%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU469^1 : 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 : n011.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 08:28:15 AM UTC 2026
% Result : Theorem 5.19s 2.48s
% Output : Refutation 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 29 ( 10 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 95 ( 2 ~; 4 |; 11 &; 65 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 42 ( 11 ^; 31 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(subrel_decl,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(refl_decl,type,
refl: ( $i > $i > $o ) > $o ).
thf(rc_decl,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(trans_decl,type,
trans: ( $i > $i > $o ) > $o ).
thf(tc_decl,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(trc_decl,type,
trc: ( $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(refl_def,definition,
( refl
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(rc_def,definition,
( rc
= ( ^ [A: $i > $i > $o,B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) ) ) ).
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(trc_def,definition,
( trc
= ( ^ [A: $i > $i > $o] : ( rc @ ( tc @ A ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( trans @ ( trc @ A ) )
& ( refl @ ( trc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_closure_is_transitive_reflexive) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( trans @ ( trc @ A ) )
& ( refl @ ( trc @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i,C: $i,D: $i] :
( ( ( ( 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 @ B @ C ) ) )
& ( ( 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 @ C @ D ) ) ) )
=> ( ( B = 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(45,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU469^1 : 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
% 0.09/0.23 % Computer : n011.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 13:42:31 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 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
% 1.17/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.78/1.14 % [INFO] Parsing done (214ms).
% 1.78/1.15 % [INFO] Running in sequential loop mode.
% 2.24/1.40 % [INFO] eprover registered as external prover.
% 2.49/1.40 % [INFO] Scanning for conjecture ...
% 2.80/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.80/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.80/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.80/1.57 % [INFO] Type checking passed.
% 2.80/1.58 % [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 ...
% 5.19/2.48 % External prover 'e' found a proof!
% 5.19/2.48 % [INFO] Killing All external provers ...
% 5.19/2.48 % Time passed: 2036ms (effective reasoning time: 1324ms)
% 5.19/2.48 % 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)>
% 5.19/2.48 % Axioms used in derivation (0):
% 5.19/2.48 % No. of inferences in proof: 4
% 5.19/2.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2036 ms resp. 1324 ms w/o parsing
% 5.47/2.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.47/2.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------