TSTP Solution File: SET592+3 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET592+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 03:06:21 EDT 2024
% Result : Theorem 34.58s 6.56s
% Output : Refutation 34.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 8 unt; 6 typ; 0 def)
% Number of atoms : 59 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 149 ( 21 ~; 14 |; 10 &; 96 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 0 ^ 29 !; 2 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C )
& ( ( intersection @ B @ C )
= empty_set ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th51) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C )
& ( ( intersection @ B @ C )
= empty_set ) )
=> ( A = empty_set ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C )
& ( ( intersection @ B @ C )
= empty_set ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
~ ! [A: $i] :
( ? [B: $i] :
( ( subset @ A @ B )
& ? [C: $i] :
( ( subset @ A @ C )
& ( ( intersection @ B @ C )
= empty_set ) ) )
=> ( A = empty_set ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(17,plain,
subset @ sk1 @ sk3,
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
( ( intersection @ sk2 @ sk3 )
= empty_set ),
inference(cnf,[status(esa)],[14]) ).
thf(20,plain,
( ( intersection @ sk2 @ sk3 )
= empty_set ),
inference(lifteq,[status(thm)],[16]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_subsets) ).
thf(24,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( intersection @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( intersection @ B @ C ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ empty_set )
| ( ( intersection @ sk2 @ sk3 )
!= ( intersection @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,25]) ).
thf(177,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( subset @ A @ sk3 )
| ( subset @ A @ empty_set ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(6142,plain,
! [A: $i] :
( ~ ( subset @ A @ sk2 )
| ( subset @ A @ empty_set )
| ( ( subset @ sk1 @ sk3 )
!= ( subset @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[17,177]) ).
thf(6143,plain,
( ~ ( subset @ sk1 @ sk2 )
| ( subset @ sk1 @ empty_set ) ),
inference(pattern_uni,[status(thm)],[6142:[bind(A,$thf( sk1 ))]]) ).
thf(18,plain,
subset @ sk1 @ sk2,
inference(cnf,[status(esa)],[14]) ).
thf(3,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_empty_set_is_empty_set) ).
thf(21,plain,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,plain,
! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( subset @ A @ empty_set ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(15,plain,
sk1 != empty_set,
inference(cnf,[status(esa)],[14]) ).
thf(19,plain,
sk1 != empty_set,
inference(lifteq,[status(thm)],[15]) ).
thf(109,plain,
! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[23,19]) ).
thf(110,plain,
~ ( subset @ sk1 @ empty_set ),
inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( sk1 ))]]) ).
thf(6220,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[6143,18,110]) ).
thf(6221,plain,
$false,
inference(simp,[status(thm)],[6220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SET592+3 : TPTP v8.2.0. Released v2.2.0.
% 0.05/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n021.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 12:09:09 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.90/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.08 % [INFO] Parsing done (161ms).
% 1.31/1.09 % [INFO] Running in sequential loop mode.
% 1.69/1.44 % [INFO] nitpick registered as external prover.
% 1.69/1.45 % [INFO] Scanning for conjecture ...
% 2.00/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.03/1.57 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.03/1.59 % [INFO] Problem is first-order (TPTP FOF).
% 2.03/1.60 % [INFO] Type checking passed.
% 2.03/1.60 % [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 ...
% 34.58/6.55 % [INFO] Killing All external provers ...
% 34.58/6.56 % Time passed: 6100ms (effective reasoning time: 5455ms)
% 34.58/6.56 % 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)>
% 34.58/6.56 % Axioms used in derivation (2): intersection_of_subsets, subset_of_empty_set_is_empty_set
% 34.58/6.56 % No. of inferences in proof: 25
% 34.58/6.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6100 ms resp. 5455 ms w/o parsing
% 34.58/6.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.58/6.64 % [INFO] Killing All external provers ...
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