TSTP Solution File: SEU519^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU519^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 03:37:57 EDT 2024
% Result : Theorem 3.67s 2.30s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 9 unt; 7 typ; 2 def)
% Number of atoms : 42 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 112 ( 10 ~; 5 |; 0 &; 80 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 0 ^ 32 !; 1 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
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(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( emptysetE
=> ( powersetI
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( powersetI
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
~ ( in @ emptyset @ ( powerset @ sk2 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ B )
| ( in @ B @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ B )
| ( in @ B @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(8,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ( B
!= ( in @ emptyset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,5]) ).
thf(12,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( A )),bind(B,$thf( in @ emptyset @ ( powerset @ sk2 ) ))]]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ C @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[9,12]) ).
thf(35,plain,
! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( E )),bind(B,$thf( emptyset )),bind(C,$thf( sk1 @ emptyset @ E ))]]) ).
thf(40,plain,
! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
inference(simp,[status(thm)],[35]) ).
thf(43,plain,
~ $true,
inference(rewrite,[status(thm)],[5,40]) ).
thf(44,plain,
$false,
inference(simp,[status(thm)],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SEU519^2 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 15:39:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 1.04/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.12 % [INFO] Parsing done (161ms).
% 1.29/1.14 % [INFO] Running in sequential loop mode.
% 1.91/1.50 % [INFO] eprover registered as external prover.
% 1.91/1.50 % [INFO] cvc4 registered as external prover.
% 1.91/1.51 % [INFO] Scanning for conjecture ...
% 2.02/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.14/1.64 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.14/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.64 % [INFO] Type checking passed.
% 2.14/1.65 % [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 ...
% 3.67/2.30 % [INFO] Killing All external provers ...
% 3.67/2.30 % Time passed: 1826ms (effective reasoning time: 1155ms)
% 3.67/2.30 % 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)>
% 3.67/2.30 % Axioms used in derivation (0):
% 3.67/2.30 % No. of inferences in proof: 15
% 3.67/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1826 ms resp. 1155 ms w/o parsing
% 3.67/2.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.67/2.34 % [INFO] Killing All external provers ...
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