TSTP Solution File: SEV444^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV444^1 : 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 15:59:02 EDT 2024
% Result : Theorem 4.83s 2.23s
% Output : Refutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 41 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 140 ( 20 ~; 12 |; 0 &; 108 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 36 ( 0 ^ 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
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 ).
thf(sk3_type,type,
sk3: skt1 ).
thf(sk7_type,type,
sk7: skt1 ).
thf(1,conjecture,
! [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/sandbox/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).
thf(2,negated_conjecture,
~ ! [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(neg_conjecture,[status(cth)],[1]) ).
thf(4,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)],[2]) ).
thf(5,plain,
( ( sk1 = sk2 )
!= ( ! [A: skt1] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 )
= ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( sk1 = sk2 )
!= ( ! [A: skt1] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 )
= ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(10,plain,
( ( sk1 != sk2 )
| ~ ! [A: skt1] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 )
= ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(12,plain,
( ( sk2 != sk1 )
| ~ ! [A: skt1] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 )
= ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(14,plain,
( ( ( '\'const/sets/IN\'' @ skt1 @ sk3 @ sk1 )
!= ( '\'const/sets/IN\'' @ skt1 @ sk3 @ sk2 ) )
| ( sk2 != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(15,plain,
( ( ( '\'const/sets/IN\'' @ skt1 @ sk3 @ sk2 )
!= ( '\'const/sets/IN\'' @ skt1 @ sk3 @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(55,plain,
( ( sk3 != sk3 )
| ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[15]) ).
thf(63,plain,
sk2 != sk1,
inference(simp,[status(thm)],[55]) ).
thf(65,plain,
( ( sk2 @ sk7 )
!= ( sk1 @ sk7 ) ),
inference(func_ext,[status(esa)],[63]) ).
thf(3,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(7,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(11,plain,
( ( sk1 = sk2 )
| ! [A: skt1] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 )
= ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(13,plain,
( ( sk2 = sk1 )
| ! [A: skt1] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 )
= ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(16,plain,
! [A: skt1] :
( ( ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 )
= ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 ) )
| ( sk2 = sk1 ) ),
inference(cnf,[status(esa)],[13]) ).
thf(17,plain,
! [A: skt1] :
( ( ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 )
= ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 ) )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(66,plain,
! [A: skt1] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 )
= ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 ) ),
inference(simplifyReflect,[status(thm)],[17,63]) ).
thf(87,plain,
( ~ ( sk2 @ sk7 )
| ~ ( sk1 @ sk7 ) ),
inference(bool_ext,[status(thm)],[65]) ).
thf(18,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(183,plain,
$false,
inference(e,[status(thm)],[65,9,7,66,87,4,63,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV444^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 21 19:02:25 EDT 2024
% 0.13/0.33 % CPUTime :
% 1.06/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/1.05 % [INFO] Parsing done (115ms).
% 1.34/1.06 % [INFO] Running in sequential loop mode.
% 1.64/1.26 % [INFO] eprover registered as external prover.
% 1.64/1.26 % [INFO] Scanning for conjecture ...
% 1.75/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.75/1.33 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.94/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 1.94/1.34 % [INFO] Type checking passed.
% 1.94/1.34 % [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 ...
% 4.83/2.23 % External prover 'e' found a proof!
% 4.83/2.23 % [INFO] Killing All external provers ...
% 4.83/2.23 % Time passed: 1685ms (effective reasoning time: 1173ms)
% 4.83/2.23 % 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)>
% 4.83/2.23 % Axioms used in derivation (1): thm/sets/IN_
% 4.83/2.23 % No. of inferences in proof: 24
% 4.83/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1685 ms resp. 1173 ms w/o parsing
% 5.24/2.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.24/2.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------