SET007 Axioms: SET007+134.ax
%------------------------------------------------------------------------------
% File : SET007+134 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Calculus of Quantifiers. Deduction Theorem
% 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 : cqc_the2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 96 ( 4 unt; 0 def)
% Number of atoms : 463 ( 19 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 397 ( 30 ~; 14 |; 25 &)
% ( 15 <=>; 313 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 4 con; 0-3 aty)
% Number of variables : 268 ( 268 !; 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(t1_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(B,C)))
=> v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,B),C)) ) ) ) ) ).
fof(t2_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(B,C)))
=> v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(B,A),C)) ) ) ) ) ).
fof(t3_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,B),C))
=> v2_cqc_the1(k12_cqc_lang(A,k12_cqc_lang(B,C))) ) ) ) ) ).
fof(t4_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,B),C))
=> v2_cqc_the1(k12_cqc_lang(B,k12_cqc_lang(A,C))) ) ) ) ) ).
fof(t5_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( r2_hidden(B,k24_qc_lang1(k14_qc_lang1(C,A)))
<=> ( r2_hidden(B,k24_qc_lang1(A))
& B != C ) ) ) ) ) ).
fof(t6_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( r2_hidden(B,k24_qc_lang1(k5_qc_lang2(C,A)))
<=> ( r2_hidden(B,k24_qc_lang1(A))
& B != C ) ) ) ) ) ).
fof(t7_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( r2_hidden(C,k24_qc_lang1(k2_qc_lang2(A,B)))
<=> ( r2_hidden(C,k24_qc_lang1(A))
| r2_hidden(C,k24_qc_lang1(B)) ) ) ) ) ) ).
fof(t8_cqc_the2,axiom,
$true ).
fof(t9_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( r2_hidden(C,k24_qc_lang1(k13_qc_lang1(A,B)))
<=> ( r2_hidden(C,k24_qc_lang1(A))
| r2_hidden(C,k24_qc_lang1(B)) ) ) ) ) ) ).
fof(t10_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( r2_hidden(C,k24_qc_lang1(k3_qc_lang2(A,B)))
<=> ( r2_hidden(C,k24_qc_lang1(A))
| r2_hidden(C,k24_qc_lang1(B)) ) ) ) ) ) ).
fof(t11_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(B,k24_qc_lang1(k6_qc_lang2(B,C,A)))
& ~ r2_hidden(C,k24_qc_lang1(k6_qc_lang2(B,C,A))) ) ) ) ) ).
fof(t12_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(B,k24_qc_lang1(k7_qc_lang2(B,C,A)))
& ~ r2_hidden(C,k24_qc_lang1(k7_qc_lang2(B,C,A))) ) ) ) ) ).
fof(t13_cqc_the2,axiom,
$true ).
fof(t14_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> k17_cqc_lang(k2_qc_lang2(A,B),C) = k2_qc_lang2(k17_cqc_lang(A,C),k17_cqc_lang(B,C)) ) ) ) ).
fof(t15_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> k17_cqc_lang(k3_qc_lang2(A,B),C) = k3_qc_lang2(k17_cqc_lang(A,C),k17_cqc_lang(B,C)) ) ) ) ).
fof(t16_cqc_the2,axiom,
$true ).
fof(t17_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( B != C
=> k17_cqc_lang(k16_cqc_lang(B,A),C) = k5_qc_lang2(B,k17_cqc_lang(A,C)) ) ) ) ) ).
fof(t18_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(A,k16_cqc_lang(B,A))) ) ) ).
fof(t19_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(A)
=> v2_cqc_the1(k16_cqc_lang(B,A)) ) ) ) ).
fof(t20_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,A),k16_cqc_lang(B,A))) ) ) ).
fof(t21_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,A),k16_cqc_lang(C,A))) ) ) ) ).
fof(t22_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(A,B))
=> ( r2_hidden(C,k24_qc_lang1(B))
| v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,A),B)) ) ) ) ) ) ).
fof(t23_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(B,k24_qc_lang1(A))
=> v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,A),A)) ) ) ) ).
fof(t24_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k16_cqc_lang(B,A))
=> ( r2_hidden(B,k24_qc_lang1(A))
| v2_cqc_the1(A) ) ) ) ) ).
fof(t25_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ( ( A = k17_cqc_lang(C,D)
& B = k17_cqc_lang(C,E) )
=> ( r2_hidden(E,k24_qc_lang1(C))
| v2_cqc_the1(k12_cqc_lang(A,k16_cqc_lang(E,B))) ) ) ) ) ) ) ) ).
fof(t26_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(A)
=> v2_cqc_the1(k15_cqc_lang(B,A)) ) ) ) ).
fof(t27_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(B,k24_qc_lang1(A))
=> v2_cqc_the1(k12_cqc_lang(A,k15_cqc_lang(B,A))) ) ) ) ).
fof(t28_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ( ( A = k17_cqc_lang(C,D)
& B = k17_cqc_lang(C,E) )
=> ( r2_hidden(D,k24_qc_lang1(C))
| v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(D,A),B)) ) ) ) ) ) ) ) ).
fof(t29_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(B,k24_qc_lang1(A))
=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(B,A))) ) ) ) ) ).
fof(t30_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ( ( A = k17_cqc_lang(C,D)
& B = k17_cqc_lang(C,E) )
=> ( r2_hidden(D,k24_qc_lang1(C))
| r2_hidden(E,k24_qc_lang1(A))
| v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(D,A),k15_cqc_lang(E,B))) ) ) ) ) ) ) ) ).
fof(t31_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(B,k24_qc_lang1(A))
=> v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,A),k16_cqc_lang(C,A))) ) ) ) ) ).
fof(t32_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ( ( A = k17_cqc_lang(C,D)
& B = k17_cqc_lang(C,E) )
=> ( r2_hidden(D,k24_qc_lang1(B))
| r2_hidden(E,k24_qc_lang1(C))
| v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(D,A),k16_cqc_lang(E,B))) ) ) ) ) ) ) ) ).
fof(t33_cqc_the2,axiom,
$true ).
fof(t34_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)))) ) ) ) ).
fof(t35_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k15_cqc_lang(C,k12_cqc_lang(A,B)))
=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B))) ) ) ) ) ).
fof(t36_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k14_cqc_lang(A,B)),k14_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)))) ) ) ) ).
fof(t37_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k15_cqc_lang(C,k14_cqc_lang(A,B)))
=> v2_cqc_the1(k14_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B))) ) ) ) ) ).
fof(t38_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B)))) ) ) ) ).
fof(t39_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k15_cqc_lang(C,k12_cqc_lang(A,B)))
=> v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B))) ) ) ) ) ).
fof(t40_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B))))
& v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)),k15_cqc_lang(C,k11_cqc_lang(A,B)))) ) ) ) ) ).
fof(t41_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k14_cqc_lang(k15_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)))) ) ) ) ).
fof(t42_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k15_cqc_lang(C,k11_cqc_lang(A,B)))
<=> v2_cqc_the1(k11_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B))) ) ) ) ) ).
fof(t43_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k13_cqc_lang(k15_cqc_lang(C,A),k15_cqc_lang(C,B)),k15_cqc_lang(C,k13_cqc_lang(A,B)))) ) ) ) ).
fof(t44_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k13_cqc_lang(A,B)),k13_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B))))
& v2_cqc_the1(k12_cqc_lang(k13_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B)),k16_cqc_lang(C,k13_cqc_lang(A,B)))) ) ) ) ) ).
fof(t45_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k14_cqc_lang(k16_cqc_lang(C,k13_cqc_lang(A,B)),k13_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B)))) ) ) ) ).
fof(t46_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k16_cqc_lang(C,k13_cqc_lang(A,B)))
<=> v2_cqc_the1(k13_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B))) ) ) ) ) ).
fof(t47_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B)))) ) ) ) ).
fof(t48_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k16_cqc_lang(C,k11_cqc_lang(A,B)))
=> v2_cqc_the1(k11_cqc_lang(k16_cqc_lang(C,A),k16_cqc_lang(C,B))) ) ) ) ) ).
fof(t49_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))),k15_cqc_lang(B,A)))
& v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,A),k15_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))))) ) ) ) ).
fof(t50_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k14_cqc_lang(k15_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))),k15_cqc_lang(B,A))) ) ) ).
fof(t51_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))),k16_cqc_lang(B,A)))
& v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,A),k16_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))))) ) ) ) ).
fof(t52_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k14_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))),k16_cqc_lang(B,A))) ) ) ).
fof(t53_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A))),k15_cqc_lang(B,A)))
& v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,A),k10_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A))))) ) ) ) ).
fof(t54_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k14_cqc_lang(k10_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A))),k15_cqc_lang(B,A))) ) ) ).
fof(t55_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k15_cqc_lang(B,A)),k16_cqc_lang(B,k10_cqc_lang(A))))
& v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A)),k10_cqc_lang(k15_cqc_lang(B,A)))) ) ) ) ).
fof(t56_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k14_cqc_lang(k10_cqc_lang(k15_cqc_lang(B,A)),k16_cqc_lang(B,k10_cqc_lang(A)))) ) ) ).
fof(t57_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k16_cqc_lang(B,A)),k15_cqc_lang(B,k10_cqc_lang(A))))
& v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,k10_cqc_lang(A)),k10_cqc_lang(k16_cqc_lang(B,A)))) ) ) ) ).
fof(t58_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k14_cqc_lang(k15_cqc_lang(B,k10_cqc_lang(A)),k10_cqc_lang(k16_cqc_lang(B,A)))) ) ) ).
fof(t59_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(B,k15_cqc_lang(C,A)),k15_cqc_lang(C,k15_cqc_lang(B,A))))
& v2_cqc_the1(k2_qc_lang2(k6_qc_lang2(B,C,A),k6_qc_lang2(C,B,A))) ) ) ) ) ).
fof(t60_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ( ( A = k17_cqc_lang(C,D)
& B = k17_cqc_lang(C,E) )
=> ( r2_hidden(E,k24_qc_lang1(C))
| v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(D,k15_cqc_lang(E,B)),k15_cqc_lang(D,A))) ) ) ) ) ) ) ) ).
fof(t61_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,k16_cqc_lang(C,A)),k16_cqc_lang(C,k16_cqc_lang(B,A))))
& v2_cqc_the1(k2_qc_lang2(k7_qc_lang2(B,C,A),k7_qc_lang2(C,B,A))) ) ) ) ) ).
fof(t62_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ( ( A = k17_cqc_lang(C,D)
& B = k17_cqc_lang(C,E) )
=> ( r2_hidden(E,k24_qc_lang1(C))
| v2_cqc_the1(k2_qc_lang2(k16_cqc_lang(D,A),k7_qc_lang2(D,E,B))) ) ) ) ) ) ) ) ).
fof(t63_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(B,k15_cqc_lang(C,A)),k15_cqc_lang(C,k16_cqc_lang(B,A)))) ) ) ) ).
fof(t64_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k16_cqc_lang(B,k14_cqc_lang(A,A))) ) ) ).
fof(t65_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(k15_cqc_lang(C,A),k16_cqc_lang(C,B))))
& v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k15_cqc_lang(C,A),k16_cqc_lang(C,B)),k16_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ) ).
fof(t66_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k14_cqc_lang(k16_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(k15_cqc_lang(C,A),k16_cqc_lang(C,B)))) ) ) ) ).
fof(t67_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k16_cqc_lang(C,k12_cqc_lang(A,B)))
<=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,A),k16_cqc_lang(C,B))) ) ) ) ) ).
fof(t68_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(A,k15_cqc_lang(C,B)))) ) ) ) ).
fof(t69_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(k15_cqc_lang(C,A),B))) ) ) ) ).
fof(t70_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k11_cqc_lang(A,B)))) ) ) ) ) ).
fof(t71_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( v2_cqc_the1(k11_cqc_lang(A,k15_cqc_lang(C,B)))
=> ( r2_hidden(C,k24_qc_lang1(A))
| v2_cqc_the1(k15_cqc_lang(C,k11_cqc_lang(A,B))) ) ) ) ) ) ).
fof(t72_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k12_cqc_lang(k13_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k13_cqc_lang(A,B))))
& v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k13_cqc_lang(A,B)),k13_cqc_lang(A,k15_cqc_lang(C,B)))) ) ) ) ) ) ).
fof(t73_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> v2_cqc_the1(k14_cqc_lang(k13_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k13_cqc_lang(A,B)))) ) ) ) ) ).
fof(t74_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k13_cqc_lang(A,k15_cqc_lang(C,B)))
<=> v2_cqc_the1(k15_cqc_lang(C,k13_cqc_lang(A,B))) ) ) ) ) ) ).
fof(t75_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k12_cqc_lang(k11_cqc_lang(A,k16_cqc_lang(C,B)),k16_cqc_lang(C,k11_cqc_lang(A,B))))
& v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k11_cqc_lang(A,B)),k11_cqc_lang(A,k16_cqc_lang(C,B)))) ) ) ) ) ) ).
fof(t76_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> v2_cqc_the1(k14_cqc_lang(k11_cqc_lang(A,k16_cqc_lang(C,B)),k16_cqc_lang(C,k11_cqc_lang(A,B)))) ) ) ) ) ).
fof(t77_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k11_cqc_lang(A,k16_cqc_lang(C,B)))
<=> v2_cqc_the1(k16_cqc_lang(C,k11_cqc_lang(A,B))) ) ) ) ) ) ).
fof(t78_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(A,k15_cqc_lang(C,B))))
& v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ) ) ).
fof(t79_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> v2_cqc_the1(k14_cqc_lang(k12_cqc_lang(A,k15_cqc_lang(C,B)),k15_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ) ).
fof(t80_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k15_cqc_lang(C,k12_cqc_lang(A,B)))
<=> v2_cqc_the1(k12_cqc_lang(A,k15_cqc_lang(C,B))) ) ) ) ) ) ).
fof(t81_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k12_cqc_lang(B,A)),k12_cqc_lang(k15_cqc_lang(C,B),A))) ) ) ) ) ).
fof(t82_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k15_cqc_lang(C,A),B),k16_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ).
fof(t83_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,B),A))
<=> v2_cqc_the1(k16_cqc_lang(C,k12_cqc_lang(B,A))) ) ) ) ) ) ).
fof(t84_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(k16_cqc_lang(C,B),A),k15_cqc_lang(C,k12_cqc_lang(B,A))))
& v2_cqc_the1(k12_cqc_lang(k15_cqc_lang(C,k12_cqc_lang(B,A)),k12_cqc_lang(k16_cqc_lang(C,B),A))) ) ) ) ) ) ).
fof(t85_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> v2_cqc_the1(k14_cqc_lang(k12_cqc_lang(k16_cqc_lang(C,B),A),k15_cqc_lang(C,k12_cqc_lang(B,A)))) ) ) ) ) ).
fof(t86_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,B),A))
<=> v2_cqc_the1(k15_cqc_lang(C,k12_cqc_lang(B,A))) ) ) ) ) ) ).
fof(t87_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> v2_cqc_the1(k12_cqc_lang(k16_cqc_lang(C,k12_cqc_lang(A,B)),k12_cqc_lang(A,k16_cqc_lang(C,B)))) ) ) ) ) ).
fof(t88_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(A,k16_cqc_lang(C,B)),k16_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ).
fof(t89_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> v2_cqc_the1(k14_cqc_lang(k12_cqc_lang(A,k16_cqc_lang(C,B)),k16_cqc_lang(C,k12_cqc_lang(A,B)))) ) ) ) ) ).
fof(t90_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(C,k24_qc_lang1(A))
=> ( v2_cqc_the1(k12_cqc_lang(A,k16_cqc_lang(C,B)))
<=> v2_cqc_the1(k16_cqc_lang(C,k12_cqc_lang(A,B))) ) ) ) ) ) ).
fof(t91_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r3_cqc_the1(k6_domain_1(k7_cqc_lang,A),A) ) ).
fof(t92_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> k1_cqc_the1(k4_subset_1(k7_cqc_lang,k6_domain_1(k7_cqc_lang,A),k6_domain_1(k7_cqc_lang,B))) = k1_cqc_the1(k6_domain_1(k7_cqc_lang,k11_cqc_lang(A,B))) ) ) ).
fof(t93_cqc_the2,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( r3_cqc_the1(k7_domain_1(k7_cqc_lang,A,B),C)
<=> r3_cqc_the1(k6_domain_1(k7_cqc_lang,k11_cqc_lang(A,B)),C) ) ) ) ) ).
fof(t94_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( r3_cqc_the1(A,B)
=> r3_cqc_the1(A,k15_cqc_lang(C,B)) ) ) ) ) ).
fof(t95_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ( ~ r2_hidden(D,k24_qc_lang1(B))
=> r3_cqc_the1(A,k12_cqc_lang(k15_cqc_lang(D,k12_cqc_lang(B,C)),k12_cqc_lang(B,k15_cqc_lang(D,C)))) ) ) ) ) ) ).
fof(t96_cqc_the2,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( ( v6_qc_lang1(B)
& r3_cqc_the1(k4_subset_1(k7_cqc_lang,A,k6_domain_1(k7_cqc_lang,B)),C) )
=> r3_cqc_the1(A,k12_cqc_lang(B,C)) ) ) ) ) ).
%------------------------------------------------------------------------------