TSTP Solution File: SEV472^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV472^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n029.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 15:59:07 EDT 2024
% Result : Theorem 3.63s 2.20s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 2 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 102 ( 2 ~; 0 |; 7 &; 88 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 35 ( 5 ^ 25 !; 5 ?; 35 :)
% 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/SETSPEC\'_type',type,
'\'const/sets/SETSPEC\'':
!>[TA: $tType] : ( TA > $o > TA > $o ) ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/GSPEC\'_type',type,
'\'const/sets/GSPEC\'':
!>[TA: $tType] : ( ( TA > $o ) > TA > $o ) ).
thf('\'const/sets/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( '\'const/sets/SUBSET\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [C: TA] :
? [D: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ C
@ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( B @ D ) )
@ D ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_RESTRICT_') ).
thf(14,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( '\'const/sets/SUBSET\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [C: TA] :
? [D: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ C
@ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( B @ D ) )
@ D ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ A )
=> ( '\'const/sets/FINITE\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [C: TA] :
? [D: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ C
@ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( B @ D ) )
@ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_RESTRICT_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ A )
=> ( '\'const/sets/FINITE\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [C: TA] :
? [D: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ C
@ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( B @ D ) )
@ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ A )
=> ( '\'const/sets/FINITE\'' @ TA
@ ( '\'const/sets/GSPEC\'' @ TA
@ ^ [C: TA] :
? [D: TA] :
( '\'const/sets/SETSPEC\'' @ TA @ C
@ ( ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( B @ D ) )
@ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(9,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
=> ( '\'const/sets/FINITE\'' @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(12,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
=> ( '\'const/sets/FINITE\'' @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,plain,
'\'const/sets/FINITE\'' @ skt1 @ sk1,
inference(cnf,[status(esa)],[6]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[14,6,9,12,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEV472^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.30 % Computer : n029.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Jun 21 19:14:40 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.89/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.03 % [INFO] Parsing done (134ms).
% 1.24/1.05 % [INFO] Running in sequential loop mode.
% 1.69/1.35 % [INFO] eprover registered as external prover.
% 1.69/1.35 % [INFO] Scanning for conjecture ...
% 1.81/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.98/1.45 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.98/1.46 % [INFO] Problem is higher-order (TPTP THF).
% 1.98/1.46 % [INFO] Type checking passed.
% 1.98/1.47 % [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 ...
% 3.63/2.20 % External prover 'e' found a proof!
% 3.63/2.20 % [INFO] Killing All external provers ...
% 3.63/2.20 % Time passed: 1733ms (effective reasoning time: 1147ms)
% 3.63/2.20 % 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)>
% 3.63/2.20 % Axioms used in derivation (3): thm/sets/SUBSET_RESTRICT_, thm/trivia/I_THM_, thm/sets/FINITE_SUBSET_
% 3.63/2.20 % No. of inferences in proof: 11
% 3.63/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1733 ms resp. 1147 ms w/o parsing
% 3.86/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.86/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------