TSTP Solution File: SEV461^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV461^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n032.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 15:59:05 EDT 2024
% Result : Theorem 3.12s 1.73s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 29 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 111 ( 7 ~; 0 |; 2 &; 97 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 47 ( 0 ^ 45 !; 2 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/trivia/I\'_type',type,
'\'const/trivia/I\'':
!>[TA: $tType] : ( TA > TA ) ).
thf('\'const/sets/UNIONS\'_type',type,
'\'const/sets/UNIONS\'':
!>[TA: $tType] : ( ( ( TA > $o ) > $o ) > TA > $o ) ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/EMPTY\'_type',type,
'\'const/sets/EMPTY\'':
!>[TA: $tType] : ( TA > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: ( skt1 > $o ) > $o ).
thf(1,conjecture,
! [TA: $tType,A: ( TA > $o ) > $o] :
( ( ( '\'const/sets/UNIONS\'' @ TA @ A )
= ( '\'const/sets/EMPTY\'' @ TA ) )
= ( ! [B: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ B @ A )
=> ( B
= ( '\'const/sets/EMPTY\'' @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EMPTY_UNIONS_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: ( TA > $o ) > $o] :
( ( ( '\'const/sets/UNIONS\'' @ TA @ A )
= ( '\'const/sets/EMPTY\'' @ TA ) )
= ( ! [B: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ B @ A )
=> ( B
= ( '\'const/sets/EMPTY\'' @ TA ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [TA: $tType,A: ( TA > $o ) > $o] :
( ( ( '\'const/sets/UNIONS\'' @ TA @ A )
= ( '\'const/sets/EMPTY\'' @ TA ) )
= ( ! [B: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ B @ A )
=> ( B
= ( '\'const/sets/EMPTY\'' @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk1 )
= ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( ! [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk1 )
=> ( A
= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
( ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk1 )
= ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( ! [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk1 )
=> ( A
= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(4,axiom,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_') ).
thf(14,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/trivia/I_THM_') ).
thf(11,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(lifteq,[status(thm)],[12]) ).
thf(7,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).
thf(22,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(16,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [TA: $tType,A: ( TA > $o ) > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
= ( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNIONS_') ).
thf(19,plain,
! [TA: $tType,A: ( TA > $o ) > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ 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)],[6]) ).
thf(15,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(cnf,[status(esa)],[14]) ).
thf(50,plain,
$false,
inference(e,[status(thm)],[10,14,13,22,16,11,8,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SEV461^1 : TPTP v8.2.0. Released v7.0.0.
% 0.06/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Fri Jun 21 18:36:40 EDT 2024
% 0.10/0.29 % CPUTime :
% 0.71/0.75 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.02/0.86 % [INFO] Parsing done (104ms).
% 1.02/0.87 % [INFO] Running in sequential loop mode.
% 1.43/1.06 % [INFO] eprover registered as external prover.
% 1.43/1.07 % [INFO] Scanning for conjecture ...
% 1.58/1.12 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.58/1.15 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.66/1.16 % [INFO] Problem is higher-order (TPTP THF).
% 1.66/1.16 % [INFO] Type checking passed.
% 1.66/1.16 % [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 ...
% 3.12/1.73 % External prover 'e' found a proof!
% 3.12/1.73 % [INFO] Killing All external provers ...
% 3.12/1.73 % Time passed: 1302ms (effective reasoning time: 865ms)
% 3.12/1.73 % 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)>
% 3.12/1.73 % Axioms used in derivation (5): thm/sets/NOT_IN_EMPTY_, thm/sets/IN_UNIONS_, thm/sets/EXTENSION_, thm/trivia/I_THM_, thm/sets/IN_
% 3.12/1.73 % No. of inferences in proof: 19
% 3.12/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1302 ms resp. 865 ms w/o parsing
% 3.39/1.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------