SET007 Axioms: SET007+77.ax
%------------------------------------------------------------------------------
% File : SET007+77 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Connectives and Subformulae of the First Order Language
% 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 : qc_lang2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 160 ( 27 unt; 0 def)
% Number of atoms : 673 ( 148 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 547 ( 34 ~; 6 |; 127 &)
% ( 24 <=>; 356 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 43 ( 43 usr; 9 con; 0-7 aty)
% Number of variables : 336 ( 325 !; 11 ?)
% 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_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( k12_qc_lang1(A) = k12_qc_lang1(B)
=> A = B ) ) ) ).
fof(t2_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> k17_qc_lang1(k12_qc_lang1(A)) = A ) ).
fof(t3_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ( k13_qc_lang1(A,B) = k13_qc_lang1(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t4_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v4_qc_lang1(A)
=> A = k13_qc_lang1(k18_qc_lang1(A),k19_qc_lang1(A)) ) ) ).
fof(t5_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( k18_qc_lang1(k13_qc_lang1(A,B)) = A
& k19_qc_lang1(k13_qc_lang1(A,B)) = B ) ) ) ).
fof(t6_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ( k14_qc_lang1(A,C) = k14_qc_lang1(B,D)
=> ( A = B
& C = D ) ) ) ) ) ) ).
fof(t7_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v5_qc_lang1(A)
=> A = k14_qc_lang1(k20_qc_lang1(A),k21_qc_lang1(A)) ) ) ).
fof(t8_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( k20_qc_lang1(k14_qc_lang1(A,B)) = A
& k21_qc_lang1(k14_qc_lang1(A,B)) = B ) ) ) ).
fof(d1_qc_lang2,axiom,
k1_qc_lang2 = k12_qc_lang1(k11_qc_lang1) ).
fof(d2_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k2_qc_lang2(A,B) = k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))) ) ) ).
fof(d3_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k3_qc_lang2(A,B) = k12_qc_lang1(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B))) ) ) ).
fof(d4_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k4_qc_lang2(A,B) = k13_qc_lang1(k2_qc_lang2(A,B),k2_qc_lang2(B,A)) ) ) ).
fof(d5_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k5_qc_lang2(A,B) = k12_qc_lang1(k14_qc_lang1(A,k12_qc_lang1(B))) ) ) ).
fof(t9_qc_lang2,axiom,
$true ).
fof(t10_qc_lang2,axiom,
$true ).
fof(t11_qc_lang2,axiom,
$true ).
fof(t12_qc_lang2,axiom,
$true ).
fof(t13_qc_lang2,axiom,
( v3_qc_lang1(k1_qc_lang2)
& k17_qc_lang1(k1_qc_lang2) = k11_qc_lang1 ) ).
fof(t14_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k3_qc_lang2(A,B) = k2_qc_lang2(k12_qc_lang1(A),B) ) ) ).
fof(t15_qc_lang2,axiom,
$true ).
fof(t16_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ( k3_qc_lang2(A,B) = k3_qc_lang2(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t17_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ( k2_qc_lang2(A,B) = k2_qc_lang2(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t18_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ( k4_qc_lang2(A,B) = k4_qc_lang2(C,D)
=> ( A = C
& B = D ) ) ) ) ) ) ).
fof(t19_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ( k5_qc_lang2(A,C) = k5_qc_lang2(B,D)
=> ( A = B
& C = D ) ) ) ) ) ) ).
fof(d6_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C)) ) ) ) ).
fof(d7_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> k7_qc_lang2(A,B,C) = k5_qc_lang2(A,k5_qc_lang2(B,C)) ) ) ) ).
fof(t20_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C))
& k7_qc_lang2(A,B,C) = k5_qc_lang2(A,k5_qc_lang2(B,C)) ) ) ) ) ).
fof(t21_qc_lang2,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)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ( k6_qc_lang2(C,E,A) = k6_qc_lang2(D,F,B)
=> ( C = D
& E = F
& A = B ) ) ) ) ) ) ) ) ).
fof(t22_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ! [E] :
( m1_subset_1(E,k8_qc_lang1)
=> ( k6_qc_lang2(A,B,D) = k14_qc_lang1(C,E)
=> ( A = C
& k14_qc_lang1(B,D) = E ) ) ) ) ) ) ) ).
fof(t23_qc_lang2,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)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ( k7_qc_lang2(C,E,A) = k7_qc_lang2(D,F,B)
=> ( C = D
& E = F
& A = B ) ) ) ) ) ) ) ) ).
fof(t24_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ! [E] :
( m1_subset_1(E,k8_qc_lang1)
=> ( k7_qc_lang2(A,B,D) = k5_qc_lang2(C,E)
=> ( A = C
& k5_qc_lang2(B,D) = E ) ) ) ) ) ) ) ).
fof(t25_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( v5_qc_lang1(k6_qc_lang2(A,B,C))
& k20_qc_lang1(k6_qc_lang2(A,B,C)) = A
& k21_qc_lang1(k6_qc_lang2(A,B,C)) = k14_qc_lang1(B,C) ) ) ) ) ).
fof(d8_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> k8_qc_lang2(A,B,C,D) = k14_qc_lang1(A,k6_qc_lang2(B,C,D)) ) ) ) ) ).
fof(d9_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)) ) ) ) ) ).
fof(t26_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ( k8_qc_lang2(A,B,C,D) = k14_qc_lang1(A,k6_qc_lang2(B,C,D))
& k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)) ) ) ) ) ) ).
fof(t27_qc_lang2,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)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
=> ! [H] :
( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
=> ( k8_qc_lang2(C,E,G,A) = k8_qc_lang2(D,F,H,B)
=> ( C = D
& E = F
& G = H
& A = B ) ) ) ) ) ) ) ) ) ) ).
fof(t28_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ! [E] :
( m1_subset_1(E,k8_qc_lang1)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ( k8_qc_lang2(A,B,C,D) = k14_qc_lang1(F,E)
=> ( A = F
& k6_qc_lang2(B,C,D) = E ) ) ) ) ) ) ) ) ).
fof(t29_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ! [E] :
( m1_subset_1(E,k8_qc_lang1)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
=> ( k8_qc_lang2(A,B,C,D) = k6_qc_lang2(F,G,E)
=> ( A = F
& B = G
& k14_qc_lang1(C,D) = E ) ) ) ) ) ) ) ) ) ).
fof(t30_qc_lang2,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)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
=> ! [H] :
( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
=> ( k9_qc_lang2(C,E,G,A) = k9_qc_lang2(D,F,H,B)
=> ( C = D
& E = F
& G = H
& A = B ) ) ) ) ) ) ) ) ) ) ).
fof(t31_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ! [E] :
( m1_subset_1(E,k8_qc_lang1)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ( k9_qc_lang2(A,B,C,D) = k5_qc_lang2(F,E)
=> ( A = F
& k7_qc_lang2(B,C,D) = E ) ) ) ) ) ) ) ) ).
fof(t32_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ! [E] :
( m1_subset_1(E,k8_qc_lang1)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
=> ( k9_qc_lang2(A,B,C,D) = k7_qc_lang2(F,G,E)
=> ( A = F
& B = G
& k5_qc_lang2(C,D) = E ) ) ) ) ) ) ) ) ) ).
fof(t33_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ( v5_qc_lang1(k8_qc_lang2(A,B,C,D))
& k20_qc_lang1(k8_qc_lang2(A,B,C,D)) = A
& k21_qc_lang1(k8_qc_lang2(A,B,C,D)) = k6_qc_lang2(B,C,D) ) ) ) ) ) ).
fof(d10_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v1_qc_lang2(A)
<=> ? [B] :
( m1_subset_1(B,k8_qc_lang1)
& ? [C] :
( m1_subset_1(C,k8_qc_lang1)
& A = k3_qc_lang2(B,C) ) ) ) ) ).
fof(d11_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v2_qc_lang2(A)
<=> ? [B] :
( m1_subset_1(B,k8_qc_lang1)
& ? [C] :
( m1_subset_1(C,k8_qc_lang1)
& A = k2_qc_lang2(B,C) ) ) ) ) ).
fof(d12_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v3_qc_lang2(A)
<=> ? [B] :
( m1_subset_1(B,k8_qc_lang1)
& ? [C] :
( m1_subset_1(C,k8_qc_lang1)
& A = k4_qc_lang2(B,C) ) ) ) ) ).
fof(d13_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v4_qc_lang2(A)
<=> ? [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
& ? [C] :
( m1_subset_1(C,k8_qc_lang1)
& A = k5_qc_lang2(B,C) ) ) ) ) ).
fof(t34_qc_lang2,axiom,
$true ).
fof(t35_qc_lang2,axiom,
$true ).
fof(t36_qc_lang2,axiom,
$true ).
fof(t37_qc_lang2,axiom,
$true ).
fof(t38_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k8_qc_lang1)
=> ( v4_qc_lang2(k7_qc_lang2(A,B,D))
& v4_qc_lang2(k9_qc_lang2(A,B,C,D)) ) ) ) ) ) ).
fof(d14_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> k10_qc_lang2(A) = k17_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) ) ).
fof(d15_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> k11_qc_lang2(A) = k17_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) ) ).
fof(d16_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> k12_qc_lang2(A) = k18_qc_lang1(k17_qc_lang1(A)) ) ).
fof(d17_qc_lang2,axiom,
$true ).
fof(d18_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> k13_qc_lang2(A) = k12_qc_lang2(k18_qc_lang1(A)) ) ).
fof(d19_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> k14_qc_lang2(A) = k11_qc_lang2(k18_qc_lang1(A)) ) ).
fof(t39_qc_lang2,axiom,
$true ).
fof(t40_qc_lang2,axiom,
$true ).
fof(t41_qc_lang2,axiom,
$true ).
fof(t42_qc_lang2,axiom,
$true ).
fof(t43_qc_lang2,axiom,
$true ).
fof(t44_qc_lang2,axiom,
$true ).
fof(t45_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( k10_qc_lang2(k3_qc_lang2(A,B)) = A
& k11_qc_lang2(k3_qc_lang2(A,B)) = B
& k17_qc_lang1(k3_qc_lang2(A,B)) = k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)) ) ) ) ).
fof(t46_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( k12_qc_lang2(k2_qc_lang2(A,B)) = A
& k11_qc_lang2(k2_qc_lang2(A,B)) = B
& k17_qc_lang1(k2_qc_lang2(A,B)) = k13_qc_lang1(A,k12_qc_lang1(B)) ) ) ) ).
fof(t47_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( k13_qc_lang2(k4_qc_lang2(A,B)) = A
& k14_qc_lang2(k4_qc_lang2(A,B)) = B
& k18_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(A,B)
& k19_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(B,A) ) ) ) ).
fof(t48_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k17_qc_lang1(k5_qc_lang2(A,B)) = k14_qc_lang1(A,k12_qc_lang1(B)) ) ) ).
fof(t49_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v1_qc_lang2(A)
=> ( v2_qc_lang2(A)
& v3_qc_lang1(A)
& v4_qc_lang1(k17_qc_lang1(A))
& v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A)))
& v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) ) ) ) ).
fof(t50_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v2_qc_lang2(A)
=> ( v3_qc_lang1(A)
& v4_qc_lang1(k17_qc_lang1(A))
& v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) ) ) ) ).
fof(t51_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v3_qc_lang2(A)
=> ( v4_qc_lang1(A)
& v2_qc_lang2(k18_qc_lang1(A))
& v2_qc_lang2(k19_qc_lang1(A)) ) ) ) ).
fof(t52_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v4_qc_lang2(A)
=> ( v3_qc_lang1(A)
& v5_qc_lang1(k17_qc_lang1(A))
& v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))) ) ) ) ).
fof(t53_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v1_qc_lang2(A)
=> A = k3_qc_lang2(k10_qc_lang2(A),k11_qc_lang2(A)) ) ) ).
fof(t54_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v2_qc_lang2(A)
=> A = k2_qc_lang2(k12_qc_lang2(A),k11_qc_lang2(A)) ) ) ).
fof(t55_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v3_qc_lang2(A)
=> A = k4_qc_lang2(k13_qc_lang2(A),k14_qc_lang2(A)) ) ) ).
fof(t56_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v4_qc_lang2(A)
=> A = k5_qc_lang2(k20_qc_lang1(k17_qc_lang1(A)),k17_qc_lang1(k21_qc_lang1(k17_qc_lang1(A)))) ) ) ).
fof(d20_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r1_qc_lang2(A,B)
<=> ~ ( B != k12_qc_lang1(A)
& ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( B != k13_qc_lang1(A,C)
& B != k13_qc_lang1(C,A) ) )
& ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> B != k14_qc_lang1(C,A) ) ) ) ) ) ).
fof(t57_qc_lang2,axiom,
$true ).
fof(t58_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ~ r1_qc_lang2(A,k11_qc_lang1) ) ).
fof(t59_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B))
=> ! [D] :
( m1_qc_lang1(D,B)
=> ~ r1_qc_lang2(A,k9_qc_lang1(C,D)) ) ) ) ) ).
fof(t60_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r1_qc_lang2(A,k12_qc_lang1(B))
<=> A = B ) ) ) ).
fof(t61_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( r1_qc_lang2(A,k1_qc_lang2)
<=> A = k11_qc_lang1 ) ) ).
fof(t62_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( r1_qc_lang2(A,k13_qc_lang1(B,C))
<=> ( A = B
| A = C ) ) ) ) ) ).
fof(t63_qc_lang2,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)
=> ( r1_qc_lang2(A,k14_qc_lang1(C,B))
<=> A = B ) ) ) ) ).
fof(t64_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ~ ( v2_qc_lang1(A)
& r1_qc_lang2(B,A) ) ) ) ).
fof(t65_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( v3_qc_lang1(A)
=> ( r1_qc_lang2(B,A)
<=> B = k17_qc_lang1(A) ) ) ) ) ).
fof(t66_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( v4_qc_lang1(A)
=> ( r1_qc_lang2(B,A)
<=> ( B = k18_qc_lang1(A)
| B = k19_qc_lang1(A) ) ) ) ) ) ).
fof(t67_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( v5_qc_lang1(A)
=> ( r1_qc_lang2(B,A)
<=> B = k21_qc_lang1(A) ) ) ) ) ).
fof(d21_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r2_qc_lang2(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D)
& r1_xreal_0(np__1,C)
& k3_finseq_1(D) = C
& k1_funct_1(D,np__1) = A
& k1_funct_1(D,C) = B
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& ~ r1_xreal_0(C,E)
& ! [F] :
( m1_subset_1(F,k8_qc_lang1)
=> ! [G] :
( m1_subset_1(G,k8_qc_lang1)
=> ~ ( k1_funct_1(D,E) = F
& k1_funct_1(D,k1_nat_1(E,np__1)) = G
& r1_qc_lang2(F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(d22_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r3_qc_lang2(A,B)
<=> ( r2_qc_lang2(A,B)
& A != B ) ) ) ) ).
fof(t68_qc_lang2,axiom,
$true ).
fof(t69_qc_lang2,axiom,
$true ).
fof(t70_qc_lang2,axiom,
$true ).
fof(t71_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ~ ( r1_qc_lang2(A,B)
& r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) ) ) ) ).
fof(t72_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r1_qc_lang2(A,B)
=> r2_qc_lang2(A,B) ) ) ) ).
fof(t73_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r1_qc_lang2(A,B)
=> r3_qc_lang2(A,B) ) ) ) ).
fof(t74_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ~ ( r3_qc_lang2(A,B)
& r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) ) ) ) ).
fof(t75_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ~ ( r3_qc_lang2(A,B)
& ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ~ r1_qc_lang2(C,B) ) ) ) ) ).
fof(t76_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( ( r3_qc_lang2(A,B)
& r3_qc_lang2(B,C) )
=> r3_qc_lang2(A,C) ) ) ) ) ).
fof(t77_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( ( r2_qc_lang2(A,B)
& r2_qc_lang2(B,C) )
=> r2_qc_lang2(A,C) ) ) ) ) ).
fof(t78_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( ( r2_qc_lang2(A,B)
& r2_qc_lang2(B,A) )
=> A = B ) ) ) ).
fof(t79_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ~ ( r3_qc_lang2(A,B)
& r2_qc_lang2(B,A) ) ) ) ).
fof(t80_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ~ ( r3_qc_lang2(A,B)
& r3_qc_lang2(B,A) ) ) ) ).
fof(t81_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ~ ( r2_qc_lang2(A,B)
& r1_qc_lang2(B,A) ) ) ) ).
fof(t82_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ~ ( r3_qc_lang2(A,B)
& r1_qc_lang2(B,A) ) ) ) ).
fof(t83_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( ~ ( ~ ( r3_qc_lang2(A,B)
& r2_qc_lang2(B,C) )
& ~ ( r2_qc_lang2(A,B)
& r3_qc_lang2(B,C) )
& ~ ( r2_qc_lang2(A,B)
& r1_qc_lang2(B,C) )
& ~ ( r1_qc_lang2(A,B)
& r2_qc_lang2(B,C) )
& ~ ( r3_qc_lang2(A,B)
& r1_qc_lang2(B,C) )
& ~ ( r1_qc_lang2(A,B)
& r3_qc_lang2(B,C) ) )
=> r3_qc_lang2(A,C) ) ) ) ) ).
fof(t84_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ~ r3_qc_lang2(A,k11_qc_lang1) ) ).
fof(t85_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B))
=> ! [D] :
( m1_qc_lang1(D,B)
=> ~ r3_qc_lang2(A,k9_qc_lang1(C,D)) ) ) ) ) ).
fof(t86_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r2_qc_lang2(A,B)
<=> r3_qc_lang2(A,k12_qc_lang1(B)) ) ) ) ).
fof(t87_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r2_qc_lang2(k12_qc_lang1(A),B)
=> r3_qc_lang2(A,B) ) ) ) ).
fof(t88_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( r3_qc_lang2(A,k1_qc_lang2)
<=> r2_qc_lang2(A,k11_qc_lang1) ) ) ).
fof(t89_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( ( r2_qc_lang2(A,B)
| r2_qc_lang2(A,C) )
<=> r3_qc_lang2(A,k13_qc_lang1(B,C)) ) ) ) ) ).
fof(t90_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( r2_qc_lang2(k13_qc_lang1(A,B),C)
=> ( r3_qc_lang2(A,C)
& r3_qc_lang2(B,C) ) ) ) ) ) ).
fof(t91_qc_lang2,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_qc_lang2(A,B)
<=> r3_qc_lang2(A,k14_qc_lang1(C,B)) ) ) ) ) ).
fof(t92_qc_lang2,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_qc_lang2(k14_qc_lang1(C,A),B)
=> r3_qc_lang2(A,B) ) ) ) ) ).
fof(t93_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r3_qc_lang2(k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B))
& r3_qc_lang2(A,k2_qc_lang2(A,B))
& r3_qc_lang2(k12_qc_lang1(B),k2_qc_lang2(A,B))
& r3_qc_lang2(B,k2_qc_lang2(A,B)) ) ) ) ).
fof(t94_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r3_qc_lang2(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B))
& r3_qc_lang2(k12_qc_lang1(A),k3_qc_lang2(A,B))
& r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B))
& r3_qc_lang2(A,k3_qc_lang2(A,B))
& r3_qc_lang2(B,k3_qc_lang2(A,B)) ) ) ) ).
fof(t95_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ~ ( v2_qc_lang1(A)
& r3_qc_lang2(B,A) ) ) ) ).
fof(t96_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v3_qc_lang1(A)
=> r3_qc_lang2(k17_qc_lang1(A),A) ) ) ).
fof(t97_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v4_qc_lang1(A)
=> ( r3_qc_lang2(k18_qc_lang1(A),A)
& r3_qc_lang2(k19_qc_lang1(A),A) ) ) ) ).
fof(t98_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v5_qc_lang1(A)
=> r3_qc_lang2(k21_qc_lang1(A),A) ) ) ).
fof(t99_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( r2_qc_lang2(A,k11_qc_lang1)
<=> A = k11_qc_lang1 ) ) ).
fof(t100_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B))
=> ! [D] :
( m1_qc_lang1(D,B)
=> ( r2_qc_lang2(A,k9_qc_lang1(C,D))
<=> A = k9_qc_lang1(C,D) ) ) ) ) ) ).
fof(t101_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( r2_qc_lang2(A,k1_qc_lang2)
<=> ( A = k1_qc_lang2
| A = k11_qc_lang1 ) ) ) ).
fof(d23_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( B = k15_qc_lang2(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( m1_subset_1(D,k8_qc_lang1)
& D = C
& r2_qc_lang2(D,A) ) ) ) ) ).
fof(t102_qc_lang2,axiom,
$true ).
fof(t103_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r2_hidden(A,k15_qc_lang2(B))
=> r2_qc_lang2(A,B) ) ) ) ).
fof(t104_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r2_qc_lang2(A,B)
=> r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B)) ) ) ) ).
fof(t105_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( r2_hidden(A,k15_qc_lang2(B))
=> r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B)) ) ) ) ).
fof(t106_qc_lang2,axiom,
$true ).
fof(t107_qc_lang2,axiom,
k15_qc_lang2(k11_qc_lang1) = k1_tarski(k11_qc_lang1) ).
fof(t108_qc_lang2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
=> ! [C] :
( m1_qc_lang1(C,A)
=> k15_qc_lang2(k9_qc_lang1(B,C)) = k1_tarski(k9_qc_lang1(B,C)) ) ) ) ).
fof(t109_qc_lang2,axiom,
k15_qc_lang2(k1_qc_lang2) = k2_tarski(k11_qc_lang1,k1_qc_lang2) ).
fof(t110_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> k15_qc_lang2(k12_qc_lang1(A)) = k2_xboole_0(k15_qc_lang2(A),k1_tarski(k12_qc_lang1(A))) ) ).
fof(t111_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k15_qc_lang2(k13_qc_lang1(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_tarski(k13_qc_lang1(A,B))) ) ) ).
fof(t112_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> k15_qc_lang2(k14_qc_lang1(B,A)) = k2_xboole_0(k15_qc_lang2(A),k1_tarski(k14_qc_lang1(B,A))) ) ) ).
fof(t113_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k15_qc_lang2(k2_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B))) ) ) ).
fof(t114_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k15_qc_lang2(k3_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k2_enumset1(k12_qc_lang1(B),k12_qc_lang1(A),k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B))) ) ) ).
fof(t115_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k15_qc_lang2(k4_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k5_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B),k12_qc_lang1(A),k13_qc_lang1(B,k12_qc_lang1(A)),k2_qc_lang2(B,A),k4_qc_lang2(A,B))) ) ) ).
fof(t116_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( ( A = k11_qc_lang1
| v2_qc_lang1(A) )
<=> k15_qc_lang2(A) = k1_tarski(A) ) ) ).
fof(t117_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v3_qc_lang1(A)
=> k15_qc_lang2(A) = k2_xboole_0(k15_qc_lang2(k17_qc_lang1(A)),k1_tarski(A)) ) ) ).
fof(t118_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v4_qc_lang1(A)
=> k15_qc_lang2(A) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(k18_qc_lang1(A)),k15_qc_lang2(k19_qc_lang1(A))),k1_tarski(A)) ) ) ).
fof(t119_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v5_qc_lang1(A)
=> k15_qc_lang2(A) = k2_xboole_0(k15_qc_lang2(k21_qc_lang1(A)),k1_tarski(A)) ) ) ).
fof(t120_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( r2_hidden(B,k15_qc_lang2(C))
=> ( ( ~ r1_qc_lang2(A,B)
& ~ r3_qc_lang2(A,B)
& ~ r2_qc_lang2(A,B) )
| r2_hidden(A,k15_qc_lang2(C)) ) ) ) ) ) ).
fof(reflexivity_r2_qc_lang2,axiom,
! [A,B] :
( ( m1_subset_1(A,k8_qc_lang1)
& m1_subset_1(B,k8_qc_lang1) )
=> r2_qc_lang2(A,A) ) ).
fof(irreflexivity_r3_qc_lang2,axiom,
! [A,B] :
( ( m1_subset_1(A,k8_qc_lang1)
& m1_subset_1(B,k8_qc_lang1) )
=> ~ r3_qc_lang2(A,A) ) ).
fof(dt_k1_qc_lang2,axiom,
m1_subset_1(k1_qc_lang2,k8_qc_lang1) ).
fof(dt_k2_qc_lang2,axiom,
! [A,B] :
( ( m1_subset_1(A,k8_qc_lang1)
& m1_subset_1(B,k8_qc_lang1) )
=> m1_subset_1(k2_qc_lang2(A,B),k8_qc_lang1) ) ).
fof(dt_k3_qc_lang2,axiom,
! [A,B] :
( ( m1_subset_1(A,k8_qc_lang1)
& m1_subset_1(B,k8_qc_lang1) )
=> m1_subset_1(k3_qc_lang2(A,B),k8_qc_lang1) ) ).
fof(dt_k4_qc_lang2,axiom,
! [A,B] :
( ( m1_subset_1(A,k8_qc_lang1)
& m1_subset_1(B,k8_qc_lang1) )
=> m1_subset_1(k4_qc_lang2(A,B),k8_qc_lang1) ) ).
fof(dt_k5_qc_lang2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_qc_lang1)
& m1_subset_1(B,k8_qc_lang1) )
=> m1_subset_1(k5_qc_lang2(A,B),k8_qc_lang1) ) ).
fof(dt_k6_qc_lang2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k2_qc_lang1)
& m1_subset_1(B,k2_qc_lang1)
& m1_subset_1(C,k8_qc_lang1) )
=> m1_subset_1(k6_qc_lang2(A,B,C),k8_qc_lang1) ) ).
fof(dt_k7_qc_lang2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k2_qc_lang1)
& m1_subset_1(B,k2_qc_lang1)
& m1_subset_1(C,k8_qc_lang1) )
=> m1_subset_1(k7_qc_lang2(A,B,C),k8_qc_lang1) ) ).
fof(dt_k8_qc_lang2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k2_qc_lang1)
& m1_subset_1(B,k2_qc_lang1)
& m1_subset_1(C,k2_qc_lang1)
& m1_subset_1(D,k8_qc_lang1) )
=> m1_subset_1(k8_qc_lang2(A,B,C,D),k8_qc_lang1) ) ).
fof(dt_k9_qc_lang2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k2_qc_lang1)
& m1_subset_1(B,k2_qc_lang1)
& m1_subset_1(C,k2_qc_lang1)
& m1_subset_1(D,k8_qc_lang1) )
=> m1_subset_1(k9_qc_lang2(A,B,C,D),k8_qc_lang1) ) ).
fof(dt_k10_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> m1_subset_1(k10_qc_lang2(A),k8_qc_lang1) ) ).
fof(dt_k11_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> m1_subset_1(k11_qc_lang2(A),k8_qc_lang1) ) ).
fof(dt_k12_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> m1_subset_1(k12_qc_lang2(A),k8_qc_lang1) ) ).
fof(dt_k13_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> m1_subset_1(k13_qc_lang2(A),k8_qc_lang1) ) ).
fof(dt_k14_qc_lang2,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> m1_subset_1(k14_qc_lang2(A),k8_qc_lang1) ) ).
fof(dt_k15_qc_lang2,axiom,
$true ).
%------------------------------------------------------------------------------