%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU461^1 : 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 : n016.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 08:28:14 AM UTC 2026
% Result : Theorem 4.34s 1.94s
% Output : Refutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 13 ( 3 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 79 ( 2 ~; 0 |; 9 &; 55 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-3 aty)
% Number of variables : 36 ( 6 ^; 30 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(subrel_decl,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(trans_decl,type,
trans: ( $i > $i > $o ) > $o ).
thf(tc_decl,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(subrel_def,definition,
( subrel
= ( ^ [A: $i > $i > $o,B: $i > $i > $o] :
! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( B @ C @ D ) ) ) ) ).
thf(trans_def,definition,
( trans
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(tc_def,definition,
( tc
= ( ^ [A: $i > $i > $o,B: $i,C: $i] :
! [D: $i > $i > $o] :
( ( ( trans @ D )
& ( subrel @ A @ D ) )
=> ( D @ B @ C ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] : ( trans @ ( tc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure_is_transitive) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] : ( trans @ ( tc @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i,C: $i,D: $i] :
( ( ! [E: $i > $i > $o] :
( ( ! [F: $i,G: $i,H: $i] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) )
& ! [F: $i,G: $i] :
( ( A @ F @ G )
=> ( E @ F @ G ) ) )
=> ( E @ B @ C ) )
& ! [E: $i > $i > $o] :
( ( ! [F: $i,G: $i,H: $i] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) )
& ! [F: $i,G: $i] :
( ( A @ F @ G )
=> ( E @ F @ G ) ) )
=> ( E @ C @ D ) ) )
=> ! [E: $i > $i > $o] :
( ( ! [F: $i,G: $i,H: $i] :
( ( ( E @ F @ G )
& ( E @ G @ H ) )
=> ( E @ F @ H ) )
& ! [F: $i,G: $i] :
( ( A @ F @ G )
=> ( E @ F @ G ) ) )
=> ( E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU461^1 : 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 : n016.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 13:46:49 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
% 0.64/0.51 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.06/0.65 % [INFO] Parsing done (135ms).
% 1.06/0.65 % [INFO] Running in sequential loop mode.
% 1.70/1.05 % [INFO] eprover registered as external prover.
% 2.00/1.06 % [INFO] Scanning for conjecture ...
% 2.60/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.60/1.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.60/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.60/1.35 % [INFO] Type checking passed.
% 2.60/1.35 % [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 ...
% 4.34/1.93 % External prover 'e' found a proof!
% 4.34/1.93 % [INFO] Killing All external provers ...
% 4.34/1.93 % Time passed: 1638ms (effective reasoning time: 1274ms)
% 4.34/1.93 % 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)>
% 4.34/1.93 % Axioms used in derivation (0):
% 4.34/1.93 % No. of inferences in proof: 4
% 4.34/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1638 ms resp. 1274 ms w/o parsing
% 4.34/1.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.34/1.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------