%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT034-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 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 : Sun Sep 27 07:46:31 AM UTC 2026
% Result : Unsatisfiable 3.16s 17.25s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 70 ( 2 ~; 0 |; 0 &; 68 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(xx_decl,type,
xx: $i ).
thf(join_decl,type,
join: $i > $i > $i ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( xx @ ( xx @ meet ) )
!= xx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(8,plain,
( ( xx @ ( xx @ meet ) )
!= xx ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
$false,
inference(e,[status(thm)],[21,13,17,11,8,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT034-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 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
% 0.15/15.43 % Computer : n006.cluster.edu
% 0.15/15.43 % Model : x86_64 x86_64
% 0.15/15.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.43 % Memory : 8046.5625MB
% 0.15/15.43 % OS : Linux 6.8.0-71-generic
% 0.15/15.43 % CPULimit : 300
% 0.15/15.43 % WCLimit : 300
% 0.15/15.43 % DateTime : Fri Sep 25 19:58:26 UTC 2026
% 0.15/15.43 % CPUTime :
% 0.15/15.43 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
% 0.19/16.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/16.20 % [INFO] Parsing done (180ms).
% 1.38/16.21 % [INFO] Running in sequential loop mode.
% 1.98/16.62 % [INFO] eprover registered as external prover.
% 1.98/16.62 % [INFO] Scanning for conjecture ...
% 2.16/16.71 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.16/16.74 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.16/16.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.16/16.76 % [INFO] Type checking passed.
% 2.16/16.76 % [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 ...
% 3.16/17.24 % External prover 'e' found a proof!
% 3.16/17.24 % [INFO] Killing All external provers ...
% 3.16/17.24 % Time passed: 1671ms (effective reasoning time: 1024ms)
% 3.16/17.25 % Axioms used in derivation (6): commutativity_of_join, absorption1, associativity_of_meet, absorption2, commutativity_of_meet, associativity_of_join
% 3.16/17.25 % No. of inferences in proof: 15
% 3.16/17.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1671 ms resp. 1024 ms w/o parsing
% 3.16/17.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.16/17.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------