%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET609^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 08:23:00 AM UTC 2026
% Result : Theorem 3.32s 1.63s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 18 unt; 0 typ; 6 def)
% Number of atoms : 133 ( 18 equ; 0 cnn)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 297 ( 65 ~; 42 |; 51 &; 139 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 @ ( setminus @ B @ C ) )
= ( union @ ( setminus @ A @ B ) @ ( intersection @ 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 @ ( setminus @ B @ C ) )
= ( union @ ( setminus @ A @ B ) @ ( intersection @ 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 )
& ~ ( sk3 @ A ) ) ) )
!= ( ^ [A: $i] :
( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
| ( ( sk1 @ A )
& ( sk3 @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) ) )
!= ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ( sk1 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(8,plain,
( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ( sk1 @ sk4 )
& ( sk3 @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(16,plain,
( ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(19,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(31,plain,
sk1 @ sk4,
inference(simp,[status(thm)],[19]) ).
thf(32,plain,
( ( $true
& ~ ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) ) )
!= ( ( $true
& ~ ( sk2 @ sk4 ) )
| ( $true
& ( sk3 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[6,31]) ).
thf(33,plain,
( ( ~ ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) ) )
!= ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(34,plain,
( ~ ~ ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ~ ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[33]) ).
thf(36,plain,
( ( ( sk2 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(39,plain,
( ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(cnfConj,[status(thm)],[36]) ).
thf(41,plain,
~ ( sk3 @ sk4 ),
inference(simp,[status(thm)],[39]) ).
thf(44,plain,
( ( ~ ( ( sk2 @ sk4 )
& ~ $false ) )
!= ( ~ ( sk2 @ sk4 )
| $false ) ),
inference(rewrite,[status(thm)],[33,41]) ).
thf(45,plain,
$false,
inference(simp,[status(thm)],[44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET609^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:34:22 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.69/0.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.89/0.61 % [INFO] Parsing done (113ms).
% 1.10/0.63 % [INFO] Running in sequential loop mode.
% 1.44/0.84 % [INFO] eprover registered as external prover.
% 1.44/0.84 % [INFO] Scanning for conjecture ...
% 1.72/0.90 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.72/0.94 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.72/0.94 % [INFO] Problem is higher-order (TPTP THF).
% 1.72/0.94 % [INFO] Type checking passed.
% 1.72/0.95 % [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 ...
% 3.32/1.62 % [INFO] Killing All external provers ...
% 3.32/1.63 % Time passed: 1346ms (effective reasoning time: 989ms)
% 3.32/1.63 % 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)>
% 3.32/1.63 % Axioms used in derivation (0):
% 3.32/1.63 % No. of inferences in proof: 18
% 3.32/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1346 ms resp. 989 ms w/o parsing
% 3.61/1.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.61/1.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------