TPTP Problem File: CAT031+3.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : CAT031+3 : TPTP v8.2.0. Released v3.4.0.
% Domain : Category Theory
% Problem : Some Isomorphisms Between Functor Categories T45
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Try92] Trybulec (1992), Some Isomorphisms Between Functor Cat
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t45_isocat_2 [Urb08]
% Status : Theorem
% Rating : 0.97 v7.5.0, 1.00 v7.4.0, 0.97 v7.1.0, 0.96 v7.0.0, 0.97 v6.4.0, 0.96 v6.2.0, 1.00 v6.0.0, 0.96 v5.4.0, 1.00 v3.4.0
% Syntax : Number of formulae : 11807 (2638 unt; 0 def)
% Number of atoms : 70866 (8376 equ)
% Maximal formula atoms : 52 ( 6 avg)
% Number of connectives : 66944 (7885 ~; 418 |;33521 &)
% (1901 <=>;23219 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 7 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 640 ( 638 usr; 2 prp; 0-6 aty)
% Number of functors : 1718 (1718 usr; 483 con; 0-10 aty)
% Number of variables : 29302 (27955 !;1347 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Chainy small version: includes all preceding MML articles that
% are included in any Bushy version.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
include('Axioms/SET007/SET007+0.ax').
include('Axioms/SET007/SET007+1.ax').
include('Axioms/SET007/SET007+2.ax').
include('Axioms/SET007/SET007+3.ax').
include('Axioms/SET007/SET007+4.ax').
include('Axioms/SET007/SET007+5.ax').
include('Axioms/SET007/SET007+6.ax').
include('Axioms/SET007/SET007+7.ax').
include('Axioms/SET007/SET007+8.ax').
include('Axioms/SET007/SET007+9.ax').
include('Axioms/SET007/SET007+10.ax').
include('Axioms/SET007/SET007+11.ax').
include('Axioms/SET007/SET007+13.ax').
include('Axioms/SET007/SET007+14.ax').
include('Axioms/SET007/SET007+15.ax').
include('Axioms/SET007/SET007+16.ax').
include('Axioms/SET007/SET007+17.ax').
include('Axioms/SET007/SET007+18.ax').
include('Axioms/SET007/SET007+19.ax').
include('Axioms/SET007/SET007+20.ax').
include('Axioms/SET007/SET007+21.ax').
include('Axioms/SET007/SET007+22.ax').
include('Axioms/SET007/SET007+23.ax').
include('Axioms/SET007/SET007+24.ax').
include('Axioms/SET007/SET007+25.ax').
include('Axioms/SET007/SET007+26.ax').
include('Axioms/SET007/SET007+31.ax').
include('Axioms/SET007/SET007+32.ax').
include('Axioms/SET007/SET007+33.ax').
include('Axioms/SET007/SET007+34.ax').
include('Axioms/SET007/SET007+35.ax').
include('Axioms/SET007/SET007+40.ax').
include('Axioms/SET007/SET007+48.ax').
include('Axioms/SET007/SET007+50.ax').
include('Axioms/SET007/SET007+51.ax').
include('Axioms/SET007/SET007+54.ax').
include('Axioms/SET007/SET007+55.ax').
include('Axioms/SET007/SET007+59.ax').
include('Axioms/SET007/SET007+60.ax').
include('Axioms/SET007/SET007+61.ax').
include('Axioms/SET007/SET007+64.ax').
include('Axioms/SET007/SET007+66.ax').
include('Axioms/SET007/SET007+67.ax').
include('Axioms/SET007/SET007+68.ax').
include('Axioms/SET007/SET007+71.ax').
include('Axioms/SET007/SET007+75.ax').
include('Axioms/SET007/SET007+76.ax').
include('Axioms/SET007/SET007+77.ax').
include('Axioms/SET007/SET007+79.ax').
include('Axioms/SET007/SET007+80.ax').
include('Axioms/SET007/SET007+86.ax').
include('Axioms/SET007/SET007+91.ax').
include('Axioms/SET007/SET007+117.ax').
include('Axioms/SET007/SET007+125.ax').
include('Axioms/SET007/SET007+126.ax').
include('Axioms/SET007/SET007+148.ax').
include('Axioms/SET007/SET007+159.ax').
include('Axioms/SET007/SET007+165.ax').
include('Axioms/SET007/SET007+170.ax').
include('Axioms/SET007/SET007+182.ax').
include('Axioms/SET007/SET007+186.ax').
include('Axioms/SET007/SET007+188.ax').
include('Axioms/SET007/SET007+190.ax').
include('Axioms/SET007/SET007+200.ax').
include('Axioms/SET007/SET007+202.ax').
include('Axioms/SET007/SET007+205.ax').
include('Axioms/SET007/SET007+206.ax').
include('Axioms/SET007/SET007+207.ax').
include('Axioms/SET007/SET007+209.ax').
include('Axioms/SET007/SET007+210.ax').
include('Axioms/SET007/SET007+211.ax').
include('Axioms/SET007/SET007+212.ax').
include('Axioms/SET007/SET007+213.ax').
include('Axioms/SET007/SET007+217.ax').
include('Axioms/SET007/SET007+218.ax').
include('Axioms/SET007/SET007+223.ax').
include('Axioms/SET007/SET007+224.ax').
include('Axioms/SET007/SET007+225.ax').
include('Axioms/SET007/SET007+227.ax').
include('Axioms/SET007/SET007+237.ax').
include('Axioms/SET007/SET007+241.ax').
include('Axioms/SET007/SET007+242.ax').
include('Axioms/SET007/SET007+246.ax').
include('Axioms/SET007/SET007+247.ax').
include('Axioms/SET007/SET007+248.ax').
include('Axioms/SET007/SET007+252.ax').
include('Axioms/SET007/SET007+253.ax').
include('Axioms/SET007/SET007+255.ax').
include('Axioms/SET007/SET007+256.ax').
include('Axioms/SET007/SET007+276.ax').
include('Axioms/SET007/SET007+278.ax').
include('Axioms/SET007/SET007+279.ax').
include('Axioms/SET007/SET007+280.ax').
include('Axioms/SET007/SET007+281.ax').
include('Axioms/SET007/SET007+293.ax').
include('Axioms/SET007/SET007+295.ax').
include('Axioms/SET007/SET007+297.ax').
include('Axioms/SET007/SET007+298.ax').
include('Axioms/SET007/SET007+299.ax').
include('Axioms/SET007/SET007+301.ax').
include('Axioms/SET007/SET007+308.ax').
include('Axioms/SET007/SET007+309.ax').
include('Axioms/SET007/SET007+311.ax').
include('Axioms/SET007/SET007+312.ax').
include('Axioms/SET007/SET007+317.ax').
include('Axioms/SET007/SET007+321.ax').
include('Axioms/SET007/SET007+322.ax').
include('Axioms/SET007/SET007+327.ax').
include('Axioms/SET007/SET007+335.ax').
include('Axioms/SET007/SET007+338.ax').
%------------------------------------------------------------------------------
fof(dt_k1_isocat_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,k1_fraenkel(B,C))
& m1_relset_1(D,A,k1_fraenkel(B,C)) )
=> ( v1_funct_1(k1_isocat_2(A,B,C,D))
& v1_funct_2(k1_isocat_2(A,B,C,D),k2_zfmisc_1(A,B),C)
& m2_relset_1(k1_isocat_2(A,B,C,D),k2_zfmisc_1(A,B),C) ) ) ).
fof(redefinition_k1_isocat_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,k1_fraenkel(B,C))
& m1_relset_1(D,A,k1_fraenkel(B,C)) )
=> k1_isocat_2(A,B,C,D) = k4_funct_5(D) ) ).
fof(dt_k2_isocat_2,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& m1_subset_1(C,u1_cat_1(A)) )
=> m2_cat_1(k2_isocat_2(A,B,C),k12_nattra_1(A,B),B) ) ).
fof(dt_k3_isocat_2,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,k11_cat_2(A,B),C)
& m1_subset_1(E,u2_cat_1(A)) )
=> ( v1_funct_1(k3_isocat_2(A,B,C,D,E))
& v1_funct_2(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C))
& m2_relset_1(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C)) ) ) ).
fof(dt_k4_isocat_2,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,k11_cat_2(A,B),C)
& m1_subset_1(E,u2_cat_1(A)) )
=> m2_nattra_1(k4_isocat_2(A,B,C,D,E),B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))) ) ).
fof(dt_k5_isocat_2,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,k11_cat_2(A,B),C) )
=> m2_cat_1(k5_isocat_2(A,B,C,D),A,k12_nattra_1(B,C)) ) ).
fof(dt_k6_isocat_2,axiom,
! [A,B,C,D,E,F] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,k11_cat_2(A,B),C)
& m2_cat_1(E,k11_cat_2(A,B),C)
& m2_nattra_1(F,k11_cat_2(A,B),C,D,E) )
=> m2_nattra_1(k6_isocat_2(A,B,C,D,E,F),A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) ) ).
fof(dt_k7_isocat_2,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C) )
=> m2_cat_1(k7_isocat_2(A,B,C),k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) ) ).
fof(dt_k8_isocat_2,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> m2_cat_1(k8_isocat_2(A,B),k11_cat_2(A,B),A) ) ).
fof(redefinition_k8_isocat_2,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> k8_isocat_2(A,B) = k16_cat_2(A,B) ) ).
fof(dt_k9_isocat_2,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> m2_cat_1(k9_isocat_2(A,B),k11_cat_2(A,B),B) ) ).
fof(redefinition_k9_isocat_2,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> k9_isocat_2(A,B) = k17_cat_2(A,B) ) ).
fof(dt_k10_isocat_2,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,A,C) )
=> m2_cat_1(k10_isocat_2(A,B,C,D,E),A,k11_cat_2(B,C)) ) ).
fof(redefinition_k10_isocat_2,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,A,C) )
=> k10_isocat_2(A,B,C,D,E) = k13_funct_3(D,E) ) ).
fof(dt_k11_isocat_2,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,k11_cat_2(B,C)) )
=> m2_cat_1(k11_isocat_2(A,B,C,D),A,B) ) ).
fof(dt_k12_isocat_2,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,k11_cat_2(B,C)) )
=> m2_cat_1(k12_isocat_2(A,B,C,D),A,C) ) ).
fof(dt_k13_isocat_2,axiom,
! [A,B,C,D,E,F] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,k11_cat_2(B,C))
& m2_cat_1(E,A,k11_cat_2(B,C))
& m2_nattra_1(F,A,k11_cat_2(B,C),D,E) )
=> m2_nattra_1(k13_isocat_2(A,B,C,D,E,F),A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E)) ) ).
fof(dt_k14_isocat_2,axiom,
! [A,B,C,D,E,F] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,k11_cat_2(B,C))
& m2_cat_1(E,A,k11_cat_2(B,C))
& m2_nattra_1(F,A,k11_cat_2(B,C),D,E) )
=> m2_nattra_1(k14_isocat_2(A,B,C,D,E,F),A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) ) ).
fof(dt_k15_isocat_2,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,A,B)
& m2_cat_1(F,A,C)
& m2_cat_1(G,A,C)
& m1_nattra_1(H,A,B,D,E)
& m1_nattra_1(I,A,C,F,G) )
=> m1_nattra_1(k15_isocat_2(A,B,C,D,E,F,G,H,I),A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) ).
fof(dt_k16_isocat_2,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,A,B)
& m2_cat_1(F,A,C)
& m2_cat_1(G,A,C)
& m2_nattra_1(H,A,B,D,E)
& m2_nattra_1(I,A,C,F,G) )
=> m2_nattra_1(k16_isocat_2(A,B,C,D,E,F,G,H,I),A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) ).
fof(dt_k17_isocat_2,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C) )
=> m2_cat_1(k17_isocat_2(A,B,C),k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))) ) ).
fof(t1_isocat_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k1_fraenkel(B,C))
& m2_relset_1(D,A,k1_fraenkel(B,C)) )
=> r4_nattra_1(A,k1_fraenkel(B,C),A,k1_fraenkel(B,C),k2_cat_2(A,B,C,k1_isocat_2(A,B,C,D)),D) ) ) ) ) ).
fof(t2_isocat_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k1_fraenkel(B,C))
& m2_relset_1(D,A,k1_fraenkel(B,C)) )
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,B)
=> k1_funct_1(k1_isocat_2(A,B,C,D),k4_tarski(E,F)) = k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),D,E),F) ) ) ) ) ) ) ).
fof(t3_isocat_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_tarski(A),B)
& m2_relset_1(C,k1_tarski(A),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_tarski(A),B)
& m2_relset_1(D,k1_tarski(A),B) )
=> ( k1_funct_1(C,A) = k1_funct_1(D,A)
=> r4_nattra_1(k1_tarski(A),B,k1_tarski(A),B,C,D) ) ) ) ) ).
fof(t4_isocat_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> r2_hidden(k8_funct_2(A,B,D,C),k2_relat_1(D)) ) ) ) ) ).
fof(t5_isocat_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,k2_zfmisc_1(B,C))
& m2_relset_1(E,A,k2_zfmisc_1(B,C)) )
=> ( ( r4_nattra_1(A,B,A,B,k7_funct_2(A,k2_zfmisc_1(B,C),B,D,k9_funct_3(B,C)),k7_funct_2(A,k2_zfmisc_1(B,C),B,E,k9_funct_3(B,C)))
& r4_nattra_1(A,C,A,C,k7_funct_2(A,k2_zfmisc_1(B,C),C,D,k10_funct_3(B,C)),k7_funct_2(A,k2_zfmisc_1(B,C),C,E,k10_funct_3(B,C))) )
=> r4_nattra_1(A,k2_zfmisc_1(B,C),A,k2_zfmisc_1(B,C),D,E) ) ) ) ) ) ) ).
fof(t6_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k4_cat_1(A,B,k10_cat_1(A,k3_cat_1(A,B))) = B ) ) ).
fof(t7_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k4_cat_1(A,k10_cat_1(A,k2_cat_1(A,B)),B) = B ) ) ).
fof(t8_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(k12_nattra_1(A,B)))
<=> m2_cat_1(C,A,B) ) ) ) ).
fof(t9_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(k12_nattra_1(A,B)))
=> ? [D] :
( m2_cat_1(D,A,B)
& ? [E] :
( m2_cat_1(E,A,B)
& ? [F] :
( m2_nattra_1(F,A,B,D,E)
& r2_nattra_1(A,B,D,E)
& k2_cat_1(k12_nattra_1(A,B),C) = D
& k3_cat_1(k12_nattra_1(A,B),C) = E
& C = k4_tarski(k4_tarski(D,E),F) ) ) ) ) ) ) ).
fof(d1_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m2_cat_1(D,k12_nattra_1(A,B),B)
=> ( D = k2_isocat_2(A,B,C)
<=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,A,B)
=> ! [G] :
( m2_nattra_1(G,A,B,E,F)
=> ( r2_nattra_1(A,B,E,F)
=> k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k5_nattra_1(A,B,E,F,G,C) ) ) ) ) ) ) ) ) ) ).
fof(l11_isocat_2,axiom,
! [A,B] :
( u1_cat_1(k8_cat_1(A,B)) = k1_tarski(A)
& u2_cat_1(k8_cat_1(A,B)) = k1_tarski(B) ) ).
fof(t10_isocat_2,axiom,
$true ).
fof(t11_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] : r1_isocat_1(k12_nattra_1(k8_cat_1(B,C),A),A) ) ).
fof(t12_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> k13_cat_1(B,C,k14_cat_2(A,B,C,D,E),F) = k13_cat_1(k11_cat_2(A,B),C,D,k12_cat_2(A,B,E,F)) ) ) ) ) ) ) ).
fof(t13_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(B))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> ( ( k6_cat_1(A,C,D) != k1_xboole_0
& k6_cat_1(B,E,F) != k1_xboole_0 )
<=> k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) != k1_xboole_0 ) ) ) ) ) ) ) ).
fof(t14_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(B))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> ( k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) != k1_xboole_0
=> ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ! [H] :
( m1_subset_1(H,u2_cat_1(B))
=> ( m1_cat_1(k13_cat_2(A,B,G,H),k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F))
<=> ( m1_cat_1(G,A,C,D)
& m1_cat_1(H,B,E,F) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
=> ! [F] :
( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
=> ! [G] :
( m1_subset_1(G,u1_cat_1(A))
=> ( r2_nattra_1(B,C,k14_cat_2(A,B,C,D,G),k14_cat_2(A,B,C,E,G))
& m2_nattra_1(k1_funct_1(k3_funct_5(F),G),B,C,k14_cat_2(A,B,C,D,G),k14_cat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) ) ).
fof(d2_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> k3_isocat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),E) ) ) ) ) ) ).
fof(t16_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(B))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ! [H] :
( m1_subset_1(H,u2_cat_1(B))
=> ( ( r2_hidden(G,k6_cat_1(A,C,D))
& r2_hidden(H,k6_cat_1(B,E,F)) )
=> r2_hidden(k13_cat_2(A,B,G,H),k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F))) ) ) ) ) ) ) ) ) ) ).
fof(t17_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> ( k6_cat_1(A,E,F) != k1_xboole_0
=> ! [G] :
( m1_cat_1(G,A,E,F)
=> ( r2_nattra_1(B,C,k14_cat_2(A,B,C,D,E),k14_cat_2(A,B,C,D,F))
& m2_nattra_1(k7_funct_2(u1_cat_1(B),u2_cat_1(B),u2_cat_1(C),u6_cat_1(B),k3_isocat_2(A,B,C,D,G)),B,C,k14_cat_2(A,B,C,D,E),k14_cat_2(A,B,C,D,F)) ) ) ) ) ) ) ) ) ) ).
fof(d3_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> k4_isocat_2(A,B,C,D,E) = k7_funct_2(u1_cat_1(B),u2_cat_1(B),u2_cat_1(C),u6_cat_1(B),k3_isocat_2(A,B,C,D,E)) ) ) ) ) ) ).
fof(t18_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> r2_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))) ) ) ) ) ) ).
fof(t19_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> k5_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E)),k4_isocat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,E,k10_cat_1(B,F))) ) ) ) ) ) ) ).
fof(t20_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),k7_nattra_1(B,C,k14_cat_2(A,B,C,D,E)),k4_isocat_2(A,B,C,D,k10_cat_1(A,E))) ) ) ) ) ) ).
fof(t21_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ( k2_cat_1(A,E) = k3_cat_1(A,F)
=> ! [G] :
( m2_nattra_1(G,B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k2_cat_1(A,E)))
=> ( r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),G,k4_isocat_2(A,B,C,D,F))
=> r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),k4_isocat_2(A,B,C,D,k4_cat_1(A,F,E)),k8_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E)),G,k4_isocat_2(A,B,C,D,E))) ) ) ) ) ) ) ) ) ) ).
fof(d4_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,A,k12_nattra_1(B,C))
=> ( E = k5_isocat_2(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),E,F) = k4_tarski(k4_tarski(k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k3_cat_1(A,F))),k4_isocat_2(A,B,C,D,F)) ) ) ) ) ) ) ) ).
fof(l27_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m2_cat_1(D,A,B)
=> ( r1_nattra_1(A,B,C,D)
=> ! [E] :
( m1_nattra_1(E,A,B,C,D)
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> r2_hidden(k5_nattra_1(A,B,C,D,E,F),k6_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F))) ) ) ) ) ) ) ) ).
fof(t22_isocat_2,axiom,
$true ).
fof(t23_isocat_2,axiom,
$true ).
fof(t24_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),E) = k14_cat_2(A,B,C,D,E) ) ) ) ) ) ).
fof(t25_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> m2_cat_1(k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),E),B,C) ) ) ) ) ) ).
fof(t26_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r4_nattra_1(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
=> r4_nattra_1(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,E) ) ) ) ) ) ) ).
fof(t27_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
=> ! [F] :
( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
=> ( r2_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
& ? [G] :
( m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
& ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C))
& m2_relset_1(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) )
=> ( r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C),F,H)
=> ! [I] :
( m1_subset_1(I,u1_cat_1(A))
=> k5_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),G,I) = k4_tarski(k12_cat_2(k12_nattra_1(B,C),k12_nattra_1(B,C),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),I),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,E),I)),k1_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k1_fraenkel(u1_cat_1(B),u2_cat_1(C)),k2_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),H),I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
=> ! [F] :
( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
=> ! [G] :
( m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
=> ( G = k6_isocat_2(A,B,C,D,E,F)
<=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C))
& m2_relset_1(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) )
=> ( r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C),F,H)
=> ! [I] :
( m1_subset_1(I,u1_cat_1(A))
=> k5_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),G,I) = k4_tarski(k12_cat_2(k12_nattra_1(B,C),k12_nattra_1(B,C),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),I),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,E),I)),k1_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k1_fraenkel(u1_cat_1(B),u2_cat_1(C)),k2_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),H),I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k7_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D)),k6_isocat_2(A,B,C,D,D,k7_nattra_1(k11_cat_2(A,B),C,D))) ) ) ) ) ).
fof(t29_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ! [F] :
( m2_cat_1(F,k11_cat_2(A,B),C)
=> ( ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
& r2_nattra_1(k11_cat_2(A,B),C,E,F) )
=> ! [G] :
( m2_nattra_1(G,k11_cat_2(A,B),C,D,E)
=> ! [H] :
( m2_nattra_1(H,k11_cat_2(A,B),C,E,F)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k6_isocat_2(A,B,C,D,F,k8_nattra_1(k11_cat_2(A,B),C,D,E,F,G,H)),k8_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),k5_isocat_2(A,B,C,F),k6_isocat_2(A,B,C,D,E,G),k6_isocat_2(A,B,C,E,F,H))) ) ) ) ) ) ) ) ) ) ).
fof(t30_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
=> ! [F] :
( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
=> ! [G] :
( m2_nattra_1(G,k11_cat_2(A,B),C,D,E)
=> ( r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k6_isocat_2(A,B,C,D,E,F),k6_isocat_2(A,B,C,D,E,G))
=> r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),F,G) ) ) ) ) ) ) ) ) ) ).
fof(t31_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k12_nattra_1(B,C))
=> ? [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
& r4_nattra_1(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),D,k5_isocat_2(A,B,C,E)) ) ) ) ) ) ).
fof(t32_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
=> ! [F] :
( m2_nattra_1(F,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
& ? [G] :
( m2_nattra_1(G,k11_cat_2(A,B),C,D,E)
& r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),F,k6_isocat_2(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) ) ).
fof(d6_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C)))
=> ( D = k7_isocat_2(A,B,C)
<=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ! [F] :
( m2_cat_1(F,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,E,F)
=> ! [G] :
( m2_nattra_1(G,k11_cat_2(A,B),C,E,F)
=> k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k4_tarski(k4_tarski(k5_isocat_2(A,B,C,E),k5_isocat_2(A,B,C,F)),k6_isocat_2(A,B,C,E,F,G)) ) ) ) ) ) ) ) ) ) ).
fof(t33_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> v8_cat_1(k7_isocat_2(A,B,C),k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) ) ) ) ).
fof(t34_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> r1_isocat_1(k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) ) ) ) ).
fof(t35_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,B,C)
=> ( r2_nattra_1(A,B,D,E)
=> ! [G] :
( m2_nattra_1(G,A,B,D,E)
=> k6_isocat_1(A,B,C,D,E,G,F) = k5_relat_1(G,F) ) ) ) ) ) ) ) ) ).
fof(d7_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k11_cat_2(B,C))
=> k11_isocat_2(A,B,C,D) = k2_isocat_1(A,k11_cat_2(B,C),B,D,k8_isocat_2(B,C)) ) ) ) ) ).
fof(d8_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k11_cat_2(B,C))
=> k12_isocat_2(A,B,C,D) = k2_isocat_1(A,k11_cat_2(B,C),C,D,k9_isocat_2(B,C)) ) ) ) ) ).
fof(t36_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,C)
=> ( r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k11_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,E)),D)
& r4_nattra_1(u2_cat_1(A),u2_cat_1(C),u2_cat_1(A),u2_cat_1(C),k12_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,E)),E) ) ) ) ) ) ) ).
fof(t37_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ( ( r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E))
& r4_nattra_1(u2_cat_1(A),u2_cat_1(C),u2_cat_1(A),u2_cat_1(C),k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) )
=> r4_nattra_1(u2_cat_1(A),u2_cat_1(k11_cat_2(B,C)),u2_cat_1(A),u2_cat_1(k11_cat_2(B,C)),D,E) ) ) ) ) ) ) ).
fof(d9_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ! [F] :
( m2_nattra_1(F,A,k11_cat_2(B,C),D,E)
=> k13_isocat_2(A,B,C,D,E,F) = k6_isocat_1(A,k11_cat_2(B,C),B,D,E,F,k8_isocat_2(B,C)) ) ) ) ) ) ) ).
fof(d10_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ! [F] :
( m2_nattra_1(F,A,k11_cat_2(B,C),D,E)
=> k14_isocat_2(A,B,C,D,E,F) = k6_isocat_1(A,k11_cat_2(B,C),C,D,E,F,k9_isocat_2(B,C)) ) ) ) ) ) ) ).
fof(t38_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ( r2_nattra_1(A,k11_cat_2(B,C),D,E)
=> ( r2_nattra_1(A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E))
& r2_nattra_1(A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) ) ) ) ) ) ) ) ).
fof(t39_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ! [F] :
( m2_cat_1(F,A,k11_cat_2(B,C))
=> ! [G] :
( m2_cat_1(G,A,k11_cat_2(B,C))
=> ( ( r2_nattra_1(A,k11_cat_2(B,C),D,E)
& r2_nattra_1(A,k11_cat_2(B,C),F,G) )
=> ! [H] :
( m2_nattra_1(H,A,k11_cat_2(B,C),D,E)
=> ! [I] :
( m2_nattra_1(I,A,k11_cat_2(B,C),F,G)
=> ( ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,D,E,H),k13_isocat_2(A,B,C,F,G,I))
& r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,D,E,H),k14_isocat_2(A,B,C,F,G,I)) )
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(k11_cat_2(B,C)),u1_cat_1(A),u2_cat_1(k11_cat_2(B,C)),H,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k11_cat_2(B,C))
=> ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k7_nattra_1(A,B,k11_isocat_2(A,B,C,D)),k13_isocat_2(A,B,C,D,D,k7_nattra_1(A,k11_cat_2(B,C),D)))
& r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_nattra_1(A,C,k12_isocat_2(A,B,C,D)),k14_isocat_2(A,B,C,D,D,k7_nattra_1(A,k11_cat_2(B,C),D))) ) ) ) ) ) ).
fof(t41_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ! [F] :
( m2_cat_1(F,A,k11_cat_2(B,C))
=> ( ( r2_nattra_1(A,k11_cat_2(B,C),D,E)
& r2_nattra_1(A,k11_cat_2(B,C),E,F) )
=> ! [G] :
( m2_nattra_1(G,A,k11_cat_2(B,C),D,E)
=> ! [H] :
( m2_nattra_1(H,A,k11_cat_2(B,C),E,F)
=> ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,D,F,k8_nattra_1(A,k11_cat_2(B,C),D,E,F,G,H)),k8_nattra_1(A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E),k11_isocat_2(A,B,C,F),k13_isocat_2(A,B,C,D,E,G),k13_isocat_2(A,B,C,E,F,H)))
& r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,D,F,k8_nattra_1(A,k11_cat_2(B,C),D,E,F,G,H)),k8_nattra_1(A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E),k12_isocat_2(A,B,C,F),k14_isocat_2(A,B,C,D,E,G),k14_isocat_2(A,B,C,E,F,H))) ) ) ) ) ) ) ) ) ) ) ).
fof(l54_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,A,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r1_nattra_1(A,B,D,E)
& r1_nattra_1(A,C,F,G) )
=> ! [H] :
( m1_nattra_1(H,A,B,D,E)
=> ! [I] :
( m1_nattra_1(I,A,C,F,G)
=> ! [J] :
( m1_subset_1(J,u1_cat_1(A))
=> k8_funct_2(u1_cat_1(A),k2_zfmisc_1(u2_cat_1(B),u2_cat_1(C)),k14_funct_3(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),H,I),J) = k13_cat_2(B,C,k5_nattra_1(A,B,D,E,H,J),k5_nattra_1(A,C,F,G,I,J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,C)
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> ! [G] :
( m1_subset_1(G,u1_cat_1(A))
=> ( k6_cat_1(A,F,G) != k1_xboole_0
=> ! [H] :
( m1_cat_1(H,A,F,G)
=> k3_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,E),F,G,H) = k13_cat_2(B,C,k3_nattra_1(A,B,D,F,G,H),k3_nattra_1(A,C,E,F,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(t43_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,C)
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> k13_cat_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,E),F) = k12_cat_2(B,C,k13_cat_1(A,B,D,F),k13_cat_1(A,C,E,F)) ) ) ) ) ) ) ).
fof(l57_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,A,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r1_nattra_1(A,B,D,E)
& r1_nattra_1(A,C,F,G) )
=> ! [H] :
( m1_nattra_1(H,A,B,D,E)
=> ! [I] :
( m1_nattra_1(I,A,C,F,G)
=> ! [J] :
( m1_subset_1(J,u1_cat_1(A))
=> r2_hidden(k8_funct_2(u1_cat_1(A),k2_zfmisc_1(u2_cat_1(B),u2_cat_1(C)),k14_funct_3(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),H,I),J),k6_cat_1(k11_cat_2(B,C),k13_cat_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),J),k13_cat_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,E,G),J))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,A,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r1_nattra_1(A,B,D,E)
& r1_nattra_1(A,C,F,G) )
=> r1_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) ).
fof(d11_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,A,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r1_nattra_1(A,B,D,E)
& r1_nattra_1(A,C,F,G) )
=> ! [H] :
( m1_nattra_1(H,A,B,D,E)
=> ! [I] :
( m1_nattra_1(I,A,C,F,G)
=> k15_isocat_2(A,B,C,D,E,F,G,H,I) = k14_funct_3(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),H,I) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_isocat_2,conjecture,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,A,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r1_nattra_1(A,B,D,E)
& r1_nattra_1(A,C,F,G) )
=> ! [H] :
( m1_nattra_1(H,A,B,D,E)
=> ! [I] :
( m1_nattra_1(I,A,C,F,G)
=> ! [J] :
( m1_subset_1(J,u1_cat_1(A))
=> k5_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k15_isocat_2(A,B,C,D,E,F,G,H,I),J) = k13_cat_2(B,C,k5_nattra_1(A,B,D,E,H,J),k5_nattra_1(A,C,F,G,I,J)) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------