SET007 Axioms: SET007+168.ax
%------------------------------------------------------------------------------
% File : SET007+168 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Logical Equivalence of Formulae
% 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_the3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 79 ( 3 unt; 0 def)
% Number of atoms : 386 ( 11 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 313 ( 6 ~; 2 |; 49 &)
% ( 24 <=>; 232 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 9 con; 0-3 aty)
% Number of variables : 199 ( 197 !; 2 ?)
% 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_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r2_hidden(A,B)
=> r3_cqc_the1(B,A) ) ) ) ).
fof(t2_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r1_tarski(A,k1_cqc_the1(B))
=> r1_tarski(k1_cqc_the1(A),k1_cqc_the1(B)) ) ) ) ).
fof(t3_cqc_the3,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,k1_zfmisc_1(k7_cqc_lang))
=> ( ( r3_cqc_the1(C,A)
& r3_cqc_the1(k6_domain_1(k7_cqc_lang,A),B) )
=> r3_cqc_the1(C,B) ) ) ) ) ).
fof(t4_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang))
=> ( ( r3_cqc_the1(B,A)
& r1_tarski(B,C) )
=> r3_cqc_the1(C,A) ) ) ) ) ).
fof(d1_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r1_cqc_the3(A,B)
<=> r3_cqc_the1(k6_domain_1(k7_cqc_lang,A),B) ) ) ) ).
fof(t5_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r1_cqc_the3(A,A) ) ).
fof(t6_cqc_the3,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)
=> ( ( r1_cqc_the3(A,B)
& r1_cqc_the3(B,C) )
=> r1_cqc_the3(A,C) ) ) ) ) ).
fof(d2_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r2_cqc_the3(A,B)
<=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(C,B)
=> r3_cqc_the1(A,C) ) ) ) ) ) ).
fof(t7_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r2_cqc_the3(A,B)
<=> r1_tarski(B,k1_cqc_the1(A)) ) ) ) ).
fof(t8_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> r2_cqc_the3(A,A) ) ).
fof(t9_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang))
=> ( ( r2_cqc_the3(A,B)
& r2_cqc_the3(B,C) )
=> r2_cqc_the3(A,C) ) ) ) ) ).
fof(t10_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r2_cqc_the3(B,k6_domain_1(k7_cqc_lang,A))
<=> r3_cqc_the1(B,A) ) ) ) ).
fof(t11_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_cqc_the3(k6_domain_1(k7_cqc_lang,A),k6_domain_1(k7_cqc_lang,B))
<=> r1_cqc_the3(A,B) ) ) ) ).
fof(t12_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r1_tarski(A,B)
=> r2_cqc_the3(B,A) ) ) ) ).
fof(t13_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> r2_cqc_the3(A,k4_cqc_the1) ) ).
fof(t14_cqc_the3,axiom,
r2_cqc_the3(k1_subset_1(k7_cqc_lang),k4_cqc_the1) ).
fof(d3_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ( r3_cqc_the3(A)
<=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(B,A)
=> v2_cqc_the1(B) ) ) ) ) ).
fof(t15_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ( r3_cqc_the3(A)
<=> r2_cqc_the3(k1_subset_1(k7_cqc_lang),A) ) ) ).
fof(t16_cqc_the3,axiom,
r3_cqc_the3(k4_cqc_the1) ).
fof(t17_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ( r3_cqc_the3(A)
<=> r1_tarski(A,k4_cqc_the1) ) ) ).
fof(d4_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r4_cqc_the3(A,B)
<=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( r3_cqc_the1(A,C)
<=> r3_cqc_the1(B,C) ) ) ) ) ) ).
fof(t18_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r4_cqc_the3(A,B)
<=> ( r2_cqc_the3(A,B)
& r2_cqc_the3(B,A) ) ) ) ) ).
fof(t19_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang))
=> ( ( r4_cqc_the3(A,B)
& r4_cqc_the3(B,C) )
=> r4_cqc_the3(A,C) ) ) ) ) ).
fof(t20_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r4_cqc_the3(A,B)
<=> k1_cqc_the1(A) = k1_cqc_the1(B) ) ) ) ).
fof(t21_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> r1_tarski(k4_subset_1(k7_cqc_lang,k1_cqc_the1(A),k1_cqc_the1(B)),k1_cqc_the1(k4_subset_1(k7_cqc_lang,A,B))) ) ) ).
fof(t22_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> k1_cqc_the1(k4_subset_1(k7_cqc_lang,A,B)) = k1_cqc_the1(k4_subset_1(k7_cqc_lang,k1_cqc_the1(A),k1_cqc_the1(B))) ) ) ).
fof(t23_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> r4_cqc_the3(A,k1_cqc_the1(A)) ) ).
fof(t24_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> r4_cqc_the3(k4_subset_1(k7_cqc_lang,A,B),k4_subset_1(k7_cqc_lang,k1_cqc_the1(A),k1_cqc_the1(B))) ) ) ).
fof(t25_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang))
=> ( r4_cqc_the3(A,B)
=> r4_cqc_the3(k4_subset_1(k7_cqc_lang,A,C),k4_subset_1(k7_cqc_lang,B,C)) ) ) ) ) ).
fof(t26_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
=> ( ( r4_cqc_the3(A,B)
& r2_cqc_the3(k4_subset_1(k7_cqc_lang,A,C),D) )
=> r2_cqc_the3(k4_subset_1(k7_cqc_lang,B,C),D) ) ) ) ) ) ).
fof(t27_cqc_the3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang))
=> ( ( r4_cqc_the3(A,B)
& r2_cqc_the3(C,A) )
=> r2_cqc_the3(C,B) ) ) ) ) ).
fof(d5_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r5_cqc_the3(A,B)
<=> ( r1_cqc_the3(A,B)
& r1_cqc_the3(B,A) ) ) ) ) ).
fof(t28_cqc_the3,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)
=> ( ( r5_cqc_the3(A,B)
& r5_cqc_the3(B,C) )
=> r5_cqc_the3(A,C) ) ) ) ) ).
fof(t29_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r5_cqc_the3(A,B)
<=> r4_cqc_the3(k6_domain_1(k7_cqc_lang,A),k6_domain_1(k7_cqc_lang,B)) ) ) ) ).
fof(t30_cqc_the3,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,k1_zfmisc_1(k7_cqc_lang))
=> ( ( r5_cqc_the3(A,B)
& r3_cqc_the1(C,A) )
=> r3_cqc_the1(C,B) ) ) ) ) ).
fof(t31_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r4_cqc_the3(k7_domain_1(k7_cqc_lang,A,B),k6_domain_1(k7_cqc_lang,k11_cqc_lang(A,B))) ) ) ).
fof(t32_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r5_cqc_the3(k11_cqc_lang(A,B),k11_cqc_lang(B,A)) ) ) ).
fof(t33_cqc_the3,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,k1_zfmisc_1(k7_cqc_lang))
=> ( r3_cqc_the1(C,k11_cqc_lang(A,B))
<=> ( r3_cqc_the1(C,A)
& r3_cqc_the1(C,B) ) ) ) ) ) ).
fof(t34_cqc_the3,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)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( ( r5_cqc_the3(A,B)
& r5_cqc_the3(C,D) )
=> r5_cqc_the3(k11_cqc_lang(A,C),k11_cqc_lang(B,D)) ) ) ) ) ) ).
fof(t35_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( r3_cqc_the1(B,k15_cqc_lang(C,A))
<=> r3_cqc_the1(B,A) ) ) ) ) ).
fof(t36_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> r5_cqc_the3(k15_cqc_lang(B,A),A) ) ) ).
fof(t37_cqc_the3,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)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ( r5_cqc_the3(A,B)
=> r5_cqc_the3(k15_cqc_lang(C,A),k15_cqc_lang(D,B)) ) ) ) ) ) ).
fof(d6_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r6_cqc_the3(A,B)
<=> ( v6_qc_lang1(A)
& ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ? [D] :
( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D)
& k3_finseq_1(D) = C
& k1_funct_1(D,np__1) = B
& k1_funct_1(D,C) = A
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& ~ r1_xreal_0(C,E)
& ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k8_qc_lang1,k7_cqc_lang)
=> ~ ( G = k1_funct_1(D,E)
& k1_funct_1(D,k1_nat_1(E,np__1)) = k15_cqc_lang(F,G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r6_cqc_the3(A,B)
=> r5_cqc_the3(A,B) ) ) ) ).
fof(t39_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( v2_cqc_the1(k12_cqc_lang(A,B))
=> r1_cqc_the3(A,B) ) ) ) ).
fof(t40_cqc_the3,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,k1_zfmisc_1(k7_cqc_lang))
=> ( r3_cqc_the1(C,k12_cqc_lang(A,B))
=> r3_cqc_the1(k4_subset_1(k7_cqc_lang,C,k6_domain_1(k7_cqc_lang,A)),B) ) ) ) ) ).
fof(t41_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( ( v6_qc_lang1(A)
& r1_cqc_the3(A,B) )
=> v2_cqc_the1(k12_cqc_lang(A,B)) ) ) ) ).
fof(t42_cqc_the3,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)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k7_cqc_lang))
=> ( r6_cqc_the3(A,B)
=> ( r3_cqc_the1(k4_subset_1(k7_cqc_lang,D,k6_domain_1(k7_cqc_lang,B)),C)
<=> r3_cqc_the1(D,k12_cqc_lang(A,C)) ) ) ) ) ) ) ).
fof(t43_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( ( v6_qc_lang1(A)
& r1_cqc_the3(A,B) )
=> r1_cqc_the3(k10_cqc_lang(B),k10_cqc_lang(A)) ) ) ) ).
fof(t44_cqc_the3,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,k1_zfmisc_1(k7_cqc_lang))
=> ( ( v6_qc_lang1(A)
& r3_cqc_the1(k4_subset_1(k7_cqc_lang,C,k6_domain_1(k7_cqc_lang,A)),B) )
=> r3_cqc_the1(k4_subset_1(k7_cqc_lang,C,k6_domain_1(k7_cqc_lang,k10_cqc_lang(B))),k10_cqc_lang(A)) ) ) ) ) ).
fof(t45_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( ( v6_qc_lang1(A)
& r1_cqc_the3(k10_cqc_lang(A),k10_cqc_lang(B)) )
=> r1_cqc_the3(B,A) ) ) ) ).
fof(t46_cqc_the3,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,k1_zfmisc_1(k7_cqc_lang))
=> ( ( v6_qc_lang1(A)
& r3_cqc_the1(k4_subset_1(k7_cqc_lang,C,k6_domain_1(k7_cqc_lang,k10_cqc_lang(A))),k10_cqc_lang(B)) )
=> r3_cqc_the1(k4_subset_1(k7_cqc_lang,C,k6_domain_1(k7_cqc_lang,B)),A) ) ) ) ) ).
fof(t47_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( ( v6_qc_lang1(A)
& v6_qc_lang1(B) )
=> ( r1_cqc_the3(A,B)
<=> r1_cqc_the3(k10_cqc_lang(B),k10_cqc_lang(A)) ) ) ) ) ).
fof(t48_cqc_the3,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)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( ( r6_cqc_the3(A,B)
& r6_cqc_the3(C,D) )
=> ( r1_cqc_the3(B,D)
<=> r1_cqc_the3(k10_cqc_lang(C),k10_cqc_lang(A)) ) ) ) ) ) ) ).
fof(t49_cqc_the3,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)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( ( r6_cqc_the3(A,B)
& r6_cqc_the3(C,D) )
=> ( r5_cqc_the3(B,D)
<=> r5_cqc_the3(k10_cqc_lang(A),k10_cqc_lang(C)) ) ) ) ) ) ) ).
fof(d7_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r7_cqc_the3(A,B)
<=> v2_cqc_the1(k14_cqc_lang(A,B)) ) ) ) ).
fof(t50_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r7_cqc_the3(A,B)
<=> ( v2_cqc_the1(k12_cqc_lang(A,B))
& v2_cqc_the1(k12_cqc_lang(B,A)) ) ) ) ) ).
fof(t51_cqc_the3,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)
=> ( ( r7_cqc_the3(A,B)
& r7_cqc_the3(B,C) )
=> r7_cqc_the3(A,C) ) ) ) ) ).
fof(t52_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r7_cqc_the3(A,B)
=> r5_cqc_the3(A,B) ) ) ) ).
fof(t53_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r7_cqc_the3(A,B)
<=> r7_cqc_the3(k10_cqc_lang(A),k10_cqc_lang(B)) ) ) ) ).
fof(t54_cqc_the3,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)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( ( r7_cqc_the3(A,B)
& r7_cqc_the3(C,D) )
=> r7_cqc_the3(k11_cqc_lang(A,C),k11_cqc_lang(B,D)) ) ) ) ) ) ).
fof(t55_cqc_the3,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)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( ( r7_cqc_the3(A,B)
& r7_cqc_the3(C,D) )
=> r7_cqc_the3(k12_cqc_lang(A,C),k12_cqc_lang(B,D)) ) ) ) ) ) ).
fof(t56_cqc_the3,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)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( ( r7_cqc_the3(A,B)
& r7_cqc_the3(C,D) )
=> r7_cqc_the3(k13_cqc_lang(A,C),k13_cqc_lang(B,D)) ) ) ) ) ) ).
fof(t57_cqc_the3,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)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( ( r7_cqc_the3(A,B)
& r7_cqc_the3(C,D) )
=> r7_cqc_the3(k14_cqc_lang(A,C),k14_cqc_lang(B,D)) ) ) ) ) ) ).
fof(t58_cqc_the3,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)
=> ( r7_cqc_the3(A,B)
=> r7_cqc_the3(k15_cqc_lang(C,A),k15_cqc_lang(C,B)) ) ) ) ) ).
fof(t59_cqc_the3,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)
=> ( r7_cqc_the3(A,B)
=> r7_cqc_the3(k16_cqc_lang(C,A),k16_cqc_lang(C,B)) ) ) ) ) ).
fof(t60_cqc_the3,axiom,
$true ).
fof(t61_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_qc_lang1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k4_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> r1_tarski(k22_qc_lang1(B),k22_qc_lang1(k5_cqc_lang(A,B,k6_cqc_lang(C,D)))) ) ) ) ) ).
fof(t62_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_qc_lang1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k4_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> r1_tarski(k22_qc_lang1(k5_cqc_lang(A,B,k6_cqc_lang(C,D))),k4_subset_1(k2_qc_lang1,k22_qc_lang1(B),k23_qc_lang1(D))) ) ) ) ) ).
fof(t63_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> r1_tarski(k24_qc_lang1(B),k24_qc_lang1(k17_cqc_lang(B,A))) ) ) ).
fof(t64_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> r1_tarski(k24_qc_lang1(k17_cqc_lang(B,A)),k4_subset_1(k2_qc_lang1,k24_qc_lang1(B),k23_qc_lang1(A))) ) ) ).
fof(t65_cqc_the3,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [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)
=> ~ ( A = k17_cqc_lang(B,C)
& C != D
& ~ r2_hidden(D,k24_qc_lang1(B))
& r2_hidden(D,k24_qc_lang1(A)) ) ) ) ) ) ).
fof(t66_cqc_the3,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(C))
| r7_cqc_the3(k15_cqc_lang(D,A),k15_cqc_lang(E,B)) ) ) ) ) ) ) ) ).
fof(symmetry_r4_cqc_the3,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
& m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
=> ( r4_cqc_the3(A,B)
=> r4_cqc_the3(B,A) ) ) ).
fof(reflexivity_r4_cqc_the3,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
& m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
=> r4_cqc_the3(A,A) ) ).
fof(symmetry_r5_cqc_the3,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> ( r5_cqc_the3(A,B)
=> r5_cqc_the3(B,A) ) ) ).
fof(reflexivity_r5_cqc_the3,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> r5_cqc_the3(A,A) ) ).
fof(symmetry_r7_cqc_the3,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> ( r7_cqc_the3(A,B)
=> r7_cqc_the3(B,A) ) ) ).
fof(reflexivity_r7_cqc_the3,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> r7_cqc_the3(A,A) ) ).
%------------------------------------------------------------------------------