TSTP Solution File: SET171^3 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET171^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 03:02:00 EDT 2024
% Result : Theorem 3.01s 1.64s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 11 unt; 6 typ; 2 def)
% Number of atoms : 61 ( 9 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 114 ( 12 ~; 22 |; 13 &; 67 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 21 ( 12 ^ 9 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_type,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(union_def,definition,
( union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
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] :
( ( union @ A @ ( intersection @ B @ C ) )
= ( intersection @ ( union @ A @ B ) @ ( union @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_distributes_over_intersection) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( union @ A @ ( intersection @ B @ C ) )
= ( intersection @ ( union @ A @ B ) @ ( union @ A @ 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 ) )
& ( ( A @ 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 ) )
& ( ( sk1 @ A )
| ( sk3 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ( ( sk1 @ A )
| ( sk3 @ A ) ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ A )
| ( ( sk2 @ A )
& ( sk3 @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk3 @ sk4 ) ) )
!= ( ( sk1 @ sk4 )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(7,plain,
( ~ ( ( ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ~ ( ( sk1 @ sk4 )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(9,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(19,plain,
~ ( sk1 @ sk4 ),
inference(simp,[status(thm)],[9]) ).
thf(30,plain,
( ( ( $false
| ( sk2 @ sk4 ) )
& ( $false
| ( sk3 @ sk4 ) ) )
!= ( $false
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[6,19]) ).
thf(31,plain,
$false,
inference(simp,[status(thm)],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET171^3 : TPTP v8.2.0. Released v3.6.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 13:12:54 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.89/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/0.94 % [INFO] Parsing done (112ms).
% 1.26/0.95 % [INFO] Running in sequential loop mode.
% 1.61/1.15 % [INFO] eprover registered as external prover.
% 1.61/1.15 % [INFO] cvc4 registered as external prover.
% 1.61/1.15 % [INFO] Scanning for conjecture ...
% 1.94/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.97/1.24 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.97/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.97/1.24 % [INFO] Type checking passed.
% 1.97/1.24 % [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 ...
% 2.82/1.59 % [INFO] Killing All external provers ...
% 3.01/1.63 % Time passed: 1143ms (effective reasoning time: 681ms)
% 3.01/1.63 % 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)>
% 3.01/1.64 % Axioms used in derivation (0):
% 3.01/1.64 % No. of inferences in proof: 11
% 3.01/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1143 ms resp. 681 ms w/o parsing
% 3.01/1.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.01/1.66 % [INFO] Killing All external provers ...
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