%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT005-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n008.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 07:46:27 AM UTC 2026
% Result : Unsatisfiable 36.19s 8.41s
% Output : Refutation 36.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 59 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 123 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 496 ( 66 ~; 64 |; 0 &; 366 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 14 usr; 13 con; 0-3 aty)
% Number of variables : 132 ( 0 ^; 132 !; 0 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_decl,type,
meet: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(join_decl,type,
join: $i > $i > $i > $o ).
thf(r2_decl,type,
r2: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n0_decl,type,
n0: $i ).
thf(e_decl,type,
e: $i ).
thf(c2_decl,type,
c2: $i ).
thf(r1_decl,type,
r1: $i ).
thf(d_decl,type,
d: $i ).
thf(a2_decl,type,
a2: $i ).
thf(b2_decl,type,
b2: $i ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ meet ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ meet ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(23,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ join ) ) )
| ~ ( F @ ( D @ ( A @ meet ) ) )
| ~ ( E @ ( C @ ( A @ meet ) ) )
| ~ ( D @ ( B @ ( C @ join ) ) )
| ~ ( B @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity3) ).
thf(61,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ join ) ) )
| ~ ( F @ ( D @ ( A @ meet ) ) )
| ~ ( E @ ( C @ ( A @ meet ) ) )
| ~ ( D @ ( B @ ( C @ join ) ) )
| ~ ( B @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(22,axiom,
! [A: $i] : ( n1 @ ( A @ ( n1 @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_1_and_x) ).
thf(60,plain,
! [A: $i] : ( n1 @ ( A @ ( n1 @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(25,axiom,
! [A: $i] : ( A @ ( A @ ( A @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_x_and_x) ).
thf(65,plain,
! [A: $i] : ( A @ ( A @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ meet ) ) )
| ~ ( F @ ( D @ ( C @ meet ) ) )
| ~ ( E @ ( D @ ( B @ meet ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet2) ).
thf(53,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ meet ) ) )
| ~ ( F @ ( D @ ( C @ meet ) ) )
| ~ ( E @ ( D @ ( B @ meet ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,negated_conjecture,
d @ ( a @ ( r2 @ meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_r2_and_a) ).
thf(39,plain,
d @ ( a @ ( r2 @ meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ meet ) ) )
| ~ ( F @ ( E @ ( A @ meet ) ) )
| ~ ( E @ ( D @ ( B @ meet ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet1) ).
thf(66,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ meet ) ) )
| ~ ( F @ ( E @ ( A @ meet ) ) )
| ~ ( E @ ( D @ ( B @ meet ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(2,negated_conjecture,
n1 @ ( r2 @ ( c @ join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_c_and_r2) ).
thf(35,plain,
n1 @ ( r2 @ ( c @ join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,negated_conjecture,
b2 @ ( d @ ( r1 @ join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_r1_and_d) ).
thf(31,plain,
b2 @ ( d @ ( r1 @ join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(27,axiom,
! [A: $i] : ( A @ ( A @ ( n1 @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_1_and_x) ).
thf(68,plain,
! [A: $i] : ( A @ ( A @ ( n1 @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(12,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ join ) ) )
| ~ ( F @ ( D @ ( B @ meet ) ) )
| ~ ( E @ ( B @ ( C @ meet ) ) )
| ~ ( D @ ( C @ ( A @ join ) ) )
| ~ ( A @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity1) ).
thf(42,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ join ) ) )
| ~ ( F @ ( D @ ( B @ meet ) ) )
| ~ ( E @ ( B @ ( C @ meet ) ) )
| ~ ( D @ ( C @ ( A @ join ) ) )
| ~ ( A @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,negated_conjecture,
n0 @ ( r2 @ ( c @ meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_c_and_r2) ).
thf(37,plain,
n0 @ ( r2 @ ( c @ meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ meet ) ) )
| ~ ( C @ ( B @ ( A @ join ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion2) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ meet ) ) )
| ~ ( C @ ( B @ ( A @ join ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( B @ meet ) ) )
| ~ ( F @ ( E @ ( A @ join ) ) )
| ~ ( E @ ( B @ ( C @ meet ) ) )
| ~ ( D @ ( C @ ( A @ join ) ) )
| ~ ( A @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity2) ).
thf(57,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( B @ meet ) ) )
| ~ ( F @ ( E @ ( A @ join ) ) )
| ~ ( E @ ( B @ ( C @ meet ) ) )
| ~ ( D @ ( C @ ( A @ join ) ) )
| ~ ( A @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,negated_conjecture,
~ ( r1 @ ( b2 @ ( a2 @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_a2_and_b2) ).
thf(38,plain,
~ ( r1 @ ( b2 @ ( a2 @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,negated_conjecture,
n1 @ ( r1 @ ( c2 @ join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_c2_and_r1) ).
thf(33,plain,
n1 @ ( r1 @ ( c2 @ join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
c @ ( b @ ( a @ meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_a_and_b) ).
thf(32,plain,
c @ ( b @ ( a @ meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,negated_conjecture,
a2 @ ( e @ ( r1 @ join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_r1_and_e) ).
thf(34,plain,
a2 @ ( e @ ( r1 @ join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ join ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion1) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ join ) ) )
| ~ ( C @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [A: $i] : ( n0 @ ( A @ ( n0 @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_0_and_x) ).
thf(59,plain,
! [A: $i] : ( n0 @ ( A @ ( n0 @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
! [A: $i] : ( A @ ( A @ ( A @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_x_and_x) ).
thf(71,plain,
! [A: $i] : ( A @ ( A @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ join ) ) )
| ~ ( F @ ( D @ ( C @ join ) ) )
| ~ ( E @ ( D @ ( B @ join ) ) )
| ~ ( C @ ( B @ ( A @ join ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join2) ).
thf(49,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ join ) ) )
| ~ ( F @ ( D @ ( C @ join ) ) )
| ~ ( E @ ( D @ ( B @ join ) ) )
| ~ ( C @ ( B @ ( A @ join ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(15,axiom,
! [A: $i] : ( A @ ( A @ ( n0 @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_0_and_x) ).
thf(48,plain,
! [A: $i] : ( A @ ( A @ ( n0 @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( A @ meet ) ) )
| ~ ( F @ ( E @ ( B @ join ) ) )
| ~ ( E @ ( C @ ( A @ meet ) ) )
| ~ ( D @ ( B @ ( C @ join ) ) )
| ~ ( B @ ( B @ ( A @ meet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity4) ).
thf(63,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( A @ meet ) ) )
| ~ ( F @ ( E @ ( B @ join ) ) )
| ~ ( E @ ( C @ ( A @ meet ) ) )
| ~ ( D @ ( B @ ( C @ join ) ) )
| ~ ( B @ ( B @ ( A @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,negated_conjecture,
e @ ( b @ ( r2 @ meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_r2_and_b) ).
thf(40,plain,
e @ ( b @ ( r2 @ meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ join ) ) )
| ~ ( F @ ( E @ ( A @ join ) ) )
| ~ ( E @ ( D @ ( B @ join ) ) )
| ~ ( C @ ( B @ ( A @ join ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join1) ).
thf(55,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ join ) ) )
| ~ ( F @ ( E @ ( A @ join ) ) )
| ~ ( E @ ( D @ ( B @ join ) ) )
| ~ ( C @ ( B @ ( A @ join ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,negated_conjecture,
n0 @ ( r1 @ ( c2 @ meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_c2_and_r1) ).
thf(36,plain,
n0 @ ( r1 @ ( c2 @ meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,negated_conjecture,
c2 @ ( b @ ( a @ join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_a_and_b) ).
thf(30,plain,
c2 @ ( b @ ( a @ join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ join ) ) )
| ~ ( C @ ( B @ ( A @ join ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ join ) ) )
| ~ ( C @ ( B @ ( A @ join ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14769,plain,
$false,
inference(e,[status(thm)],[69,61,60,65,53,39,66,35,31,68,42,37,46,57,38,33,32,34,44,59,71,49,48,63,40,55,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.15/0.42 % Computer : n008.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 19:55:10 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 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
% 0.66/0.75 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.89/0.86 % [INFO] Parsing done (111ms).
% 0.89/0.87 % [INFO] Running in sequential loop mode.
% 1.42/1.08 % [INFO] eprover registered as external prover.
% 1.42/1.08 % [INFO] Scanning for conjecture ...
% 1.68/1.13 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 1.68/1.18 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.83/1.21 % [INFO] Problem is propositional (TPTP CNF).
% 1.83/1.22 % [INFO] Type checking passed.
% 1.83/1.22 % [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 ...
% 40.37/8.40 % External prover 'e' found a proof!
% 40.37/8.40 % [INFO] Killing All external provers ...
% 36.19/8.40 % Time passed: 7872ms (effective reasoning time: 7525ms)
% 36.19/8.40 % Axioms used in derivation (18): meet_0_and_x, modularity3, commutativity_of_join, join_x_and_x, modularity4, meet_1_and_x, associativity_of_join2, absorbtion1, join_0_and_x, modularity2, absorbtion2, modularity1, associativity_of_meet1, commutativity_of_meet, associativity_of_join1, meet_x_and_x, join_1_and_x, associativity_of_meet2
% 36.19/8.40 % No. of inferences in proof: 59
% 36.19/8.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 7872 ms resp. 7525 ms w/o parsing
% 36.19/8.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.19/8.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------