TSTP Solution File: SET609+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET609+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 11:53:45 EDT 2023
% Result : Theorem 9.07s 2.76s
% Output : Refutation 9.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 119 ( 19 unt; 9 typ; 0 def)
% Number of atoms : 303 ( 72 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1152 ( 123 ~; 109 |; 28 &; 854 @)
% ( 7 <=>; 31 =>; 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 : 355 ( 0 ^; 355 !; 0 ?; 355 :)
% Comments :
%------------------------------------------------------------------------------
thf(difference_type,type,
difference: $i > $i > $i ).
thf(union_type,type,
union: $i > $i > $i ).
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(7,axiom,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(lifteq,[status(thm)],[46]) ).
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(15,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(16,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)],[15]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( difference @ A @ B ) )
<=> ( ( member @ C @ A )
& ~ ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
thf(28,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( difference @ A @ B ) )
=> ( ( member @ C @ A )
& ~ ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
& ~ ( member @ C @ B ) )
=> ( member @ C @ ( difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( difference @ A @ B ) )
=> ( ( member @ C @ A )
& ~ ( member @ C @ B ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ A )
& ~ ( member @ C @ B ) )
=> ( member @ C @ ( difference @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[28]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( difference @ A @ B ) )
| ~ ( member @ C @ B ) ),
inference(cnf,[status(esa)],[29]) ).
thf(91,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ F @ ( difference @ D @ E ) )
| ( ( member @ C @ ( union @ A @ B ) )
!= ( member @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[20,32]) ).
thf(92,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ A @ ( difference @ B @ ( union @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( union @ G @ H )),bind(F,$thf( C ))]]) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ A @ ( difference @ B @ ( union @ C @ D ) ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ( ( member @ A @ ( difference @ B @ ( union @ C @ D ) ) )
!= ( member @ A @ C ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[104]) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ( A != A )
| ( ( difference @ B @ ( union @ C @ D ) )
!= C ) ),
inference(simp,[status(thm)],[180]) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ( ( difference @ B @ ( union @ C @ D ) )
!= C ) ),
inference(simp,[status(thm)],[182]) ).
thf(194,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ E )
| ( ( difference @ D @ ( union @ B @ A ) )
!= E )
| ( ( union @ A @ B )
!= ( union @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[47,185]) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( ( difference @ D @ ( union @ B @ A ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(456,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ E @ C )
| ( ( difference @ F @ ( union @ B @ A ) )
!= C )
| ( ( union @ A @ B )
!= ( union @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[47,195]) ).
thf(457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( difference @ D @ ( union @ B @ A ) )
!= B ) ),
inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( difference @ D @ ( union @ B @ A ) )
!= B ) ),
inference(simp,[status(thm)],[457]) ).
thf(9,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(51,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)],[9]) ).
thf(52,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)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[53]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( difference @ B @ C ) )
= ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th81) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( difference @ B @ C ) )
= ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( difference @ B @ C ) )
= ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
( ( difference @ sk1 @ ( difference @ sk2 @ sk3 ) )
!= ( union @ ( difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
( ( union @ ( difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )
!= ( difference @ sk1 @ ( difference @ sk2 @ sk3 ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(202,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)],[56,21]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( sk4 @ F @ G ))]]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ A @ C ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(93,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)],[47,20]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(58,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(34,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)],[6]) ).
thf(35,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)],[34]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[35]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(42,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[41]) ).
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(22,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(23,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)],[22]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ A ) ),
inference(cnf,[status(esa)],[23]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[54]) ).
thf(218,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( difference @ D @ ( union @ E @ F ) )
!= E )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[56,185]) ).
thf(219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ C )
| ( ( difference @ A @ ( union @ D @ B ) )
!= D ) ),
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( sk4 @ G @ H )),bind(D,$thf( D )),bind(E,$thf( H ))]]) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ C )
| ( ( difference @ A @ ( union @ D @ B ) )
!= D ) ),
inference(simp,[status(thm)],[219]) ).
thf(11,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(60,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)],[11]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(cnf,[status(esa)],[48]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[23]) ).
thf(154,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)],[50,26]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ B ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ B ) ),
inference(simp,[status(thm)],[155]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ B )
| ( member @ C @ ( difference @ A @ B ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ B )
| ( member @ C @ ( difference @ A @ B ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(196,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ E )
| ( ( difference @ D @ ( union @ A @ B ) )
!= E )
| ( ( union @ B @ A )
!= ( union @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[47,185]) ).
thf(197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( difference @ D @ ( union @ A @ B ) )
!= B ) ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(200,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)],[56,20]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( sk4 @ F @ G ))]]) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ C @ A ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( member @ C @ ( intersection @ A @ B ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( difference @ A @ B ) )
| ( member @ C @ A ) ),
inference(cnf,[status(esa)],[29]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[35]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(simp,[status(thm)],[39]) ).
thf(125,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)],[47,21]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(142,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)],[50,25]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ A ) ),
inference(pattern_uni,[status(thm)],[142:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ B @ A ) )
| ( member @ C @ A ) ),
inference(simp,[status(thm)],[143]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( union @ A @ B ) )
| ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[16]) ).
thf(865,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B
!= ( difference @ sk1 @ ( difference @ sk2 @ sk3 ) ) )
| ( A
!= ( union @ ( difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,14]) ).
thf(866,plain,
! [A: $i] :
( ~ ( subset @ ( union @ ( difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) @ A )
| ~ ( subset @ A @ ( union @ ( difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) )
| ( A
!= ( difference @ sk1 @ ( difference @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[865:[bind(A,$thf( union @ ( difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) )),bind(B,$thf( B ))]]) ).
thf(1093,plain,
( ~ ( subset @ ( union @ ( difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) @ ( difference @ sk1 @ ( difference @ sk2 @ sk3 ) ) )
| ~ ( subset @ ( difference @ sk1 @ ( difference @ sk2 @ sk3 ) ) @ ( union @ ( difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[866]) ).
thf(448,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( difference @ F @ ( union @ D @ C ) )
!= C )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[56,195]) ).
thf(449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ C )
| ( ( difference @ B @ ( union @ A @ D ) )
!= D ) ),
inference(pattern_uni,[status(thm)],[448:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( sk4 @ G @ H ))]]) ).
thf(464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ C )
| ( ( difference @ B @ ( union @ A @ D ) )
!= D ) ),
inference(simp,[status(thm)],[449]) ).
thf(458,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ E @ C )
| ( ( difference @ F @ ( union @ A @ B ) )
!= C )
| ( ( union @ B @ A )
!= ( union @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[47,195]) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( ( difference @ D @ ( union @ A @ B ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[458:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( ( difference @ D @ ( union @ A @ B ) )
!= A ) ),
inference(simp,[status(thm)],[459]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( member @ C @ ( difference @ A @ B ) )
!= ( member @ C @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( C != C )
| ( ( difference @ A @ B )
!= B ) ),
inference(simp,[status(thm)],[80]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( difference @ A @ B )
!= B ) ),
inference(simp,[status(thm)],[82]) ).
thf(523,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)],[224,57]) ).
thf(524,plain,
! [B: $i,A: $i] :
( ( subset @ A @ ( union @ A @ B ) )
| ( subset @ A @ ( union @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[523:[bind(A,$thf( G )),bind(B,$thf( union @ F @ G )),bind(C,$thf( F )),bind(D,$thf( F )),bind(E,$thf( union @ F @ G ))]]) ).
thf(543,plain,
! [B: $i,A: $i] : ( subset @ A @ ( union @ A @ B ) ),
inference(simp,[status(thm)],[524]) ).
thf(559,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)],[47,543]) ).
thf(560,plain,
! [B: $i,A: $i] : ( subset @ A @ ( union @ B @ A ) ),
inference(pattern_uni,[status(thm)],[559:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(216,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( ( difference @ C @ D )
!= D )
| ( ( member @ ( sk4 @ B @ A ) @ A )
!= ( member @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[56,83]) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( ( difference @ A @ C )
!= C ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( sk4 @ F @ G ))]]) ).
thf(232,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( ( difference @ A @ C )
!= C ) ),
inference(simp,[status(thm)],[217]) ).
thf(1488,plain,
$false,
inference(cvc4,[status(thm)],[468,56,14,225,105,12,48,104,58,195,185,42,25,20,57,233,60,28,160,21,33,197,224,45,32,34,22,27,50,31,40,26,139,151,51,19,1093,464,47,15,469,83,543,560,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET609+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 19:00:03 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.85/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.96 % [INFO] Parsing done (120ms).
% 1.17/0.96 % [INFO] Running in sequential loop mode.
% 1.49/1.16 % [INFO] eprover registered as external prover.
% 1.49/1.16 % [INFO] cvc4 registered as external prover.
% 1.49/1.17 % [INFO] Scanning for conjecture ...
% 1.80/1.23 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.80/1.25 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.80/1.27 % [INFO] Problem is first-order (TPTP FOF).
% 1.80/1.27 % [INFO] Type checking passed.
% 1.80/1.27 % [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 ...
% 9.07/2.75 % External prover 'cvc4' found a proof!
% 9.07/2.75 % [INFO] Killing All external provers ...
% 9.07/2.76 % Time passed: 2251ms (effective reasoning time: 1789ms)
% 9.07/2.76 % 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)>
% 9.07/2.76 % Axioms used in derivation (9): reflexivity_of_subset, equal_member_defn, equal_defn, intersection_defn, commutativity_of_intersection, difference_defn, commutativity_of_union, union_defn, subset_defn
% 9.07/2.76 % No. of inferences in proof: 110
% 9.07/2.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2251 ms resp. 1789 ms w/o parsing
% 9.13/2.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.13/2.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------