%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT010-1 : TPTP v9.3.1. Released v2.2.0.
% 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 : n018.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 07:46:28 AM UTC 2026
% Result : Unsatisfiable 53.77s 11.26s
% Output : Refutation 53.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 278 ( 2 ~; 0 |; 0 &; 276 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(join_decl,type,
join: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(d_decl,type,
d: $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,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(28,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)],[8]) ).
thf(1,negated_conjecture,
( ( d @ ( b @ join ) @ ( c @ ( b @ join ) @ meet ) @ ( a @ meet ) )
!= ( d @ ( a @ meet ) @ ( c @ ( a @ meet ) @ join ) @ ( d @ ( c @ meet ) @ ( b @ join ) @ ( a @ meet ) @ join ) @ ( d @ ( b @ join ) @ ( c @ ( b @ join ) @ meet ) @ ( a @ meet ) @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(13,plain,
( ( d @ ( b @ join ) @ ( c @ ( b @ join ) @ meet ) @ ( a @ meet ) )
!= ( d @ ( a @ meet ) @ ( c @ ( a @ meet ) @ join ) @ ( d @ ( c @ meet ) @ ( b @ join ) @ ( a @ meet ) @ join ) @ ( d @ ( b @ join ) @ ( c @ ( b @ join ) @ meet ) @ ( a @ meet ) @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(18,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ join ) @ ( C @ meet ) @ ( B @ join ) @ ( A @ meet ) )
= ( D @ ( C @ meet ) @ ( B @ ( A @ meet ) @ join ) @ ( A @ meet ) @ ( C @ ( A @ meet ) @ ( B @ join ) @ ( A @ meet ) @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n5_1) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ join ) @ ( C @ meet ) @ ( B @ join ) @ ( A @ meet ) )
= ( D @ ( C @ meet ) @ ( B @ ( A @ meet ) @ join ) @ ( A @ meet ) @ ( C @ ( A @ meet ) @ ( B @ join ) @ ( A @ meet ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ meet ) @ ( C @ join ) @ ( B @ meet ) @ ( A @ join ) )
= ( D @ ( C @ join ) @ ( B @ ( A @ join ) @ meet ) @ ( A @ join ) @ ( C @ ( A @ join ) @ ( B @ meet ) @ ( A @ join ) @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n5_2) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ meet ) @ ( C @ join ) @ ( B @ meet ) @ ( A @ join ) )
= ( D @ ( C @ join ) @ ( B @ ( A @ join ) @ meet ) @ ( A @ join ) @ ( C @ ( A @ join ) @ ( B @ meet ) @ ( A @ join ) @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( C @ join ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ meet ) )
= ( C @ ( B @ join ) @ ( A @ meet ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ ( C @ meet ) @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nr_3) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( C @ join ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ meet ) )
= ( C @ ( B @ join ) @ ( A @ meet ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ ( C @ meet ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,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(30,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)],[9]) ).
thf(17112,plain,
$false,
inference(e,[status(thm)],[24,20,28,13,22,18,16,26,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT010-1 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 19:58:20 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.58/0.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.80 % [INFO] Parsing done (99ms).
% 0.96/0.80 % [INFO] Running in sequential loop mode.
% 1.20/0.99 % [INFO] eprover registered as external prover.
% 1.20/1.00 % [INFO] Scanning for conjecture ...
% 1.50/1.04 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.50/1.06 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.50/1.07 % [INFO] Problem is propositional (TPTP CNF).
% 1.50/1.08 % [INFO] Type checking passed.
% 1.50/1.08 % [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 ...
% 53.77/11.25 % External prover 'e' found a proof!
% 53.77/11.25 % [INFO] Killing All external provers ...
% 53.77/11.25 % Time passed: 10764ms (effective reasoning time: 10448ms)
% 53.77/11.26 % Axioms used in derivation (11): nr_3, commutativity_of_join, absorption1, associativity_of_meet, commutativity_of_meet, n5_2, associativity_of_join, idempotence_of_meet, n5_1, idempotence_of_join, absorption2
% 53.77/11.26 % No. of inferences in proof: 25
% 53.77/11.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10764 ms resp. 10448 ms w/o parsing
% 53.77/11.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.77/11.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------