%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL159-1 : 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 : n006.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 07:50:59 AM UTC 2026
% Result : Unsatisfiable 3.76s 2.82s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 214 ( 2 ~; 0 |; 0 &; 212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(xor_decl,type,
xor: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(truth_decl,type,
truth: $i ).
thf(y_decl,type,
y: $i ).
thf(and_star_decl,type,
and_star: $i > $i > $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(falsehood_decl,type,
falsehood: $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) )
= ( A @ ( B @ or ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutativity) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) )
= ( A @ ( B @ or ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ xor ) )
= ( A @ ( B @ xor ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ xor ) )
= ( A @ ( B @ xor ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,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(45,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)],[14]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ or ) @ or ) )
= ( C @ ( B @ or ) @ ( A @ or ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_associativity) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ or ) @ or ) )
= ( C @ ( B @ or ) @ ( A @ or ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( truth @ implies ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( A @ ( B @ and ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutativity) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( A @ ( B @ and ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,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(35,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ implies ) @ implies ) )
= ( A @ ( A @ ( B @ implies ) @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( y @ ( truth @ xor ) @ ( x @ xor ) )
!= ( y @ ( truth @ ( x @ xor ) @ xor ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
thf(18,plain,
( ( y @ ( truth @ xor ) @ ( x @ xor ) )
!= ( y @ ( truth @ ( x @ xor ) @ xor ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ and ) @ and ) )
= ( C @ ( B @ and ) @ ( A @ and ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_associativity) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ and ) @ and ) )
= ( C @ ( B @ and ) @ ( A @ and ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,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(43,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ not @ implies ) @ implies ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ and_star ) @ and_star ) )
= ( C @ ( B @ and_star ) @ ( A @ and_star ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_associativity) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ and_star ) @ and_star ) )
= ( C @ ( B @ and_star ) @ ( A @ and_star ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
( ( truth @ not )
= falsehood ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_definition) ).
thf(51,plain,
( ( truth @ not )
= falsehood ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ xor ) )
= ( B @ ( A @ not @ and ) @ ( B @ not @ ( A @ and ) @ or ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ xor ) )
= ( B @ ( A @ not @ and ) @ ( B @ not @ ( A @ and ) @ or ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ and_star ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_definition) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and_star ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ and_star ) )
= ( A @ ( B @ and_star ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and_star ) )
= ( A @ ( B @ and_star ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) )
= ( B @ ( A @ not @ implies ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) )
= ( B @ ( A @ not @ implies ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL159-1 : 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
% 0.13/0.40 % Computer : n006.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 21:55:56 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.68/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.08/1.27 % [INFO] Parsing done (261ms).
% 1.08/1.29 % [INFO] Running in sequential loop mode.
% 1.77/1.65 % [INFO] eprover registered as external prover.
% 1.77/1.67 % [INFO] Scanning for conjecture ...
% 1.93/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.07/1.86 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.07/1.89 % [INFO] Problem is propositional (TPTP CNF).
% 2.22/1.90 % [INFO] Type checking passed.
% 2.22/1.91 % [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 ...
% 3.76/2.81 % External prover 'e' found a proof!
% 3.76/2.81 % [INFO] Killing All external provers ...
% 3.76/2.81 % Time passed: 2211ms (effective reasoning time: 1512ms)
% 3.76/2.82 % Axioms used in derivation (16): wajsberg_3, or_definition, and_definition, xor_definition, and_commutativity, false_definition, and_associativity, or_associativity, and_star_definition, and_star_commutativity, wajsberg_4, and_star_associativity, or_commutativity, wajsberg_1, wajsberg_2, xor_commutativity
% 3.76/2.82 % No. of inferences in proof: 35
% 3.76/2.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2211 ms resp. 1512 ms w/o parsing
% 3.90/2.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.90/2.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------