%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MSC008-1.002 : 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 : n013.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 08:03:10 AM UTC 2026
% Result : Unsatisfiable 5.01s 2.59s
% Output : Refutation 5.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 338 ( 44 ~; 54 |; 0 &; 240 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 102 ( 0 ^; 102 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(greek_decl,type,
greek: $i > $i > $i > $o ).
thf(latin_decl,type,
latin: $i > $i > $i > $o ).
thf(eq_decl,type,
eq: $i > $i > $o ).
thf(p_1_decl,type,
p_1: $i ).
thf(p_2_decl,type,
p_2: $i ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( p_2 @ ( B @ ( A @ greek ) ) )
| ( p_1 @ ( B @ ( A @ greek ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_cell_element) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( p_2 @ ( B @ ( A @ greek ) ) )
| ( p_1 @ ( B @ ( A @ greek ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( p_2 @ greek ) ) )
| ( B @ ( A @ ( p_1 @ greek ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_row_required) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( p_2 @ greek ) ) )
| ( B @ ( A @ ( p_1 @ greek ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ eq ) )
| ~ ( D @ ( B @ ( A @ greek ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_element_is_unique) ).
thf(22,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ eq ) )
| ~ ( D @ ( B @ ( A @ greek ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ eq ) )
| ~ ( C @ ( B @ ( D @ latin ) ) )
| ~ ( C @ ( B @ ( A @ latin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_row_is_unique) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ eq ) )
| ~ ( C @ ( B @ ( D @ latin ) ) )
| ~ ( C @ ( B @ ( A @ latin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( p_2 @ latin ) ) )
| ( B @ ( A @ ( p_1 @ latin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_row_required) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( p_2 @ latin ) ) )
| ( B @ ( A @ ( p_1 @ latin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( B @ eq ) )
| ~ ( D @ ( F @ ( E @ latin ) ) )
| ~ ( C @ ( F @ ( E @ greek ) ) )
| ~ ( D @ ( B @ ( A @ latin ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_two_same1) ).
thf(18,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( B @ eq ) )
| ~ ( D @ ( F @ ( E @ latin ) ) )
| ~ ( C @ ( F @ ( E @ greek ) ) )
| ~ ( D @ ( B @ ( A @ latin ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ eq ) )
| ~ ( D @ ( B @ ( A @ latin ) ) )
| ~ ( C @ ( B @ ( A @ latin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_element_is_unique) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ eq ) )
| ~ ( D @ ( B @ ( A @ latin ) ) )
| ~ ( C @ ( B @ ( A @ latin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ eq ) )
| ~ ( C @ ( D @ ( A @ greek ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_column_is_unique) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ eq ) )
| ~ ( C @ ( D @ ( A @ greek ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ eq ) )
| ~ ( C @ ( B @ ( D @ greek ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_row_is_unique) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ eq ) )
| ~ ( C @ ( B @ ( D @ greek ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ eq ) )
| ~ ( B @ ( A @ eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ eq ) )
| ~ ( B @ ( A @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i] : ( A @ ( A @ eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(38,plain,
! [A: $i] : ( A @ ( A @ eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( p_2 @ ( A @ greek ) ) )
| ( B @ ( p_1 @ ( A @ greek ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_column_required) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( p_2 @ ( A @ greek ) ) )
| ( B @ ( p_1 @ ( A @ greek ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( p_2 @ ( B @ ( A @ latin ) ) )
| ( p_1 @ ( B @ ( A @ latin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_cell_element) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( p_2 @ ( B @ ( A @ latin ) ) )
| ( p_1 @ ( B @ ( A @ latin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
~ ( p_2 @ ( p_1 @ eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p_1_is_not_p_2) ).
thf(34,plain,
~ ( p_2 @ ( p_1 @ eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( p_2 @ ( A @ latin ) ) )
| ( B @ ( p_1 @ ( A @ latin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_column_required) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( p_2 @ ( A @ latin ) ) )
| ( B @ ( p_1 @ ( A @ latin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ eq ) )
| ~ ( C @ ( D @ ( A @ latin ) ) )
| ~ ( C @ ( B @ ( A @ latin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_column_is_unique) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ eq ) )
| ~ ( C @ ( D @ ( A @ latin ) ) )
| ~ ( C @ ( B @ ( A @ latin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ eq ) )
| ~ ( D @ ( F @ ( E @ latin ) ) )
| ~ ( C @ ( F @ ( E @ greek ) ) )
| ~ ( D @ ( B @ ( A @ latin ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_two_same2) ).
thf(19,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ eq ) )
| ~ ( D @ ( F @ ( E @ latin ) ) )
| ~ ( C @ ( F @ ( E @ greek ) ) )
| ~ ( D @ ( B @ ( A @ latin ) ) )
| ~ ( C @ ( B @ ( A @ greek ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(74,plain,
$false,
inference(e,[status(thm)],[24,41,22,49,39,18,43,26,47,28,38,45,32,34,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MSC008-1.002 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.25/0.52 % Computer : n013.cluster.edu
% 0.25/0.52 % Model : x86_64 x86_64
% 0.25/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.52 % Memory : 8046.5625MB
% 0.25/0.52 % OS : Linux 6.8.0-71-generic
% 0.25/0.52 % CPULimit : 300
% 0.25/0.52 % WCLimit : 300
% 0.25/0.52 % DateTime : Sat Sep 26 00:14:23 UTC 2026
% 0.25/0.52 % CPUTime :
% 0.25/0.52 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
% 1.19/1.06 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/1.24 % [INFO] Parsing done (172ms).
% 1.54/1.25 % [INFO] Running in sequential loop mode.
% 2.37/1.62 % [INFO] eprover registered as external prover.
% 2.37/1.63 % [INFO] Scanning for conjecture ...
% 2.60/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.84/1.80 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.84/1.82 % [INFO] Problem is propositional (TPTP CNF).
% 2.84/1.82 % [INFO] Type checking passed.
% 2.84/1.83 % [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 ...
% 5.01/2.59 % External prover 'e' found a proof!
% 5.01/2.59 % [INFO] Killing All external provers ...
% 5.01/2.59 % Time passed: 1922ms (effective reasoning time: 1329ms)
% 5.01/2.59 % Axioms used in derivation (15): greek_cell_element, greek_element_is_unique, latin_column_required, reflexivity, greek_column_required, latin_cell_element, greek_row_is_unique, greek_row_required, symmetry, p_1_is_not_p_2, latin_element_is_unique, latin_row_required, latin_row_is_unique, latin_column_is_unique, greek_column_is_unique
% 5.01/2.59 % No. of inferences in proof: 35
% 5.01/2.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1922 ms resp. 1329 ms w/o parsing
% 5.57/2.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.57/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------