%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT021-1 : 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 : n001.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 07:46:29 AM UTC 2026
% Result : Unsatisfiable 5.87s 3.51s
% Output : Refutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 154 ( 2 ~; 0 |; 0 &; 152 @)
% ( 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 : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% 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(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(24,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(2,axiom,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(14,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quasi_lattice2) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(22,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(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( b @ ( a @ meet ) @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
thf(11,plain,
( ( c @ ( b @ join ) @ ( a @ meet ) )
!= ( c @ ( a @ meet ) @ ( b @ ( a @ meet ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( C @ ( B @ join ) @ ( A @ meet ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quasi_lattice1) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( C @ ( B @ join ) @ ( A @ meet ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ meet ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ join ) )
= ( C @ ( B @ meet ) @ ( A @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bowden) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ meet ) @ ( C @ ( B @ meet ) @ ( A @ join ) @ join ) )
= ( C @ ( B @ meet ) @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(54,plain,
$false,
inference(e,[status(thm)],[24,14,20,28,22,18,16,11,26,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT021-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.24/0.51 % Computer : n001.cluster.edu
% 0.24/0.51 % Model : x86_64 x86_64
% 0.24/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.51 % Memory : 8046.5625MB
% 0.24/0.51 % OS : Linux 6.8.0-71-generic
% 0.24/0.51 % CPULimit : 300
% 0.24/0.51 % WCLimit : 300
% 0.24/0.51 % DateTime : Fri Sep 25 20:03:11 UTC 2026
% 0.24/0.51 % CPUTime :
% 0.24/0.51 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
% 1.41/1.36 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.89/1.63 % [INFO] Parsing done (264ms).
% 1.89/1.65 % [INFO] Running in sequential loop mode.
% 2.90/2.26 % [INFO] eprover registered as external prover.
% 2.90/2.27 % [INFO] Scanning for conjecture ...
% 3.10/2.40 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.25/2.44 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.25/2.47 % [INFO] Problem is propositional (TPTP CNF).
% 3.25/2.48 % [INFO] Type checking passed.
% 3.25/2.48 % [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 ...
% 5.87/3.50 % External prover 'e' found a proof!
% 5.87/3.50 % [INFO] Killing All external provers ...
% 5.87/3.50 % Time passed: 2779ms (effective reasoning time: 1839ms)
% 5.87/3.50 % Axioms used in derivation (9): quasi_lattice1, commutativity_of_join, bowden, associativity_of_meet, quasi_lattice2, idempotence_of_join, commutativity_of_meet, associativity_of_join, idempotence_of_meet
% 5.87/3.50 % No. of inferences in proof: 21
% 5.87/3.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2779 ms resp. 1839 ms w/o parsing
% 5.87/3.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.87/3.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------