%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT038-1 : TPTP v9.3.1. Released v2.4.0.
% 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 07:46:31 AM UTC 2026
% Result : Unsatisfiable 10.66s 4.05s
% Output : Refutation 10.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 210 ( 2 ~; 0 |; 0 &; 208 @)
% ( 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 : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $i > $i > $i ).
thf(aa_decl,type,
aa: $i ).
thf(dd_decl,type,
dd: $i ).
thf(cc_decl,type,
cc: $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(join_decl,type,
join: $i > $i > $i ).
thf(bb_decl,type,
bb: $i ).
thf(n0_decl,type,
n0: $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
( ( dd @ ( bb @ ( aa @ join ) @ f ) )
= ( dd @ ( bb @ ( cc @ join ) @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs1) ).
thf(41,plain,
( ( dd @ ( bb @ ( aa @ join ) @ f ) )
= ( dd @ ( bb @ ( cc @ join ) @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( n0 @ f ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_left_bottom) ).
thf(45,plain,
! [A: $i] :
( ( A @ ( n0 @ f ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ f ) )
= ( C @ ( B @ f ) @ ( C @ ( A @ f ) @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_left_join) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ join ) @ f ) )
= ( C @ ( B @ f ) @ ( C @ ( A @ f ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,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(39,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)],[11]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( dd @ ( aa @ f ) )
!= ( dd @ ( cc @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).
thf(18,plain,
( ( dd @ ( aa @ f ) )
!= ( dd @ ( cc @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ join ) @ ( A @ f ) )
= ( C @ ( A @ f ) @ ( B @ ( A @ f ) @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_right_join) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ join ) @ ( A @ f ) )
= ( C @ ( A @ f ) @ ( B @ ( A @ f ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $i] :
( ( n0 @ ( A @ f ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_right_bottom) ).
thf(51,plain,
! [A: $i] :
( ( n0 @ ( A @ f ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
( ( dd @ ( bb @ f ) @ ( dd @ ( aa @ f ) @ meet ) )
= ( dd @ ( bb @ f ) @ ( dd @ ( cc @ f ) @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs2) ).
thf(47,plain,
( ( dd @ ( bb @ f ) @ ( dd @ ( aa @ f ) @ meet ) )
= ( dd @ ( bb @ f ) @ ( dd @ ( cc @ f ) @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ join ) @ ( A @ meet ) )
= ( C @ ( A @ meet ) @ ( B @ ( A @ meet ) @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_meet) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ join ) @ ( A @ meet ) )
= ( C @ ( A @ meet ) @ ( B @ ( A @ meet ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ meet ) @ ( A @ join ) )
= ( C @ ( A @ join ) @ ( B @ ( A @ join ) @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_join) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ meet ) @ ( A @ join ) )
= ( C @ ( A @ join ) @ ( B @ ( A @ join ) @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,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(33,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)],[8]) ).
thf(1127,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT038-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % 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
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 19:58:38 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.18 % [INFO] Parsing done (195ms).
% 1.28/1.19 % [INFO] Running in sequential loop mode.
% 1.87/1.59 % [INFO] eprover registered as external prover.
% 2.07/1.60 % [INFO] Scanning for conjecture ...
% 2.07/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.26/1.76 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.26/1.78 % [INFO] Problem is propositional (TPTP CNF).
% 2.26/1.79 % [INFO] Type checking passed.
% 2.26/1.80 % [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 ...
% 10.66/4.04 % External prover 'e' found a proof!
% 10.66/4.04 % [INFO] Killing All external provers ...
% 10.66/4.04 % Time passed: 3510ms (effective reasoning time: 2847ms)
% 10.66/4.05 % Axioms used in derivation (16): f_on_right_bottom, commutativity_of_join, absorption1, lhs1, f_on_right_join, commutativity_of_meet, lhs2, associativity_of_join, idempotence_of_meet, dist_meet, dist_join, f_on_left_join, associativity_of_meet, f_on_left_bottom, idempotence_of_join, absorption2
% 10.66/4.05 % No. of inferences in proof: 35
% 10.66/4.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3510 ms resp. 2847 ms w/o parsing
% 10.66/4.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.66/4.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------