%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET606^3 : 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 : n014.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 4.37s 2.43s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 13 unt; 0 typ; 4 def)
% Number of atoms : 65 ( 13 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 134 ( 31 ~; 8 |; 29 &; 66 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 25 ( 16 ^; 7 !; 0 ?; 25 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
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 ).
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] :
( ( A @ C )
& ~ ( ( A @ C )
& ( B @ C ) ) ) )
= ( ^ [C: $i] :
( ( A @ C )
& ~ ( B @ C ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
( ( ^ [B: $i] :
( ( sk1 @ B )
& ~ ( ( sk1 @ B )
& ( A @ B ) ) ) )
!= ( ^ [B: $i] :
( ( sk1 @ B )
& ~ ( A @ B ) ) ) ) ) ) ).
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(40,plain,
( ( ( sk1 @ sk3 )
& ~ ( ( sk1 @ sk3 )
& ( sk2 @ sk3 ) ) )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(53,plain,
( ( ( sk1 @ sk3 )
| ( sk1 @ sk3 ) )
& ( ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 ) )
& ( ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ( sk1 @ sk3 ) )
& ( ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk3 )
| ~ ( sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(54,plain,
( ( sk1 @ sk3 )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(58,plain,
sk1 @ sk3,
inference(simp,[status(thm)],[54]) ).
thf(67,plain,
( ( $true
& ~ ( $true
& ( sk2 @ sk3 ) ) )
!= ( $true
& ~ ( sk2 @ sk3 ) ) ),
inference(rewrite,[status(thm)],[7,58]) ).
thf(68,plain,
$false,
inference(simp,[status(thm)],[67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET606^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n014.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:38:45 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.02 % [INFO] Parsing done (216ms).
% 1.53/1.03 % [INFO] Running in sequential loop mode.
% 2.10/1.45 % [INFO] eprover registered as external prover.
% 2.10/1.46 % [INFO] Scanning for conjecture ...
% 2.31/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.53/1.62 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.53/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.53/1.62 % [INFO] Type checking passed.
% 2.53/1.63 % [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 ...
% 4.37/2.42 % [INFO] Killing All external provers ...
% 4.37/2.43 % Time passed: 2056ms (effective reasoning time: 1385ms)
% 4.37/2.43 % 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)>
% 4.37/2.43 % Axioms used in derivation (0):
% 4.37/2.43 % No. of inferences in proof: 12
% 4.37/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2056 ms resp. 1385 ms w/o parsing
% 4.37/2.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.37/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------