%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET624^3 : 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 : 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 08:23:03 AM UTC 2026
% Result : Theorem 3.75s 2.21s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 6 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 16 ( 5 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 38 ( 2 ~; 5 |; 4 &; 27 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 18 ( 5 ^; 9 !; 4 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(meets_decl,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(union_def,definition,
( union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(meets_def,definition,
( meets
= ( ^ [A: $i > $o,B: $i > $o] :
? [C: $i] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( meets @ A @ ( union @ B @ C ) )
= ( ( meets @ A @ B )
| ( meets @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( meets @ A @ ( union @ B @ C ) )
= ( ( meets @ A @ B )
| ( meets @ 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 ) )
| ? [D: $i] :
( ( A @ D )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % 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
% 0.12/0.22 % Computer : n017.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 13:35:07 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 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
% 1.02/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.50/1.03 % [INFO] Parsing done (220ms).
% 1.50/1.05 % [INFO] Running in sequential loop mode.
% 2.05/1.45 % [INFO] eprover registered as external prover.
% 2.05/1.46 % [INFO] Scanning for conjecture ...
% 2.26/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.44/1.62 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.44/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.44/1.62 % [INFO] Type checking passed.
% 2.44/1.63 % [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 ...
% 3.75/2.21 % External prover 'e' found a proof!
% 3.75/2.21 % [INFO] Killing All external provers ...
% 3.75/2.21 % Time passed: 1840ms (effective reasoning time: 1157ms)
% 3.75/2.21 % 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)>
% 3.75/2.21 % Axioms used in derivation (0):
% 3.75/2.21 % No. of inferences in proof: 4
% 3.75/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1840 ms resp. 1157 ms w/o parsing
% 3.75/2.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.75/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------