TSTP Solution File: SET984+1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET984+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 : Tue May 21 03:07:31 EDT 2024
% Result : Theorem 139.68s 20.88s
% Output : Refutation 139.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 28 unt; 8 typ; 0 def)
% Number of atoms : 148 ( 115 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 434 ( 46 ~; 59 |; 7 &; 310 @)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 127 ( 0 ^ 127 !; 0 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( ( cartesian_product2 @ A @ B )
= empty_set )
| ( ( subset @ A @ C )
& ( subset @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( ( cartesian_product2 @ A @ B )
= empty_set )
| ( ( subset @ A @ C )
& ( subset @ B @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( ( cartesian_product2 @ A @ B )
= empty_set )
| ( ( subset @ A @ C )
& ( subset @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
subset @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ),
inference(cnf,[status(esa)],[14]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ A @ B )
= A )
| ~ ( subset @ A @ B ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(851,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ A @ B )
= A )
| ( ( subset @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17,55]) ).
thf(852,plain,
( ( set_intersection2 @ ( cartesian_product2 @ sk1 @ sk2 ) @ ( cartesian_product2 @ sk3 @ sk4 ) )
= ( cartesian_product2 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[851:[bind(A,$thf( cartesian_product2 @ sk1 @ sk2 )),bind(B,$thf( cartesian_product2 @ sk3 @ sk4 ))]]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(43,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
= ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) )
= ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(884,plain,
( ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk2 @ sk4 ) )
= ( cartesian_product2 @ sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[852,45]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ C @ D ) )
=> ( ( A = empty_set )
| ( B = empty_set )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(46,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ C @ D ) )
=> ( ( A = empty_set )
| ( B = empty_set )
| ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ A @ B )
!= ( cartesian_product2 @ C @ D ) )
| ( A = empty_set )
| ( B = empty_set )
| ( B = D ) ),
inference(cnf,[status(esa)],[46]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ A @ B )
!= ( cartesian_product2 @ C @ D ) )
| ( A = empty_set )
| ( B = empty_set )
| ( B = D ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(903,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ sk1 @ sk2 )
!= ( cartesian_product2 @ A @ B ) )
| ( A = empty_set )
| ( B = empty_set )
| ( B = D )
| ( ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk2 @ sk4 ) )
!= ( cartesian_product2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[884,50]) ).
thf(904,plain,
! [B: $i,A: $i] :
( ( ( cartesian_product2 @ sk1 @ sk2 )
!= ( cartesian_product2 @ A @ B ) )
| ( A = empty_set )
| ( B = empty_set )
| ( B
= ( set_intersection2 @ sk2 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[903:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( set_intersection2 @ sk1 @ sk3 )),bind(D,$thf( set_intersection2 @ sk2 @ sk4 ))]]) ).
thf(40642,plain,
( ( ( set_intersection2 @ sk2 @ sk4 )
= sk2 )
| ( sk2 = empty_set )
| ( sk1 = empty_set ) ),
inference(pattern_uni,[status(thm)],[904:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= empty_set )
<=> ( ( A = empty_set )
| ( B = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( ( cartesian_product2 @ A @ B )
= empty_set )
=> ( ( A = empty_set )
| ( B = empty_set ) ) )
& ( ( ( A = empty_set )
| ( B = empty_set ) )
=> ( ( cartesian_product2 @ A @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,plain,
( ! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= empty_set )
=> ( ( A = empty_set )
| ( B = empty_set ) ) )
& ! [A: $i,B: $i] :
( ( ( A = empty_set )
| ( B = empty_set ) )
=> ( ( cartesian_product2 @ A @ B )
= empty_set ) ) ),
inference(miniscope,[status(thm)],[33]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B != empty_set )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) ),
inference(cnf,[status(esa)],[34]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B != empty_set )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(41,plain,
! [A: $i] :
( ( cartesian_product2 @ A @ empty_set )
= empty_set ),
inference(simp,[status(thm)],[40]) ).
thf(16,plain,
( ( cartesian_product2 @ sk1 @ sk2 )
!= empty_set ),
inference(cnf,[status(esa)],[14]) ).
thf(18,plain,
( ( cartesian_product2 @ sk1 @ sk2 )
!= empty_set ),
inference(lifteq,[status(thm)],[16]) ).
thf(84,plain,
! [A: $i] :
( ( cartesian_product2 @ A @ empty_set )
!= ( cartesian_product2 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[41,18]) ).
thf(86,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[84]) ).
thf(89,plain,
sk2 != empty_set,
inference(simp,[status(thm)],[86]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(12,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(51,plain,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(52,plain,
! [B: $i,A: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
inference(cnf,[status(esa)],[51]) ).
thf(152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subset @ ( set_intersection2 @ B @ A ) @ C )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[21,52]) ).
thf(153,plain,
! [B: $i,A: $i] : ( subset @ ( set_intersection2 @ B @ A ) @ A ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ A @ B )
!= ( cartesian_product2 @ C @ D ) )
| ( A = empty_set )
| ( B = empty_set )
| ( A = C ) ),
inference(cnf,[status(esa)],[46]) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ A @ B )
!= ( cartesian_product2 @ C @ D ) )
| ( A = empty_set )
| ( B = empty_set )
| ( A = C ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cartesian_product2 @ sk1 @ sk2 )
!= ( cartesian_product2 @ A @ B ) )
| ( A = empty_set )
| ( B = empty_set )
| ( A = C )
| ( ( cartesian_product2 @ ( set_intersection2 @ sk1 @ sk3 ) @ ( set_intersection2 @ sk2 @ sk4 ) )
!= ( cartesian_product2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[884,49]) ).
thf(900,plain,
! [B: $i,A: $i] :
( ( ( cartesian_product2 @ sk1 @ sk2 )
!= ( cartesian_product2 @ A @ B ) )
| ( A = empty_set )
| ( B = empty_set )
| ( A
= ( set_intersection2 @ sk1 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[899:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( set_intersection2 @ sk1 @ sk3 )),bind(D,$thf( set_intersection2 @ sk2 @ sk4 ))]]) ).
thf(37666,plain,
( ( ( set_intersection2 @ sk1 @ sk3 )
= sk1 )
| ( sk2 = empty_set )
| ( sk1 = empty_set ) ),
inference(pattern_uni,[status(thm)],[900:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A != empty_set )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) ),
inference(cnf,[status(esa)],[34]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( A != empty_set )
| ( ( cartesian_product2 @ A @ B )
= empty_set ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(39,plain,
! [A: $i] :
( ( cartesian_product2 @ empty_set @ A )
= empty_set ),
inference(simp,[status(thm)],[38]) ).
thf(71,plain,
! [A: $i] :
( ( cartesian_product2 @ empty_set @ A )
!= ( cartesian_product2 @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[39,18]) ).
thf(74,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[71]) ).
thf(77,plain,
sk1 != empty_set,
inference(simp,[status(thm)],[74]) ).
thf(40092,plain,
( ( set_intersection2 @ sk1 @ sk3 )
= sk1 ),
inference(simplifyReflect,[status(thm)],[37666,89,77]) ).
thf(15,plain,
( ~ ( subset @ sk1 @ sk3 )
| ~ ( subset @ sk2 @ sk4 ) ),
inference(cnf,[status(esa)],[14]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk2 @ sk4 )
| ( ( subset @ ( set_intersection2 @ B @ A ) @ A )
!= ( subset @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[153,15]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ~ ( subset @ sk2 @ sk4 )
| ( ( set_intersection2 @ B @ A )
!= sk1 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[189]) ).
thf(202,plain,
! [A: $i] :
( ~ ( subset @ sk2 @ sk4 )
| ( ( set_intersection2 @ A @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[193]) ).
thf(40118,plain,
! [A: $i] :
( ~ ( subset @ sk2 @ sk4 )
| ( ( set_intersection2 @ sk1 @ sk3 )
!= ( set_intersection2 @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[40092,202]) ).
thf(40119,plain,
~ ( subset @ sk2 @ sk4 ),
inference(pattern_uni,[status(thm)],[40118:[bind(A,$thf( sk1 ))]]) ).
thf(40566,plain,
! [B: $i,A: $i] :
( ( subset @ ( set_intersection2 @ B @ A ) @ A )
!= ( subset @ sk2 @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[153,40119]) ).
thf(40603,plain,
! [B: $i,A: $i] :
( ( ( set_intersection2 @ B @ A )
!= sk2 )
| ( A != sk4 ) ),
inference(simp,[status(thm)],[40566]) ).
thf(40633,plain,
! [A: $i] :
( ( set_intersection2 @ A @ sk4 )
!= sk2 ),
inference(simp,[status(thm)],[40603]) ).
thf(43998,plain,
$false,
inference(simplifyReflect,[status(thm)],[40642,89,40633,77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : SET984+1 : TPTP v8.2.0. Released v3.2.0.
% 0.08/0.11 % Command : run_Leo-III %s %d
% 0.10/0.31 % Computer : n012.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 11:57:24 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.87/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.06 % [INFO] Parsing done (157ms).
% 1.28/1.07 % [INFO] Running in sequential loop mode.
% 1.70/1.42 % [INFO] nitpick registered as external prover.
% 1.82/1.42 % [INFO] Scanning for conjecture ...
% 1.91/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.02/1.55 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.17/1.57 % [INFO] Problem is first-order (TPTP FOF).
% 2.17/1.58 % [INFO] Type checking passed.
% 2.17/1.58 % [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 ...
% 139.68/20.83 % [INFO] Killing All external provers ...
% 139.68/20.84 % Time passed: 20380ms (effective reasoning time: 19755ms)
% 139.68/20.84 % 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)>
% 139.68/20.87 % Axioms used in derivation (6): t17_xboole_1, t113_zfmisc_1, commutativity_k3_xboole_0, t123_zfmisc_1, t28_xboole_1, t134_zfmisc_1
% 139.68/20.87 % No. of inferences in proof: 64
% 139.68/20.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20380 ms resp. 19755 ms w/o parsing
% 139.80/21.03 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 139.80/21.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------