SET007 Axioms: SET007+116.ax
%------------------------------------------------------------------------------
% File : SET007+116 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Propositional Calculus
% 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 : lukasi_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 93 ( 0 unt; 0 def)
% Number of atoms : 391 ( 0 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 298 ( 0 ~; 0 |; 19 &)
% ( 12 <=>; 267 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 226 ( 226 !; 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_lukasi_1,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)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C))),k4_cqc_the1) ) ) ) ).
fof(t2_lukasi_1,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)
=> ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C)),k4_cqc_the1) ) ) ) ) ).
fof(t3_lukasi_1,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)
=> ( ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
& r2_hidden(k12_cqc_lang(B,C),k4_cqc_the1) )
=> r2_hidden(k12_cqc_lang(A,C),k4_cqc_the1) ) ) ) ) ).
fof(t4_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(A,A),k4_cqc_the1) ) ).
fof(t5_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,A)),k4_cqc_the1) ) ) ).
fof(t6_lukasi_1,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)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(k12_cqc_lang(A,B),C),k12_cqc_lang(B,C)),k4_cqc_the1) ) ) ) ).
fof(t7_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(A,k12_cqc_lang(k12_cqc_lang(A,B),B)),k4_cqc_the1) ) ) ).
fof(t8_lukasi_1,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)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k12_cqc_lang(B,C)),k12_cqc_lang(B,k12_cqc_lang(A,C))),k4_cqc_the1) ) ) ) ).
fof(t9_lukasi_1,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)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k12_cqc_lang(C,A),k12_cqc_lang(C,B))),k4_cqc_the1) ) ) ) ).
fof(t10_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k12_cqc_lang(A,B)),k12_cqc_lang(A,B)),k4_cqc_the1) ) ) ).
fof(t11_lukasi_1,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)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k12_cqc_lang(B,C)),k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,C))),k4_cqc_the1) ) ) ) ).
fof(t12_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k10_cqc_lang(k9_cqc_lang),A),k4_cqc_the1) ) ).
fof(t13_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(A,k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(B,A),k4_cqc_the1) ) ) ) ).
fof(t14_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(A,k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),B),k4_cqc_the1) ) ) ) ).
fof(t15_lukasi_1,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)
=> ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(B,k12_cqc_lang(A,C)),k4_cqc_the1) ) ) ) ) ).
fof(t16_lukasi_1,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)
=> ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
& r2_hidden(B,k4_cqc_the1) )
=> r2_hidden(k12_cqc_lang(A,C),k4_cqc_the1) ) ) ) ) ).
fof(t17_lukasi_1,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)
=> ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
& r2_hidden(B,k4_cqc_the1)
& r2_hidden(A,k4_cqc_the1) )
=> r2_hidden(C,k4_cqc_the1) ) ) ) ) ).
fof(t18_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(A,B)),k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1) ) ) ) ).
fof(t19_lukasi_1,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)
=> ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,C)),k4_cqc_the1) ) ) ) ) ).
fof(t20_lukasi_1,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)
=> ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
& r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1) )
=> r2_hidden(k12_cqc_lang(A,C),k4_cqc_the1) ) ) ) ) ).
fof(t21_lukasi_1,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)
=> ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
& r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
& r2_hidden(A,k4_cqc_the1) )
=> r2_hidden(C,k4_cqc_the1) ) ) ) ) ).
fof(t22_lukasi_1,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)
=> ( ( r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,C)),k4_cqc_the1)
& r2_hidden(k12_cqc_lang(A,k12_cqc_lang(C,D)),k4_cqc_the1) )
=> r2_hidden(k12_cqc_lang(A,k12_cqc_lang(B,D)),k4_cqc_the1) ) ) ) ) ) ).
fof(t23_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(A,k9_cqc_lang),k4_cqc_the1) ) ).
fof(t24_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k12_cqc_lang(B,A)),k4_cqc_the1) ) ) ).
fof(t25_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),A),k4_cqc_the1) ) ).
fof(t26_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(B),k10_cqc_lang(A))),k4_cqc_the1) ) ) ).
fof(t27_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(A))),k4_cqc_the1) ) ).
fof(t28_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B),k12_cqc_lang(A,B)),k4_cqc_the1)
& r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B)),k4_cqc_the1) ) ) ) ).
fof(t29_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B))),k12_cqc_lang(A,B)),k4_cqc_the1)
& r2_hidden(k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B)))),k4_cqc_the1) ) ) ) ).
fof(t30_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(B)),k12_cqc_lang(B,k10_cqc_lang(A))),k4_cqc_the1) ) ) ).
fof(t31_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(A),B),k12_cqc_lang(k10_cqc_lang(B),A)),k4_cqc_the1) ) ) ).
fof(t32_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(A)),k10_cqc_lang(A)),k4_cqc_the1) ) ).
fof(t33_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k10_cqc_lang(A),k12_cqc_lang(A,B)),k4_cqc_the1) ) ) ).
fof(t34_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
<=> r2_hidden(k12_cqc_lang(k10_cqc_lang(B),k10_cqc_lang(A)),k4_cqc_the1) ) ) ) ).
fof(t35_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(k12_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(B,A),k4_cqc_the1) ) ) ) ).
fof(t36_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(A,k4_cqc_the1)
<=> r2_hidden(k10_cqc_lang(k10_cqc_lang(A)),k4_cqc_the1) ) ) ).
fof(t37_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
<=> r2_hidden(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B))),k4_cqc_the1) ) ) ) ).
fof(t38_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1)
<=> r2_hidden(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B),k4_cqc_the1) ) ) ) ).
fof(t39_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(k12_cqc_lang(A,k10_cqc_lang(B)),k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(B,k10_cqc_lang(A)),k4_cqc_the1) ) ) ) ).
fof(t40_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(k12_cqc_lang(k10_cqc_lang(A),B),k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(k10_cqc_lang(B),A),k4_cqc_the1) ) ) ) ).
fof(t41_lukasi_1,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(k12_cqc_lang(A,B),k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C)))) ) ) ) ).
fof(t42_lukasi_1,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,B))
=> v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C))) ) ) ) ) ).
fof(t43_lukasi_1,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,B))
& v2_cqc_the1(k12_cqc_lang(B,C)) )
=> v2_cqc_the1(k12_cqc_lang(A,C)) ) ) ) ) ).
fof(t44_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> v2_cqc_the1(k12_cqc_lang(A,A)) ) ).
fof(t45_lukasi_1,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,k12_cqc_lang(B,A))) ) ) ).
fof(t46_lukasi_1,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(A)
=> v2_cqc_the1(k12_cqc_lang(B,A)) ) ) ) ).
fof(t47_lukasi_1,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(k12_cqc_lang(A,k12_cqc_lang(B,C)),k12_cqc_lang(B,k12_cqc_lang(A,C)))) ) ) ) ).
fof(t48_lukasi_1,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(B,k12_cqc_lang(A,C))) ) ) ) ) ).
fof(t49_lukasi_1,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(B) )
=> v2_cqc_the1(k12_cqc_lang(A,C)) ) ) ) ) ).
fof(t50_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ( v2_cqc_the1(k12_cqc_lang(A,k9_cqc_lang))
& v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k9_cqc_lang),A)) ) ) ).
fof(t51_lukasi_1,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,k12_cqc_lang(k12_cqc_lang(A,B),B))) ) ) ).
fof(t52_lukasi_1,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(k12_cqc_lang(A,k12_cqc_lang(A,B)),k12_cqc_lang(A,B))) ) ) ).
fof(t53_lukasi_1,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,k12_cqc_lang(A,B)))
=> v2_cqc_the1(k12_cqc_lang(A,B)) ) ) ) ).
fof(t54_lukasi_1,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(k12_cqc_lang(A,k12_cqc_lang(B,C)),k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,C)))) ) ) ) ).
fof(t55_lukasi_1,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(k12_cqc_lang(A,B),k12_cqc_lang(A,C))) ) ) ) ) ).
fof(t56_lukasi_1,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(A,B)) )
=> v2_cqc_the1(k12_cqc_lang(A,C)) ) ) ) ) ).
fof(t57_lukasi_1,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(k12_cqc_lang(k12_cqc_lang(A,B),C),k12_cqc_lang(B,C))) ) ) ) ).
fof(t58_lukasi_1,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(k12_cqc_lang(A,B),C))
=> v2_cqc_the1(k12_cqc_lang(B,C)) ) ) ) ) ).
fof(t59_lukasi_1,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(k12_cqc_lang(A,B),k12_cqc_lang(k12_cqc_lang(C,A),k12_cqc_lang(C,B)))) ) ) ) ).
fof(t60_lukasi_1,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,B))
=> v2_cqc_the1(k12_cqc_lang(k12_cqc_lang(C,A),k12_cqc_lang(C,B))) ) ) ) ) ).
fof(t61_lukasi_1,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(k12_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(B),k10_cqc_lang(A)))) ) ) ).
fof(t62_lukasi_1,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(k12_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k12_cqc_lang(B,A))) ) ) ).
fof(t63_lukasi_1,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(k10_cqc_lang(A),k10_cqc_lang(B)))
<=> v2_cqc_the1(k12_cqc_lang(B,A)) ) ) ) ).
fof(t64_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> v2_cqc_the1(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(A)))) ) ).
fof(t65_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),A)) ) ).
fof(t66_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ( v2_cqc_the1(k10_cqc_lang(k10_cqc_lang(A)))
<=> v2_cqc_the1(A) ) ) ).
fof(t67_lukasi_1,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(k12_cqc_lang(k10_cqc_lang(k10_cqc_lang(A)),B),k12_cqc_lang(A,B))) ) ) ).
fof(t68_lukasi_1,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(k10_cqc_lang(k10_cqc_lang(A)),B))
<=> v2_cqc_the1(k12_cqc_lang(A,B)) ) ) ) ).
fof(t69_lukasi_1,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(k12_cqc_lang(A,k10_cqc_lang(k10_cqc_lang(B))),k12_cqc_lang(A,B))) ) ) ).
fof(t70_lukasi_1,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,k10_cqc_lang(k10_cqc_lang(B))))
<=> v2_cqc_the1(k12_cqc_lang(A,B)) ) ) ) ).
fof(t71_lukasi_1,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(k12_cqc_lang(A,k10_cqc_lang(B)),k12_cqc_lang(B,k10_cqc_lang(A)))) ) ) ).
fof(t72_lukasi_1,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,k10_cqc_lang(B)))
=> v2_cqc_the1(k12_cqc_lang(B,k10_cqc_lang(A))) ) ) ) ).
fof(t73_lukasi_1,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(k12_cqc_lang(k10_cqc_lang(A),B),k12_cqc_lang(k10_cqc_lang(B),A))) ) ) ).
fof(t74_lukasi_1,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(k10_cqc_lang(A),B))
=> v2_cqc_the1(k12_cqc_lang(k10_cqc_lang(B),A)) ) ) ) ).
fof(t75_lukasi_1,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))
=> ( r3_cqc_the1(D,k12_cqc_lang(A,B))
=> r3_cqc_the1(D,k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(A,C))) ) ) ) ) ) ).
fof(t76_lukasi_1,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))
=> ( ( r3_cqc_the1(D,k12_cqc_lang(A,B))
& r3_cqc_the1(D,k12_cqc_lang(B,C)) )
=> r3_cqc_the1(D,k12_cqc_lang(A,C)) ) ) ) ) ) ).
fof(t77_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> r3_cqc_the1(B,k12_cqc_lang(A,A)) ) ) ).
fof(t78_lukasi_1,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(C,k12_cqc_lang(B,A)) ) ) ) ) ).
fof(t79_lukasi_1,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(C,k12_cqc_lang(k12_cqc_lang(A,B),B)) ) ) ) ) ).
fof(t80_lukasi_1,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))
=> ( r3_cqc_the1(D,k12_cqc_lang(A,k12_cqc_lang(B,C)))
=> r3_cqc_the1(D,k12_cqc_lang(B,k12_cqc_lang(A,C))) ) ) ) ) ) ).
fof(t81_lukasi_1,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))
=> ( ( r3_cqc_the1(D,k12_cqc_lang(A,k12_cqc_lang(B,C)))
& r3_cqc_the1(D,B) )
=> r3_cqc_the1(D,k12_cqc_lang(A,C)) ) ) ) ) ) ).
fof(t82_lukasi_1,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,k12_cqc_lang(A,B)))
=> r3_cqc_the1(C,k12_cqc_lang(A,B)) ) ) ) ) ).
fof(t83_lukasi_1,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))
=> ( r3_cqc_the1(D,k12_cqc_lang(k12_cqc_lang(A,B),C))
=> r3_cqc_the1(D,k12_cqc_lang(B,C)) ) ) ) ) ) ).
fof(t84_lukasi_1,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))
=> ( r3_cqc_the1(D,k12_cqc_lang(A,k12_cqc_lang(B,C)))
=> r3_cqc_the1(D,k12_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(A,C))) ) ) ) ) ) ).
fof(t85_lukasi_1,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))
=> ( ( r3_cqc_the1(D,k12_cqc_lang(A,k12_cqc_lang(B,C)))
& r3_cqc_the1(D,k12_cqc_lang(A,B)) )
=> r3_cqc_the1(D,k12_cqc_lang(A,C)) ) ) ) ) ) ).
fof(t86_lukasi_1,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(k10_cqc_lang(A),k10_cqc_lang(B)))
<=> r3_cqc_the1(C,k12_cqc_lang(B,A)) ) ) ) ) ).
fof(t87_lukasi_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r3_cqc_the1(B,k10_cqc_lang(k10_cqc_lang(A)))
<=> r3_cqc_the1(B,A) ) ) ) ).
fof(t88_lukasi_1,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,k10_cqc_lang(k10_cqc_lang(B))))
<=> r3_cqc_the1(C,k12_cqc_lang(A,B)) ) ) ) ) ).
fof(t89_lukasi_1,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(k10_cqc_lang(k10_cqc_lang(A)),B))
<=> r3_cqc_the1(C,k12_cqc_lang(A,B)) ) ) ) ) ).
fof(t90_lukasi_1,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,k10_cqc_lang(B)))
=> r3_cqc_the1(C,k12_cqc_lang(B,k10_cqc_lang(A))) ) ) ) ) ).
fof(t91_lukasi_1,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(k10_cqc_lang(A),B))
=> r3_cqc_the1(C,k12_cqc_lang(k10_cqc_lang(B),A)) ) ) ) ) ).
fof(t92_lukasi_1,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,k10_cqc_lang(B)))
& r3_cqc_the1(C,B) )
=> r3_cqc_the1(C,k10_cqc_lang(A)) ) ) ) ) ).
fof(t93_lukasi_1,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(k10_cqc_lang(A),B))
& r3_cqc_the1(C,k10_cqc_lang(B)) )
=> r3_cqc_the1(C,A) ) ) ) ) ).
%------------------------------------------------------------------------------