TSTP Solution File: SET169+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:52:53 EDT 2023
% Result : Theorem 15.10s 3.61s
% Output : Refutation 15.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 117 ( 19 unt; 10 typ; 0 def)
% Number of atoms : 295 ( 98 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1346 ( 124 ~; 115 |; 24 &;1044 @)
% ( 6 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 272 ( 0 ^; 272 !; 0 ?; 272 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
<=> ( ( member @ C @ A )
| ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(14,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(45,plain,
( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[45]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[46]) ).
thf(15,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[14]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(408,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ E @ ( union @ C @ D ) )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[49,19]) ).
thf(409,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( sk4 @ F @ G ))]]) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ C @ A ) ) ),
inference(simp,[status(thm)],[409]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[45]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[47]) ).
thf(782,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( subset @ D @ E )
| ( ( member @ ( sk4 @ B @ C ) @ ( union @ C @ A ) )
!= ( member @ ( sk4 @ E @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[422,50]) ).
thf(783,plain,
! [B: $i,A: $i] :
( ( subset @ A @ ( union @ A @ B ) )
| ( subset @ A @ ( union @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[782:[bind(A,$thf( G )),bind(B,$thf( union @ F @ G )),bind(C,$thf( F )),bind(D,$thf( F )),bind(E,$thf( union @ F @ G ))]]) ).
thf(798,plain,
! [B: $i,A: $i] : ( subset @ A @ ( union @ A @ B ) ),
inference(simp,[status(thm)],[783]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[28]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(simp,[status(thm)],[32]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( intersection @ A @ ( union @ B @ C ) )
= ( union @ ( intersection @ A @ B ) @ ( intersection @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_distributes_over_union) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( intersection @ A @ ( union @ B @ C ) )
= ( union @ ( intersection @ A @ B ) @ ( intersection @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( intersection @ A @ ( union @ B @ C ) )
= ( union @ ( intersection @ A @ B ) @ ( intersection @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
( ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) )
!= ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
( ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( union @ ( intersection @ A @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33,13]) ).
thf(100,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( union @ ( intersection @ A @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ C @ sk1 )
| ( ( union @ ( intersection @ C @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( subset @ A @ ( union @ A @ B ) )
!= ( subset @ sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[798,100]) ).
thf(812,plain,
! [A: $i] :
( ~ ( subset @ ( union @ sk1 @ A ) @ sk1 )
| ( ( union @ ( intersection @ ( union @ sk1 @ A ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[811:[bind(A,$thf( sk1 )),bind(B,$thf( E )),bind(C,$thf( union @ sk1 @ E ))]]) ).
thf(834,plain,
! [A: $i] :
( ~ ( subset @ ( union @ sk1 @ A ) @ sk1 )
| ( ( union @ ( intersection @ ( union @ sk1 @ A ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[812]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( member @ C @ A )
<=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ! [C: $i] :
( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(54,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
& ! [C: $i] :
( ( member @ C @ B )
=> ( member @ C @ A ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
& ! [C: $i] :
( ( member @ C @ B )
=> ( member @ C @ A ) ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[53]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( member @ ( sk5 @ B @ A ) @ A )
| ( member @ ( sk6 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[54]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( member @ ( sk5 @ B @ A ) @ A )
| ( member @ ( sk6 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( member @ ( sk5 @ B @ A ) @ A )
| ( member @ ( sk6 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[63]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(503,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ E @ ( union @ C @ D ) )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[49,20]) ).
thf(504,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[503:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( sk4 @ F @ G ))]]) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ A @ C ) ) ),
inference(simp,[status(thm)],[504]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[28]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(35,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[34]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ( ( union @ ( intersection @ ( union @ sk1 @ B ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( subset @ A @ A )
!= ( subset @ ( union @ sk1 @ B ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[35,834]) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( ( union @ ( intersection @ ( union @ sk1 @ B ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( A
!= ( union @ sk1 @ B ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[888]) ).
thf(923,plain,
! [A: $i] :
( ( ( union @ ( intersection @ ( union @ sk1 @ A ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[912]) ).
thf(1001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( union @ ( intersection @ ( union @ A @ B ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ C )
!= sk1 )
| ( ( union @ B @ A )
!= ( union @ sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[40,923]) ).
thf(1002,plain,
! [A: $i] :
( ( ( union @ ( intersection @ ( union @ A @ sk1 ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ A )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[1001:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( union @ ( intersection @ B @ A ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ C )
!= sk1 )
| ( ( intersection @ A @ B )
!= ( intersection @ ( union @ C @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[43,1002]) ).
thf(1116,plain,
! [A: $i] :
( ( ( union @ ( intersection @ sk2 @ ( union @ A @ sk1 ) ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ A )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[1115:[bind(A,$thf( union @ D @ sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( D ))]]) ).
thf(1145,plain,
! [A: $i] :
( ( ( union @ ( intersection @ sk2 @ ( union @ A @ sk1 ) ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[1116]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
<=> ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
thf(21,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( intersection @ A @ B ) )
=> ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( member @ C @ ( intersection @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
=> ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( member @ C @ ( intersection @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ A ) ),
inference(cnf,[status(esa)],[22]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[22]) ).
thf(816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ ( union @ B @ A ) )
| ( ( union @ A @ B )
!= ( union @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[40,798]) ).
thf(817,plain,
! [B: $i,A: $i] : ( subset @ A @ ( union @ B @ A ) ),
inference(pattern_uni,[status(thm)],[816:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ A @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[33,13]) ).
thf(102,plain,
! [A: $i] :
( ~ ( subset @ A @ sk1 )
| ~ ( subset @ sk1 @ A )
| ( ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ A @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( union @ B @ A )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ C )
!= sk1 )
| ( ( union @ A @ B )
!= ( union @ ( intersection @ ( union @ sk1 @ C ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,923]) ).
thf(994,plain,
! [A: $i] :
( ( ( union @ ( intersection @ sk1 @ sk3 ) @ ( intersection @ ( union @ sk1 @ A ) @ sk2 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ A )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[993:[bind(A,$thf( intersection @ ( union @ sk1 @ G ) @ sk2 )),bind(B,$thf( intersection @ sk1 @ sk3 )),bind(C,$thf( G ))]]) ).
thf(1021,plain,
! [A: $i] :
( ( ( union @ ( intersection @ sk1 @ sk3 ) @ ( intersection @ ( union @ sk1 @ A ) @ sk2 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[994]) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( union @ ( intersection @ ( union @ C @ sk1 ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ A @ B )
!= sk1 )
| ( ( union @ B @ A )
!= ( union @ sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[40,1002]) ).
thf(1131,plain,
! [A: $i] :
( ( ( union @ ( intersection @ ( union @ A @ sk1 ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ A @ sk1 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[1130:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(507,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ E @ D )
| ( member @ E @ ( union @ B @ A ) )
| ( ( union @ A @ B )
!= ( union @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[40,20]) ).
thf(508,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[507:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(521,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(simp,[status(thm)],[508]) ).
thf(387,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ E @ C )
| ( member @ E @ ( union @ B @ A ) )
| ( ( union @ A @ B )
!= ( union @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[40,19]) ).
thf(388,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(394,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(simp,[status(thm)],[388]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[45]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( union @ A @ B ) )
| ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[15]) ).
thf(534,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ E @ ( intersection @ B @ A ) )
| ( member @ E @ C )
| ( ( intersection @ A @ B )
!= ( intersection @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[43,24]) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ A ) ),
inference(pattern_uni,[status(thm)],[534:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ A ) ),
inference(simp,[status(thm)],[535]) ).
thf(585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ E @ D )
| ( member @ ( sk4 @ D @ E ) @ ( union @ B @ A ) )
| ( ( union @ A @ B )
!= ( union @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[40,422]) ).
thf(586,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( member @ ( sk4 @ C @ A ) @ ( union @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[585:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( member @ ( sk4 @ C @ A ) @ ( union @ B @ A ) ) ),
inference(simp,[status(thm)],[586]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(9,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(51,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( B
!= ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,13]) ).
thf(96,plain,
! [A: $i] :
( ~ ( subset @ A @ ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) )
| ~ ( subset @ ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) @ A )
| ( A
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( A )),bind(B,$thf( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ))]]) ).
thf(107,plain,
( ~ ( subset @ ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) @ ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) )
| ~ ( subset @ ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) @ ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ A ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[33,13]) ).
thf(94,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( union @ ( intersection @ sk1 @ sk2 ) @ ( intersection @ sk1 @ A ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(988,plain,
! [C: $i,B: $i,A: $i] :
( ( ( union @ ( intersection @ B @ A ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ C )
!= sk1 )
| ( ( intersection @ A @ B )
!= ( intersection @ ( union @ sk1 @ C ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[43,923]) ).
thf(989,plain,
! [A: $i] :
( ( ( union @ ( intersection @ sk2 @ ( union @ sk1 @ A ) ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ A )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[988:[bind(A,$thf( union @ sk1 @ E )),bind(B,$thf( sk2 )),bind(C,$thf( E ))]]) ).
thf(1019,plain,
! [A: $i] :
( ( ( union @ ( intersection @ sk2 @ ( union @ sk1 @ A ) ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ sk1 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[989]) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ( ( union @ ( intersection @ ( union @ sk1 @ C ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ A @ B )
!= sk1 )
| ( ( union @ B @ A )
!= ( union @ sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[40,923]) ).
thf(1004,plain,
! [A: $i] :
( ( ( union @ ( intersection @ ( union @ sk1 @ A ) @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( intersection @ sk1 @ ( union @ sk2 @ sk3 ) ) )
| ( ( union @ A @ sk1 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[1003:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(3963,plain,
$false,
inference(cvc4,[status(thm)],[14,834,53,64,49,520,1145,24,25,817,20,102,798,1021,38,21,33,1131,13,1002,41,44,27,521,394,35,48,18,50,544,11,612,43,40,26,51,19,422,107,94,1019,1004,923,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 18:52:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (114ms).
% 1.20/0.96 % [INFO] Running in sequential loop mode.
% 1.65/1.15 % [INFO] eprover registered as external prover.
% 1.65/1.16 % [INFO] cvc4 registered as external prover.
% 1.65/1.16 % [INFO] Scanning for conjecture ...
% 1.65/1.21 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.65/1.23 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.87/1.25 % [INFO] Problem is first-order (TPTP FOF).
% 1.87/1.25 % [INFO] Type checking passed.
% 1.87/1.25 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 15.10/3.61 % External prover 'cvc4' found a proof!
% 15.10/3.61 % [INFO] Killing All external provers ...
% 15.10/3.61 % Time passed: 3095ms (effective reasoning time: 2651ms)
% 15.10/3.61 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 15.10/3.61 % Axioms used in derivation (8): reflexivity_of_subset, equal_member_defn, equal_defn, intersection_defn, commutativity_of_intersection, commutativity_of_union, union_defn, subset_defn
% 15.10/3.61 % No. of inferences in proof: 107
% 15.10/3.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3095 ms resp. 2651 ms w/o parsing
% 15.10/3.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.10/3.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------