%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT005-4 : TPTP v9.3.1. Released v1.1.0.
% 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 : n004.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 07:46:27 AM UTC 2026
% Result : Unsatisfiable 18.53s 4.16s
% Output : Refutation 18.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 42 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 166 ( 4 ~; 2 |; 0 &; 160 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 ^; 46 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_decl,type,
join: $i > $i > $i ).
thf(r2_decl,type,
r2: $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n0_decl,type,
n0: $i ).
thf(r1_decl,type,
r1: $i ).
thf(b2_decl,type,
b2: $i ).
thf(a2_decl,type,
a2: $i ).
thf(18,axiom,
! [A: $i] :
( ( n1 @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).
thf(56,plain,
! [A: $i] :
( ( n1 @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [A: $i] :
( ( n0 @ ( A @ meet ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).
thf(52,plain,
! [A: $i] :
( ( n0 @ ( A @ meet ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ join ) @ ( B @ meet ) )
= ( B @ ( C @ meet ) @ ( A @ join ) ) )
| ( ( B @ ( A @ meet ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ join ) @ ( B @ meet ) )
= ( B @ ( C @ meet ) @ ( A @ join ) ) )
| ( ( B @ ( A @ meet ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [A: $i] :
( ( n0 @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
thf(54,plain,
! [A: $i] :
( ( n0 @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ meet ) @ meet ) )
= ( C @ ( B @ meet ) @ ( A @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(48,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)],[14]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ join ) )
= ( C @ ( B @ join ) @ ( A @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
thf(50,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)],[15]) ).
thf(19,axiom,
! [A: $i] :
( ( n1 @ ( A @ join ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_1) ).
thf(58,plain,
! [A: $i] :
( ( n1 @ ( A @ join ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,negated_conjecture,
( ( b @ ( a @ meet ) @ ( r2 @ meet ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_complement_meet_a_b_2) ).
thf(24,plain,
( ( b @ ( a @ meet ) @ ( r2 @ meet ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,negated_conjecture,
( ( b2 @ ( a2 @ meet ) )
!= r1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_SAMs_lemma) ).
thf(25,plain,
( ( b2 @ ( a2 @ meet ) )
!= r1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(38,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,negated_conjecture,
( ( r2 @ ( a @ meet ) @ ( r1 @ join ) )
= b2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',define_b2) ).
thf(21,plain,
( ( r2 @ ( a @ meet ) @ ( r1 @ join ) )
= b2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
( ( b @ ( a @ meet ) @ ( r2 @ join ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_complement_meet_a_b_1) ).
thf(22,plain,
( ( b @ ( a @ meet ) @ ( r2 @ join ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,negated_conjecture,
( ( b @ ( a @ join ) @ ( r1 @ meet ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1_complement_join_a_b_2) ).
thf(27,plain,
( ( b @ ( a @ join ) @ ( r1 @ meet ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,negated_conjecture,
( ( b @ ( a @ join ) @ ( r1 @ join ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1_complement_join_a_b_1) ).
thf(26,plain,
( ( b @ ( a @ join ) @ ( r1 @ join ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,negated_conjecture,
( ( r2 @ ( b @ meet ) @ ( r1 @ join ) )
= a2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',define_a2) ).
thf(23,plain,
( ( r2 @ ( b @ meet ) @ ( r1 @ join ) )
= a2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3074,plain,
$false,
inference(e,[status(thm)],[56,52,46,60,54,48,50,58,36,42,24,25,38,21,22,44,27,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT005-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n004.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 19:55:06 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.68/0.73 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.92/0.84 % [INFO] Parsing done (110ms).
% 0.92/0.85 % [INFO] Running in sequential loop mode.
% 1.47/1.06 % [INFO] eprover registered as external prover.
% 1.47/1.06 % [INFO] Scanning for conjecture ...
% 1.47/1.11 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 1.75/1.13 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.75/1.14 % [INFO] Problem is propositional (TPTP CNF).
% 1.75/1.15 % [INFO] Type checking passed.
% 1.75/1.15 % [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 ...
% 18.53/4.15 % External prover 'e' found a proof!
% 18.53/4.15 % [INFO] Killing All external provers ...
% 18.53/4.16 % Time passed: 3648ms (effective reasoning time: 3304ms)
% 18.53/4.16 % Axioms used in derivation (13): commutativity_of_join, associativity_of_meet, commutativity_of_meet, x_join_0, x_meet_1, associativity_of_join, idempotence_of_meet, x_meet_0, absorption1, x_join_1, modular, idempotence_of_join, absorption2
% 18.53/4.16 % No. of inferences in proof: 41
% 18.53/4.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3648 ms resp. 3304 ms w/o parsing
% 18.53/4.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.53/4.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------