TSTP Solution File: SEV476^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV476^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 04:10:37 EDT 2024
% Result : Theorem 3.72s 1.87s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 22 ( 4 unt; 7 typ; 0 def)
% Number of atoms : 50 ( 3 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 101 ( 10 ~; 3 |; 2 &; 81 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 27 ( 0 ^ 24 !; 0 ?; 27 :)
% ( 3 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/SUBSET\'_type',type,
'\'const/sets/SUBSET\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf('\'const/sets/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('\'const/sets/DIFF\'_type',type,
'\'const/sets/DIFF\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(sk2_type,type,
sk2: skt1 > $o ).
thf(sk3_type,type,
sk3: skt1 ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ A )
=> ( '\'const/sets/FINITE\'' @ TA @ ( '\'const/sets/DIFF\'' @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_DIFF_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ A )
=> ( '\'const/sets/FINITE\'' @ TA @ ( '\'const/sets/DIFF\'' @ TA @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ A )
=> ( '\'const/sets/FINITE\'' @ TA @ ( '\'const/sets/DIFF\'' @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(10,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(7,plain,
'\'const/sets/FINITE\'' @ skt1 @ sk1,
inference(cnf,[status(esa)],[5]) ).
thf(6,plain,
~ ( '\'const/sets/FINITE\'' @ skt1 @ ( '\'const/sets/DIFF\'' @ skt1 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(12,plain,
( ( '\'const/sets/FINITE\'' @ skt1 @ ( '\'const/sets/DIFF\'' @ skt1 @ sk1 @ sk2 ) )
!= ( '\'const/sets/FINITE\'' @ skt1 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[7,6]) ).
thf(13,plain,
( ( '\'const/sets/DIFF\'' @ skt1 @ sk1 @ sk2 )
!= sk1 ),
inference(simp,[status(thm)],[12]) ).
thf(14,plain,
( ( '\'const/sets/DIFF\'' @ skt1 @ sk1 @ sk2 @ sk3 )
!= ( sk1 @ sk3 ) ),
inference(func_ext,[status(esa)],[13]) ).
thf(11,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ B )
| ~ ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
| ( '\'const/sets/FINITE\'' @ TA @ A ) ),
inference(cnf,[status(esa)],[10]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( '\'const/sets/SUBSET\'' @ TA @ ( '\'const/sets/DIFF\'' @ TA @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_DIFF_') ).
thf(8,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( '\'const/sets/SUBSET\'' @ TA @ ( '\'const/sets/DIFF\'' @ TA @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,plain,
( ~ ( '\'const/sets/DIFF\'' @ skt1 @ sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk3 ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[5,10,14,6,13,7,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV476^1 : TPTP v8.2.0. Released v7.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:50:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (99ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.64/1.17 % [INFO] eprover registered as external prover.
% 1.64/1.18 % [INFO] cvc4 registered as external prover.
% 1.64/1.18 % [INFO] Scanning for conjecture ...
% 1.74/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.85/1.25 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.85/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 1.85/1.26 % [INFO] Type checking passed.
% 1.85/1.26 % [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 ...
% 3.72/1.87 % External prover 'e' found a proof!
% 3.72/1.87 % [INFO] Killing All external provers ...
% 3.72/1.87 % Time passed: 1340ms (effective reasoning time: 893ms)
% 3.72/1.87 % 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)>
% 3.72/1.87 % Axioms used in derivation (2): thm/sets/FINITE_SUBSET_, thm/sets/SUBSET_DIFF_
% 3.72/1.87 % No. of inferences in proof: 15
% 3.72/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1340 ms resp. 893 ms w/o parsing
% 3.72/1.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.72/1.90 % [INFO] Killing All external provers ...
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