TSTP Solution File: SEV463^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV463^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n026.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 : Mon Jun 24 15:59:06 EDT 2024
% Result : Theorem 8.50s 2.90s
% Output : Refutation 8.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 15 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 124 ( 4 ~; 0 |; 0 &; 111 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 44 ( 0 ^ 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/trivia/I\'_type',type,
'\'const/trivia/I\'':
!>[TA: $tType] : ( TA > TA ) ).
thf('\'const/sets/SUBSET\'_type',type,
'\'const/sets/SUBSET\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf('\'const/sets/INTERS\'_type',type,
'\'const/sets/INTERS\'':
!>[TA: $tType] : ( ( ( TA > $o ) > $o ) > TA > $o ) ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(sk2_type,type,
sk2: ( skt1 > $o ) > $o ).
thf(3,axiom,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/trivia/I_THM_') ).
thf(10,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ ( '\'const/sets/INTERS\'' @ TA @ B ) )
= ( ! [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
=> ( '\'const/sets/SUBSET\'' @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_INTERS_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ ( '\'const/sets/INTERS\'' @ TA @ B ) )
= ( ! [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
=> ( '\'const/sets/SUBSET\'' @ TA @ A @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ ( '\'const/sets/INTERS\'' @ TA @ B ) )
= ( ! [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
=> ( '\'const/sets/SUBSET\'' @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( '\'const/sets/SUBSET\'' @ skt1 @ sk1 @ ( '\'const/sets/INTERS\'' @ skt1 @ sk2 ) )
!= ( ! [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
=> ( '\'const/sets/SUBSET\'' @ skt1 @ sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( '\'const/sets/SUBSET\'' @ skt1 @ sk1 @ ( '\'const/sets/INTERS\'' @ skt1 @ sk2 ) )
!= ( ! [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
=> ( '\'const/sets/SUBSET\'' @ skt1 @ sk1 @ A ) ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(13,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(lifteq,[status(thm)],[11]) ).
thf(5,axiom,
! [TA: $tType,A: ( TA > $o ) > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/INTERS\'' @ TA @ A ) )
= ( ! [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_INTERS_') ).
thf(16,plain,
! [TA: $tType,A: ( TA > $o ) > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/INTERS\'' @ TA @ A ) )
= ( ! [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_') ).
thf(19,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(488,plain,
$false,
inference(e,[status(thm)],[10,9,13,12,7,16,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEV463^1 : TPTP v8.2.0. Released v7.0.0.
% 0.04/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 21 18:27:10 EDT 2024
% 0.13/0.35 % CPUTime :
% 1.07/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/1.07 % [INFO] Parsing done (114ms).
% 1.32/1.08 % [INFO] Running in sequential loop mode.
% 1.74/1.31 % [INFO] eprover registered as external prover.
% 1.74/1.31 % [INFO] Scanning for conjecture ...
% 2.01/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.01/1.39 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.01/1.41 % [INFO] Problem is higher-order (TPTP THF).
% 2.01/1.41 % [INFO] Type checking passed.
% 2.01/1.41 % [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 ...
% 8.50/2.90 % External prover 'e' found a proof!
% 8.50/2.90 % [INFO] Killing All external provers ...
% 8.50/2.90 % Time passed: 2334ms (effective reasoning time: 1812ms)
% 8.50/2.90 % 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)>
% 8.50/2.90 % Axioms used in derivation (4): thm/trivia/I_THM_, thm/sets/IN_, thm/sets/IN_INTERS_, thm/sets/SUBSET_
% 8.50/2.90 % No. of inferences in proof: 16
% 8.50/2.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2334 ms resp. 1812 ms w/o parsing
% 8.50/2.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.50/2.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------