%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL109-3 : 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 : n002.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 8.16s 3.44s
% Output : Refutation 8.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 182 ( 6 ~; 4 |; 0 &; 172 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(truth_decl,type,
truth: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ implies ) )
!= ( A @ ( B @ implies ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_2) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ implies ) )
!= ( A @ ( B @ implies ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_6) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ implies ) @ ( A @ ( C @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( A @ implies ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ not @ implies ) )
= ( A @ ( B @ implies ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ not @ implies ) )
= ( A @ ( B @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,negated_conjecture,
( ( a @ ( b @ implies ) @ ( a @ ( b @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) )
!= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
thf(16,plain,
( ( a @ ( b @ implies ) @ ( a @ ( b @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ implies ) )
!= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) )
= ( C @ ( A @ implies ) @ ( B @ implies ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_7) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( A @ implies ) )
= ( C @ ( A @ implies ) @ ( B @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ implies ) @ implies ) )
= ( A @ ( A @ ( B @ implies ) @ implies ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ implies ) @ implies ) )
= ( A @ ( A @ ( B @ implies ) @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ not @ not )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_9) ).
thf(47,plain,
! [A: $i] :
( ( A @ not @ not )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
= truth )
| ( ( B @ ( A @ implies ) )
!= ( C @ ( B @ implies ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_5) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
= truth )
| ( ( B @ ( A @ implies ) )
!= ( C @ ( B @ implies ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
thf(21,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)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ( truth @ ( A @ implies ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3) ).
thf(34,plain,
! [A: $i] :
( ( truth @ ( A @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ( truth @ not @ ( A @ implies ) )
= ( A @ not ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_8) ).
thf(45,plain,
! [A: $i] :
( ( truth @ not @ ( A @ implies ) )
= ( A @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
= truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
thf(19,plain,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(681,plain,
$false,
inference(e,[status(thm)],[25,29,41,27,49,16,43,23,47,38,21,34,45,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-3 : 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
% 0.14/0.38 % Computer : n002.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Fri Sep 25 21:54:38 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.90/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.16 % [INFO] Parsing done (195ms).
% 1.31/1.17 % [INFO] Running in sequential loop mode.
% 1.96/1.58 % [INFO] eprover registered as external prover.
% 1.96/1.58 % [INFO] Scanning for conjecture ...
% 2.17/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.34/1.71 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.34/1.73 % [INFO] Problem is propositional (TPTP CNF).
% 2.34/1.74 % [INFO] Type checking passed.
% 2.34/1.74 % [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 ...
% 8.16/3.44 % External prover 'e' found a proof!
% 8.16/3.44 % [INFO] Killing All external provers ...
% 8.16/3.44 % Time passed: 2919ms (effective reasoning time: 2258ms)
% 8.16/3.44 % Axioms used in derivation (14): wajsberg_3, lemma_4, wajsberg_4, lemma_1, lemma_6, wajsberg_2, lemma_8, lemma_3, lemma_7, lemma_10, lemma_5, wajsberg_1, lemma_9, lemma_2
% 8.16/3.44 % No. of inferences in proof: 31
% 8.16/3.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2919 ms resp. 2258 ms w/o parsing
% 8.16/3.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.16/3.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------