TSTP Solution File: SEU573^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU573^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 03:42:46 EDT 2024
% Result : Theorem 5.13s 2.15s
% Output : Refutation 5.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 7 unt; 8 typ; 2 def)
% Number of atoms : 77 ( 5 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 228 ( 15 ~; 20 |; 0 &; 169 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 0 ^ 55 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(powersetI_type,type,
powersetI: $o ).
thf(powersetI_def,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ) ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(subsetE_def,definition,
( subsetE
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( powersetI
=> ( subsetE
=> ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(2,negated_conjecture,
~ ( powersetI
=> ( subsetE
=> ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(8,plain,
subset @ sk2 @ sk3,
inference(cnf,[status(esa)],[4]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ B )
| ( in @ B @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( in @ C @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( in @ C @ A )
| ( in @ C @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(18,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ~ ( subset @ C @ D )
| ( in @ E @ D )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5,10]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ C ) )
| ~ ( subset @ B @ A )
| ( in @ ( sk1 @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( D )),bind(E,$thf( sk1 @ F @ G ))]]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ C ) )
| ~ ( subset @ B @ A )
| ( in @ ( sk1 @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[19]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ C ) )
| ( in @ ( sk1 @ B @ C ) @ A )
| ( ( subset @ sk2 @ sk3 )
!= ( subset @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,25]) ).
thf(56,plain,
! [A: $i] :
( ( in @ sk2 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk2 @ A ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(63,plain,
! [A: $i] :
( ( in @ sk2 @ ( powerset @ A ) )
| ( in @ ( sk1 @ sk2 @ A ) @ sk3 ) ),
inference(simp,[status(thm)],[56]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ B @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ sk2 @ ( powerset @ A ) )
| ( in @ C @ ( powerset @ B ) )
| ( ( in @ ( sk1 @ sk2 @ A ) @ sk3 )
!= ( in @ ( sk1 @ C @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[63,6]) ).
thf(200,plain,
( ( in @ sk2 @ ( powerset @ sk3 ) )
| ( in @ sk2 @ ( powerset @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 )),bind(C,$thf( sk2 ))]]) ).
thf(216,plain,
in @ sk2 @ ( powerset @ sk3 ),
inference(simp,[status(thm)],[200]) ).
thf(7,plain,
~ ( in @ sk2 @ ( powerset @ sk3 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(219,plain,
$false,
inference(rewrite,[status(thm)],[216,7]) ).
thf(220,plain,
$false,
inference(simp,[status(thm)],[219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU573^2 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n005.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sun May 19 16:19:24 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.13/0.99 % [INFO] Parsing done (105ms).
% 1.13/1.00 % [INFO] Running in sequential loop mode.
% 1.73/1.23 % [INFO] nitpick registered as external prover.
% 1.73/1.23 % [INFO] Scanning for conjecture ...
% 1.84/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.84/1.32 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.84/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.32 % [INFO] Type checking passed.
% 1.84/1.33 % [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 ...
% 5.00/2.15 % [INFO] Killing All external provers ...
% 5.13/2.15 % Time passed: 1607ms (effective reasoning time: 1148ms)
% 5.13/2.15 % 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)>
% 5.13/2.15 % Axioms used in derivation (0):
% 5.13/2.15 % No. of inferences in proof: 21
% 5.13/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1607 ms resp. 1148 ms w/o parsing
% 5.13/2.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.13/2.19 % [INFO] Killing All external provers ...
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