%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 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 : 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 07:50:51 AM UTC 2026
% Result : Unsatisfiable 3.73s 2.41s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 26 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 268 ( 14 ~; 12 |; 0 &; 242 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_V_decl,type,
big_V: $i > $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(truth_decl,type,
truth: $i ).
thf(big_hat_decl,type,
big_hat: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(ordered_decl,type,
ordered: $i > $i > $o ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( B @ ordered ) )
| ~ ( C @ ( B @ implies ) @ ( A @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_2) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( B @ ordered ) )
| ~ ( C @ ( B @ implies ) @ ( A @ ordered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
= truth )
| ~ ( B @ ( A @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_definition1) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
= truth )
| ~ ( B @ ( A @ ordered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ implies ) @ ( A @ ( C @ implies ) @ ordered ) )
| ~ ( B @ ( A @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_2) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ implies ) @ ( A @ ( C @ implies ) @ ordered ) )
| ~ ( B @ ( A @ ordered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ big_V ) @ not )
= ( B @ not @ ( A @ not @ big_hat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_4) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_V ) @ not )
= ( B @ not @ ( A @ not @ big_hat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ big_hat ) @ not )
= ( B @ not @ ( A @ not @ big_V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_5) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_hat ) @ not )
= ( B @ not @ ( A @ not @ big_V ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( B @ ordered ) )
| ~ ( C @ ( B @ implies ) @ ( A @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_1) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( B @ ordered ) )
| ~ ( C @ ( B @ implies ) @ ( A @ ordered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ big_V ) )
= ( B @ ( B @ ( A @ implies ) @ implies ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_V_definition) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_V ) )
= ( B @ ( B @ ( A @ implies ) @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ big_V ) @ implies ) )
= ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ big_hat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_6) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ big_V ) @ implies ) )
= ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ big_hat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ ordered ) )
| ~ ( B @ ( A @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ ( A @ implies ) @ ordered ) )
| ~ ( B @ ( A @ ordered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,negated_conjecture,
( ( x @ ( y @ implies ) @ ( y @ ( x @ implies ) @ big_V ) )
!= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mv_4) ).
thf(18,plain,
( ( x @ ( y @ implies ) @ ( y @ ( x @ implies ) @ big_V ) )
!= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered ) )
| ( ( B @ ( A @ implies ) )
!= truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_definition2) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered ) )
| ( ( B @ ( A @ implies ) )
!= truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ implies ) @ implies ) )
= ( A @ ( A @ ( B @ implies ) @ implies ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ implies ) @ implies ) )
= ( A @ ( A @ ( B @ implies ) @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ big_hat ) @ ( A @ implies ) )
= ( C @ ( A @ implies ) @ ( B @ ( A @ implies ) @ big_hat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_7) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ big_hat ) @ ( A @ implies ) )
= ( C @ ( A @ implies ) @ ( B @ ( A @ implies ) @ big_hat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ big_hat ) )
= ( B @ not @ ( A @ not @ big_V ) @ not ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_hat_definition) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_hat ) )
= ( B @ not @ ( A @ not @ big_V ) @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(61,plain,
$false,
inference(e,[status(thm)],[53,35,42,25,46,29,38,21,33,44,27,48,18,50,31,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n003.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 21:53:39 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.83/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.19 % [INFO] Parsing done (196ms).
% 1.35/1.21 % [INFO] Running in sequential loop mode.
% 1.98/1.61 % [INFO] eprover registered as external prover.
% 1.98/1.61 % [INFO] Scanning for conjecture ...
% 2.15/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.15/1.76 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.15/1.79 % [INFO] Problem is propositional (TPTP CNF).
% 2.15/1.80 % [INFO] Type checking passed.
% 2.31/1.80 % [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 ...
% 3.73/2.41 % External prover 'e' found a proof!
% 3.73/2.41 % [INFO] Killing All external provers ...
% 3.73/2.41 % Time passed: 1855ms (effective reasoning time: 1191ms)
% 3.73/2.41 % Axioms used in derivation (16): partial_order_definition1, lemma_4, big_V_definition, lemma_3_1, lemma_1, lemma_2, big_hat_definition, lemma_6, wajsberg_2, lemma_7, wajsberg_3, lemma_3_2, partial_order_definition2, wajsberg_4, lemma_5, wajsberg_1
% 3.73/2.41 % No. of inferences in proof: 35
% 3.73/2.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1855 ms resp. 1191 ms w/o parsing
% 3.73/2.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.73/2.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------