TPTP Problem File: SEU417+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SEU417+2 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Problem : First and Second Order Cutting of Binary Relations T07
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Ret05] Retel (2005), Properties of First and Second Order Cut
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t7_relset_2 [Urb08]
% Status : ContradictoryAxioms
% Rating : 0.83 v8.2.0, 0.86 v8.1.0, 0.89 v7.5.0, 0.88 v7.4.0, 0.90 v7.3.0, 0.93 v7.1.0, 0.91 v7.0.0, 0.90 v6.4.0, 0.85 v6.3.0, 0.88 v6.2.0, 0.96 v6.1.0, 0.97 v6.0.0, 0.96 v5.5.0, 1.00 v3.4.0
% Syntax : Number of formulae : 4475 (1181 unt; 0 def)
% Number of atoms : 19413 (3268 equ)
% Maximal formula atoms : 49 ( 4 avg)
% Number of connectives : 17085 (2147 ~; 197 |;7402 &)
% ( 632 <=>;6707 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 270 ( 268 usr; 1 prp; 0-4 aty)
% Number of functors : 625 ( 625 usr; 177 con; 0-9 aty)
% Number of variables : 10402 (9886 !; 516 ?)
% SPC : FOF_CAX_RFO_SEQ
% Comments : Bushy version: includes all articles that contribute axioms to the
% Normal 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+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+16.ax').
include('Axioms/SET007/SET007+17.ax').
include('Axioms/SET007/SET007+18.ax').
include('Axioms/SET007/SET007+20.ax').
include('Axioms/SET007/SET007+22.ax').
include('Axioms/SET007/SET007+24.ax').
include('Axioms/SET007/SET007+26.ax').
include('Axioms/SET007/SET007+31.ax').
include('Axioms/SET007/SET007+35.ax').
include('Axioms/SET007/SET007+40.ax').
include('Axioms/SET007/SET007+48.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+80.ax').
include('Axioms/SET007/SET007+117.ax').
include('Axioms/SET007/SET007+126.ax').
include('Axioms/SET007/SET007+188.ax').
include('Axioms/SET007/SET007+200.ax').
include('Axioms/SET007/SET007+210.ax').
include('Axioms/SET007/SET007+212.ax').
include('Axioms/SET007/SET007+213.ax').
include('Axioms/SET007/SET007+225.ax').
include('Axioms/SET007/SET007+363.ax').
include('Axioms/SET007/SET007+393.ax').
include('Axioms/SET007/SET007+441.ax').
%------------------------------------------------------------------------------
fof(dt_k1_relset_2,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> m1_subset_1(k1_relset_2(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ).
fof(commutativity_k1_relset_2,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> k1_relset_2(A,B,C) = k1_relset_2(A,C,B) ) ).
fof(idempotence_k1_relset_2,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> k1_relset_2(A,B,B) = B ) ).
fof(redefinition_k1_relset_2,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> k1_relset_2(A,B,C) = k3_xboole_0(B,C) ) ).
fof(dt_k2_relset_2,axiom,
! [A,B,C,D] :
( ( m1_relset_1(C,A,B)
& m1_subset_1(D,A) )
=> m1_subset_1(k2_relset_2(A,B,C,D),k1_zfmisc_1(B)) ) ).
fof(dt_k3_relset_2,axiom,
! [A,B,C,D] :
( ( m1_relset_1(C,A,B)
& m1_subset_1(D,A) )
=> m1_subset_1(k3_relset_2(A,B,C,D),k1_zfmisc_1(A)) ) ).
fof(dt_k4_relset_2,axiom,
! [A,B,C,D] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_zfmisc_1(B))))
=> m1_subset_1(k4_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ).
fof(redefinition_k4_relset_2,axiom,
! [A,B,C,D] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_zfmisc_1(B))))
=> k4_relset_2(A,B,C,D) = k9_relat_1(C,D) ) ).
fof(dt_k5_relset_2,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( v1_relat_1(k5_relset_2(A,B))
& v1_funct_1(k5_relset_2(A,B)) ) ) ).
fof(dt_k6_relset_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A)))
=> ( v1_funct_1(k6_relset_2(A,B,C))
& v1_funct_2(k6_relset_2(A,B,C),k1_zfmisc_1(B),k1_zfmisc_1(A))
& m2_relset_1(k6_relset_2(A,B,C),k1_zfmisc_1(B),k1_zfmisc_1(A)) ) ) ).
fof(redefinition_k6_relset_2,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A)))
=> k6_relset_2(A,B,C) = k5_relset_2(B,C) ) ).
fof(dt_k7_relset_2,axiom,
$true ).
fof(dt_k8_relset_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
=> m1_subset_1(k8_relset_2(A,B,C,D),k1_zfmisc_1(B)) ) ).
fof(redefinition_k8_relset_2,axiom,
! [A,B,C,D] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
=> k8_relset_2(A,B,C,D) = k7_relset_2(A,B,C,D) ) ).
fof(dt_k9_relset_2,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
& m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) )
=> m2_relset_1(k9_relset_2(A,B,C,D,E),A,C) ) ).
fof(redefinition_k9_relset_2,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
& m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) )
=> k9_relset_2(A,B,C,D,E) = k5_relat_1(D,E) ) ).
fof(t1_relset_2,axiom,
! [A,B] :
( r2_hidden(A,k3_pua2mss1(B))
<=> ? [C] :
( A = k1_tarski(C)
& r2_hidden(C,B) ) ) ).
fof(t2_relset_2,axiom,
! [A] :
( A = k1_xboole_0
<=> k3_pua2mss1(A) = k1_xboole_0 ) ).
fof(t3_relset_2,axiom,
! [A,B] : k3_pua2mss1(k2_xboole_0(A,B)) = k2_xboole_0(k3_pua2mss1(A),k3_pua2mss1(B)) ).
fof(t4_relset_2,axiom,
! [A,B] : k3_pua2mss1(k3_xboole_0(A,B)) = k3_xboole_0(k3_pua2mss1(A),k3_pua2mss1(B)) ).
fof(t5_relset_2,axiom,
! [A,B] : k3_pua2mss1(k4_xboole_0(A,B)) = k4_xboole_0(k3_pua2mss1(A),k3_pua2mss1(B)) ).
fof(t6_relset_2,axiom,
! [A,B] :
( r1_tarski(A,B)
<=> r1_tarski(k3_pua2mss1(A),k3_pua2mss1(B)) ) ).
fof(t7_relset_2,conjecture,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> r1_tarski(k5_subset_1(A,k8_setfam_1(A,B),k8_setfam_1(A,C)),k8_setfam_1(A,k1_relset_2(A,B,C))) ) ) ).
%------------------------------------------------------------------------------