TSTP Solution File: SET143+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET143+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 11:52:46 EDT 2023
% Result : Theorem 16.15s 4.23s
% Output : Refutation 16.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 111 ( 19 unt; 9 typ; 0 def)
% Number of atoms : 305 ( 92 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1080 ( 133 ~; 133 |; 22 &; 758 @)
% ( 5 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 249 ( 0 ^; 249 !; 0 ?; 249 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_type,type,
intersection: $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(8,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(41,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)],[8]) ).
thf(42,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)],[41]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( member @ ( sk5 @ B @ A ) @ A )
| ( member @ ( sk6 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[42]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( member @ ( sk5 @ B @ A ) @ A )
| ( member @ ( sk6 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( member @ ( sk5 @ B @ A ) @ A )
| ( member @ ( sk6 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[55]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(29,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(6,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(32,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)],[6]) ).
thf(33,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)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[33]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[34]) ).
thf(3,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(12,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)],[3]) ).
thf(13,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)],[12]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(239,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ E @ D )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ E @ ( intersection @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,16]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ C ) @ A )
| ( member @ ( sk4 @ A @ ( intersection @ B @ C ) ) @ C ) ),
inference(pattern_uni,[status(thm)],[239:[bind(A,$thf( intersection @ H @ I )),bind(B,$thf( F )),bind(C,$thf( H )),bind(D,$thf( I )),bind(E,$thf( sk4 @ F @ ( intersection @ H @ I ) ))]]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ C ) @ A )
| ( member @ ( sk4 @ A @ ( intersection @ B @ C ) ) @ C ) ),
inference(simp,[status(thm)],[240]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[33]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[35]) ).
thf(328,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ C ) @ A )
| ( subset @ D @ E )
| ( ( member @ ( sk4 @ A @ ( intersection @ B @ C ) ) @ C )
!= ( member @ ( sk4 @ E @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[241,38]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( subset @ ( intersection @ A @ B ) @ B )
| ( subset @ ( intersection @ A @ B ) @ B ) ),
inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( intersection @ F @ G )),bind(E,$thf( G ))]]) ).
thf(362,plain,
! [B: $i,A: $i] : ( subset @ ( intersection @ A @ B ) @ B ),
inference(simp,[status(thm)],[329]) ).
thf(420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ A ) @ D )
| ( ( intersection @ A @ B )
!= ( intersection @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[31,362]) ).
thf(421,plain,
! [B: $i,A: $i] : ( subset @ ( intersection @ B @ A ) @ B ),
inference(pattern_uni,[status(thm)],[420:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ A ) @ D )
| ( ( intersection @ A @ B )
!= ( intersection @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[31,421]) ).
thf(443,plain,
! [B: $i,A: $i] : ( subset @ ( intersection @ B @ A ) @ A ),
inference(pattern_uni,[status(thm)],[442:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_intersection) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 )
!= ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
( ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 )
!= ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(61,plain,
( ( ( intersection @ sk1 @ sk2 )
!= sk1 )
| ( ( intersection @ sk2 @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(18,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)],[4]) ).
thf(19,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)],[18]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[19]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(simp,[status(thm)],[23]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( ( intersection @ B @ A )
!= ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) )
| ( ( intersection @ A @ B )
!= ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[31,11]) ).
thf(141,plain,
( ( intersection @ sk3 @ ( intersection @ sk1 @ sk2 ) )
!= ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( intersection @ sk1 @ sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(149,plain,
( ( sk3 != sk1 )
| ( ( intersection @ sk2 @ sk3 )
!= ( intersection @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(180,plain,
( ( sk3 != sk1 )
| ( sk2 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[149]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B != sk1 )
| ( sk2 != sk1 )
| ( sk3 != sk2 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[24,180]) ).
thf(259,plain,
! [A: $i] :
( ~ ( subset @ sk3 @ A )
| ~ ( subset @ A @ sk3 )
| ( A != sk1 )
| ( sk2 != sk1 )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( sk3 ))]]) ).
thf(270,plain,
( ~ ( subset @ sk3 @ sk1 )
| ~ ( subset @ sk1 @ sk3 )
| ( sk2 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[259]) ).
thf(422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ A @ B ) @ D )
| ( ( intersection @ B @ A )
!= ( intersection @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[31,362]) ).
thf(423,plain,
! [B: $i,A: $i] : ( subset @ ( intersection @ A @ B ) @ A ),
inference(pattern_uni,[status(thm)],[422:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[33]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ E @ C )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ E @ ( intersection @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,15]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ C ) @ A )
| ( member @ ( sk4 @ A @ ( intersection @ B @ C ) ) @ B ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( intersection @ H @ I )),bind(B,$thf( F )),bind(C,$thf( H )),bind(D,$thf( I )),bind(E,$thf( sk4 @ F @ ( intersection @ H @ I ) ))]]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ C ) @ A )
| ( member @ ( sk4 @ A @ ( intersection @ B @ C ) ) @ B ) ),
inference(simp,[status(thm)],[230]) ).
thf(221,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ E @ ( intersection @ B @ A ) )
| ( member @ E @ D )
| ( ( intersection @ A @ B )
!= ( intersection @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[31,16]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ B ) ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ B ) ),
inference(simp,[status(thm)],[222]) ).
thf(350,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ A ) @ C )
| ( member @ ( sk4 @ C @ ( intersection @ D @ E ) ) @ E )
| ( ( intersection @ A @ B )
!= ( intersection @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[31,241]) ).
thf(351,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ A ) @ C )
| ( member @ ( sk4 @ C @ ( intersection @ A @ B ) ) @ B ) ),
inference(pattern_uni,[status(thm)],[350:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(1284,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ B @ A ) @ C )
| ( subset @ D @ E )
| ( ( member @ ( sk4 @ C @ ( intersection @ A @ B ) ) @ B )
!= ( member @ ( sk4 @ E @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[351,38]) ).
thf(1285,plain,
! [B: $i,A: $i] :
( ( subset @ ( intersection @ B @ A ) @ B )
| ( subset @ ( intersection @ A @ B ) @ B ) ),
inference(pattern_uni,[status(thm)],[1284:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( intersection @ F @ G )),bind(E,$thf( G ))]]) ).
thf(1358,plain,
! [B: $i,A: $i] :
( ( subset @ ( intersection @ B @ A ) @ B )
| ( subset @ ( intersection @ A @ B ) @ B ) ),
inference(simp,[status(thm)],[1285]) ).
thf(2486,plain,
! [B: $i,A: $i] :
( ( subset @ ( intersection @ B @ A ) @ B )
| ( ( subset @ ( intersection @ A @ B ) @ B )
!= ( subset @ ( intersection @ B @ A ) @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1358]) ).
thf(2505,plain,
! [A: $i] : ( subset @ ( intersection @ A @ A ) @ A ),
inference(pattern_uni,[status(thm)],[2486:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(39,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk3 != sk1 )
| ( B != sk1 )
| ( sk3 != sk2 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[24,180]) ).
thf(261,plain,
! [A: $i] :
( ~ ( subset @ sk2 @ A )
| ~ ( subset @ A @ sk2 )
| ( sk3 != sk1 )
| ( A != sk1 )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( sk2 ))]]) ).
thf(271,plain,
( ~ ( subset @ sk2 @ sk1 )
| ~ ( subset @ sk1 @ sk2 )
| ( sk3 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[261]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk5 @ B @ A ) @ B )
| ~ ( member @ ( sk6 @ B @ A ) @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[42]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( member @ ( sk5 @ B @ A ) @ B )
| ~ ( member @ ( sk6 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( member @ ( sk5 @ B @ A ) @ B )
| ~ ( member @ ( sk6 @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[49]) ).
thf(578,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ E @ C )
| ( member @ E @ D )
| ( ( subset @ ( intersection @ B @ A ) @ B )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[421,36]) ).
thf(579,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(pattern_uni,[status(thm)],[578:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( intersection @ F @ G )),bind(D,$thf( F ))]]) ).
thf(613,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(simp,[status(thm)],[579]) ).
thf(608,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ E @ C )
| ( member @ E @ D )
| ( ( subset @ ( intersection @ A @ B ) @ B )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[362,36]) ).
thf(609,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(pattern_uni,[status(thm)],[608:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( intersection @ F @ G )),bind(D,$thf( G ))]]) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(simp,[status(thm)],[609]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[19]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(26,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[25]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( sk3 != sk1 )
| ( sk2 != sk1 )
| ( B != sk2 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[24,180]) ).
thf(263,plain,
! [A: $i] :
( ~ ( subset @ sk3 @ A )
| ~ ( subset @ A @ sk3 )
| ( sk3 != sk1 )
| ( sk2 != sk1 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( sk3 ))]]) ).
thf(272,plain,
( ~ ( subset @ sk3 @ sk2 )
| ~ ( subset @ sk2 @ sk3 )
| ( sk3 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[263]) ).
thf(209,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)],[31,15]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ A ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ A ) ),
inference(simp,[status(thm)],[210]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B
!= ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) )
| ( A
!= ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[24,11]) ).
thf(75,plain,
! [A: $i] :
( ~ ( subset @ ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) @ A )
| ~ ( subset @ A @ ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) )
| ( A
!= ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 )),bind(B,$thf( B ))]]) ).
thf(119,plain,
( ~ ( subset @ ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) @ ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) )
| ~ ( subset @ ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) @ ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk5 @ B @ A ) @ B )
| ( member @ ( sk6 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[42]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( member @ ( sk5 @ B @ A ) @ B )
| ( member @ ( sk6 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( member @ ( sk5 @ B @ A ) @ B )
| ( member @ ( sk6 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[57]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B != sk1 )
| ( ( intersection @ sk2 @ sk3 )
!= ( intersection @ sk1 @ sk2 ) )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[24,149]) ).
thf(182,plain,
! [A: $i] :
( ~ ( subset @ sk3 @ A )
| ~ ( subset @ A @ sk3 )
| ( A != sk1 )
| ( ( intersection @ sk2 @ sk3 )
!= ( intersection @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( sk3 ))]]) ).
thf(200,plain,
( ~ ( subset @ sk3 @ sk1 )
| ~ ( subset @ sk1 @ sk3 )
| ( ( intersection @ sk2 @ sk3 )
!= ( intersection @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(3754,plain,
$false,
inference(cvc4,[status(thm)],[56,443,61,270,38,423,12,241,18,36,242,24,37,421,228,29,9,141,2505,41,32,180,17,149,362,39,271,50,16,31,1358,613,11,612,26,351,272,214,119,58,15,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET143+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n022.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Thu May 18 19:14:48 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.90/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.03 % [INFO] Parsing done (139ms).
% 1.21/1.04 % [INFO] Running in sequential loop mode.
% 1.57/1.29 % [INFO] eprover registered as external prover.
% 1.57/1.29 % [INFO] cvc4 registered as external prover.
% 1.57/1.29 % [INFO] Scanning for conjecture ...
% 1.72/1.35 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.84/1.37 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.84/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 1.84/1.39 % [INFO] Type checking passed.
% 1.84/1.39 % [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 ...
% 16.15/4.22 % External prover 'cvc4' found a proof!
% 16.15/4.23 % [INFO] Killing All external provers ...
% 16.15/4.23 % Time passed: 3702ms (effective reasoning time: 3183ms)
% 16.15/4.23 % 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)>
% 16.15/4.23 % Axioms used in derivation (6): reflexivity_of_subset, equal_member_defn, commutativity_of_intersection, equal_defn, subset_defn, intersection_defn
% 16.15/4.23 % No. of inferences in proof: 102
% 16.15/4.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3702 ms resp. 3183 ms w/o parsing
% 16.26/4.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.26/4.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------