TSTP Solution File: SET615^3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET615^3 : 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 10:50:07 EDT 2024
% Result : Theorem 2.49s 1.51s
% Output : Refutation 2.49s
% 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 : 131 ( 29 ~; 16 |; 19 &; 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(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 @ ( union @ A @ B ) @ C )
= ( union @ ( setminus @ A @ C ) @ ( setminus @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( setminus @ ( union @ A @ B ) @ C )
= ( union @ ( setminus @ A @ C ) @ ( setminus @ 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 )
& ~ ( C @ 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 )
& ~ ( sk3 @ 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 )
& ~ ( sk3 @ A ) )
| ( ( sk2 @ A )
& ~ ( sk3 @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ~ ( sk3 @ sk4 ) )
!= ( ( ( sk1 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(8,plain,
( ( ( ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ~ ( sk3 @ sk4 ) )
| ( ( sk1 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(19,plain,
( ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(28,plain,
~ ( sk3 @ sk4 ),
inference(simp,[status(thm)],[19]) ).
thf(30,plain,
( ( ( ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ~ $false )
!= ( ( ( sk1 @ sk4 )
& ~ $false )
| ( ( sk2 @ sk4 )
& ~ $false ) ) ),
inference(rewrite,[status(thm)],[6,28]) ).
thf(31,plain,
$false,
inference(simp,[status(thm)],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET615^3 : TPTP v8.1.2. Released v3.6.0.
% 0.06/0.14 % 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 20:46:54 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.92/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (125ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.70/1.17 % [INFO] nitpick registered as external prover.
% 1.70/1.17 % [INFO] Scanning for conjecture ...
% 1.91/1.24 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 1.91/1.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.91/1.26 % [INFO] Problem is higher-order (TPTP THF).
% 1.91/1.26 % [INFO] Type checking passed.
% 1.91/1.26 % [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 ...
% 2.49/1.50 % [INFO] Killing All external provers ...
% 2.49/1.51 % Time passed: 996ms (effective reasoning time: 535ms)
% 2.49/1.51 % 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)>
% 2.49/1.51 % Axioms used in derivation (0):
% 2.49/1.51 % No. of inferences in proof: 11
% 2.49/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 996 ms resp. 535 ms w/o parsing
% 2.49/1.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.49/1.53 % [INFO] Killing All external provers ...
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