp_1(B,F,G)) = k1_midsp_1(B,k1_midsp_1(B,D,F),k1_midsp_1(B,E,G)) ) ) ) ) ) ) ) ) ).
fof(t23_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_midsp_2(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_midsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( ( r2_midsp_2(u1_struct_0(B),A,C)
& r1_midsp_2(B,A,C) )
=> ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_1(B) ) ) ) ) ) ).
fof(d7_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_midsp_2(A,B,C) = k12_midsp_1(A,B,C) ) ) ) ).
fof(d8_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k19_midsp_1(A)))
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k19_midsp_1(A))) )
=> ( B = k5_midsp_2(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k19_midsp_1(A)),B,C,D) = k12_midsp_1(A,C,D) ) ) ) ) ) ).
fof(t24_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> r2_midsp_2(u1_struct_0(A),k19_midsp_1(A),k5_midsp_2(A)) ) ).
fof(t25_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k12_midsp_1(A,B,C) = k12_midsp_1(A,D,E)
<=> k4_midsp_1(A,B,E) = k4_midsp_1(A,C,D) ) ) ) ) ) ) ).
fof(t26_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( k4_midsp_1(A,B,C) = D
<=> k12_midsp_1(A,B,D) = k12_midsp_1(A,D,C) ) ) ) ) ) ).
fof(t27_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> r1_midsp_2(A,k19_midsp_1(A),k5_midsp_2(A)) ) ).
fof(d9_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_midsp_2(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( r2_midsp_2(A,B,C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( D = k6_midsp_2(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> k2_binop_1(A,A,u1_struct_0(B),C,E,k2_binop_1(A,A,A,D,E,F)) = k2_binop_1(A,A,u1_struct_0(B),C,k2_binop_1(A,A,A,D,E,F),F) ) ) ) ) ) ) ) ) ).
fof(t28_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_midsp_2(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( r2_midsp_2(A,B,C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ( k2_binop_1(A,A,A,k6_midsp_2(A,B,C),D,E) = F
<=> k2_binop_1(A,A,u1_struct_0(B),C,D,F) = k2_binop_1(A,A,u1_struct_0(B),C,F,E) ) ) ) ) ) ) ) ) ).
fof(d10_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_midsp_2(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> k7_midsp_2(A,B,C) = C ) ) ) ).
fof(t29_midsp_2,axiom,
$true ).
fof(t30_midsp_2,axiom,
$true ).
fof(t31_midsp_2,axiom,
$true ).
fof(t32_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_midsp_2(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( r2_midsp_2(A,B,C)
=> r1_midsp_2(g1_midsp_1(A,k6_midsp_2(A,B,C)),B,k7_midsp_2(A,B,C)) ) ) ) ) ).
fof(d11_midsp_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_midsp_2(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( r2_midsp_2(A,B,C)
=> k8_midsp_2(A,B,C) = g1_midsp_1(A,k6_midsp_2(A,B,C)) ) ) ) ) ).
fof(t33_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A) )
=> ( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
<=> ? [B] :
( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_midsp_2(B)
& l1_rlvect_1(B)
& ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
& r2_midsp_2(u1_struct_0(A),B,C)
& r1_midsp_2(A,B,C) ) ) ) ) ).
fof(d12_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A) )
=> ! [B] :
( l1_midsp_2(B,A)
=> ( v3_midsp_2(B,A)
<=> ( v1_midsp_2(u1_midsp_2(A,B))
& v4_rlvect_1(u1_midsp_2(A,B))
& v5_rlvect_1(u1_midsp_2(A,B))
& v6_rlvect_1(u1_midsp_2(A,B))
& v3_rlvect_1(u1_midsp_2(A,B))
& r1_midsp_2(A,u1_midsp_2(A,B),u2_midsp_2(A,B))
& r2_midsp_2(u1_struct_0(A),u1_midsp_2(A,B),u2_midsp_2(A,B)) ) ) ) ) ).
fof(d13_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( l1_midsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k9_midsp_2(A,B,C,D) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(u1_midsp_2(A,B)),u2_midsp_2(A,B),C,D) ) ) ) ) ).
fof(d14_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( l1_midsp_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(u1_midsp_2(A,B)))
=> k10_midsp_2(A,B,C,D) = k2_midsp_2(u1_struct_0(A),u1_midsp_2(A,B),u2_midsp_2(A,B),C,D) ) ) ) ) ).
fof(d15_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( v3_midsp_2(B,A)
& l1_midsp_2(B,A) )
=> k11_midsp_2(A,B) = k1_rlvect_1(u1_midsp_2(A,B)) ) ) ).
fof(t34_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_midsp_2(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_midsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( ( r2_midsp_2(u1_struct_0(B),A,C)
& r1_midsp_2(B,A,C) )
=> ( k1_midsp_1(B,D,E) = k1_midsp_1(B,F,G)
<=> k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,E) = k4_rlvect_1(A,k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,F),k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,G)) ) ) ) ) ) ) ) ) ) ).
fof(t35_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_midsp_2(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_midsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r2_midsp_2(u1_struct_0(B),A,C)
& r1_midsp_2(B,A,C) )
=> ( k1_midsp_1(B,D,E) = F
<=> k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,E) = k1_midsp_2(A,k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,F)) ) ) ) ) ) ) ) ) ).
fof(t36_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( v3_midsp_2(B,A)
& l1_midsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( k4_midsp_1(A,C,D) = k4_midsp_1(A,E,F)
<=> k9_midsp_2(A,B,C,D) = k2_rlvect_1(u1_midsp_2(A,B),k9_midsp_2(A,B,C,E),k9_midsp_2(A,B,C,F)) ) ) ) ) ) ) ) ).
fof(t37_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( v3_midsp_2(B,A)
& l1_midsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k4_midsp_1(A,C,D) = E
<=> k9_midsp_2(A,B,C,D) = k1_midsp_2(u1_midsp_2(A,B),k9_midsp_2(A,B,C,E)) ) ) ) ) ) ) ).
fof(t38_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( v3_midsp_2(B,A)
& l1_midsp_2(B,A) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(u1_midsp_2(A,B)))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& k9_midsp_2(A,B,C,E) = D ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k9_midsp_2(A,B,C,D) = k9_midsp_2(A,B,C,E)
=> D = E ) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k2_rlvect_1(u1_midsp_2(A,B),k9_midsp_2(A,B,C,D),k9_midsp_2(A,B,D,E)) = k9_midsp_2(A,B,C,E) ) ) ) ) ) ) ).
fof(t39_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( v3_midsp_2(B,A)
& l1_midsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(u1_midsp_2(A,B)))
=> ( k9_midsp_2(A,B,C,C) = k11_midsp_2(A,B)
& ( k9_midsp_2(A,B,C,D) = k11_midsp_2(A,B)
=> C = D )
& k9_midsp_2(A,B,C,D) = k5_rlvect_1(u1_midsp_2(A,B),k9_midsp_2(A,B,D,C))
& ( k9_midsp_2(A,B,C,D) = k9_midsp_2(A,B,E,F)
=> k9_midsp_2(A,B,D,C) = k9_midsp_2(A,B,F,E) )
& ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(u1_midsp_2(A,B)))
=> ? [J] :
( m1_subset_1(J,u1_struct_0(A))
& k9_midsp_2(A,B,J,H) = I ) ) )
& ( k9_midsp_2(A,B,D,C) = k9_midsp_2(A,B,E,C)
=> D = E )
& ( k4_midsp_1(A,C,D) = E
=> k9_midsp_2(A,B,C,E) = k9_midsp_2(A,B,E,D) )
& ( k9_midsp_2(A,B,C,E) = k9_midsp_2(A,B,E,D)
=> k4_midsp_1(A,C,D) = E )
& ( k4_midsp_1(A,C,D) = k4_midsp_1(A,E,F)
=> k9_midsp_2(A,B,C,F) = k9_midsp_2(A,B,E,D) )
& ( k9_midsp_2(A,B,C,F) = k9_midsp_2(A,B,E,D)
=> k4_midsp_1(A,C,D) = k4_midsp_1(A,E,F) )
& ( k9_midsp_2(A,B,C,D) = G
=> k10_midsp_2(A,B,C,G) = D )
& ( k10_midsp_2(A,B,C,G) = D
=> k9_midsp_2(A,B,C,D) = G ) ) ) ) ) ) ) ) ) ).
fof(t40_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( v3_midsp_2(B,A)
& l1_midsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k10_midsp_2(A,B,C,k11_midsp_2(A,B)) = C ) ) ) ).
fof(dt_l1_midsp_2,axiom,
$true ).
fof(existence_l1_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A) )
=> ? [B] : l1_midsp_2(B,A) ) ).
fof(abstractness_v2_midsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A)
& l1_midsp_2(B,A) )
=> ( v2_midsp_2(B,A)
=> B = g1_midsp_2(A,u1_midsp_2(A,B),u2_midsp_2(A,B)) ) ) ).
fof(dt_k1_midsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k1_midsp_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_midsp_2,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_rlvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_subset_1(D,A)
& m1_subset_1(E,u1_struct_0(B)) )
=> m1_subset_1(k2_midsp_2(A,B,C,D,E),A) ) ).
fof(dt_k3_midsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v1_midsp_2(A)
& l1_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k3_midsp_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k4_midsp_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k4_midsp_2(A,B,C),u1_struct_0(k19_midsp_1(A))) ) ).
fof(dt_k5_midsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ( v1_funct_1(k5_midsp_2(A))
& v1_funct_2(k5_midsp_2(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k19_midsp_1(A)))
& m2_relset_1(k5_midsp_2(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k19_midsp_1(A))) ) ) ).
fof(dt_k6_midsp_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_midsp_2(B)
& l1_rlvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( v1_funct_1(k6_midsp_2(A,B,C))
& v1_funct_2(k6_midsp_2(A,B,C),k2_zfmisc_1(A,A),A)
& m2_relset_1(k6_midsp_2(A,B,C),k2_zfmisc_1(A,A),A) ) ) ).
fof(dt_k7_midsp_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_midsp_2(B)
& l1_rlvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( v1_funct_1(k7_midsp_2(A,B,C))
& v1_funct_2(k7_midsp_2(A,B,C),k2_zfmisc_1(u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C)))),u1_struct_0(B))
& m2_relset_1(k7_midsp_2(A,B,C),k2_zfmisc_1(u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C)))),u1_struct_0(B)) ) ) ).
fof(dt_k8_midsp_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_midsp_2(B)
& l1_rlvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
=> ( ~ v3_struct_0(k8_midsp_2(A,B,C))
& v1_midsp_1(k8_midsp_2(A,B,C))
& v2_midsp_1(k8_midsp_2(A,B,C))
& l1_midsp_1(k8_midsp_2(A,B,C)) ) ) ).
fof(dt_k9_midsp_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& l1_midsp_2(B,A)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k9_midsp_2(A,B,C,D),u1_struct_0(u1_midsp_2(A,B))) ) ).
fof(dt_k10_midsp_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& l1_midsp_2(B,A)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(u1_midsp_2(A,B))) )
=> m1_subset_1(k10_midsp_2(A,B,C,D),u1_struct_0(A)) ) ).
fof(dt_k11_midsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& v3_midsp_2(B,A)
& l1_midsp_2(B,A) )
=> m1_subset_1(k11_midsp_2(A,B),u1_struct_0(u1_midsp_2(A,B))) ) ).
fof(dt_u1_midsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A)
& l1_midsp_2(B,A) )
=> ( ~ v3_struct_0(u1_midsp_2(A,B))
& l1_rlvect_1(u1_midsp_2(A,B)) ) ) ).
fof(dt_u2_midsp_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A)
& l1_midsp_2(B,A) )
=> ( v1_funct_1(u2_midsp_2(A,B))
& v1_funct_2(u2_midsp_2(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(u1_midsp_2(A,B)))
& m2_relset_1(u2_midsp_2(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(u1_midsp_2(A,B))) ) ) ).
fof(dt_g1_midsp_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A)
& ~ v3_struct_0(B)
& l1_rlvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B)) )
=> ( v2_midsp_2(g1_midsp_2(A,B,C),A)
& l1_midsp_2(g1_midsp_2(A,B,C),A) ) ) ).
fof(free_g1_midsp_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A)
& ~ v3_struct_0(B)
& l1_rlvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B)) )
=> ! [D,E,F] :
( g1_midsp_2(A,B,C) = g1_midsp_2(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
%------------------------------------------------------------------------------