TSTP Solution File: SET606^3 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SET606^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 7 08:07:35 EDT 2024
% Result : Theorem 3.61s 1.86s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 11 unt; 5 typ; 2 def)
% Number of atoms : 46 ( 9 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 87 ( 19 ~; 2 |; 20 &; 46 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 12 ^ 6 !; 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(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 ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $o] :
( ( setminus @ A @ ( intersection @ A @ B ) )
= ( setminus @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o] :
( ( setminus @ A @ ( intersection @ A @ B ) )
= ( setminus @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $o] :
( ( ^ [C: $i] :
( ( A @ C )
& ~ ( ( A @ C )
& ( B @ C ) ) ) )
= ( ^ [C: $i] :
( ( A @ C )
& ~ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( ( sk1 @ A )
& ( sk2 @ A ) ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( ( sk1 @ A )
& ( sk2 @ A ) ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk1 @ sk3 )
& ~ ( ( sk1 @ sk3 )
& ( sk2 @ sk3 ) ) )
!= ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(37,plain,
( ( ( sk1 @ sk3 )
& ~ ( ( sk1 @ sk3 )
& ( sk2 @ sk3 ) ) )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(49,plain,
( ( sk1 @ sk3 )
| ( sk1 @ sk3 ) ),
inference(cnf,[status(esa)],[37]) ).
thf(52,plain,
sk1 @ sk3,
inference(simp,[status(thm)],[49]) ).
thf(58,plain,
( ( $true
& ~ ( $true
& ( sk2 @ sk3 ) ) )
!= ( $true
& ~ ( sk2 @ sk3 ) ) ),
inference(rewrite,[status(thm)],[7,52]) ).
thf(59,plain,
$false,
inference(simp,[status(thm)],[58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET606^3 : TPTP v8.1.2. Released v3.6.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n025.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 6 13:16:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.86/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.95 % [INFO] Parsing done (138ms).
% 1.16/0.96 % [INFO] Running in sequential loop mode.
% 1.59/1.19 % [INFO] eprover registered as external prover.
% 1.59/1.19 % [INFO] cvc4 registered as external prover.
% 1.59/1.19 % [INFO] Scanning for conjecture ...
% 1.80/1.27 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 1.93/1.29 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.93/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.93/1.29 % [INFO] Type checking passed.
% 1.93/1.30 % [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 ...
% 3.61/1.85 % [INFO] Killing All external provers ...
% 3.61/1.85 % Time passed: 1350ms (effective reasoning time: 889ms)
% 3.61/1.85 % 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)>
% 3.61/1.86 % Axioms used in derivation (0):
% 3.61/1.86 % No. of inferences in proof: 11
% 3.61/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1350 ms resp. 889 ms w/o parsing
% 3.61/1.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.61/1.88 % [INFO] Killing All external provers ...
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