%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET601^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:22:59 AM UTC 2026
% Result : Theorem 5.69s 2.64s
% Output : Refutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 5 def)
% Number of atoms : 88 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 7 avg)
% Number of connectives : 208 ( 8 ~; 36 |; 36 &; 128 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 33 ( 18 ^; 12 !; 0 ?; 33 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(intersection_decl,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i > $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(union_def,definition,
( union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(intersection_def,definition,
( intersection
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ! [B: $i > $o,C: $i > $o] :
( ( ^ [D: $i] :
( ( ( A @ D )
& ( B @ D ) )
| ( ( B @ D )
& ( C @ D ) )
| ( ( C @ D )
& ( A @ D ) ) ) )
= ( ^ [D: $i] :
( ( ( A @ D )
| ( B @ D ) )
& ( ( B @ D )
| ( C @ D ) )
& ( ( C @ D )
| ( A @ D ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
~ ! [B: $i > $o] :
( ( ^ [C: $i] :
( ( ( sk1 @ C )
& ( A @ C ) )
| ( ( A @ C )
& ( B @ C ) )
| ( ( B @ C )
& ( sk1 @ C ) ) ) )
= ( ^ [C: $i] :
( ( ( sk1 @ C )
| ( A @ C ) )
& ( ( A @ C )
| ( B @ C ) )
& ( ( B @ C )
| ( sk1 @ C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $o] :
( ( ^ [B: $i] :
( ( ( sk1 @ B )
& ( sk2 @ B ) )
| ( ( sk2 @ B )
& ( A @ B ) )
| ( ( A @ B )
& ( sk1 @ B ) ) ) )
!= ( ^ [B: $i] :
( ( ( sk1 @ B )
| ( sk2 @ B ) )
& ( ( sk2 @ B )
| ( A @ B ) )
& ( ( A @ B )
| ( sk1 @ B ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( union @ ( intersection @ A @ B ) @ ( union @ ( intersection @ B @ C ) @ ( intersection @ C @ A ) ) )
= ( intersection @ ( union @ A @ B ) @ ( intersection @ ( union @ B @ C ) @ ( union @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( union @ ( intersection @ A @ B ) @ ( union @ ( intersection @ B @ C ) @ ( intersection @ C @ A ) ) )
= ( intersection @ ( union @ A @ B ) @ ( intersection @ ( union @ B @ C ) @ ( union @ C @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( ^ [D: $i] :
( ( ( A @ D )
& ( B @ D ) )
| ( ( B @ D )
& ( C @ D ) )
| ( ( C @ D )
& ( A @ D ) ) ) )
= ( ^ [D: $i] :
( ( ( A @ D )
| ( B @ D ) )
& ( ( B @ D )
| ( C @ D ) )
& ( ( C @ D )
| ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i] :
( ( ( sk1 @ A )
& ( sk2 @ A ) )
| ( ( sk2 @ A )
& ( sk3 @ A ) )
| ( ( sk3 @ A )
& ( sk1 @ A ) ) ) )
!= ( ^ [A: $i] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ( ( sk2 @ A )
| ( sk3 @ A ) )
& ( ( sk3 @ A )
| ( sk1 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ( ( sk2 @ A )
| ( sk3 @ A ) )
& ( ( sk3 @ A )
| ( sk1 @ A ) ) ) )
!= ( ^ [A: $i] :
( ( ( sk1 @ A )
& ( sk2 @ A ) )
| ( ( sk2 @ A )
& ( sk3 @ A ) )
| ( ( sk3 @ A )
& ( sk1 @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk3 @ sk4 )
| ( sk1 @ sk4 ) ) )
!= ( ( ( sk1 @ sk4 )
& ( sk2 @ sk4 ) )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ( sk1 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(73,plain,
$false,
inference(e,[status(thm)],[3,5,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET601^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n026.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 13:40:57 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.02/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.50/1.04 % [INFO] Parsing done (214ms).
% 1.50/1.05 % [INFO] Running in sequential loop mode.
% 2.18/1.46 % [INFO] eprover registered as external prover.
% 2.18/1.47 % [INFO] Scanning for conjecture ...
% 2.60/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.60/1.63 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.60/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.60/1.64 % [INFO] Type checking passed.
% 2.60/1.64 % [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 ...
% 5.69/2.63 % External prover 'e' found a proof!
% 5.69/2.64 % [INFO] Killing All external provers ...
% 5.69/2.64 % Time passed: 2259ms (effective reasoning time: 1575ms)
% 5.69/2.64 % 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)>
% 5.69/2.64 % Axioms used in derivation (0):
% 5.69/2.64 % No. of inferences in proof: 7
% 5.69/2.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2259 ms resp. 1575 ms w/o parsing
% 5.69/2.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.69/2.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------