%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT035-1 : TPTP v9.3.1. Released v2.4.0.
% 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 : 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 07:46:31 AM UTC 2026
% Result : Unsatisfiable 5.50s 3.48s
% Output : Refutation 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 44 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 190 ( 6 ~; 4 |; 0 &; 180 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $i > $i ).
thf(k_decl,type,
k: $i > $i ).
thf(join_decl,type,
join: $i > $i > $i ).
thf(aa_decl,type,
aa: $i ).
thf(bb_decl,type,
bb: $i ).
thf(n0_decl,type,
n0: $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(n1_decl,type,
n1: $i ).
thf(20,axiom,
( ( n1 @ k )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_on_top) ).
thf(61,plain,
( ( n1 @ k )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,axiom,
( ( n0 @ k )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_on_bottom) ).
thf(53,plain,
( ( n0 @ k )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,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(48,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)],[14]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ join ) @ ( B @ meet ) )
= ( B @ ( C @ meet ) @ ( A @ join ) ) )
| ( ( B @ ( A @ meet ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular) ).
thf(50,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)],[15]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ f )
= ( B @ f @ ( A @ f @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_meet) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ f )
= ( B @ f @ ( A @ f @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i] :
( ( n0 @ ( A @ meet ) )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_meet_0) ).
thf(46,plain,
! [A: $i] :
( ( n0 @ ( A @ meet ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i] :
( ( n0 @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_join_0) ).
thf(57,plain,
! [A: $i] :
( ( n0 @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,negated_conjecture,
( ( ( n0 @ k @ f )
!= n0 )
| ( ( bb @ ( aa @ join ) @ k @ f )
!= ( bb @ k @ f @ ( aa @ k @ f @ join ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comp_join_hemimorphism) ).
thf(21,plain,
( ( ( n0 @ k @ f )
!= n0 )
| ( ( bb @ ( aa @ join ) @ k @ f )
!= ( bb @ k @ f @ ( aa @ k @ f @ join ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ k )
= ( B @ k @ ( A @ k @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_on_meet) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ k )
= ( B @ k @ ( A @ k @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
( ( n1 @ ( A @ join ) )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_join_1) ).
thf(32,plain,
! [A: $i] :
( ( n1 @ ( A @ join ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ k )
= ( B @ k @ ( A @ k @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_on_join) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ k )
= ( B @ k @ ( A @ k @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i] :
( ( n1 @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_meet_1) ).
thf(26,plain,
! [A: $i] :
( ( n1 @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
( ( n1 @ f )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_top) ).
thf(55,plain,
( ( n1 @ f )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,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(30,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)],[5]) ).
thf(67,plain,
$false,
inference(e,[status(thm)],[61,53,48,50,42,24,46,57,21,28,38,32,34,44,59,40,26,55,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT035-1 : TPTP v9.3.1. Released v2.4.0.
% 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
% 0.23/0.49 % Computer : n004.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Fri Sep 25 19:58:21 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 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
% 1.39/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.87/1.63 % [INFO] Parsing done (281ms).
% 1.87/1.65 % [INFO] Running in sequential loop mode.
% 2.85/2.27 % [INFO] eprover registered as external prover.
% 2.85/2.28 % [INFO] Scanning for conjecture ...
% 3.21/2.42 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 3.39/2.51 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 3.39/2.55 % [INFO] Problem is propositional (TPTP CNF).
% 3.39/2.56 % [INFO] Type checking passed.
% 3.39/2.57 % [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 ...
% 5.50/3.47 % External prover 'e' found a proof!
% 5.50/3.47 % [INFO] Killing All external provers ...
% 5.50/3.47 % Time passed: 2762ms (effective reasoning time: 1808ms)
% 5.50/3.47 % Axioms used in derivation (19): f_on_top, commutativity_of_join, associativity_of_meet, k_on_top, commutativity_of_meet, k_on_meet, x_meet_1, associativity_of_join, idempotence_of_meet, x_meet_0, absorption1, x_join_1, modular, f_on_meet, k_on_join, idempotence_of_join, absorption2, k_on_bottom, x_join_0
% 5.50/3.47 % No. of inferences in proof: 41
% 5.50/3.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2762 ms resp. 1808 ms w/o parsing
% 5.82/3.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.82/3.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------