SET007 Axioms: SET007+24.ax
%------------------------------------------------------------------------------
% File : SET007+24 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Binary Operations Applied to Functions
% 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 : funcop_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 117 ( 18 unt; 0 def)
% Number of atoms : 793 ( 108 equ)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 774 ( 98 ~; 2 |; 366 &)
% ( 2 <=>; 306 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 1 con; 0-6 aty)
% Number of variables : 395 ( 394 !; 1 ?)
% 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_funcop_1,axiom,
! [A,B] :
( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B)) ) ).
fof(fc2_funcop_1,axiom,
! [A] :
( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
& v1_relat_1(k2_funcop_1(k1_xboole_0,A))
& v1_funct_1(k2_funcop_1(k1_xboole_0,A))
& v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ).
fof(fc3_funcop_1,axiom,
! [A,B] :
( v1_xboole_0(B)
=> ( v1_xboole_0(k2_funcop_1(B,A))
& v1_relat_1(k2_funcop_1(B,A))
& v1_funct_1(k2_funcop_1(B,A))
& v2_funct_1(k2_funcop_1(B,A)) ) ) ).
fof(fc4_funcop_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_relat_1(C)
& v1_funct_1(C) )
=> ( v1_relat_1(k3_funcop_1(A,B,C))
& v1_funct_1(k3_funcop_1(A,B,C)) ) ) ).
fof(fc5_funcop_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B) )
=> ( v1_relat_1(k4_funcop_1(A,B,C))
& v1_funct_1(k4_funcop_1(A,B,C)) ) ) ).
fof(fc6_funcop_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(C)
& v1_funct_1(C) )
=> ( v1_relat_1(k5_funcop_1(A,B,C))
& v1_funct_1(k5_funcop_1(A,B,C)) ) ) ).
fof(rc1_funcop_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) ) ).
fof(fc7_funcop_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ( v1_relat_1(k1_funct_1(A,B))
& v1_funct_1(k1_funct_1(A,B)) ) ) ).
fof(fc8_funcop_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A)
& v1_relat_1(B)
& v1_funct_1(B) )
=> ( v1_relat_1(k5_relat_1(B,A))
& v1_funct_1(k5_relat_1(B,A))
& v1_funcop_1(k5_relat_1(B,A)) ) ) ).
fof(fc9_funcop_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( v1_relat_1(k2_funcop_1(A,B))
& v2_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B)) ) ) ).
fof(t1_funcop_1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B,C] :
( A = k2_zfmisc_1(B,C)
=> ( B = k1_xboole_0
| C = k1_xboole_0
| ( k1_relat_1(A) = B
& k2_relat_1(A) = C ) ) ) ) ).
fof(t2_funcop_1,axiom,
! [A] : k12_funct_3(A) = k13_funct_3(k6_partfun1(A),k6_partfun1(A)) ).
fof(t3_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( k1_relat_1(A) = k1_relat_1(B)
=> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B)) ) ) ) ) ).
fof(t4_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( ( k1_relat_1(A) = k1_xboole_0
& k1_relat_1(B) = k1_xboole_0 )
=> A = B ) ) ) ).
fof(d1_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( B = k1_funcop_1(A)
<=> ( k1_relat_1(B) = k1_relat_1(A)
& ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> ( ! [D,E] :
( k1_funct_1(A,C) = k4_tarski(D,E)
=> k1_funct_1(B,C) = k4_tarski(E,D) )
& ~ ( k1_funct_1(A,C) != k1_funct_1(B,C)
& ! [D,E] : k1_funct_1(A,C) != k4_tarski(D,E) ) ) ) ) ) ) ) ).
fof(t5_funcop_1,axiom,
$true ).
fof(t6_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)) ) ) ).
fof(t7_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] : k1_funcop_1(k7_relat_1(A,B)) = k7_relat_1(k1_funcop_1(A),B) ) ).
fof(t8_funcop_1,axiom,
$true ).
fof(t9_funcop_1,axiom,
! [A] : k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A) ).
fof(t10_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] : k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(k7_relat_1(A,C),B) ) ) ).
fof(t11_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] : k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(A,k7_relat_1(B,C)) ) ) ).
fof(d2_funcop_1,axiom,
! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ).
fof(t12_funcop_1,axiom,
$true ).
fof(t13_funcop_1,axiom,
! [A,B,C] :
( r2_hidden(B,A)
=> k1_funct_1(k2_funcop_1(A,C),B) = C ) ).
fof(t14_funcop_1,axiom,
! [A,B] :
( A != k1_xboole_0
=> k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B) ) ).
fof(t15_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( k2_relat_1(A) = k1_tarski(B)
=> A = k2_funcop_1(k1_relat_1(A),B) ) ) ).
fof(t16_funcop_1,axiom,
! [A] :
( k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0
& k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 ) ).
fof(t17_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> k1_funct_1(A,C) = B )
=> A = k2_funcop_1(k1_relat_1(A),B) ) ) ).
fof(t18_funcop_1,axiom,
! [A,B,C] : k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B) ).
fof(t19_funcop_1,axiom,
! [A,B] :
( k1_relat_1(k2_funcop_1(A,B)) = A
& r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ).
fof(t20_funcop_1,axiom,
! [A,B,C] :
( r2_hidden(B,C)
=> k10_relat_1(k2_funcop_1(A,B),C) = A ) ).
fof(t21_funcop_1,axiom,
! [A,B] : k10_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A ).
fof(t22_funcop_1,axiom,
! [A,B,C] :
( ~ r2_hidden(B,C)
=> k10_relat_1(k2_funcop_1(A,B),C) = k1_xboole_0 ) ).
fof(t23_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( r2_hidden(C,k1_relat_1(A))
=> k5_relat_1(k2_funcop_1(B,C),A) = k2_funcop_1(B,k1_funct_1(A,C)) ) ) ).
fof(t24_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
~ ( B != k1_xboole_0
& r2_hidden(C,k1_relat_1(A))
& k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0 ) ) ).
fof(t25_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] : k5_relat_1(A,k2_funcop_1(B,C)) = k2_funcop_1(k10_relat_1(A,B),C) ) ).
fof(t26_funcop_1,axiom,
! [A,B,C] : k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C))) = k2_funcop_1(A,k4_tarski(C,B)) ).
fof(d3_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A) ) ) ) ).
fof(t27_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( k1_relat_1(D) = k1_relat_1(k3_funcop_1(C,A,B))
& ! [E] :
( r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B)))
=> k1_funct_1(D,E) = k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) ) )
=> D = k3_funcop_1(C,A,B) ) ) ) ) ) ).
fof(t28_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B)))
=> k1_funct_1(k3_funcop_1(C,A,B),D) = k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ).
fof(t29_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D,E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( k7_relat_1(A,D) = k7_relat_1(B,D)
=> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D) ) ) ) ) ) ).
fof(t30_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D,E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( k7_relat_1(A,D) = k7_relat_1(B,D)
=> k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D) ) ) ) ) ) ).
fof(t31_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) ) ).
fof(t32_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C) ) ) ) ) ).
fof(d4_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] : k4_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A) ) ) ).
fof(t33_funcop_1,axiom,
$true ).
fof(t34_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] : k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C)) ) ) ).
fof(t35_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D] :
( r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D)))
=> k1_funct_1(k4_funcop_1(B,A,D),C) = k1_binop_1(B,k1_funct_1(A,C),D) ) ) ) ).
fof(t36_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( k7_relat_1(A,C) = k7_relat_1(B,C)
=> k7_relat_1(k4_funcop_1(D,A,E),C) = k7_relat_1(k4_funcop_1(D,B,E),C) ) ) ) ) ).
fof(t37_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] : k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D) ) ) ) ).
fof(t38_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] : k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D) ) ) ) ).
fof(t39_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] : k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D) ) ) ).
fof(d5_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> k5_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A) ) ) ).
fof(t40_funcop_1,axiom,
$true ).
fof(t41_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] : k5_funcop_1(B,C,A) = k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A) ) ) ).
fof(t42_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D] :
( r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A)))
=> k1_funct_1(k5_funcop_1(B,D,A),C) = k1_binop_1(B,D,k1_funct_1(A,C)) ) ) ) ).
fof(t43_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( k7_relat_1(A,C) = k7_relat_1(B,C)
=> k7_relat_1(k5_funcop_1(D,E,A),C) = k7_relat_1(k5_funcop_1(D,E,B),C) ) ) ) ) ).
fof(t44_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] : k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A)) ) ) ) ).
fof(t45_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] : k5_relat_1(k5_funcop_1(C,D,B),A) = k5_funcop_1(k5_relat_1(C,A),D,B) ) ) ) ).
fof(t46_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] : k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B)) ) ) ).
fof(t47_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ( v1_funct_1(k3_funcop_1(C,D,E))
& v1_funct_2(k3_funcop_1(C,D,E),A,B)
& m2_relset_1(k3_funcop_1(C,D,E),A,B) ) ) ) ) ) ) ).
fof(t48_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,A)
& m2_relset_1(E,B,A) )
=> ! [F] :
( m1_subset_1(F,B)
=> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)) ) ) ) ) ) ) ).
fof(t49_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( ! [G] :
( m1_subset_1(G,A)
=> k8_funct_2(A,B,F,G) = k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)) )
=> F = k6_funcop_1(B,A,C,D,E) ) ) ) ) ) ) ) ).
fof(t50_funcop_1,axiom,
$true ).
fof(t51_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,B)
& m2_relset_1(E,B,B) )
=> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)) ) ) ) ) ) ).
fof(t52_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,B)
& m2_relset_1(E,B,B) )
=> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))) = k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) ) ) ) ) ) ).
fof(t53_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))) = k6_funcop_1(B,A,C,D,D) ) ) ) ) ).
fof(t54_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)) ) ) ) ) ).
fof(t55_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) ) ) ) ) ).
fof(t56_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m1_subset_1(C,A)
=> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C) ) ) ) ).
fof(t57_funcop_1,axiom,
! [A,B,C] :
( r2_hidden(C,B)
=> ( v1_funct_1(k2_funcop_1(A,C))
& v1_funct_2(k2_funcop_1(A,C),A,B)
& m2_relset_1(k2_funcop_1(A,C),A,B) ) ) ).
fof(t58_funcop_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ( v1_funct_1(k2_funcop_1(A,C))
& v1_funct_2(k2_funcop_1(A,C),A,B)
& m2_relset_1(k2_funcop_1(A,C),A,B) ) ) ) ).
fof(t59_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,B)
=> ( v1_funct_1(k4_funcop_1(C,D,E))
& v1_funct_2(k4_funcop_1(C,D,E),A,B)
& m2_relset_1(k4_funcop_1(C,D,E),A,B) ) ) ) ) ) ) ).
fof(t60_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,B)
=> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) ) ) ) ) ) ) ).
fof(t61_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,A)
& m2_relset_1(E,B,A) )
=> ! [F] :
( m1_subset_1(F,A)
=> ( ! [G] :
( m1_subset_1(G,B)
=> k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) )
=> D = k7_funcop_1(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(t62_funcop_1,axiom,
$true ).
fof(t63_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,B)
=> k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E) ) ) ) ) ) ).
fof(t64_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m1_subset_1(C,A)
=> k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C) ) ) ) ).
fof(t65_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,B)
=> ( v1_funct_1(k5_funcop_1(C,E,D))
& v1_funct_2(k5_funcop_1(C,E,D),A,B)
& m2_relset_1(k5_funcop_1(C,E,D),A,B) ) ) ) ) ) ) ).
fof(t66_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,B)
=> k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)) ) ) ) ) ) ) ).
fof(t67_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,A)
& m2_relset_1(E,B,A) )
=> ! [F] :
( m1_subset_1(F,A)
=> ( ! [G] :
( m1_subset_1(G,B)
=> k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) )
=> D = k8_funcop_1(A,B,C,F,E) ) ) ) ) ) ) ) ).
fof(t68_funcop_1,axiom,
$true ).
fof(t69_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,B)
=> k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D) ) ) ) ) ) ).
fof(t70_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m1_subset_1(C,A)
=> k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C) ) ) ) ).
fof(t71_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> ! [E] :
( m1_subset_1(E,A)
=> k1_funct_1(k1_funcop_1(D),E) = k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))) ) ) ) ) ) ).
fof(t72_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> m2_relset_1(k2_relat_1(D),B,C) ) ) ) ) ).
fof(t73_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)) = k4_relat_1(k9_funcop_1(A,B,C,D)) ) ) ) ) ).
fof(t74_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( m1_subset_1(F,B)
=> ( v2_binop_1(C,B)
=> k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F)) ) ) ) ) ) ) ) ).
fof(t75_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,B)
=> ( v2_binop_1(C,B)
=> k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E) = k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) ) ) ) ) ) ) ) ).
fof(t76_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( v2_binop_1(C,B)
=> k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F) = k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F)) ) ) ) ) ) ) ) ).
fof(t77_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( m1_subset_1(F,B)
=> ( v2_binop_1(C,B)
=> k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D) = k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D)) ) ) ) ) ) ) ) ).
fof(t78_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( m1_subset_1(F,B)
=> ( v2_binop_1(C,B)
=> k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F)) = k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) ) ) ) ) ) ) ) ).
fof(t79_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,B)
=> ( v1_binop_1(C,B)
=> k8_funcop_1(B,A,C,E,D) = k7_funcop_1(B,A,C,D,E) ) ) ) ) ) ) ).
fof(t80_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ( v1_binop_1(C,B)
=> k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D) ) ) ) ) ) ) ).
fof(t81_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( v3_binop_1(C,B)
=> k6_funcop_1(B,A,C,D,D) = D ) ) ) ) ) ).
fof(t82_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( m1_subset_1(E,B)
=> ( v3_binop_1(C,A)
=> k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E) = k8_funct_2(B,A,D,E) ) ) ) ) ) ) ).
fof(t83_funcop_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( m1_subset_1(E,B)
=> ( v3_binop_1(C,A)
=> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E) ) ) ) ) ) ) ).
fof(t84_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A))
=> k1_relat_1(k3_funcop_1(A,B,C)) = k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) ) ) ) ) ).
fof(d6_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_funcop_1(A)
<=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> ( v1_relat_1(k1_funct_1(A,B))
& v1_funct_1(k1_funct_1(A,B)) ) ) ) ) ).
fof(dt_k1_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_relat_1(k1_funcop_1(A))
& v1_funct_1(k1_funcop_1(A)) ) ) ).
fof(involutiveness_k1_funcop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> k1_funcop_1(k1_funcop_1(A)) = A ) ).
fof(dt_k2_funcop_1,axiom,
$true ).
fof(dt_k3_funcop_1,axiom,
$true ).
fof(dt_k4_funcop_1,axiom,
$true ).
fof(dt_k5_funcop_1,axiom,
$true ).
fof(dt_k6_funcop_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& v1_funct_1(E)
& v1_funct_2(E,B,A)
& m1_relset_1(E,B,A) )
=> ( v1_funct_1(k6_funcop_1(A,B,C,D,E))
& v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A)
& m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) ) ) ).
fof(redefinition_k6_funcop_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& v1_funct_1(E)
& v1_funct_2(E,B,A)
& m1_relset_1(E,B,A) )
=> k6_funcop_1(A,B,C,D,E) = k3_funcop_1(C,D,E) ) ).
fof(dt_k7_funcop_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& m1_subset_1(E,A) )
=> ( v1_funct_1(k7_funcop_1(A,B,C,D,E))
& v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A)
& m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) ) ) ).
fof(redefinition_k7_funcop_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& m1_subset_1(E,A) )
=> k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E) ) ).
fof(dt_k8_funcop_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_subset_1(D,A)
& v1_funct_1(E)
& v1_funct_2(E,B,A)
& m1_relset_1(E,B,A) )
=> ( v1_funct_1(k8_funcop_1(A,B,C,D,E))
& v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A)
& m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) ) ) ).
fof(redefinition_k8_funcop_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_subset_1(D,A)
& v1_funct_1(E)
& v1_funct_2(E,B,A)
& m1_relset_1(E,B,A) )
=> k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E) ) ).
fof(dt_k9_funcop_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> m2_relset_1(k9_funcop_1(A,B,C,D),B,C) ) ).
fof(redefinition_k9_funcop_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> k9_funcop_1(A,B,C,D) = k2_relat_1(D) ) ).
fof(dt_k10_funcop_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> ( v1_funct_1(k10_funcop_1(A,B,C,D))
& v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B))
& m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) ) ) ).
fof(involutiveness_k10_funcop_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)) = D ) ).
fof(redefinition_k10_funcop_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m1_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> k10_funcop_1(A,B,C,D) = k1_funcop_1(D) ) ).
%------------------------------------------------------------------------------