TSTP Solution File: SET612^3 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET612^3 : 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 03:06:28 EDT 2024
% Result : Theorem 2.66s 1.54s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 28 ( 13 unt; 7 typ; 3 def)
% Number of atoms : 80 ( 9 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 172 ( 37 ~; 22 |; 26 &; 87 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 24 ( 15 ^ 9 !; 0 ?; 24 :)
% 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(setminus_type,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(setminus_def,definition,
( setminus
= ( ^ [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] :
( ( setminus @ A @ ( union @ B @ C ) )
= ( intersection @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( setminus @ A @ ( union @ B @ C ) )
= ( intersection @ ( setminus @ A @ B ) @ ( setminus @ 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(7,plain,
( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 )
& ( sk1 @ sk4 )
& ~ ( sk3 @ sk4 ) )
!= ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(9,plain,
( ~ ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 )
& ( sk1 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ~ ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(11,plain,
( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(12,plain,
( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[11]) ).
thf(10,plain,
( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 )
& ( sk1 @ 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(17,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 ) ),
inference(cnf,[status(esa)],[10]) ).
thf(20,plain,
sk1 @ sk4,
inference(simp,[status(thm)],[17]) ).
thf(15,plain,
( ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[10]) ).
thf(21,plain,
~ ( sk3 @ sk4 ),
inference(simp,[status(thm)],[15]) ).
thf(26,plain,
( ~ $true
| $false
| $false ),
inference(rewrite,[status(thm)],[12,19,20,21]) ).
thf(27,plain,
$false,
inference(simp,[status(thm)],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET612^3 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.14 % 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 13:31:54 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.86/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.02/0.92 % [INFO] Parsing done (122ms).
% 1.02/0.93 % [INFO] Running in sequential loop mode.
% 1.67/1.14 % [INFO] nitpick registered as external prover.
% 1.67/1.15 % [INFO] Scanning for conjecture ...
% 1.76/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.93/1.24 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.93/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.93/1.25 % [INFO] Type checking passed.
% 1.93/1.25 % [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 ...
% 2.66/1.53 % [INFO] Killing All external provers ...
% 2.66/1.54 % Time passed: 1028ms (effective reasoning time: 602ms)
% 2.66/1.54 % 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)>
% 2.66/1.54 % Axioms used in derivation (0):
% 2.66/1.54 % No. of inferences in proof: 18
% 2.66/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1028 ms resp. 602 ms w/o parsing
% 2.74/1.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.74/1.57 % [INFO] Killing All external provers ...
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