%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET612^3 : 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 : n001.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 08:23:01 AM UTC 2026
% Result : Theorem 4.02s 2.33s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 16 unt; 0 typ; 6 def)
% Number of atoms : 121 ( 15 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 281 ( 63 ~; 37 |; 49 &; 132 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 36 ( 21 ^; 12 !; 0 ?; 36 :)
% ( 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(setminus_decl,type,
setminus: ( $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(setminus_def,definition,
( setminus
= ( ^ [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 )
| ( C @ D ) ) ) )
= ( ^ [D: $i] :
( ( A @ D )
& ~ ( B @ D )
& ( A @ D )
& ~ ( C @ D ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
~ ! [B: $i > $o] :
( ( ^ [C: $i] :
( ( sk1 @ C )
& ~ ( ( A @ C )
| ( B @ C ) ) ) )
= ( ^ [C: $i] :
( ( sk1 @ C )
& ~ ( A @ C )
& ( sk1 @ C )
& ~ ( B @ C ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $o] :
( ( ^ [B: $i] :
( ( sk1 @ B )
& ~ ( ( sk2 @ B )
| ( A @ B ) ) ) )
!= ( ^ [B: $i] :
( ( sk1 @ B )
& ~ ( sk2 @ B )
& ( sk1 @ B )
& ~ ( A @ B ) ) ) ) ) ) ).
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/sandbox2/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 )
| ~ ( sk1 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ 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(13,plain,
( ( ( sk1 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk3 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(18,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(20,plain,
sk1 @ sk4,
inference(simp,[status(thm)],[18]) ).
thf(16,plain,
( ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(21,plain,
~ ( sk3 @ sk4 ),
inference(simp,[status(thm)],[16]) ).
thf(15,plain,
( ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(22,plain,
~ ( sk2 @ sk4 ),
inference(simp,[status(thm)],[15]) ).
thf(27,plain,
( ~ $true
| $false
| $false ),
inference(rewrite,[status(thm)],[12,20,21,22]) ).
thf(28,plain,
$false,
inference(simp,[status(thm)],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET612^3 : 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
% 0.10/0.21 % Computer : n001.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:45:05 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.98/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.07 % [INFO] Parsing done (206ms).
% 1.35/1.08 % [INFO] Running in sequential loop mode.
% 1.99/1.47 % [INFO] eprover registered as external prover.
% 1.99/1.48 % [INFO] Scanning for conjecture ...
% 2.40/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.40/1.64 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.40/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.40/1.64 % [INFO] Type checking passed.
% 2.40/1.65 % [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 ...
% 4.02/2.32 % [INFO] Killing All external provers ...
% 4.02/2.33 % Time passed: 1953ms (effective reasoning time: 1235ms)
% 4.02/2.33 % 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)>
% 4.02/2.33 % Axioms used in derivation (0):
% 4.02/2.33 % No. of inferences in proof: 19
% 4.02/2.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1953 ms resp. 1235 ms w/o parsing
% 4.02/2.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.02/2.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------