%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT223-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n020.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 07:46:46 AM UTC 2026
% Result : Unsatisfiable 48.07s 10.73s
% Output : Refutation 48.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 30 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 174 ( 2 ~; 0 |; 0 &; 172 @)
% ( 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; 5 con; 0-4 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_decl,type,
join: $i > $i > $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(b_decl,type,
b: $i ).
thf(a_decl,type,
a: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(zero_decl,type,
zero: $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) )
= ( A @ ( B @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ complement @ ( zero @ ( B @ ( A @ meet ) @ ifeq ) ) ) @ ( one @ ( B @ ( A @ join ) @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_join_complement) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ complement @ ( zero @ ( B @ ( A @ meet ) @ ifeq ) ) ) @ ( one @ ( B @ ( A @ join ) @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
( ( a @ ( b @ meet ) )
= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
thf(45,plain,
( ( a @ ( b @ meet ) )
= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ meet ) @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ complement @ ( A @ meet ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
thf(39,plain,
! [A: $i] :
( ( A @ complement @ ( A @ meet ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,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(35,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)],[10]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ meet ) @ ( B @ join ) @ ( A @ meet ) )
= ( B @ ( A @ join ) @ ( C @ meet ) @ ( B @ ( A @ meet ) @ join ) @ ( A @ meet ) @ ( B @ join ) @ ( A @ meet ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H7) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ meet ) @ ( B @ join ) @ ( A @ meet ) )
= ( B @ ( A @ join ) @ ( C @ meet ) @ ( B @ ( A @ meet ) @ join ) @ ( A @ meet ) @ ( B @ join ) @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(23,plain,
! [A: $i] :
( ( A @ ( A @ join ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ complement @ ( A @ join ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_join) ).
thf(37,plain,
! [A: $i] :
( ( A @ complement @ ( A @ join ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( A @ meet ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,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(33,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)],[9]) ).
thf(1,negated_conjecture,
( ( a @ complement @ ( b @ complement @ join ) )
!= ( a @ complement ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
thf(16,plain,
( ( a @ complement @ ( b @ complement @ join ) )
!= ( a @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7412,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,39,35,43,23,19,37,25,21,33,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT223-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.10 % 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
% 0.22/0.48 % Computer : n020.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Fri Sep 25 20:18:03 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.45/1.32 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/1.58 % [INFO] Parsing done (253ms).
% 1.81/1.60 % [INFO] Running in sequential loop mode.
% 2.93/2.20 % [INFO] eprover registered as external prover.
% 2.93/2.21 % [INFO] Scanning for conjecture ...
% 3.10/2.34 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 3.10/2.39 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 3.25/2.42 % [INFO] Problem is propositional (TPTP CNF).
% 3.25/2.43 % [INFO] Type checking passed.
% 3.25/2.44 % [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 ...
% 48.07/10.72 % External prover 'e' found a proof!
% 48.07/10.73 % [INFO] Killing All external provers ...
% 48.07/10.73 % Time passed: 10039ms (effective reasoning time: 9123ms)
% 48.07/10.73 % Axioms used in derivation (14): absorption1, meet_join_complement, complement_meet, commutativity_of_meet, associativity_of_join, idempotence_of_meet, equation_H7, prove_distributivity_hypothesis, ifeq_axiom, commutativity_of_join, associativity_of_meet, complement_join, idempotence_of_join, absorption2
% 48.07/10.73 % No. of inferences in proof: 31
% 48.07/10.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10039 ms resp. 9123 ms w/o parsing
% 48.07/10.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.07/10.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------