%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP167-1 : 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 : n007.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 07:20:17 AM UTC 2026
% Result : Unsatisfiable 9.85s 4.41s
% Output : Refutation 9.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 40 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 240 ( 2 ~; 0 |; 0 &; 238 @)
% ( 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; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 ^; 82 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_decl,type,
a: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(positive_part_decl,type,
positive_part: $i > $i ).
thf(negative_part_decl,type,
negative_part: $i > $i ).
thf(greatest_lower_bound_decl,type,
greatest_lower_bound: $i > $i > $i ).
thf(least_upper_bound_decl,type,
least_upper_bound: $i > $i > $i ).
thf(identity_decl,type,
identity: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(18,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(56,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)],[18]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ negative_part )
= ( identity @ ( A @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_2) ).
thf(52,plain,
! [A: $i] :
( ( A @ negative_part )
= ( identity @ ( A @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,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(46,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)],[13]) ).
thf(20,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(60,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)],[20]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ positive_part )
= ( identity @ ( A @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_1) ).
thf(44,plain,
! [A: $i] :
( ( A @ positive_part )
= ( identity @ ( A @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(54,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(48,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,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(50,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)],[15]) ).
thf(19,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(58,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)],[19]) ).
thf(11,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(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= ( C @ ( A @ greatest_lower_bound ) @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_4) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= ( C @ ( A @ greatest_lower_bound ) @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( a
!= ( a @ negative_part @ ( a @ positive_part @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
thf(21,plain,
( a
!= ( a @ negative_part @ ( a @ positive_part @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,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(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,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(38,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)],[9]) ).
thf(6,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(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,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(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,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(40,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)],[10]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= ( C @ ( A @ least_upper_bound ) @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_3) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= ( C @ ( A @ least_upper_bound ) @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(30,plain,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(285,plain,
$false,
inference(e,[status(thm)],[56,52,46,60,44,54,48,50,58,42,24,21,28,38,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP167-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.23/0.47 % Computer : n007.cluster.edu
% 0.23/0.47 % Model : x86_64 x86_64
% 0.23/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.47 % Memory : 8046.5625MB
% 0.23/0.47 % OS : Linux 6.8.0-71-generic
% 0.23/0.47 % CPULimit : 300
% 0.23/0.47 % WCLimit : 300
% 0.23/0.47 % DateTime : Fri Sep 25 14:30:54 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 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
% 1.25/1.29 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.82/1.51 % [INFO] Parsing done (214ms).
% 1.82/1.53 % [INFO] Running in sequential loop mode.
% 2.84/2.08 % [INFO] eprover registered as external prover.
% 2.84/2.09 % [INFO] Scanning for conjecture ...
% 3.10/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 3.10/2.30 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 3.28/2.34 % [INFO] Problem is propositional (TPTP CNF).
% 3.28/2.35 % [INFO] Type checking passed.
% 3.28/2.36 % [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 ...
% 9.85/4.40 % External prover 'e' found a proof!
% 9.85/4.40 % [INFO] Killing All external provers ...
% 9.85/4.40 % Time passed: 3724ms (effective reasoning time: 2872ms)
% 9.85/4.41 % Axioms used in derivation (19): associativity, monotony_lub1, idempotence_of_lub, monotony_glb1, left_inverse, lat4_4, monotony_glb2, glb_absorbtion, lat4_1, idempotence_of_gld, associativity_of_glb, symmetry_of_lub, monotony_lub2, left_identity, lat4_3, symmetry_of_glb, lat4_2, associativity_of_lub, lub_absorbtion
% 9.85/4.41 % No. of inferences in proof: 41
% 9.85/4.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3724 ms resp. 2872 ms w/o parsing
% 9.85/4.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.85/4.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------