TSTP Solution File: SET615+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET615+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 11:53:48 EDT 2023
% Result : Theorem 11.32s 3.15s
% Output : Refutation 11.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 118 ( 15 unt; 10 typ; 0 def)
% Number of atoms : 312 ( 76 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1192 ( 124 ~; 121 |; 24 &; 884 @)
% ( 6 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 343 ( 0 ^; 343 !; 0 ?; 343 :)
% Comments :
%------------------------------------------------------------------------------
thf(difference_type,type,
difference: $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(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( difference @ ( union @ A @ B ) @ C )
= ( union @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_distributes_over_union) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( difference @ ( union @ A @ B ) @ C )
= ( union @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( difference @ ( union @ A @ B ) @ C )
= ( union @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(40,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)],[7]) ).
thf(41,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)],[40]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[41]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[42]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
<=> ( ( member @ C @ A )
| ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(13,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(14,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)],[13]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(143,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)],[45,19]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( sk4 @ F @ G ))]]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ A @ C ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(37,plain,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( difference @ A @ B ) )
<=> ( ( member @ C @ A )
& ~ ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(20,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)],[4]) ).
thf(21,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)],[20]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( difference @ A @ B ) )
| ~ ( member @ C @ B ) ),
inference(cnf,[status(esa)],[21]) ).
thf(76,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)],[18,24]) ).
thf(77,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ A @ ( difference @ B @ ( union @ C @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$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(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ~ ( member @ A @ ( difference @ B @ ( union @ C @ D ) ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(177,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)],[91]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ( A != A )
| ( ( difference @ B @ ( union @ C @ D ) )
!= C ) ),
inference(simp,[status(thm)],[177]) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ( ( difference @ B @ ( union @ C @ D ) )
!= C ) ),
inference(simp,[status(thm)],[181]) ).
thf(191,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)],[39,185]) ).
thf(192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( difference @ D @ ( union @ A @ B ) )
!= B ) ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(78,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)],[39,18]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(26,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(27,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)],[26]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[27]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(simp,[status(thm)],[31]) ).
thf(11,plain,
( ( difference @ ( union @ sk1 @ sk2 ) @ sk3 )
!= ( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
( ( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ sk3 ) )
!= ( difference @ ( union @ sk1 @ sk2 ) @ sk3 ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(568,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B
!= ( difference @ ( union @ sk1 @ sk2 ) @ sk3 ) )
| ( A
!= ( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,12]) ).
thf(569,plain,
! [A: $i] :
( ~ ( subset @ ( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ sk3 ) ) @ A )
| ~ ( subset @ A @ ( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ sk3 ) ) )
| ( A
!= ( difference @ ( union @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[568:[bind(A,$thf( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ sk3 ) )),bind(B,$thf( B ))]]) ).
thf(742,plain,
( ~ ( subset @ ( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ sk3 ) ) @ ( difference @ ( union @ sk1 @ sk2 ) @ sk3 ) )
| ~ ( subset @ ( difference @ ( union @ sk1 @ sk2 ) @ sk3 ) @ ( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[569]) ).
thf(96,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)],[39,19]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( member @ C @ ( union @ B @ A ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( member @ C @ ( difference @ A @ B ) )
!= ( member @ C @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[24]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( C != C )
| ( ( difference @ A @ B )
!= B ) ),
inference(simp,[status(thm)],[69]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( difference @ A @ B )
!= B ) ),
inference(simp,[status(thm)],[71]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[41]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[43]) ).
thf(221,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( subset @ D @ E )
| ( ( member @ ( sk4 @ B @ C ) @ ( union @ A @ C ) )
!= ( member @ ( sk4 @ E @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[147,46]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( subset @ B @ ( union @ A @ B ) )
| ( subset @ B @ ( union @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( F )),bind(B,$thf( union @ F @ G )),bind(C,$thf( G )),bind(D,$thf( G )),bind(E,$thf( union @ F @ G ))]]) ).
thf(240,plain,
! [B: $i,A: $i] : ( subset @ B @ ( union @ A @ B ) ),
inference(simp,[status(thm)],[222]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[41]) ).
thf(1296,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ E @ C )
| ( member @ E @ D )
| ( ( subset @ B @ ( union @ A @ B ) )
!= ( subset @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[240,44]) ).
thf(1297,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ( member @ A @ ( union @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[1296:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( union @ F @ G ))]]) ).
thf(1316,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ C )
| ( member @ A @ ( union @ B @ C ) ) ),
inference(simp,[status(thm)],[1297]) ).
thf(189,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)],[39,185]) ).
thf(190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( ( difference @ D @ ( union @ B @ A ) )
!= A ) ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(372,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)],[45,190]) ).
thf(373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ C )
| ( ( difference @ B @ ( union @ A @ D ) )
!= D ) ),
inference(pattern_uni,[status(thm)],[372:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( sk4 @ G @ H ))]]) ).
thf(378,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ C )
| ( ( difference @ B @ ( union @ A @ D ) )
!= D ) ),
inference(simp,[status(thm)],[373]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ ( union @ B @ A ) )
| ( ( union @ A @ B )
!= ( union @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[39,240]) ).
thf(242,plain,
! [B: $i,A: $i] : ( subset @ B @ ( union @ B @ A ) ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(202,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 @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[39,147]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( member @ ( sk4 @ C @ B ) @ ( union @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(232,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( member @ ( sk4 @ C @ B ) @ ( union @ B @ A ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ B )
| ( member @ C @ ( difference @ A @ B ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ B )
| ( member @ C @ ( difference @ A @ B ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(139,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)],[45,72]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( ( difference @ A @ C )
!= C ) ),
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( sk4 @ F @ G ))]]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( ( difference @ A @ C )
!= C ) ),
inference(simp,[status(thm)],[140]) ).
thf(204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ E @ D )
| ( member @ ( sk4 @ D @ E ) @ ( union @ A @ B ) )
| ( ( union @ B @ A )
!= ( union @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[39,147]) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( member @ ( sk4 @ C @ A ) @ ( union @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ A @ C )
| ( member @ ( sk4 @ C @ A ) @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(197,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)],[45,185]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ C )
| ( ( difference @ A @ ( union @ D @ B ) )
!= D ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( sk4 @ G @ H )),bind(D,$thf( D )),bind(E,$thf( H ))]]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ D @ C )
| ( ( difference @ A @ ( union @ D @ B ) )
!= D ) ),
inference(simp,[status(thm)],[198]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( union @ A @ B ) )
| ( member @ C @ A )
| ( member @ C @ B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[27]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(34,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[33]) ).
thf(576,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( union @ ( difference @ sk1 @ A ) @ ( difference @ sk2 @ sk3 ) )
!= ( difference @ ( union @ sk1 @ sk2 ) @ sk3 ) )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[32,12]) ).
thf(577,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( union @ ( difference @ sk1 @ A ) @ ( difference @ sk2 @ sk3 ) )
!= ( difference @ ( union @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[576:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(578,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( ( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ A ) )
!= ( difference @ ( union @ sk1 @ sk2 ) @ sk3 ) )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[32,12]) ).
thf(579,plain,
! [A: $i] :
( ~ ( subset @ A @ sk3 )
| ~ ( subset @ sk3 @ A )
| ( ( union @ ( difference @ sk1 @ sk3 ) @ ( difference @ sk2 @ A ) )
!= ( difference @ ( union @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[578:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(364,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)],[39,190]) ).
thf(365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( difference @ D @ ( union @ B @ A ) )
!= B ) ),
inference(pattern_uni,[status(thm)],[364:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ C @ B )
| ( ( difference @ D @ ( union @ B @ A ) )
!= B ) ),
inference(simp,[status(thm)],[365]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( member @ C @ A )
<=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(49,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)],[9]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( difference @ A @ B ) )
| ( member @ C @ A ) ),
inference(cnf,[status(esa)],[21]) ).
thf(137,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)],[45,18]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( sk4 @ F @ G ))]]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk4 @ B @ C ) @ ( union @ C @ A ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(8,axiom,
! [A: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(47,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(50,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)],[49]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( member @ ( sk5 @ B @ A ) @ A )
| ( member @ ( sk6 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[50]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( member @ ( sk5 @ B @ A ) @ A )
| ( member @ ( sk6 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( member @ ( sk5 @ B @ A ) @ A )
| ( member @ ( sk6 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[61]) ).
thf(2512,plain,
$false,
inference(cvc4,[status(thm)],[10,147,192,92,742,109,13,39,18,72,1316,378,242,232,185,24,37,25,20,46,152,233,201,45,17,32,34,44,577,579,12,382,49,91,240,40,26,23,151,190,19,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET615+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 19:19:04 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (113ms).
% 1.22/0.95 % [INFO] Running in sequential loop mode.
% 1.57/1.15 % [INFO] eprover registered as external prover.
% 1.57/1.16 % [INFO] cvc4 registered as external prover.
% 1.66/1.16 % [INFO] Scanning for conjecture ...
% 1.66/1.21 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.85/1.23 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.85/1.25 % [INFO] Problem is first-order (TPTP FOF).
% 1.85/1.25 % [INFO] Type checking passed.
% 1.85/1.25 % [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 ...
% 11.32/3.15 % External prover 'cvc4' found a proof!
% 11.32/3.15 % [INFO] Killing All external provers ...
% 11.32/3.15 % Time passed: 2640ms (effective reasoning time: 2192ms)
% 11.32/3.15 % 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)>
% 11.32/3.15 % Axioms used in derivation (7): reflexivity_of_subset, equal_member_defn, equal_defn, difference_defn, commutativity_of_union, union_defn, subset_defn
% 11.32/3.15 % No. of inferences in proof: 108
% 11.32/3.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2640 ms resp. 2192 ms w/o parsing
% 11.49/3.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.49/3.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------