%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL144-1 : 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 : n012.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 07:50:57 AM UTC 2026
% Result : Unsatisfiable 3.34s 1.75s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 146 ( 8 ~; 8 |; 0 &; 130 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordered_decl,type,
ordered: $i > $i > $o ).
thf(x_decl,type,
x: $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(y_decl,type,
y: $i ).
thf(z_decl,type,
z: $i ).
thf(truth_decl,type,
truth: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(big_V_decl,type,
big_V: $i > $i > $i ).
thf(big_hat_decl,type,
big_hat: $i > $i > $i ).
thf(8,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(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_hat ) )
= ( B @ not @ ( A @ not @ big_V ) @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,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(21,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,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(17,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)],[4]) ).
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(27,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
= truth )
| ~ ( B @ ( A @ ordered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,negated_conjecture,
( ~ ( z @ ( x @ implies ) @ ( y @ ordered ) )
| ~ ( z @ ( y @ implies ) @ ( x @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
thf(12,plain,
( ~ ( z @ ( x @ implies ) @ ( y @ ordered ) )
| ~ ( z @ ( y @ implies ) @ ( x @ ordered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( z @ ( x @ implies ) @ ( y @ ordered ) )
| ( z @ ( y @ implies ) @ ( x @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antecedent) ).
thf(11,plain,
( ( z @ ( x @ implies ) @ ( y @ ordered ) )
| ( z @ ( y @ implies ) @ ( x @ ordered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,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(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ big_V ) )
= ( B @ ( B @ ( A @ implies ) @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
thf(15,plain,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered ) )
| ( ( B @ ( A @ implies ) )
!= truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_definition2) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered ) )
| ( ( B @ ( A @ implies ) )
!= truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,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(19,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ implies ) @ implies ) )
= ( A @ ( A @ ( B @ implies ) @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(265,plain,
$false,
inference(e,[status(thm)],[25,21,17,27,12,11,23,15,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % 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
% 0.07/0.33 % Computer : n012.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Fri Sep 25 21:55:35 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 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
% 0.51/0.65 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.75 % [INFO] Parsing done (99ms).
% 0.65/0.76 % [INFO] Running in sequential loop mode.
% 1.04/0.96 % [INFO] eprover registered as external prover.
% 1.04/0.97 % [INFO] Scanning for conjecture ...
% 1.27/1.02 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 1.27/1.04 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.27/1.04 % [INFO] Problem is propositional (TPTP CNF).
% 1.27/1.05 % [INFO] Type checking passed.
% 1.27/1.05 % [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 ...
% 3.34/1.74 % External prover 'e' found a proof!
% 3.34/1.74 % [INFO] Killing All external provers ...
% 3.34/1.74 % Time passed: 1334ms (effective reasoning time: 981ms)
% 3.34/1.75 % Axioms used in derivation (8): partial_order_definition1, wajsberg_3, big_V_definition, wajsberg_1, big_hat_definition, wajsberg_2, partial_order_definition2, wajsberg_4
% 3.34/1.75 % No. of inferences in proof: 21
% 3.34/1.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1334 ms resp. 981 ms w/o parsing
% 3.34/1.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.34/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------