%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET684^3 : 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 : n020.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 08:23:07 AM UTC 2026
% Result : Theorem 3.04s 1.85s
% Output : Refutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 8 ( 3 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 25 ( 2 ~; 0 |; 3 &; 20 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 1 usr; 2 con; 0-4 aty)
% Number of variables : 15 ( 4 ^; 8 !; 3 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(rel_composition_decl,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(rel_composition_def,definition,
( rel_composition
= ( ^ [A: $i > $i > $o,B: $i > $i > $o,C: $i,D: $i] :
? [E: $i] :
( ( A @ C @ E )
& ( B @ E @ D ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o,B: $i > $i > $o,C: $i,D: $i] :
( ( rel_composition @ A @ B @ C @ D )
= ( ? [E: $i] :
( ( A @ C @ E )
& ( B @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o,B: $i > $i > $o,C: $i,D: $i] :
( ( rel_composition @ A @ B @ C @ D )
= ( ? [E: $i] :
( ( A @ C @ E )
& ( B @ E @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
$false,
inference(simp,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET684^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % 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
% 0.11/0.21 % Computer : n020.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 13:41:34 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.57/1.06 % [INFO] Parsing done (260ms).
% 1.57/1.07 % [INFO] Running in sequential loop mode.
% 2.21/1.47 % [INFO] eprover registered as external prover.
% 2.21/1.48 % [INFO] Scanning for conjecture ...
% 2.68/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.68/1.69 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.68/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.68/1.69 % [INFO] Type checking passed.
% 2.88/1.70 % [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 ...
% 3.04/1.85 % [INFO] Killing All external provers ...
% 3.04/1.85 % Time passed: 1490ms (effective reasoning time: 769ms)
% 3.04/1.85 % 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)>
% 3.04/1.85 % Axioms used in derivation (0):
% 3.04/1.85 % No. of inferences in proof: 4
% 3.04/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1490 ms resp. 769 ms w/o parsing
% 3.30/1.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.30/1.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------