SET007 Axioms: SET007+120.ax
%------------------------------------------------------------------------------
% File : SET007+120 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Calculus of Propositions
% 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 : procal_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 58 ( 0 unt; 0 def)
% Number of atoms : 215 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 157 ( 0 ~; 0 |; 7 &)
% ( 0 <=>; 150 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 2 usr; 0 prp; 2-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 133 ( 133 !; 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_procal_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k10_cqc_lang(k11_cqc_lang(A,k10_cqc_lang(A))),k4_cqc_the1) ) ).
fof(t2_procal_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k13_cqc_lang(A,k10_cqc_lang(A)),k4_cqc_the1) ) ).
fof(t3_procal_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,k13_cqc_lang(A,B)),k4_cqc_the1) ) ) ).
fof(t4_procal_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,k13_cqc_lang(B,A)),k4_cqc_the1) ) ) ).
fof(t5_procal_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(k13_cqc_lang(A,B),k12_cqc_lang(k10_cqc_lang(A),B)),k4_cqc_the1) ) ) ).
fof(t6_procal_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(k13_cqc_lang(A,B)),k11_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B))),k4_cqc_the1) ) ) ).
fof(t7_procal_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(k11_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k10_cqc_lang(k13_cqc_lang(A,B))),k4_cqc_the1) ) ) ).
fof(t8_procal_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(k13_cqc_lang(A,B),k13_cqc_lang(B,A)),k4_cqc_the1) ) ) ).
fof(t9_procal_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k13_cqc_lang(k10_cqc_lang(A),A),k4_cqc_the1) ) ).
fof(t10_procal_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(k13_cqc_lang(A,B)),k10_cqc_lang(A)),k4_cqc_the1) ) ) ).
fof(t11_procal_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(k13_cqc_lang(A,A),A),k4_cqc_the1) ) ).
fof(t12_procal_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(A,k13_cqc_lang(A,A)),k4_cqc_the1) ) ).
fof(t13_procal_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(k11_cqc_lang(A,k10_cqc_lang(A)),B),k4_cqc_the1) ) ) ).
fof(t14_procal_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),k13_cqc_lang(k10_cqc_lang(A),B)),k4_cqc_the1) ) ) ).
fof(t15_procal_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(k11_cqc_lang(A,B),k10_cqc_lang(k12_cqc_lang(A,k10_cqc_lang(B)))),k4_cqc_the1) ) ) ).
fof(t16_procal_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(k12_cqc_lang(A,k10_cqc_lang(B))),k11_cqc_lang(A,B)),k4_cqc_the1) ) ) ).
fof(t17_procal_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(k11_cqc_lang(A,B)),k13_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B))),k4_cqc_the1) ) ) ).
fof(t18_procal_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(k13_cqc_lang(k10_cqc_lang(A),k10_cqc_lang(B)),k10_cqc_lang(k11_cqc_lang(A,B))),k4_cqc_the1) ) ) ).
fof(t19_procal_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(k11_cqc_lang(A,B),A),k4_cqc_the1) ) ) ).
fof(t20_procal_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(k11_cqc_lang(A,B),k13_cqc_lang(A,B)),k4_cqc_the1) ) ) ).
fof(t21_procal_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(k11_cqc_lang(A,B),B),k4_cqc_the1) ) ) ).
fof(t22_procal_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k12_cqc_lang(A,k11_cqc_lang(A,A)),k4_cqc_the1) ) ).
fof(t23_procal_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(k14_cqc_lang(A,B),k12_cqc_lang(A,B)),k4_cqc_the1) ) ) ).
fof(t24_procal_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(k14_cqc_lang(A,B),k12_cqc_lang(B,A)),k4_cqc_the1) ) ) ).
fof(t25_procal_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(k13_cqc_lang(k13_cqc_lang(A,B),C),k13_cqc_lang(A,k13_cqc_lang(B,C))),k4_cqc_the1) ) ) ) ).
fof(t26_procal_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(k11_cqc_lang(k11_cqc_lang(A,B),C),k11_cqc_lang(A,k11_cqc_lang(B,C))),k4_cqc_the1) ) ) ) ).
fof(t27_procal_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(k13_cqc_lang(A,k13_cqc_lang(B,C)),k13_cqc_lang(k13_cqc_lang(A,B),C)),k4_cqc_the1) ) ) ) ).
fof(t28_procal_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,k11_cqc_lang(A,B))),k4_cqc_the1) ) ) ).
fof(t29_procal_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(k12_cqc_lang(B,A),k14_cqc_lang(A,B))),k4_cqc_the1) ) ) ).
fof(t30_procal_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(k14_cqc_lang(k13_cqc_lang(A,B),k13_cqc_lang(B,A)),k4_cqc_the1) ) ) ).
fof(t31_procal_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(k11_cqc_lang(A,B),C),k12_cqc_lang(A,k12_cqc_lang(B,C))),k4_cqc_the1) ) ) ) ).
fof(t32_procal_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(k11_cqc_lang(A,B),C)),k4_cqc_the1) ) ) ) ).
fof(t33_procal_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(A,C),k12_cqc_lang(A,k11_cqc_lang(B,C)))),k4_cqc_the1) ) ) ) ).
fof(t34_procal_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(k13_cqc_lang(A,B),C),k13_cqc_lang(k12_cqc_lang(A,C),k12_cqc_lang(B,C))),k4_cqc_the1) ) ) ) ).
fof(t35_procal_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,B),k12_cqc_lang(k13_cqc_lang(A,C),B))),k4_cqc_the1) ) ) ) ).
fof(t36_procal_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(k11_cqc_lang(k12_cqc_lang(A,B),k12_cqc_lang(C,B)),k12_cqc_lang(k13_cqc_lang(A,C),B)),k4_cqc_the1) ) ) ) ).
fof(t37_procal_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,k11_cqc_lang(B,k10_cqc_lang(B))),k10_cqc_lang(A)),k4_cqc_the1) ) ) ).
fof(t38_procal_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(k11_cqc_lang(k13_cqc_lang(A,B),k13_cqc_lang(A,C)),k13_cqc_lang(A,k11_cqc_lang(B,C))),k4_cqc_the1) ) ) ) ).
fof(t39_procal_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(k11_cqc_lang(A,k13_cqc_lang(B,C)),k13_cqc_lang(k11_cqc_lang(A,B),k11_cqc_lang(A,C))),k4_cqc_the1) ) ) ) ).
fof(t40_procal_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(k11_cqc_lang(k13_cqc_lang(A,B),k13_cqc_lang(C,B)),k13_cqc_lang(k11_cqc_lang(A,C),B)),k4_cqc_the1) ) ) ) ).
fof(t41_procal_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(k11_cqc_lang(k13_cqc_lang(A,B),C),k13_cqc_lang(k11_cqc_lang(A,C),k11_cqc_lang(B,C))),k4_cqc_the1) ) ) ) ).
fof(t42_procal_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(k13_cqc_lang(A,B),k4_cqc_the1) ) ) ) ).
fof(t43_procal_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(k13_cqc_lang(B,A),k4_cqc_the1) ) ) ) ).
fof(t44_procal_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(k11_cqc_lang(A,B),k4_cqc_the1)
=> r2_hidden(A,k4_cqc_the1) ) ) ) ).
fof(t45_procal_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(k11_cqc_lang(A,B),k4_cqc_the1)
=> r2_hidden(B,k4_cqc_the1) ) ) ) ).
fof(t46_procal_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(k11_cqc_lang(A,B),k4_cqc_the1)
=> r2_hidden(k13_cqc_lang(A,B),k4_cqc_the1) ) ) ) ).
fof(t47_procal_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(B,k4_cqc_the1) )
=> r2_hidden(k11_cqc_lang(A,B),k4_cqc_the1) ) ) ) ).
fof(t48_procal_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(k13_cqc_lang(A,C),k13_cqc_lang(B,C)),k4_cqc_the1) ) ) ) ) ).
fof(t49_procal_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(k13_cqc_lang(C,A),k13_cqc_lang(C,B)),k4_cqc_the1) ) ) ) ) ).
fof(t50_procal_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(k11_cqc_lang(C,A),k11_cqc_lang(C,B)),k4_cqc_the1) ) ) ) ) ).
fof(t51_procal_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(k11_cqc_lang(A,C),k11_cqc_lang(B,C)),k4_cqc_the1) ) ) ) ) ).
fof(t52_procal_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(A,C),k4_cqc_the1) )
=> r2_hidden(k12_cqc_lang(A,k11_cqc_lang(B,C)),k4_cqc_the1) ) ) ) ) ).
fof(t53_procal_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(C,B),k4_cqc_the1) )
=> r2_hidden(k12_cqc_lang(k13_cqc_lang(A,C),B),k4_cqc_the1) ) ) ) ) ).
fof(t54_procal_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(k13_cqc_lang(A,B),k4_cqc_the1)
& r2_hidden(k10_cqc_lang(A),k4_cqc_the1) )
=> r2_hidden(B,k4_cqc_the1) ) ) ) ).
fof(t55_procal_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(k13_cqc_lang(A,B),k4_cqc_the1)
& r2_hidden(k10_cqc_lang(B),k4_cqc_the1) )
=> r2_hidden(A,k4_cqc_the1) ) ) ) ).
fof(t56_procal_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,B),k4_cqc_the1)
& r2_hidden(k12_cqc_lang(C,D),k4_cqc_the1) )
=> r2_hidden(k12_cqc_lang(k11_cqc_lang(A,C),k11_cqc_lang(B,D)),k4_cqc_the1) ) ) ) ) ) ).
fof(t57_procal_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,B),k4_cqc_the1)
& r2_hidden(k12_cqc_lang(C,D),k4_cqc_the1) )
=> r2_hidden(k12_cqc_lang(k13_cqc_lang(A,C),k13_cqc_lang(B,D)),k4_cqc_the1) ) ) ) ) ) ).
fof(t58_procal_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(k11_cqc_lang(A,k10_cqc_lang(B)),k10_cqc_lang(A)),k4_cqc_the1)
=> r2_hidden(k12_cqc_lang(A,B),k4_cqc_the1) ) ) ) ).
%------------------------------------------------------------------------------