%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL862^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 : n006.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 08:14:15 AM UTC 2026
% Result : Theorem 3.94s 2.29s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 22 ( 7 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 69 ( 2 ~; 0 |; 13 &; 48 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 26 ( 4 ^; 22 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mreflexive_decl,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(msymmetric_decl,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(mtransitive_decl,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(meuclidean_decl,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(msymmetric_def,definition,
( msymmetric
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) ) ) ) ).
thf(mtransitive_def,definition,
( mtransitive
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(meuclidean_def,definition,
( meuclidean
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( ( mreflexive @ A )
& ( meuclidean @ A ) )
= ( ( mreflexive @ A )
& ( mtransitive @ A )
& ( msymmetric @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( ( mreflexive @ A )
& ( meuclidean @ A ) )
= ( ( mreflexive @ A )
& ( mtransitive @ A )
& ( msymmetric @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ( ! [B: $i] : ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ B @ D ) )
=> ( A @ C @ D ) ) )
= ( ! [B: $i] : ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL862^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 : n006.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 10:12:39 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
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/1.03 % [INFO] Parsing done (241ms).
% 1.59/1.04 % [INFO] Running in sequential loop mode.
% 2.17/1.43 % [INFO] eprover registered as external prover.
% 2.17/1.44 % [INFO] Scanning for conjecture ...
% 2.58/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.58/1.63 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.58/1.63 % [INFO] Problem is higher-order (TPTP THF).
% 2.58/1.64 % [INFO] Type checking passed.
% 2.58/1.64 % [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 ...
% 3.94/2.28 % External prover 'e' found a proof!
% 3.94/2.28 % [INFO] Killing All external provers ...
% 3.94/2.28 % Time passed: 1928ms (effective reasoning time: 1238ms)
% 3.94/2.28 % 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)>
% 3.94/2.29 % Axioms used in derivation (0):
% 3.94/2.29 % No. of inferences in proof: 4
% 3.94/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1928 ms resp. 1238 ms w/o parsing
% 4.15/2.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.15/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------