%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP167-2 : 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 : n003.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 5.34s 2.95s
% Output : Refutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 47 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 46 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 260 ( 2 ~; 0 |; 0 &; 258 @)
% ( 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 : 88 ( 0 ^; 88 !; 0 ?; 88 :)
% 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(least_upper_bound_decl,type,
least_upper_bound: $i > $i > $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(23,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(69,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)],[23]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ inverse )
= ( A @ inverse @ ( B @ inverse @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_3) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ inverse )
= ( A @ inverse @ ( B @ inverse @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
( ( identity @ inverse )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_1) ).
thf(33,plain,
( ( identity @ inverse )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,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(65,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)],[21]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ positive_part )
= ( identity @ ( A @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_4) ).
thf(53,plain,
! [A: $i] :
( ( A @ positive_part )
= ( identity @ ( A @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,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(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,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(45,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)],[11]) ).
thf(13,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(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,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(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,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_7) ).
thf(35,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)],[6]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(63,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,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(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(55,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,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(51,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)],[14]) ).
thf(12,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(47,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)],[12]) ).
thf(1,negated_conjecture,
( a
!= ( a @ negative_part @ ( a @ positive_part @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
thf(24,plain,
( a
!= ( a @ negative_part @ ( a @ positive_part @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,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(57,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)],[17]) ).
thf(3,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_6) ).
thf(29,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)],[3]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ negative_part )
= ( identity @ ( A @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_5) ).
thf(59,plain,
! [A: $i] :
( ( A @ negative_part )
= ( identity @ ( A @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,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(67,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)],[22]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ inverse @ inverse )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_2) ).
thf(31,plain,
! [A: $i] :
( ( A @ inverse @ inverse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(169,plain,
$false,
inference(e,[status(thm)],[69,61,33,65,53,41,45,49,39,35,63,43,55,51,47,24,37,57,29,59,27,67,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % 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
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 14:34:38 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 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
% 0.89/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.16 % [INFO] Parsing done (206ms).
% 1.31/1.17 % [INFO] Running in sequential loop mode.
% 1.99/1.58 % [INFO] eprover registered as external prover.
% 1.99/1.59 % [INFO] Scanning for conjecture ...
% 2.21/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 2.39/1.73 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.39/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.39/1.77 % [INFO] Type checking passed.
% 2.39/1.78 % [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 ...
% 5.34/2.94 % External prover 'e' found a proof!
% 5.34/2.94 % [INFO] Killing All external provers ...
% 5.34/2.94 % Time passed: 2429ms (effective reasoning time: 1765ms)
% 5.34/2.95 % Axioms used in derivation (22): associativity, monotony_lub1, lat4_5, idempotence_of_lub, monotony_glb1, left_inverse, lat4_4, glb_absorbtion, lat4_1, idempotence_of_gld, associativity_of_glb, symmetry_of_lub, lat4_6, monotony_lub2, left_identity, lat4_3, symmetry_of_glb, lat4_2, lat4_7, monotony_glb2, associativity_of_lub, lub_absorbtion
% 5.34/2.95 % No. of inferences in proof: 47
% 5.34/2.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2429 ms resp. 1765 ms w/o parsing
% 5.34/3.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.34/3.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------