TSTP Solution File: SET596+3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET596+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 7 10:50:00 EDT 2024
% Result : Theorem 5.11s 2.33s
% Output : Refutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 11 unt; 6 typ; 0 def)
% Number of atoms : 44 ( 17 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 139 ( 12 ~; 6 |; 3 &; 110 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 ^ 32 !; 0 ?; 32 :)
% 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 )
& ( ( intersection @ B @ C )
= empty_set ) )
=> ( ( intersection @ A @ C )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th55) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( ( intersection @ B @ C )
= empty_set ) )
=> ( ( intersection @ A @ C )
= empty_set ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( ( intersection @ B @ C )
= empty_set ) )
=> ( ( intersection @ A @ C )
= empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
( ( intersection @ sk2 @ sk3 )
= empty_set ),
inference(cnf,[status(esa)],[13]) ).
thf(18,plain,
( ( intersection @ sk2 @ sk3 )
= empty_set ),
inference(lifteq,[status(thm)],[15]) ).
thf(16,plain,
subset @ sk1 @ sk2,
inference(cnf,[status(esa)],[13]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_subset) ).
thf(22,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] : ( subset @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ),
inference(miniscope,[status(thm)],[22]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(216,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) )
| ( ( subset @ sk1 @ sk2 )
!= ( subset @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,24]) ).
thf(217,plain,
! [A: $i] : ( subset @ ( intersection @ sk1 @ A ) @ ( intersection @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(243,plain,
! [A: $i] : ( subset @ ( intersection @ sk1 @ A ) @ ( intersection @ sk2 @ A ) ),
inference(simp,[status(thm)],[217]) ).
thf(266,plain,
! [A: $i] :
( ( subset @ ( intersection @ sk1 @ A ) @ empty_set )
| ( ( intersection @ sk2 @ sk3 )
!= ( intersection @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,243]) ).
thf(267,plain,
subset @ ( intersection @ sk1 @ sk3 ) @ empty_set,
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( sk3 ))]]) ).
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(19,plain,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( subset @ A @ empty_set ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(14,plain,
( ( intersection @ sk1 @ sk3 )
!= empty_set ),
inference(cnf,[status(esa)],[13]) ).
thf(17,plain,
( ( intersection @ sk1 @ sk3 )
!= empty_set ),
inference(lifteq,[status(thm)],[14]) ).
thf(91,plain,
! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A
!= ( intersection @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[21,17]) ).
thf(92,plain,
~ ( subset @ ( intersection @ sk1 @ sk3 ) @ empty_set ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( intersection @ sk1 @ sk3 ))]]) ).
thf(296,plain,
$false,
inference(rewrite,[status(thm)],[267,92]) ).
thf(297,plain,
$false,
inference(simp,[status(thm)],[296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET596+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 6 20:45:09 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.79/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.09/0.97 % [INFO] Parsing done (135ms).
% 1.09/0.97 % [INFO] Running in sequential loop mode.
% 1.50/1.24 % [INFO] nitpick registered as external prover.
% 1.50/1.24 % [INFO] Scanning for conjecture ...
% 1.81/1.32 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.88/1.35 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.88/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 1.88/1.37 % [INFO] Type checking passed.
% 1.88/1.37 % [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 ...
% 5.11/2.33 % [INFO] Killing All external provers ...
% 5.11/2.33 % Time passed: 1845ms (effective reasoning time: 1349ms)
% 5.11/2.33 % 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)>
% 5.11/2.33 % Axioms used in derivation (2): intersection_of_subset, subset_of_empty_set_is_empty_set
% 5.11/2.33 % No. of inferences in proof: 25
% 5.11/2.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1845 ms resp. 1349 ms w/o parsing
% 5.11/2.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.11/2.36 % [INFO] Killing All external provers ...
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