TSTP Solution File: SET143^3 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET143^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 03:05:31 EDT 2024
% Result : Theorem 2.73s 1.62s
% Output : Refutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 17 ( 10 unt; 5 typ; 1 def)
% Number of atoms : 51 ( 8 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 88 ( 6 ~; 2 |; 25 &; 55 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 9 ^ 9 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_type,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(intersection_def,definition,
( intersection
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $o ).
thf(sk2_type,type,
sk2: $i > $o ).
thf(sk3_type,type,
sk3: $i > $o ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( ^ [D: $i] :
( ( A @ D )
& ( B @ D )
& ( C @ D ) ) )
= ( ^ [D: $i] :
( ( A @ D )
& ( B @ D )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A )
& ( sk3 @ A ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A )
& ( sk3 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A )
& ( sk3 @ A ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A )
& ( sk3 @ A ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) )
!= ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(10,plain,
( ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(14,plain,
( ( sk2 @ sk4 )
| ( sk2 @ sk4 ) ),
inference(cnf,[status(esa)],[10]) ).
thf(19,plain,
sk2 @ sk4,
inference(simp,[status(thm)],[14]) ).
thf(22,plain,
( ( ( sk1 @ sk4 )
& $true
& ( sk3 @ sk4 ) )
!= ( ( sk1 @ sk4 )
& $true
& ( sk3 @ sk4 ) ) ),
inference(rewrite,[status(thm)],[7,19]) ).
thf(23,plain,
$false,
inference(simp,[status(thm)],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET143^3 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n027.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 12:27:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.01 % [INFO] Parsing done (131ms).
% 1.34/1.02 % [INFO] Running in sequential loop mode.
% 1.79/1.24 % [INFO] nitpick registered as external prover.
% 1.79/1.25 % [INFO] Scanning for conjecture ...
% 2.12/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.12/1.34 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.12/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.12/1.34 % [INFO] Type checking passed.
% 2.23/1.35 % [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 ...
% 2.73/1.61 % [INFO] Killing All external provers ...
% 2.73/1.62 % Time passed: 1083ms (effective reasoning time: 597ms)
% 2.73/1.62 % 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)>
% 2.73/1.62 % Axioms used in derivation (0):
% 2.73/1.62 % No. of inferences in proof: 11
% 2.73/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1083 ms resp. 597 ms w/o parsing
% 2.92/1.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.92/1.65 % [INFO] Killing All external provers ...
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