%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n011.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 07:20:16 AM UTC 2026
% Result : Unsatisfiable 4.07s 2.42s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 200 ( 2 ~; 0 |; 0 &; 198 @)
% ( 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 : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(least_upper_bound_decl,type,
least_upper_bound: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(greatest_lower_bound_decl,type,
greatest_lower_bound: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(identity_decl,type,
identity: $i ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ least_upper_bound ) )
= ( C @ ( B @ ( A @ least_upper_bound ) @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ least_upper_bound ) )
= ( C @ ( B @ ( A @ least_upper_bound ) @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(48,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ greatest_lower_bound ) )
= ( C @ ( B @ ( A @ greatest_lower_bound ) @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ greatest_lower_bound ) )
= ( C @ ( B @ ( A @ greatest_lower_bound ) @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(38,plain,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ least_upper_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ least_upper_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
( ( identity @ ( a @ least_upper_bound ) )
= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat3a_1) ).
thf(34,plain,
( ( identity @ ( a @ least_upper_bound ) )
= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
( ( identity @ ( b @ least_upper_bound ) )
= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat3a_2) ).
thf(44,plain,
( ( identity @ ( b @ least_upper_bound ) )
= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ greatest_lower_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ greatest_lower_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( a @ ( b @ multiply ) @ ( a @ least_upper_bound ) )
!= ( a @ ( b @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat3a) ).
thf(19,plain,
( ( a @ ( b @ multiply ) @ ( a @ least_upper_bound ) )
!= ( a @ ( b @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(62,plain,
$false,
inference(e,[status(thm)],[52,46,54,48,50,42,24,28,38,32,34,22,44,40,26,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.14/0.40 % Computer : n011.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 14:33:14 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.19 % [INFO] Parsing done (202ms).
% 1.42/1.21 % [INFO] Running in sequential loop mode.
% 2.19/1.62 % [INFO] eprover registered as external prover.
% 2.19/1.63 % [INFO] Scanning for conjecture ...
% 2.40/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 2.40/1.78 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.57/1.80 % [INFO] Problem is propositional (TPTP CNF).
% 2.57/1.81 % [INFO] Type checking passed.
% 2.57/1.82 % [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 ...
% 4.07/2.41 % External prover 'e' found a proof!
% 4.07/2.41 % [INFO] Killing All external provers ...
% 4.07/2.41 % Time passed: 1862ms (effective reasoning time: 1195ms)
% 4.07/2.41 % Axioms used in derivation (17): monotony_lub1, idempotence_of_lub, monotony_glb1, left_inverse, symmetry_of_glb, monotony_glb2, glb_absorbtion, associativity_of_glb, symmetry_of_lub, lat3a_1, associativity, monotony_lub2, left_identity, associativity_of_lub, lub_absorbtion, lat3a_2, idempotence_of_gld
% 4.07/2.41 % No. of inferences in proof: 37
% 4.07/2.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1862 ms resp. 1195 ms w/o parsing
% 4.07/2.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.07/2.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------