TSTP Solution File: SEU511^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU511^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 03:37:54 EDT 2024
% Result : Theorem 3.02s 1.64s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 22 ( 10 unt; 6 typ; 2 def)
% Number of atoms : 28 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 8 ~; 2 |; 0 &; 26 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 1 ^ 15 !; 5 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(nonempty_type,type,
nonempty: $i > $o ).
thf(nonempty_def,definition,
( nonempty
= ( ^ [A: $i] : ( A != emptyset ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( emptysetE
=> ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( nonempty @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( nonempty @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( A != emptyset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( A != emptyset ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(6,plain,
in @ sk2 @ sk1,
inference(cnf,[status(esa)],[4]) ).
thf(5,plain,
sk1 = emptyset,
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
sk1 = emptyset,
inference(lifteq,[status(thm)],[5]) ).
thf(9,plain,
in @ sk2 @ emptyset,
inference(rewrite,[status(thm)],[6,8]) ).
thf(7,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
! [B: $o,A: $i] :
( B
| ( ( in @ sk2 @ emptyset )
!= ( in @ A @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[9,7]) ).
thf(13,plain,
! [A: $o] : A,
inference(pattern_uni,[status(thm)],[12:[bind(A,$thf( sk2 ))]]) ).
thf(29,plain,
! [A: $o] : A,
inference(simp,[status(thm)],[13]) ).
thf(33,plain,
$false,
inference(prim_subst,[status(thm)],[29:[bind(A,$thf( $false ))]]) ).
thf(38,plain,
$false,
inference(simp,[status(thm)],[33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU511^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 16:01:24 EDT 2024
% 0.21/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.95 % [INFO] Parsing done (97ms).
% 1.19/0.95 % [INFO] Running in sequential loop mode.
% 1.63/1.16 % [INFO] eprover registered as external prover.
% 1.63/1.16 % [INFO] cvc4 registered as external prover.
% 1.63/1.17 % [INFO] Scanning for conjecture ...
% 1.71/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.82/1.24 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.82/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.86/1.24 % [INFO] Type checking passed.
% 1.86/1.25 % [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 ...
% 3.02/1.63 % [INFO] Killing All external provers ...
% 3.02/1.63 % Time passed: 1118ms (effective reasoning time: 675ms)
% 3.02/1.63 % 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)>
% 3.02/1.64 % Axioms used in derivation (0):
% 3.02/1.64 % No. of inferences in proof: 14
% 3.02/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1118 ms resp. 675 ms w/o parsing
% 3.02/1.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.02/1.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------