SET007 Axioms: SET007+187.ax
%------------------------------------------------------------------------------
% File : SET007+187 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Basic Properties of 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 : pzfmisc1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 93 ( 4 unt; 0 def)
% Number of atoms : 453 ( 14 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 398 ( 38 ~; 13 |; 66 &)
% ( 13 <=>; 268 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 1 con; 0-3 aty)
% Number of variables : 317 ( 317 !; 0 ?)
% 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_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v1_relat_1(k1_pzfmisc1(A,B))
& v2_relat_1(k1_pzfmisc1(A,B))
& v1_funct_1(k1_pzfmisc1(A,B))
& v1_pre_circ(k1_pzfmisc1(A,B),A) ) ) ).
fof(fc2_pzfmisc1,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ( v1_relat_1(k2_pzfmisc1(A,B,C))
& v2_relat_1(k2_pzfmisc1(A,B,C))
& v1_funct_1(k2_pzfmisc1(A,B,C))
& v1_pre_circ(k2_pzfmisc1(A,B,C),A) ) ) ).
fof(t1_pzfmisc1,axiom,
! [A,B,C,D] :
( m1_pboole(D,A)
=> ( r2_hidden(B,A)
=> k1_relat_1(k1_funct_4(D,k3_cqc_lang(B,C))) = A ) ) ).
fof(t2_pzfmisc1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( A = k1_xboole_0
=> m1_pboole(A,k1_xboole_0) ) ) ).
fof(t3_pzfmisc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ~ ( v3_relat_1(B)
& v2_relat_1(B) ) ) ) ).
fof(d1_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( C = k1_pzfmisc1(A,B)
<=> ! [D] :
( r2_hidden(D,A)
=> k1_funct_1(C,D) = k1_tarski(k1_funct_1(B,D)) ) ) ) ) ).
fof(d2_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( D = k2_pzfmisc1(A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k1_funct_1(D,E) = k2_tarski(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ).
fof(t4_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,B,k1_pzfmisc1(A,C))
<=> ! [D] :
( m1_pboole(D,A)
=> ( r1_pboole(A,D,B)
<=> r6_pboole(A,D,C) ) ) ) ) ) ).
fof(t5_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ! [E] :
( m1_pboole(E,A)
=> ( r1_pboole(A,E,B)
<=> ( r6_pboole(A,E,C)
| r6_pboole(A,E,D) ) ) )
=> r6_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) ).
fof(t6_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,B,k2_pzfmisc1(A,C,D))
=> ! [E] :
( m1_pboole(E,A)
=> ( ( r6_pboole(A,E,C)
| r6_pboole(A,E,D) )
=> r1_pboole(A,E,B) ) ) ) ) ) ) ).
fof(t7_pzfmisc1,axiom,
$true ).
fof(t8_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r1_pboole(A,B,k1_pzfmisc1(A,C))
=> r6_pboole(A,B,C) ) ) ) ).
fof(t9_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r1_pboole(A,B,k1_pzfmisc1(A,B)) ) ).
fof(t10_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r6_pboole(A,B,C)
| r6_pboole(A,B,D) )
=> r1_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) ).
fof(t11_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k2_pzfmisc1(A,B,C)) ) ) ).
fof(t12_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r6_pboole(A,k2_pzfmisc1(A,B,B),k1_pzfmisc1(A,B)) ) ).
fof(t13_pzfmisc1,axiom,
$true ).
fof(t14_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))
=> r6_pboole(A,B,C) ) ) ) ).
fof(t15_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))
=> r6_pboole(A,B,C) ) ) ) ).
fof(t16_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,C,D))
=> ( r6_pboole(A,B,C)
& r6_pboole(A,B,D) ) ) ) ) ) ).
fof(t17_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,C,D))
=> r6_pboole(A,C,D) ) ) ) ) ).
fof(t18_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C))
& r2_pboole(A,k1_pzfmisc1(A,C),k2_pzfmisc1(A,B,C)) ) ) ) ).
fof(t19_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,B))
| r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,C)) )
=> r6_pboole(A,B,C) ) ) ) ).
fof(t20_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C)),k2_pzfmisc1(A,B,C)) ) ) ).
fof(t21_pzfmisc1,axiom,
$true ).
fof(t22_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ~ ( ~ v1_xboole_0(A)
& r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pboole(A))
& B = C ) ) ) ).
fof(t23_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,B))
| r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,C)) )
=> r6_pboole(A,B,C) ) ) ) ).
fof(t24_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C)),k1_pzfmisc1(A,B))
& r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,C),k2_pzfmisc1(A,B,C)),k1_pzfmisc1(A,C)) ) ) ) ).
fof(t25_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ~ ( ~ v1_xboole_0(A)
& r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pzfmisc1(A,B))
& B = C ) ) ) ).
fof(t26_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)),k1_pboole(A))
=> r6_pboole(A,B,C) ) ) ) ).
fof(t27_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),k2_pzfmisc1(A,B,C)),k1_pboole(A))
& r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,C),k2_pzfmisc1(A,B,C)),k1_pboole(A)) ) ) ) ).
fof(t28_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))
=> r6_pboole(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C)) ) ) ) ).
fof(t29_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,k2_pzfmisc1(A,B,C),k1_pzfmisc1(A,D))
=> ( r6_pboole(A,B,D)
& r6_pboole(A,C,D) ) ) ) ) ) ).
fof(t30_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,k2_pzfmisc1(A,B,C),k1_pzfmisc1(A,D))
=> r6_pboole(A,k2_pzfmisc1(A,B,C),k1_pzfmisc1(A,D)) ) ) ) ) ).
fof(t31_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r6_pboole(A,k1_mboolean(A,k1_pzfmisc1(A,B)),k2_pzfmisc1(A,k1_pboole(A),k1_pzfmisc1(A,B))) ) ).
fof(t32_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r2_pboole(A,k1_pzfmisc1(A,B),k1_mboolean(A,B)) ) ).
fof(t33_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r6_pboole(A,k2_mboolean(A,k1_pzfmisc1(A,B)),B) ) ).
fof(t34_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k2_mboolean(A,k2_pzfmisc1(A,k1_pzfmisc1(A,B),k1_pzfmisc1(A,C))),k2_pzfmisc1(A,B,C)) ) ) ).
fof(t35_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> r6_pboole(A,k2_mboolean(A,k2_pzfmisc1(A,B,C)),k2_pboole(A,B,C)) ) ) ).
fof(t36_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,k1_pzfmisc1(A,B),C)
<=> r1_pboole(A,B,C) ) ) ) ).
fof(t37_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,k2_pzfmisc1(A,B,C),D)
<=> ( r1_pboole(A,B,D)
& r1_pboole(A,C,D) ) ) ) ) ) ).
fof(t38_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ~ ( ~ r6_pboole(A,B,k1_pboole(A))
& ~ r6_pboole(A,B,k1_pzfmisc1(A,C))
& ~ r6_pboole(A,B,k1_pzfmisc1(A,D))
& ~ r6_pboole(A,B,k2_pzfmisc1(A,C,D)) )
=> r2_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) ).
fof(t39_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ( r1_pboole(A,B,C)
| r6_pboole(A,B,D) )
=> r1_pboole(A,B,k2_pboole(A,C,k1_pzfmisc1(A,D))) ) ) ) ) ).
fof(t40_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r2_pboole(A,k2_pboole(A,B,k1_pzfmisc1(A,C)),D)
<=> ( r1_pboole(A,C,D)
& r2_pboole(A,B,D) ) ) ) ) ) ).
fof(t41_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),C),C)
=> r1_pboole(A,B,C) ) ) ) ).
fof(t42_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r1_pboole(A,B,C)
=> r6_pboole(A,k2_pboole(A,k1_pzfmisc1(A,B),C),C) ) ) ) ).
fof(t43_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k2_pboole(A,k2_pzfmisc1(A,B,C),D),D)
<=> ( r1_pboole(A,B,D)
& r1_pboole(A,C,D) ) ) ) ) ) ).
fof(t44_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ~ ( ~ v1_xboole_0(A)
& k2_pboole(A,k1_pzfmisc1(A,B),C) = k1_pboole(A) ) ) ) ).
fof(t45_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ~ ( ~ v1_xboole_0(A)
& k2_pboole(A,k2_pzfmisc1(A,B,C),D) = k1_pboole(A) ) ) ) ) ).
fof(t46_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k3_pboole(A,B,k1_pzfmisc1(A,C)),k1_pzfmisc1(A,C))
=> r1_pboole(A,C,B) ) ) ) ).
fof(t47_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r1_pboole(A,B,C)
=> r6_pboole(A,k3_pboole(A,C,k1_pzfmisc1(A,B)),k1_pzfmisc1(A,B)) ) ) ) ).
fof(t48_pzfmisc1,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,D,C) )
<=> r6_pboole(A,k3_pboole(A,k2_pzfmisc1(A,B,D),C),k2_pzfmisc1(A,B,D)) ) ) ) ) ).
fof(t49_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ~ ( ~ v1_xboole_0(A)
& r6_pboole(A,k3_pboole(A,k1_pzfmisc1(A,B),C),k1_pboole(A))
& r1_pboole(A,B,C) ) ) ) ).
fof(t50_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k3_pboole(A,k2_pzfmisc1(A,B,C),D),k1_pboole(A))
=> ( v1_xboole_0(A)
| ( ~ r1_pboole(A,B,D)
& ~ r1_pboole(A,C,D) ) ) ) ) ) ) ).
fof(t51_pzfmisc1,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,k1_pzfmisc1(A,D)))
=> r1_pboole(A,B,C) ) ) ) ) ).
fof(t52_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ~ ( ~ v1_xboole_0(A)
& r1_pboole(A,B,k4_pboole(A,C,k1_pzfmisc1(A,D)))
& B = D ) ) ) ) ).
fof(t53_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ~ ( ~ v1_xboole_0(A)
& r6_pboole(A,k4_pboole(A,B,k1_pzfmisc1(A,C)),B)
& r1_pboole(A,C,B) ) ) ) ).
fof(t54_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ~ ( ~ v1_xboole_0(A)
& r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),C),k1_pzfmisc1(A,B))
& r1_pboole(A,B,C) ) ) ) ).
fof(t55_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k4_pboole(A,k1_pzfmisc1(A,B),C),k1_pboole(A))
<=> r1_pboole(A,B,C) ) ) ) ).
fof(t56_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ~ ( ~ v1_xboole_0(A)
& r6_pboole(A,k4_pboole(A,k2_pzfmisc1(A,B,C),D),k1_pzfmisc1(A,B))
& r1_pboole(A,B,D) ) ) ) ) ).
fof(t57_pzfmisc1,axiom,
$true ).
fof(t58_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k4_pboole(A,k2_pzfmisc1(A,B,C),D),k2_pzfmisc1(A,B,C))
=> ( v1_xboole_0(A)
| ( ~ r1_pboole(A,B,D)
& ~ r1_pboole(A,C,D) ) ) ) ) ) ) ).
fof(t59_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k4_pboole(A,k2_pzfmisc1(A,B,C),D),k1_pboole(A))
<=> ( r1_pboole(A,B,D)
& r1_pboole(A,C,D) ) ) ) ) ) ).
fof(t60_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( ~ ( ~ r6_pboole(A,B,k1_pboole(A))
& ~ r6_pboole(A,B,k1_pzfmisc1(A,C))
& ~ r6_pboole(A,B,k1_pzfmisc1(A,D))
& ~ r6_pboole(A,B,k2_pzfmisc1(A,C,D)) )
=> r6_pboole(A,k4_pboole(A,B,k2_pzfmisc1(A,C,D)),k1_pboole(A)) ) ) ) ) ).
fof(t61_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( r6_pboole(A,B,k1_pboole(A))
| r6_pboole(A,C,k1_pboole(A)) )
=> r6_pboole(A,k11_pboole(A,B,C),k1_pboole(A)) ) ) ) ).
fof(t62_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( v2_relat_1(B)
& v2_relat_1(C)
& r6_pboole(A,k11_pboole(A,B,C),k11_pboole(A,C,B)) )
=> r6_pboole(A,B,C) ) ) ) ).
fof(t63_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r6_pboole(A,k11_pboole(A,B,B),k11_pboole(A,C,C))
=> r6_pboole(A,B,C) ) ) ) ).
fof(t64_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( v2_relat_1(B)
=> ( ( ~ r2_pboole(A,k11_pboole(A,C,B),k11_pboole(A,D,B))
& ~ r2_pboole(A,k11_pboole(A,B,C),k11_pboole(A,B,D)) )
| r2_pboole(A,C,D) ) ) ) ) ) ).
fof(t65_pzfmisc1,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,k11_pboole(A,B,D),k11_pboole(A,C,D))
& r2_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C)) ) ) ) ) ) ).
fof(t66_pzfmisc1,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,k11_pboole(A,B,D),k11_pboole(A,C,E)) ) ) ) ) ) ).
fof(t67_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k11_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D)))
& r6_pboole(A,k11_pboole(A,D,k2_pboole(A,B,C)),k2_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C))) ) ) ) ) ).
fof(t68_pzfmisc1,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,k11_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)),k2_pboole(A,k2_pboole(A,k2_pboole(A,k11_pboole(A,B,D),k11_pboole(A,B,E)),k11_pboole(A,C,D)),k11_pboole(A,C,E))) ) ) ) ) ).
fof(t69_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k11_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D)))
& r6_pboole(A,k11_pboole(A,D,k3_pboole(A,B,C)),k3_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C))) ) ) ) ) ).
fof(t70_pzfmisc1,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,k11_pboole(A,k3_pboole(A,B,C),k3_pboole(A,D,E)),k3_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,E))) ) ) ) ) ).
fof(t71_pzfmisc1,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) )
=> r6_pboole(A,k3_pboole(A,k11_pboole(A,B,E),k11_pboole(A,C,D)),k11_pboole(A,B,D)) ) ) ) ) ) ).
fof(t72_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k11_pboole(A,k4_pboole(A,B,C),D),k4_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,D)))
& r6_pboole(A,k11_pboole(A,D,k4_pboole(A,B,C)),k4_pboole(A,k11_pboole(A,D,B),k11_pboole(A,D,C))) ) ) ) ) ).
fof(t73_pzfmisc1,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,k4_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E)),k2_pboole(A,k11_pboole(A,k4_pboole(A,B,D),C),k11_pboole(A,B,k4_pboole(A,C,E)))) ) ) ) ) ).
fof(t74_pzfmisc1,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,k3_pboole(A,B,C),k1_pboole(A))
| r6_pboole(A,k3_pboole(A,D,E),k1_pboole(A)) )
=> r6_pboole(A,k3_pboole(A,k11_pboole(A,B,D),k11_pboole(A,C,E)),k1_pboole(A)) ) ) ) ) ) ).
fof(t75_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( v2_relat_1(B)
=> ( v2_relat_1(k11_pboole(A,k1_pzfmisc1(A,C),B))
& v2_relat_1(k11_pboole(A,B,k1_pzfmisc1(A,C))) ) ) ) ) ).
fof(t76_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( r6_pboole(A,k11_pboole(A,k2_pzfmisc1(A,B,C),D),k2_pboole(A,k11_pboole(A,k1_pzfmisc1(A,B),D),k11_pboole(A,k1_pzfmisc1(A,C),D)))
& r6_pboole(A,k11_pboole(A,D,k2_pzfmisc1(A,B,C)),k2_pboole(A,k11_pboole(A,D,k1_pzfmisc1(A,B)),k11_pboole(A,D,k1_pzfmisc1(A,C)))) ) ) ) ) ).
fof(t77_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,A)
=> ( ( v2_relat_1(B)
& v2_relat_1(C)
& r6_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E)) )
=> ( r6_pboole(A,B,D)
& r6_pboole(A,C,E) ) ) ) ) ) ) ).
fof(t78_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( ( r2_pboole(A,B,k11_pboole(A,B,C))
| r2_pboole(A,B,k11_pboole(A,C,B)) )
=> r6_pboole(A,B,k1_pboole(A)) ) ) ) ).
fof(t79_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,A)
=> ! [F] :
( m1_pboole(F,A)
=> ( ( r1_pboole(A,B,k11_pboole(A,C,D))
& r1_pboole(A,B,k11_pboole(A,E,F)) )
=> r1_pboole(A,B,k11_pboole(A,k3_pboole(A,C,E),k3_pboole(A,D,F))) ) ) ) ) ) ) ).
fof(t80_pzfmisc1,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,k11_pboole(A,B,C),k11_pboole(A,D,E))
& v2_relat_1(k11_pboole(A,B,C)) )
=> ( r2_pboole(A,B,D)
& r2_pboole(A,C,E) ) ) ) ) ) ) ).
fof(t81_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r2_pboole(A,B,C)
=> r2_pboole(A,k11_pboole(A,B,B),k11_pboole(A,C,C)) ) ) ) ).
fof(t82_pzfmisc1,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,k3_pboole(A,k11_pboole(A,B,C),k11_pboole(A,C,B)),k1_pboole(A)) ) ) ) ).
fof(t83_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,A)
=> ( v2_relat_1(B)
=> ( ( ~ r2_pboole(A,k11_pboole(A,B,C),k11_pboole(A,D,E))
& ~ r2_pboole(A,k11_pboole(A,C,B),k11_pboole(A,E,D)) )
| r2_pboole(A,C,E) ) ) ) ) ) ) ).
fof(t84_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,A)
=> ! [F] :
( m1_pboole(F,A)
=> ! [G] :
( m1_pboole(G,A)
=> ( ( r2_pboole(A,B,k11_pboole(A,C,D))
& r2_pboole(A,E,k11_pboole(A,F,G)) )
=> r2_pboole(A,k2_pboole(A,B,E),k11_pboole(A,k2_pboole(A,C,F),k2_pboole(A,D,G))) ) ) ) ) ) ) ) ).
fof(d3_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ( r1_pzfmisc1(A,B,C)
<=> ! [D] :
( ( r2_hidden(D,A)
& k1_funct_1(C,D) = k1_xboole_0 )
=> k1_funct_1(B,D) = k1_xboole_0 ) ) ) ) ).
fof(reflexivity_r1_pzfmisc1,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> r1_pzfmisc1(A,B,B) ) ).
fof(dt_k1_pzfmisc1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> m1_pboole(k1_pzfmisc1(A,B),A) ) ).
fof(dt_k2_pzfmisc1,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> m1_pboole(k2_pzfmisc1(A,B,C),A) ) ).
fof(commutativity_k2_pzfmisc1,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> k2_pzfmisc1(A,B,C) = k2_pzfmisc1(A,C,B) ) ).
%------------------------------------------------------------------------------