%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP002-3 : 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 : 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 07:19:42 AM UTC 2026
% Result : Unsatisfiable 4.34s 2.97s
% Output : Refutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 64 ( 2 ~; 0 |; 0 &; 62 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(commutator_decl,type,
commutator: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(identity_decl,type,
identity: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(10,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(12,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( b @ ( b @ ( a @ commutator ) @ commutator ) )
!= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator) ).
thf(7,plain,
( ( b @ ( b @ ( a @ commutator ) @ commutator ) )
!= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( A @ multiply ) @ ( A @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
thf(18,plain,
! [A: $i] :
( ( A @ ( A @ multiply ) @ ( A @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ commutator ) )
= ( B @ inverse @ ( A @ inverse @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ commutator ) )
= ( B @ inverse @ ( A @ inverse @ multiply ) @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[10,14,12,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-3 : 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
% 0.15/0.62 % Computer : n002.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.63 % DateTime : Fri Sep 25 14:18:24 UTC 2026
% 0.18/0.63 % CPUTime :
% 0.18/0.63 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
% 0.99/1.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.38 % [INFO] Parsing done (165ms).
% 1.47/1.40 % [INFO] Running in sequential loop mode.
% 2.28/1.97 % [INFO] eprover registered as external prover.
% 2.28/1.99 % [INFO] Scanning for conjecture ...
% 2.59/2.11 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.77/2.16 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.77/2.17 % [INFO] Problem is propositional (TPTP CNF).
% 2.77/2.19 % [INFO] Type checking passed.
% 2.77/2.19 % [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 ...
% 4.34/2.96 % External prover 'e' found a proof!
% 4.34/2.96 % [INFO] Killing All external provers ...
% 4.34/2.96 % Time passed: 2196ms (effective reasoning time: 1551ms)
% 4.34/2.97 % Axioms used in derivation (5): associativity, left_identity, left_inverse, x_cubed_is_identity, commutator
% 4.34/2.97 % No. of inferences in proof: 13
% 4.34/2.97 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2196 ms resp. 1551 ms w/o parsing
% 4.34/3.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.34/3.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------