SET007 Axioms: SET007+220.ax
%------------------------------------------------------------------------------
% File : SET007+220 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Midpoint 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 149 ( 34 unt; 0 def)
% Number of atoms : 785 ( 107 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 748 ( 112 ~; 0 |; 317 &)
% ( 16 <=>; 303 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-5 aty)
% Number of functors : 38 ( 38 usr; 3 con; 0-6 aty)
% Number of variables : 342 ( 316 !; 26 ?)
% 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_1,axiom,
? [A] :
( l1_midsp_1(A)
& v1_midsp_1(A) ) ).
fof(rc2_midsp_1,axiom,
? [A] :
( l1_midsp_1(A)
& ~ v3_struct_0(A) ) ).
fof(fc1_midsp_1,axiom,
( ~ v3_struct_0(k3_midsp_1)
& v1_midsp_1(k3_midsp_1) ) ).
fof(rc3_midsp_1,axiom,
? [A] :
( l1_midsp_1(A)
& ~ v3_struct_0(A)
& v1_midsp_1(A)
& v2_midsp_1(A) ) ).
fof(fc2_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> ( v1_relat_1(k8_midsp_1(A,B))
& ~ v1_xboole_0(k8_midsp_1(A,B)) ) ) ).
fof(fc3_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ~ v1_xboole_0(k14_midsp_1(A)) ) ).
fof(fc4_midsp_1,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)) ) ) ).
fof(d1_midsp_1,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))
=> k1_midsp_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_midsp_1(A),B,C) ) ) ) ).
fof(d2_midsp_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))
& m2_relset_1(A,k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) )
=> A = k2_midsp_1 ) ).
fof(d3_midsp_1,axiom,
k3_midsp_1 = g1_midsp_1(k1_tarski(k1_xboole_0),k2_midsp_1) ).
fof(t1_midsp_1,axiom,
$true ).
fof(t2_midsp_1,axiom,
$true ).
fof(t3_midsp_1,axiom,
$true ).
fof(t4_midsp_1,axiom,
$true ).
fof(t5_midsp_1,axiom,
u1_struct_0(k3_midsp_1) = k1_tarski(k1_xboole_0) ).
fof(t6_midsp_1,axiom,
u1_midsp_1(k3_midsp_1) = k2_midsp_1 ).
fof(t7_midsp_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_midsp_1))
=> A = k1_xboole_0 ) ).
fof(t8_midsp_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_midsp_1))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_midsp_1))
=> k1_midsp_1(k3_midsp_1,A,B) = k1_binop_1(k2_midsp_1,A,B) ) ) ).
fof(t9_midsp_1,axiom,
$true ).
fof(t10_midsp_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_midsp_1))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_midsp_1))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_midsp_1))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_midsp_1))
=> ( k1_midsp_1(k3_midsp_1,A,A) = A
& k1_midsp_1(k3_midsp_1,A,B) = k1_midsp_1(k3_midsp_1,B,A)
& k1_midsp_1(k3_midsp_1,k1_midsp_1(k3_midsp_1,A,B),k1_midsp_1(k3_midsp_1,C,D)) = k1_midsp_1(k3_midsp_1,k1_midsp_1(k3_midsp_1,A,C),k1_midsp_1(k3_midsp_1,B,D))
& ? [E] :
( m1_subset_1(E,u1_struct_0(k3_midsp_1))
& k1_midsp_1(k3_midsp_1,E,A) = B ) ) ) ) ) ) ).
fof(d4_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A) )
=> ( v2_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))
=> ( k1_midsp_1(A,B,B) = B
& k1_midsp_1(A,B,C) = k1_midsp_1(A,C,B)
& k1_midsp_1(A,k1_midsp_1(A,B,C),k1_midsp_1(A,D,E)) = k1_midsp_1(A,k1_midsp_1(A,B,D),k1_midsp_1(A,C,E))
& ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& k1_midsp_1(A,F,B) = C ) ) ) ) ) ) ) ) ).
fof(t11_midsp_1,axiom,
$true ).
fof(t12_midsp_1,axiom,
$true ).
fof(t13_midsp_1,axiom,
$true ).
fof(t14_midsp_1,axiom,
$true ).
fof(t15_midsp_1,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,k4_midsp_1(A,B,C),D) = k4_midsp_1(A,k4_midsp_1(A,B,D),k4_midsp_1(A,C,D)) ) ) ) ) ).
fof(t16_midsp_1,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,k4_midsp_1(A,C,D)) = k4_midsp_1(A,k4_midsp_1(A,B,C),k4_midsp_1(A,B,D)) ) ) ) ) ).
fof(t17_midsp_1,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_1(A,B,C) = B
=> B = C ) ) ) ) ).
fof(t18_midsp_1,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) = k4_midsp_1(A,D,C)
=> B = D ) ) ) ) ) ).
fof(t19_midsp_1,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) = k4_midsp_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(d5_midsp_1,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))
=> ( r1_midsp_1(A,B,C,D,E)
<=> k4_midsp_1(A,B,E) = k4_midsp_1(A,C,D) ) ) ) ) ) ) ).
fof(t20_midsp_1,axiom,
$true ).
fof(t21_midsp_1,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))
=> r1_midsp_1(A,B,B,C,C) ) ) ) ).
fof(t22_midsp_1,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))
=> ( r1_midsp_1(A,B,C,D,E)
=> r1_midsp_1(A,D,E,B,C) ) ) ) ) ) ) ).
fof(t23_midsp_1,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))
=> ( r1_midsp_1(A,B,B,C,D)
=> C = D ) ) ) ) ) ).
fof(t24_midsp_1,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))
=> ( r1_midsp_1(A,B,C,D,D)
=> B = C ) ) ) ) ) ).
fof(t25_midsp_1,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))
=> r1_midsp_1(A,B,C,B,C) ) ) ) ).
fof(t26_midsp_1,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))
& r1_midsp_1(A,B,C,D,E) ) ) ) ) ) ).
fof(t27_midsp_1,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))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r1_midsp_1(A,B,C,D,E)
& r1_midsp_1(A,B,C,D,F) )
=> E = F ) ) ) ) ) ) ) ).
fof(t28_midsp_1,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))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r1_midsp_1(A,B,C,D,E)
& r1_midsp_1(A,B,C,F,G) )
=> r1_midsp_1(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t29_midsp_1,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))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r1_midsp_1(A,B,C,D,E)
& r1_midsp_1(A,C,F,E,G) )
=> r1_midsp_1(A,B,F,D,G) ) ) ) ) ) ) ) ) ).
fof(d6_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( r2_midsp_1(A,B,C)
<=> r1_midsp_1(A,k5_midsp_1(A,B),k6_midsp_1(A,B),k5_midsp_1(A,C),k6_midsp_1(A,C)) ) ) ) ) ).
fof(t30_midsp_1,axiom,
$true ).
fof(t31_midsp_1,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))
=> ( r1_midsp_1(A,B,C,D,E)
=> r2_midsp_1(A,k7_midsp_1(A,B,C),k7_midsp_1(A,D,E)) ) ) ) ) ) ) ).
fof(t32_midsp_1,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))
=> ( r2_midsp_1(A,k7_midsp_1(A,B,C),k7_midsp_1(A,D,E))
=> r1_midsp_1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t33_midsp_1,axiom,
$true ).
fof(t34_midsp_1,axiom,
$true ).
fof(t35_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( ( r2_midsp_1(A,B,C)
& r2_midsp_1(A,B,D) )
=> r2_midsp_1(A,C,D) ) ) ) ) ) ).
fof(t36_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( ( r2_midsp_1(A,B,C)
& r2_midsp_1(A,D,C) )
=> r2_midsp_1(A,B,D) ) ) ) ) ) ).
fof(t37_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( ( r2_midsp_1(A,B,C)
& r2_midsp_1(A,C,D) )
=> r2_midsp_1(A,B,D) ) ) ) ) ) ).
fof(t38_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( r2_midsp_1(A,B,C)
=> ( r2_midsp_1(A,D,B)
<=> r2_midsp_1(A,D,C) ) ) ) ) ) ) ).
fof(t40_midsp_1,axiom,
$true ).
fof(t41_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( r2_hidden(B,k8_midsp_1(A,C))
<=> r2_midsp_1(A,B,C) ) ) ) ) ).
fof(t42_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( r2_midsp_1(A,B,C)
=> k8_midsp_1(A,B) = k8_midsp_1(A,C) ) ) ) ) ).
fof(t43_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( k8_midsp_1(A,B) = k8_midsp_1(A,C)
=> r2_midsp_1(A,B,C) ) ) ) ) ).
fof(t44_midsp_1,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))
=> ( k8_midsp_1(A,k7_midsp_1(A,B,C)) = k8_midsp_1(A,k7_midsp_1(A,D,E))
=> k4_midsp_1(A,B,E) = k4_midsp_1(A,C,D) ) ) ) ) ) ) ).
fof(t45_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> r2_hidden(B,k8_midsp_1(A,B)) ) ) ).
fof(d8_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) )
=> ( m1_midsp_1(B,A)
<=> ? [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& B = k8_midsp_1(A,C) ) ) ) ) ).
fof(t46_midsp_1,axiom,
$true ).
fof(t47_midsp_1,axiom,
$true ).
fof(t48_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ? [B] :
( m1_midsp_1(B,A)
& ! [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( r2_hidden(C,B)
<=> k5_midsp_1(A,C) = k6_midsp_1(A,C) ) ) ) ) ).
fof(t49_midsp_1,axiom,
$true ).
fof(t50_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k10_midsp_1(A) = k9_midsp_1(A,k7_midsp_1(A,B,B)) ) ) ).
fof(t51_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> ! [C] :
( m1_midsp_1(C,A)
=> ? [D] :
( m1_midsp_1(D,A)
& ? [E] :
( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& ? [F] :
( m1_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& B = k9_midsp_1(A,E)
& C = k9_midsp_1(A,F)
& k6_midsp_1(A,E) = k5_midsp_1(A,F)
& D = k9_midsp_1(A,k7_midsp_1(A,k5_midsp_1(A,E),k6_midsp_1(A,F))) ) ) ) ) ) ) ).
fof(t52_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> ! [C] :
( m1_midsp_1(C,A)
=> ! [D] :
( m1_midsp_1(D,A)
=> ! [E] :
( m1_midsp_1(E,A)
=> ~ ( ? [F] :
( m1_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& ? [G] :
( m1_subset_1(G,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& B = k9_midsp_1(A,F)
& C = k9_midsp_1(A,G)
& k6_midsp_1(A,F) = k5_midsp_1(A,G)
& D = k9_midsp_1(A,k7_midsp_1(A,k5_midsp_1(A,F),k6_midsp_1(A,G))) ) )
& ? [F] :
( m1_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& ? [G] :
( m1_subset_1(G,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& B = k9_midsp_1(A,F)
& C = k9_midsp_1(A,G)
& k6_midsp_1(A,F) = k5_midsp_1(A,G)
& E = k9_midsp_1(A,k7_midsp_1(A,k5_midsp_1(A,F),k6_midsp_1(A,G))) ) )
& D != E ) ) ) ) ) ) ).
fof(d10_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> ! [C] :
( m1_midsp_1(C,A)
=> ! [D] :
( m1_midsp_1(D,A)
=> ( D = k11_midsp_1(A,B,C)
<=> ? [E] :
( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& ? [F] :
( m1_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& B = k9_midsp_1(A,E)
& C = k9_midsp_1(A,F)
& k6_midsp_1(A,E) = k5_midsp_1(A,F)
& D = k9_midsp_1(A,k7_midsp_1(A,k5_midsp_1(A,E),k6_midsp_1(A,F))) ) ) ) ) ) ) ) ).
fof(t53_midsp_1,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_midsp_1(C,A)
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = k9_midsp_1(A,k7_midsp_1(A,B,D)) ) ) ) ) ).
fof(d11_midsp_1,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))
=> k12_midsp_1(A,B,C) = k9_midsp_1(A,k7_midsp_1(A,B,C)) ) ) ) ).
fof(t54_midsp_1,axiom,
$true ).
fof(t55_midsp_1,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_midsp_1(C,A)
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = k12_midsp_1(A,B,D) ) ) ) ) ).
fof(t56_midsp_1,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))
=> ( r2_midsp_1(A,k7_midsp_1(A,B,C),k7_midsp_1(A,D,E))
=> k12_midsp_1(A,B,C) = k12_midsp_1(A,D,E) ) ) ) ) ) ) ).
fof(t57_midsp_1,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(t58_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k10_midsp_1(A) = k12_midsp_1(A,B,B) ) ) ).
fof(t59_midsp_1,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))
=> ( k12_midsp_1(A,B,C) = k12_midsp_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t60_midsp_1,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))
=> k11_midsp_1(A,k12_midsp_1(A,B,C),k12_midsp_1(A,C,D)) = k12_midsp_1(A,B,D) ) ) ) ) ).
fof(t61_midsp_1,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))
=> r2_midsp_1(A,k7_midsp_1(A,B,k4_midsp_1(A,B,C)),k7_midsp_1(A,k4_midsp_1(A,B,C),C)) ) ) ) ).
fof(t62_midsp_1,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))
=> k11_midsp_1(A,k12_midsp_1(A,B,k4_midsp_1(A,B,C)),k12_midsp_1(A,B,k4_midsp_1(A,B,C))) = k12_midsp_1(A,B,C) ) ) ) ).
fof(t63_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> ! [C] :
( m1_midsp_1(C,A)
=> ! [D] :
( m1_midsp_1(D,A)
=> k11_midsp_1(A,k11_midsp_1(A,B,C),D) = k11_midsp_1(A,B,k11_midsp_1(A,C,D)) ) ) ) ) ).
fof(t64_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> k11_midsp_1(A,B,k10_midsp_1(A)) = B ) ) ).
fof(t65_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> ? [C] :
( m1_midsp_1(C,A)
& k11_midsp_1(A,B,C) = k10_midsp_1(A) ) ) ) ).
fof(t66_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> ! [C] :
( m1_midsp_1(C,A)
=> k11_midsp_1(A,B,C) = k11_midsp_1(A,C,B) ) ) ) ).
fof(t67_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> ! [C] :
( m1_midsp_1(C,A)
=> ! [D] :
( m1_midsp_1(D,A)
=> ( k11_midsp_1(A,B,C) = k11_midsp_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(d12_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> ! [C] :
( m1_midsp_1(C,A)
=> ( C = k13_midsp_1(A,B)
<=> k11_midsp_1(A,B,C) = k10_midsp_1(A) ) ) ) ) ).
fof(t68_midsp_1,axiom,
$true ).
fof(t69_midsp_1,axiom,
$true ).
fof(t70_midsp_1,axiom,
$true ).
fof(t71_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
<=> r2_hidden(B,k14_midsp_1(A)) ) ) ).
fof(d14_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k14_midsp_1(A))
=> ! [C] :
( m1_subset_1(C,k14_midsp_1(A))
=> ! [D] :
( m1_subset_1(D,k14_midsp_1(A))
=> ( D = k15_midsp_1(A,B,C)
<=> ! [E] :
( m1_midsp_1(E,A)
=> ! [F] :
( m1_midsp_1(F,A)
=> ( ( B = E
& C = F )
=> D = k11_midsp_1(A,E,F) ) ) ) ) ) ) ) ) ).
fof(t72_midsp_1,axiom,
$true ).
fof(t73_midsp_1,axiom,
$true ).
fof(t74_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k14_midsp_1(A))
=> ! [C] :
( m1_subset_1(C,k14_midsp_1(A))
=> k15_midsp_1(A,B,C) = k15_midsp_1(A,C,B) ) ) ) ).
fof(t75_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k14_midsp_1(A))
=> ! [C] :
( m1_subset_1(C,k14_midsp_1(A))
=> ! [D] :
( m1_subset_1(D,k14_midsp_1(A))
=> k15_midsp_1(A,k15_midsp_1(A,B,C),D) = k15_midsp_1(A,B,k15_midsp_1(A,C,D)) ) ) ) ) ).
fof(d15_midsp_1,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(k14_midsp_1(A),k14_midsp_1(A)),k14_midsp_1(A))
& m2_relset_1(B,k2_zfmisc_1(k14_midsp_1(A),k14_midsp_1(A)),k14_midsp_1(A)) )
=> ( B = k16_midsp_1(A)
<=> ! [C] :
( m1_subset_1(C,k14_midsp_1(A))
=> ! [D] :
( m1_subset_1(D,k14_midsp_1(A))
=> k2_binop_1(k14_midsp_1(A),k14_midsp_1(A),k14_midsp_1(A),B,C,D) = k15_midsp_1(A,C,D) ) ) ) ) ) ).
fof(t76_midsp_1,axiom,
$true ).
fof(t77_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k14_midsp_1(A))
=> ? [C] :
( m1_subset_1(C,k14_midsp_1(A))
& k15_midsp_1(A,B,C) = k10_midsp_1(A) ) ) ) ).
fof(t78_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k14_midsp_1(A))
=> ! [C] :
( m1_subset_1(C,k14_midsp_1(A))
=> ! [D] :
( m1_subset_1(D,k14_midsp_1(A))
=> ( ( k15_midsp_1(A,B,C) = k10_midsp_1(A)
& k15_midsp_1(A,B,D) = k10_midsp_1(A) )
=> C = D ) ) ) ) ) ).
fof(d16_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k14_midsp_1(A),k14_midsp_1(A))
& m2_relset_1(B,k14_midsp_1(A),k14_midsp_1(A)) )
=> ( B = k17_midsp_1(A)
<=> ! [C] :
( m1_subset_1(C,k14_midsp_1(A))
=> k15_midsp_1(A,C,k8_funct_2(k14_midsp_1(A),k14_midsp_1(A),B,C)) = k10_midsp_1(A) ) ) ) ) ).
fof(d17_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> k18_midsp_1(A) = k10_midsp_1(A) ) ).
fof(d18_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> k19_midsp_1(A) = g1_rlvect_1(k14_midsp_1(A),k16_midsp_1(A),k18_midsp_1(A)) ) ).
fof(t79_midsp_1,axiom,
$true ).
fof(t80_midsp_1,axiom,
$true ).
fof(t81_midsp_1,axiom,
$true ).
fof(t82_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> u1_struct_0(k19_midsp_1(A)) = k14_midsp_1(A) ) ).
fof(t83_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> u1_rlvect_1(k19_midsp_1(A)) = k16_midsp_1(A) ) ).
fof(t84_midsp_1,axiom,
$true ).
fof(t85_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> u2_struct_0(k19_midsp_1(A)) = k18_midsp_1(A) ) ).
fof(t86_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ( v4_rlvect_1(k19_midsp_1(A))
& v5_rlvect_1(k19_midsp_1(A))
& v6_rlvect_1(k19_midsp_1(A))
& v3_rlvect_1(k19_midsp_1(A)) ) ) ).
fof(dt_m1_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_midsp_1(B,A)
=> ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) ) ) ).
fof(existence_m1_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ? [B] : m1_midsp_1(B,A) ) ).
fof(dt_l1_midsp_1,axiom,
! [A] :
( l1_midsp_1(A)
=> l1_struct_0(A) ) ).
fof(existence_l1_midsp_1,axiom,
? [A] : l1_midsp_1(A) ).
fof(abstractness_v1_midsp_1,axiom,
! [A] :
( l1_midsp_1(A)
=> ( v1_midsp_1(A)
=> A = g1_midsp_1(u1_struct_0(A),u1_midsp_1(A)) ) ) ).
fof(symmetry_r2_midsp_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> ( r2_midsp_1(A,B,C)
=> r2_midsp_1(A,C,B) ) ) ).
fof(reflexivity_r2_midsp_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> r2_midsp_1(A,B,B) ) ).
fof(dt_k1_midsp_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_midsp_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k1_midsp_1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k2_midsp_1,axiom,
( v1_funct_1(k2_midsp_1)
& v1_funct_2(k2_midsp_1,k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))
& m2_relset_1(k2_midsp_1,k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) ) ).
fof(dt_k3_midsp_1,axiom,
l1_midsp_1(k3_midsp_1) ).
fof(dt_k4_midsp_1,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_1(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k4_midsp_1,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)) )
=> k4_midsp_1(A,B,C) = k4_midsp_1(A,C,B) ) ).
fof(redefinition_k4_midsp_1,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)) )
=> k4_midsp_1(A,B,C) = k1_midsp_1(A,B,C) ) ).
fof(dt_k5_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> m1_subset_1(k5_midsp_1(A,B),u1_struct_0(A)) ) ).
fof(redefinition_k5_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> k5_midsp_1(A,B) = k1_mcart_1(B) ) ).
fof(dt_k6_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> m1_subset_1(k6_midsp_1(A,B),u1_struct_0(A)) ) ).
fof(redefinition_k6_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> k6_midsp_1(A,B) = k2_mcart_1(B) ) ).
fof(dt_k7_midsp_1,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(k7_midsp_1(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
fof(redefinition_k7_midsp_1,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)) )
=> k7_midsp_1(A,B,C) = k4_tarski(B,C) ) ).
fof(dt_k8_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> m1_subset_1(k8_midsp_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) ).
fof(dt_k9_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> m1_midsp_1(k9_midsp_1(A,B),A) ) ).
fof(redefinition_k9_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
=> k9_midsp_1(A,B) = k8_midsp_1(A,B) ) ).
fof(dt_k10_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> m1_midsp_1(k10_midsp_1(A),A) ) ).
fof(dt_k11_midsp_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_midsp_1(B,A)
& m1_midsp_1(C,A) )
=> m1_midsp_1(k11_midsp_1(A,B,C),A) ) ).
fof(dt_k12_midsp_1,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_midsp_1(k12_midsp_1(A,B,C),A) ) ).
fof(dt_k13_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_midsp_1(B,A) )
=> m1_midsp_1(k13_midsp_1(A,B),A) ) ).
fof(dt_k14_midsp_1,axiom,
$true ).
fof(dt_k15_midsp_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A)
& m1_subset_1(B,k14_midsp_1(A))
& m1_subset_1(C,k14_midsp_1(A)) )
=> m1_subset_1(k15_midsp_1(A,B,C),k14_midsp_1(A)) ) ).
fof(dt_k16_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ( v1_funct_1(k16_midsp_1(A))
& v1_funct_2(k16_midsp_1(A),k2_zfmisc_1(k14_midsp_1(A),k14_midsp_1(A)),k14_midsp_1(A))
& m2_relset_1(k16_midsp_1(A),k2_zfmisc_1(k14_midsp_1(A),k14_midsp_1(A)),k14_midsp_1(A)) ) ) ).
fof(dt_k17_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ( v1_funct_1(k17_midsp_1(A))
& v1_funct_2(k17_midsp_1(A),k14_midsp_1(A),k14_midsp_1(A))
& m2_relset_1(k17_midsp_1(A),k14_midsp_1(A),k14_midsp_1(A)) ) ) ).
fof(dt_k18_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> m1_subset_1(k18_midsp_1(A),k14_midsp_1(A)) ) ).
fof(dt_k19_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> l1_rlvect_1(k19_midsp_1(A)) ) ).
fof(dt_u1_midsp_1,axiom,
! [A] :
( l1_midsp_1(A)
=> ( v1_funct_1(u1_midsp_1(A))
& v1_funct_2(u1_midsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(u1_midsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_g1_midsp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ( v1_midsp_1(g1_midsp_1(A,B))
& l1_midsp_1(g1_midsp_1(A,B)) ) ) ).
fof(free_g1_midsp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C,D] :
( g1_midsp_1(A,B) = g1_midsp_1(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(t39_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( ~ v1_xboole_0(a_2_0_midsp_1(A,B))
& m1_subset_1(a_2_0_midsp_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) ) ) ).
fof(d7_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> k8_midsp_1(A,B) = a_2_0_midsp_1(A,B) ) ) ).
fof(d9_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> k10_midsp_1(A) = a_1_0_midsp_1(A) ) ).
fof(d13_midsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_midsp_1(A)
& l1_midsp_1(A) )
=> k14_midsp_1(A) = a_1_1_midsp_1(A) ) ).
fof(fraenkel_a_2_0_midsp_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_1(B)
& m1_subset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_midsp_1(B,C))
<=> ? [D] :
( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& A = D
& r2_midsp_1(B,D,C) ) ) ) ).
fof(fraenkel_a_1_0_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_1(B) )
=> ( r2_hidden(A,a_1_0_midsp_1(B))
<=> ? [C] :
( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& A = C
& k5_midsp_1(B,C) = k6_midsp_1(B,C) ) ) ) ).
fof(fraenkel_a_1_1_midsp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_midsp_1(B)
& l1_midsp_1(B) )
=> ( r2_hidden(A,a_1_1_midsp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))))
& A = C
& m1_midsp_1(C,B) ) ) ) ).
%------------------------------------------------------------------------------