SET007 Axioms: SET007+80.ax
%------------------------------------------------------------------------------
% File : SET007+80 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Many-sorted Sets
% 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 : pboole [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 235 ( 20 unt; 0 def)
% Number of atoms : 994 ( 50 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 802 ( 43 ~; 3 |; 194 &)
% ( 35 <=>; 527 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-4 aty)
% Number of functors : 44 ( 44 usr; 9 con; 0-4 aty)
% Number of variables : 717 ( 701 !; 16 ?)
% 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_pboole,axiom,
? [A] :
( v1_relat_1(A)
& v3_relat_1(A)
& v1_funct_1(A) ) ).
fof(rc2_pboole,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v3_relat_1(B)
& v1_funct_1(B) ) ).
fof(rc3_pboole,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) ) ).
fof(cc1_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ( v2_relat_1(B)
=> ~ v3_relat_1(B) ) ) ) ).
fof(cc2_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ( v3_relat_1(B)
=> ~ v2_relat_1(B) ) ) ) ).
fof(rc4_pboole,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) ) ).
fof(cc3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ! [D] :
( m3_pboole(D,A,B,C)
=> v1_funcop_1(D) ) ) ).
fof(fc1_pboole,axiom,
! [A,B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ( v1_relat_1(k6_pboole(A,B))
& v2_relat_1(k6_pboole(A,B))
& ~ v3_relat_1(k6_pboole(A,B))
& v1_funct_1(k6_pboole(A,B)) ) ) ).
fof(fc2_pboole,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v2_relat_1(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> ~ v1_xboole_0(k1_funct_1(B,C)) ) ).
fof(rc5_pboole,axiom,
! [A,B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ? [C] :
( m4_pboole(C,A,B)
& v1_relat_1(C)
& v2_relat_1(C)
& v1_funct_1(C) ) ) ).
fof(fc3_pboole,axiom,
! [A] :
( v1_relat_1(k1_pboole(A))
& v3_relat_1(k1_pboole(A))
& v1_funct_1(k1_pboole(A)) ) ).
fof(t1_pboole,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v2_relat_1(A)
=> v1_setfam_1(k2_relat_1(A)) ) ) ).
fof(t2_pboole,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v3_relat_1(A)
<=> ( A = k1_xboole_0
| k2_relat_1(A) = k1_tarski(k1_xboole_0) ) ) ) ).
fof(d1_pboole,axiom,
$true ).
fof(d2_pboole,axiom,
$true ).
fof(d3_pboole,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( m1_pboole(B,A)
<=> k1_relat_1(B) = A ) ) ).
fof(d4_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r1_pboole(A,B,C)
<=> ! [D] :
( r2_hidden(D,A)
=> r2_hidden(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ).
fof(d5_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,B,C)
<=> ! [D] :
( r2_hidden(D,A)
=> r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ).
fof(t3_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ! [D] :
( r2_hidden(D,A)
=> k1_funct_1(B,D) = k1_funct_1(C,D) )
=> B = C ) ) ) ).
fof(d6_pboole,axiom,
! [A] : k1_pboole(A) = k2_funcop_1(A,k1_xboole_0) ).
fof(d7_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( D = k2_pboole(A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ).
fof(d8_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( D = k3_pboole(A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ).
fof(d9_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( D = k4_pboole(A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k1_funct_1(D,E) = k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ).
fof(d10_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r4_pboole(A,B,C)
<=> ! [D] :
~ ( r2_hidden(D,A)
& r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ).
fof(d11_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r5_pboole(A,B,C)
<=> ! [D] :
( r2_hidden(D,A)
=> r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ).
fof(d12_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> k5_pboole(A,B,C) = k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) ) ) ).
fof(t4_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( r2_hidden(D,A)
=> k1_funct_1(k5_pboole(A,B,C),D) = k5_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ).
fof(t5_pboole,axiom,
! [A,B] : k1_funct_1(k1_pboole(B),A) = k1_xboole_0 ).
fof(t6_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( ! [C] :
( r2_hidden(C,A)
=> k1_funct_1(B,C) = k1_xboole_0 )
=> B = k1_pboole(A) ) ) ).
fof(t7_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r1_pboole(A,B,C)
| r1_pboole(A,B,D) )
=> r1_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) ).
fof(t8_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r1_pboole(A,B,k3_pboole(A,C,D))
<=> ( r1_pboole(A,B,C)
& r1_pboole(A,B,D) ) ) ) ) ) ).
fof(t9_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r1_pboole(A,B,C)
& r2_pboole(A,C,D) )
=> r1_pboole(A,B,D) ) ) ) ) ).
fof(t10_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r1_pboole(A,B,C)
& r1_pboole(A,B,D) )
=> r4_pboole(A,C,D) ) ) ) ) ).
fof(t11_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ~ ( r4_pboole(A,B,C)
& ! [D] :
( m1_pboole(D,A)
=> ~ ( r1_pboole(A,D,B)
& r1_pboole(A,D,C) ) ) ) ) ) ).
fof(t12_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r1_pboole(A,B,k4_pboole(A,C,D))
=> r1_pboole(A,B,C) ) ) ) ) ).
fof(d13_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,B,C)
<=> ( r2_pboole(A,B,C)
& r2_pboole(A,C,B) ) ) ) ) ).
fof(t13_pboole,axiom,
$true ).
fof(t14_pboole,axiom,
$true ).
fof(t15_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r2_pboole(A,B,C)
& r2_pboole(A,C,D) )
=> r2_pboole(A,B,D) ) ) ) ) ).
fof(t16_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,B,k2_pboole(A,B,C))
& r2_pboole(A,C,k2_pboole(A,B,C)) ) ) ) ).
fof(t17_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,k3_pboole(A,B,C),B)
& r2_pboole(A,k3_pboole(A,B,C),C) ) ) ) ).
fof(t18_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r2_pboole(A,B,C)
& r2_pboole(A,D,C) )
=> r2_pboole(A,k2_pboole(A,B,D),C) ) ) ) ) ).
fof(t19_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r2_pboole(A,B,C)
& r2_pboole(A,B,D) )
=> r2_pboole(A,B,k3_pboole(A,C,D)) ) ) ) ) ).
fof(t20_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,B,C)
=> ( r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D))
& r2_pboole(A,k2_pboole(A,D,B),k2_pboole(A,D,C)) ) ) ) ) ) ).
fof(t21_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,B,C)
=> ( r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D))
& r2_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C)) ) ) ) ) ) ).
fof(t22_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,A)
=> ( ( r2_pboole(A,B,C)
& r2_pboole(A,D,E) )
=> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,E)) ) ) ) ) ) ).
fof(t23_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,A)
=> ( ( r2_pboole(A,B,C)
& r2_pboole(A,D,E) )
=> r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,E)) ) ) ) ) ) ).
fof(t24_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,B,C)
=> ( r6_pboole(A,k2_pboole(A,B,C),C)
& r6_pboole(A,k2_pboole(A,C,B),C) ) ) ) ) ).
fof(t25_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,B,C)
=> ( r6_pboole(A,k3_pboole(A,B,C),B)
& r6_pboole(A,k3_pboole(A,C,B),B) ) ) ) ) ).
fof(t26_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r2_pboole(A,k3_pboole(A,B,C),k2_pboole(A,B,D)) ) ) ) ).
fof(t27_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,B,C)
=> r6_pboole(A,k2_pboole(A,B,k3_pboole(A,D,C)),k3_pboole(A,k2_pboole(A,B,D),C)) ) ) ) ) ).
fof(t28_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,B,k2_pboole(A,C,D))
<=> ( r2_pboole(A,C,B)
& r2_pboole(A,D,B)
& ! [E] :
( m1_pboole(E,A)
=> ( ( r2_pboole(A,C,E)
& r2_pboole(A,D,E) )
=> r2_pboole(A,B,E) ) ) ) ) ) ) ) ).
fof(t29_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,B,k3_pboole(A,C,D))
<=> ( r2_pboole(A,B,C)
& r2_pboole(A,B,D)
& ! [E] :
( m1_pboole(E,A)
=> ( ( r2_pboole(A,E,C)
& r2_pboole(A,E,D) )
=> r2_pboole(A,E,B) ) ) ) ) ) ) ) ).
fof(t30_pboole,axiom,
$true ).
fof(t31_pboole,axiom,
$true ).
fof(t32_pboole,axiom,
$true ).
fof(t33_pboole,axiom,
$true ).
fof(t34_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,B,k2_pboole(A,C,D))) ) ) ) ).
fof(t35_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,B,k3_pboole(A,C,D))) ) ) ) ).
fof(t36_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k3_pboole(A,B,k2_pboole(A,B,C)),B)
& r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B)
& r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,B)),B)
& r6_pboole(A,k3_pboole(A,k2_pboole(A,C,B),B),B) ) ) ) ).
fof(t37_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k2_pboole(A,B,k3_pboole(A,B,C)),B)
& r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),B),B)
& r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B)
& r6_pboole(A,k2_pboole(A,k3_pboole(A,C,B),B),B) ) ) ) ).
fof(t38_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))) ) ) ) ).
fof(t39_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D)))
& r6_pboole(A,k2_pboole(A,k3_pboole(A,C,D),B),k3_pboole(A,k2_pboole(A,C,B),k2_pboole(A,D,B))) ) ) ) ) ).
fof(t40_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D)),B)
=> r2_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) ).
fof(t41_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D)),B)
=> r2_pboole(A,k3_pboole(A,C,D),B) ) ) ) ) ).
fof(t42_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k2_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,C,D)),k3_pboole(A,D,B)),k3_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,C,D)),k2_pboole(A,D,B))) ) ) ) ).
fof(t43_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,k2_pboole(A,B,C),D)
=> ( r2_pboole(A,B,D)
& r2_pboole(A,C,D) ) ) ) ) ) ).
fof(t44_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,B,k3_pboole(A,C,D))
=> ( r2_pboole(A,B,C)
& r2_pboole(A,B,D) ) ) ) ) ) ).
fof(t45_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D)))
& r6_pboole(A,k2_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))) ) ) ) ) ).
fof(t46_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D)))
& r6_pboole(A,k3_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))) ) ) ) ) ).
fof(t47_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k2_pboole(A,B,k2_pboole(A,B,C)),k2_pboole(A,B,C))
& r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),C),k2_pboole(A,B,C)) ) ) ) ).
fof(t48_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k3_pboole(A,B,k3_pboole(A,B,C)),k3_pboole(A,B,C))
& r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),C),k3_pboole(A,B,C)) ) ) ) ).
fof(t49_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r2_pboole(A,k1_pboole(A),B) ) ).
fof(t50_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( r2_pboole(A,B,k1_pboole(A))
=> r6_pboole(A,B,k1_pboole(A)) ) ) ).
fof(t51_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r2_pboole(A,B,C)
& r2_pboole(A,B,D)
& r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) )
=> r6_pboole(A,B,k1_pboole(A)) ) ) ) ) ).
fof(t52_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r2_pboole(A,B,C)
& r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) )
=> r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) ) ) ) ) ).
fof(t53_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B)
& r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B) ) ) ).
fof(t54_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k2_pboole(A,B,C),k1_pboole(A))
=> ( r6_pboole(A,B,k1_pboole(A))
& r6_pboole(A,C,k1_pboole(A)) ) ) ) ) ).
fof(t55_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( r6_pboole(A,k3_pboole(A,B,k1_pboole(A)),k1_pboole(A))
& r6_pboole(A,k3_pboole(A,k1_pboole(A),B),k1_pboole(A)) ) ) ).
fof(t56_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r2_pboole(A,B,k2_pboole(A,C,D))
& r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) )
=> r2_pboole(A,B,C) ) ) ) ) ).
fof(t57_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( r2_pboole(A,B,C)
& r6_pboole(A,k3_pboole(A,C,B),k1_pboole(A)) )
=> r6_pboole(A,B,k1_pboole(A)) ) ) ) ).
fof(t58_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k4_pboole(A,B,C),k1_pboole(A))
<=> r2_pboole(A,B,C) ) ) ) ).
fof(t59_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,B,C)
=> r2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D)) ) ) ) ) ).
fof(t60_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,B,C)
=> r2_pboole(A,k4_pboole(A,D,C),k4_pboole(A,D,B)) ) ) ) ) ).
fof(t61_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,A)
=> ( ( r2_pboole(A,B,C)
& r2_pboole(A,D,E) )
=> r2_pboole(A,k4_pboole(A,B,E),k4_pboole(A,C,D)) ) ) ) ) ) ).
fof(t62_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r2_pboole(A,k4_pboole(A,B,C),B) ) ) ).
fof(t63_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,B,k4_pboole(A,C,B))
=> r6_pboole(A,B,k1_pboole(A)) ) ) ) ).
fof(t64_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r6_pboole(A,k4_pboole(A,B,B),k1_pboole(A)) ) ).
fof(t65_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r6_pboole(A,k4_pboole(A,B,k1_pboole(A)),B) ) ).
fof(t66_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r6_pboole(A,k4_pboole(A,k1_pboole(A),B),k1_pboole(A)) ) ).
fof(t67_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k4_pboole(A,B,k2_pboole(A,B,C)),k1_pboole(A))
& r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,B)),k1_pboole(A)) ) ) ) ).
fof(t68_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),D)) ) ) ) ).
fof(t69_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A))
& r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)) ) ) ) ).
fof(t70_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k4_pboole(A,B,k4_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,D))) ) ) ) ).
fof(t71_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,C)),B)
& r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)),B) ) ) ) ).
fof(t72_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,B,C)
=> ( r6_pboole(A,C,k2_pboole(A,B,k4_pboole(A,C,B)))
& r6_pboole(A,C,k2_pboole(A,k4_pboole(A,C,B),B)) ) ) ) ) ).
fof(t73_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k2_pboole(A,B,k4_pboole(A,C,B)),k2_pboole(A,B,C))
& r6_pboole(A,k2_pboole(A,k4_pboole(A,C,B),B),k2_pboole(A,C,B)) ) ) ) ).
fof(t74_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k4_pboole(A,B,k4_pboole(A,B,C)),k3_pboole(A,B,C)) ) ) ).
fof(t75_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))) ) ) ) ).
fof(t76_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C))
& r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)) ) ) ) ).
fof(t77_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))
<=> r6_pboole(A,k4_pboole(A,B,C),B) ) ) ) ).
fof(t78_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))) ) ) ) ).
fof(t79_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),D),k4_pboole(A,B,k2_pboole(A,C,D))) ) ) ) ).
fof(t80_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k4_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))) ) ) ) ).
fof(t81_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),k4_pboole(A,B,C)) ) ) ).
fof(t82_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,B,k2_pboole(A,C,D))
=> ( r2_pboole(A,k4_pboole(A,B,C),D)
& r2_pboole(A,k4_pboole(A,B,D),C) ) ) ) ) ) ).
fof(t83_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B))) ) ) ).
fof(t84_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),C),k4_pboole(A,B,C)) ) ) ).
fof(t85_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))) ) ) ) ).
fof(t86_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B))
=> r6_pboole(A,B,C) ) ) ) ).
fof(t87_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))) ) ) ) ).
fof(t88_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,k4_pboole(A,B,C),D)
=> r2_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) ).
fof(t89_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r2_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,C)) ) ) ).
fof(t90_pboole,axiom,
$true ).
fof(t91_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B)
& r6_pboole(A,k5_pboole(A,k1_pboole(A),B),B) ) ) ).
fof(t92_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r6_pboole(A,k5_pboole(A,B,B),k1_pboole(A)) ) ).
fof(t93_pboole,axiom,
$true ).
fof(t94_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))) ) ) ).
fof(t95_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k5_pboole(A,B,C),k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C))) ) ) ).
fof(t96_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k4_pboole(A,k5_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k4_pboole(A,C,k2_pboole(A,B,D)))) ) ) ) ).
fof(t97_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k4_pboole(A,B,k5_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),D))) ) ) ) ).
fof(t98_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> r6_pboole(A,k5_pboole(A,k5_pboole(A,B,C),D),k5_pboole(A,B,k5_pboole(A,C,D))) ) ) ) ).
fof(t99_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r2_pboole(A,k4_pboole(A,B,C),D)
& r2_pboole(A,k4_pboole(A,C,B),D) )
=> r2_pboole(A,k5_pboole(A,B,C),D) ) ) ) ) ).
fof(t100_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,C,B))) ) ) ).
fof(t101_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,B,C))) ) ) ).
fof(t102_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,k3_pboole(A,B,C))) ) ) ).
fof(t103_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,C,k2_pboole(A,C,B))) ) ) ).
fof(t104_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))) ) ) ).
fof(t105_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k2_pboole(A,B,C))) ) ) ).
fof(t106_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r4_pboole(A,B,C)
| r4_pboole(A,B,D) )
=> r4_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) ).
fof(t107_pboole,axiom,
$true ).
fof(t108_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r4_pboole(A,B,C)
& r2_pboole(A,C,D) )
=> r4_pboole(A,B,D) ) ) ) ) ).
fof(t109_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r4_pboole(A,B,C)
& r2_pboole(A,B,D) )
=> r4_pboole(A,D,C) ) ) ) ) ).
fof(t110_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,A)
=> ( ( r2_pboole(A,B,C)
& r2_pboole(A,D,E)
& r4_pboole(A,B,D) )
=> r4_pboole(A,C,E) ) ) ) ) ) ).
fof(t111_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r4_pboole(A,B,k3_pboole(A,C,D))
=> ( r4_pboole(A,B,C)
& r4_pboole(A,B,D) ) ) ) ) ) ).
fof(t112_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r4_pboole(A,B,C)
& r2_pboole(A,B,D) )
=> r4_pboole(A,B,k3_pboole(A,C,D)) ) ) ) ) ).
fof(t113_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r4_pboole(A,B,k4_pboole(A,C,D))
=> r4_pboole(A,B,C) ) ) ) ) ).
fof(t114_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ~ ( ~ r4_pboole(A,B,C)
& r4_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C)) ) ) ) ) ).
fof(t115_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r4_pboole(A,B,k4_pboole(A,C,D))
=> r4_pboole(A,C,k4_pboole(A,B,D)) ) ) ) ) ).
fof(t116_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ~ ( ~ r5_pboole(A,B,C)
& r2_pboole(A,C,D)
& r5_pboole(A,B,D) ) ) ) ) ).
fof(t117_pboole,axiom,
$true ).
fof(t118_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r5_pboole(A,B,k4_pboole(A,C,B)) ) ) ).
fof(t119_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r5_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)) ) ) ).
fof(t120_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r5_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,C)) ) ) ).
fof(t121_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r5_pboole(A,B,C)
=> r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) ) ) ) ).
fof(t122_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ~ ( B != k1_pboole(A)
& r5_pboole(A,B,B) ) ) ).
fof(t123_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r2_pboole(A,B,C)
& r2_pboole(A,B,D)
& r5_pboole(A,C,D) )
=> r6_pboole(A,B,k1_pboole(A)) ) ) ) ) ).
fof(t124_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,A)
=> ( ( r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E))
& r5_pboole(A,D,B)
& r5_pboole(A,E,C) )
=> ( r6_pboole(A,D,C)
& r6_pboole(A,E,B) ) ) ) ) ) ) ).
fof(t125_pboole,axiom,
$true ).
fof(t126_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r5_pboole(A,B,C)
=> r6_pboole(A,k4_pboole(A,B,C),B) ) ) ) ).
fof(t127_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r5_pboole(A,B,C)
=> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),B) ) ) ) ).
fof(t128_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k4_pboole(A,B,C),B)
=> r5_pboole(A,B,C) ) ) ) ).
fof(t129_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r5_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) ) ) ).
fof(d14_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r7_pboole(A,B,C)
<=> ! [D] :
( m1_pboole(D,A)
=> ( r1_pboole(A,D,B)
=> r1_pboole(A,D,C) ) ) ) ) ) ).
fof(t130_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,B,C)
=> r7_pboole(A,B,C) ) ) ) ).
fof(t131_pboole,axiom,
$true ).
fof(t132_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r7_pboole(A,B,C)
& r7_pboole(A,C,D) )
=> r7_pboole(A,B,D) ) ) ) ) ).
fof(t133_pboole,axiom,
r1_pboole(k1_xboole_0,k1_pboole(k1_xboole_0),k1_pboole(k1_xboole_0)) ).
fof(t134_pboole,axiom,
! [A] :
( m1_pboole(A,k1_xboole_0)
=> A = k1_xboole_0 ) ).
fof(t135_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ~ ( r4_pboole(A,B,C)
& r5_pboole(A,B,C) ) ) ) ) ).
fof(t136_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ~ r3_pboole(A,B,k1_pboole(A)) ) ) ).
fof(t137_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ~ ( r3_pboole(A,B,C)
& r3_pboole(A,B,D)
& k3_pboole(A,C,D) = k1_pboole(A) ) ) ) ) ) ).
fof(t138_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ( ~ r4_pboole(A,B,k1_pboole(A))
& ~ r4_pboole(A,k1_pboole(A),B) ) ) ) ).
fof(t139_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ~ ( r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))
& r4_pboole(A,B,C) ) ) ) ) ).
fof(t140_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ~ ( r4_pboole(A,B,B)
& B = k1_pboole(A) ) ) ) ).
fof(d15_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v3_relat_1(B)
<=> ! [C] :
( r2_hidden(C,A)
=> v1_xboole_0(k1_funct_1(B,C)) ) ) ) ).
fof(d16_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v2_relat_1(B)
<=> ! [C] :
~ ( r2_hidden(C,A)
& v1_xboole_0(k1_funct_1(B,C)) ) ) ) ).
fof(t141_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v3_relat_1(B)
<=> r6_pboole(A,B,k1_pboole(A)) ) ) ).
fof(t142_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( v3_relat_1(B)
& r2_pboole(A,C,B) )
=> v3_relat_1(C) ) ) ) ).
fof(t143_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( v2_relat_1(B)
& r2_pboole(A,B,C) )
=> v2_relat_1(C) ) ) ) ).
fof(t144_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( v2_relat_1(B)
& r7_pboole(A,B,C) )
=> r2_pboole(A,B,C) ) ) ) ).
fof(t145_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( v2_relat_1(B)
& r7_pboole(A,B,C) )
=> v2_relat_1(C) ) ) ) ).
fof(t146_pboole,axiom,
! [A,B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ? [C] :
( m1_pboole(C,A)
& r1_pboole(A,C,B) ) ) ).
fof(t147_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ( ! [D] :
( m1_pboole(D,A)
=> ( r1_pboole(A,D,C)
<=> r1_pboole(A,D,B) ) )
=> r6_pboole(A,C,B) ) ) ) ).
fof(t148_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( ( v2_relat_1(D)
& m1_pboole(D,A) )
=> ( ! [E] :
( m1_pboole(E,A)
=> ( r1_pboole(A,E,D)
<=> ( r1_pboole(A,E,B)
& r1_pboole(A,E,C) ) ) )
=> r6_pboole(A,D,k3_pboole(A,B,C)) ) ) ) ) ).
fof(t149_pboole,axiom,
! [A,B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ~ r2_hidden(k1_xboole_0,k2_relat_1(B)) ) ).
fof(t150_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,k2_relat_1(B))
=> ? [D] :
( r2_hidden(D,A)
& C = k1_funct_1(B,D) ) ) ) ) ).
fof(t151_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( r2_hidden(C,A)
=> m1_subset_1(k1_funct_1(B,C),k2_relat_1(B)) ) ) ).
fof(d17_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( m2_pboole(C,A,B)
<=> ! [D] :
( r2_hidden(D,A)
=> m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D)) ) ) ) ) ).
fof(d18_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( m3_pboole(D,A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> ( v1_funct_1(k1_funct_1(D,E))
& v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
& m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ).
fof(d19_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,k3_finseq_2(A))
=> ( C = k6_pboole(A,B)
<=> ! [D] :
( m2_finseq_2(D,A,k3_finseq_2(A))
=> k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)) ) ) ) ) ).
fof(d20_pboole,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k3_finseq_2(k1_tarski(A)))
& m2_relset_1(B,k5_numbers,k3_finseq_2(k1_tarski(A))) )
=> ( B = k9_pboole(A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),B,C) = k2_finseq_2(C,A) ) ) ) ).
fof(t152_pboole,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] : k5_relat_1(k2_finseq_2(A,B),k2_funcop_1(k1_tarski(B),C)) = k2_finseq_2(A,C) ) ).
fof(t153_pboole,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C,D] :
( m1_pboole(D,k1_tarski(C))
=> ( D = k2_funcop_1(k1_tarski(C),A)
=> k1_funct_1(k7_pboole(k5_numbers,k3_finseq_2(k1_tarski(C)),k9_pboole(C),k6_pboole(k1_tarski(C),D)),B) = k1_funct_2(k2_finseq_1(B),A) ) ) ) ) ).
fof(d21_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( D = k11_pboole(A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ).
fof(d22_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( D = k12_pboole(A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k1_funct_1(D,E) = k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ).
fof(d23_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( m4_pboole(C,A,B)
<=> r2_pboole(A,C,B) ) ) ) ).
fof(d24_pboole,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_funcop_1(C) )
=> ( C = k13_pboole(A,B)
<=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
& ! [D] :
( r2_hidden(D,k1_relat_1(C))
=> k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ).
fof(d25_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v1_funcop_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( m1_pboole(D,A)
=> ( D = k14_pboole(A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k1_funct_1(D,E) = k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) ) ).
fof(s1_pboole,axiom,
( ! [A] :
~ ( r2_hidden(A,f1_s1_pboole)
& f2_s1_pboole(A) = k1_xboole_0 )
=> ? [A] :
( m1_pboole(A,f1_s1_pboole)
& ! [B] :
( r2_hidden(B,f1_s1_pboole)
=> r2_hidden(k1_funct_1(A,B),f2_s1_pboole(B)) ) ) ) ).
fof(s2_pboole,axiom,
? [A] :
( m1_pboole(A,f1_s2_pboole)
& ! [B] :
( r2_hidden(B,f1_s2_pboole)
=> ! [C] :
( r2_hidden(C,k1_funct_1(A,B))
<=> ( r2_hidden(C,k1_funct_1(f2_s2_pboole,B))
& p1_s2_pboole(B,C) ) ) ) ) ).
fof(s3_pboole,axiom,
( ! [A] :
~ ( r2_hidden(A,f1_s3_pboole)
& ! [B] : ~ p1_s3_pboole(A,B) )
=> ? [A] :
( m1_pboole(A,f1_s3_pboole)
& ! [B] :
( r2_hidden(B,f1_s3_pboole)
=> p1_s3_pboole(B,k1_funct_1(A,B)) ) ) ) ).
fof(s4_pboole,axiom,
? [A] :
( m1_pboole(A,f1_s4_pboole)
& ! [B] :
( r2_hidden(B,f1_s4_pboole)
=> k1_funct_1(A,B) = f2_s4_pboole(B) ) ) ).
fof(s5_pboole,axiom,
? [A] :
( m1_pboole(A,f1_s5_pboole)
& ! [B] :
( m1_subset_1(B,f1_s5_pboole)
=> k1_funct_1(A,B) = f2_s5_pboole(B) ) ) ).
fof(dt_m1_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ).
fof(existence_m1_pboole,axiom,
! [A] :
? [B] : m1_pboole(B,A) ).
fof(dt_m2_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m2_pboole(C,A,B)
=> m1_pboole(C,A) ) ) ).
fof(existence_m2_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ? [C] : m2_pboole(C,A,B) ) ).
fof(dt_m3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ! [D] :
( m3_pboole(D,A,B,C)
=> m1_pboole(D,A) ) ) ).
fof(existence_m3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ? [D] : m3_pboole(D,A,B,C) ) ).
fof(dt_m4_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m4_pboole(C,A,B)
=> m1_pboole(C,A) ) ) ).
fof(existence_m4_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ? [C] : m4_pboole(C,A,B) ) ).
fof(redefinition_v1_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v1_pboole(B,A)
<=> v3_relat_1(B) ) ) ).
fof(redefinition_v2_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v2_pboole(B,A)
<=> v2_relat_1(B) ) ) ).
fof(reflexivity_r2_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> r2_pboole(A,B,B) ) ).
fof(antisymmetry_r3_pboole,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& m1_pboole(C,A) )
=> ( r3_pboole(A,B,C)
=> ~ r3_pboole(A,C,B) ) ) ).
fof(redefinition_r3_pboole,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& m1_pboole(C,A) )
=> ( r3_pboole(A,B,C)
<=> r1_pboole(A,B,C) ) ) ).
fof(symmetry_r4_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ( r4_pboole(A,B,C)
=> r4_pboole(A,C,B) ) ) ).
fof(symmetry_r5_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ( r5_pboole(A,B,C)
=> r5_pboole(A,C,B) ) ) ).
fof(symmetry_r6_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ( r6_pboole(A,B,C)
=> r6_pboole(A,C,B) ) ) ).
fof(reflexivity_r6_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> r6_pboole(A,B,B) ) ).
fof(redefinition_r6_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ( r6_pboole(A,B,C)
<=> B = C ) ) ).
fof(reflexivity_r7_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> r7_pboole(A,B,B) ) ).
fof(dt_k1_pboole,axiom,
! [A] : m1_pboole(k1_pboole(A),A) ).
fof(dt_k2_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> m1_pboole(k2_pboole(A,B,C),A) ) ).
fof(commutativity_k2_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> k2_pboole(A,B,C) = k2_pboole(A,C,B) ) ).
fof(idempotence_k2_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> k2_pboole(A,B,B) = B ) ).
fof(dt_k3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> m1_pboole(k3_pboole(A,B,C),A) ) ).
fof(commutativity_k3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> k3_pboole(A,B,C) = k3_pboole(A,C,B) ) ).
fof(idempotence_k3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> k3_pboole(A,B,B) = B ) ).
fof(dt_k4_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> m1_pboole(k4_pboole(A,B,C),A) ) ).
fof(dt_k5_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> m1_pboole(k5_pboole(A,B,C),A) ) ).
fof(commutativity_k5_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> k5_pboole(A,B,C) = k5_pboole(A,C,B) ) ).
fof(dt_k6_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ).
fof(dt_k7_pboole,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,B) )
=> m1_pboole(k7_pboole(A,B,C,D),A) ) ).
fof(redefinition_k7_pboole,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,B) )
=> k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ).
fof(dt_k8_pboole,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& v2_relat_1(D)
& m1_pboole(D,B) )
=> ( v2_relat_1(k8_pboole(A,B,C,D))
& m1_pboole(k8_pboole(A,B,C,D),A) ) ) ).
fof(redefinition_k8_pboole,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& v2_relat_1(D)
& m1_pboole(D,B) )
=> k8_pboole(A,B,C,D) = k5_relat_1(C,D) ) ).
fof(dt_k9_pboole,axiom,
! [A] :
( v1_funct_1(k9_pboole(A))
& v1_funct_2(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A)))
& m2_relset_1(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) ) ).
fof(dt_k10_pboole,axiom,
! [A,B] :
( v1_funct_1(k10_pboole(A,B))
& v1_funct_2(k10_pboole(A,B),A,k1_tarski(B))
& m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) ) ).
fof(redefinition_k10_pboole,axiom,
! [A,B] : k10_pboole(A,B) = k2_funcop_1(A,B) ).
fof(dt_k11_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> m1_pboole(k11_pboole(A,B,C),A) ) ).
fof(dt_k12_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> m1_pboole(k12_pboole(A,B,C),A) ) ).
fof(dt_k13_pboole,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ( v1_relat_1(k13_pboole(A,B))
& v1_funct_1(k13_pboole(A,B))
& v1_funcop_1(k13_pboole(A,B)) ) ) ).
fof(dt_k14_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& v1_funcop_1(C)
& m1_pboole(C,A) )
=> m1_pboole(k14_pboole(A,B,C),A) ) ).
%------------------------------------------------------------------------------