TPTP Problem File: SEU172+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SEU172+1 : TPTP v8.2.0. Released v3.3.0.
% Domain : Set theory
% Problem : MPTP bushy problem t54_subset_1
% Version : [Urb07] axioms : Especial.
% English :
% Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% : [Urb07] Urban (2006), Email to G. Sutcliffe
% Source : [Urb07]
% Names : bushy-t54_subset_1 [Urb07]
% Status : Theorem
% Rating : 0.08 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.12 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.22 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.22 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.1, 0.17 v4.0.0, 0.21 v3.7.0, 0.15 v3.5.0, 0.16 v3.3.0
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 38 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 10 ~; 0 |; 7 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 31 ( 26 !; 5 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% library, www.mizar.org
%------------------------------------------------------------------------------
fof(dt_k1_xboole_0,axiom,
$true ).
fof(fc1_xboole_0,axiom,
empty(empty_set) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B) ) ) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(A)
& A != B
& empty(B) ) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A) ).
fof(dt_k1_zfmisc_1,axiom,
$true ).
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ) ).
fof(dt_k4_xboole_0,axiom,
$true ).
fof(dt_m1_subset_1,axiom,
$true ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ) ).
fof(t54_subset_1,conjecture,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,subset_complement(A,C))
& in(B,C) ) ) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ) ).
%------------------------------------------------------------------------------