%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 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 : 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 07:20:55 AM UTC 2026
% Result : Unsatisfiable 3.81s 2.45s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 90 ( 6 ~; 4 |; 0 &; 80 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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 : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(commutator_decl,type,
commutator: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(2,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_of_multiply) ).
thf(10,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)],[2]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ commutator ) @ multiply ) )
= ( B @ ( A @ commutator ) @ ( C @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nilpotency) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ commutator ) @ multiply ) )
= ( B @ ( A @ commutator ) @ ( C @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ multiply ) )
!= ( C @ ( A @ multiply ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ multiply ) )
!= ( C @ ( A @ multiply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( B @ ( A @ commutator ) @ ( A @ multiply ) @ ( B @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( B @ ( A @ commutator ) @ ( A @ multiply ) @ ( B @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ multiply ) )
!= ( B @ ( C @ multiply ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_cancellation) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ multiply ) )
!= ( B @ ( C @ multiply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ ( a @ commutator ) @ commutator ) )
!= ( c @ ( b @ commutator ) @ ( a @ commutator ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator_is_associative) ).
thf(7,plain,
( ( c @ ( b @ ( a @ commutator ) @ commutator ) )
!= ( c @ ( b @ commutator ) @ ( a @ commutator ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[10,24,17,22,12,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % 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
% 0.15/0.40 % Computer : n006.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 14:52:02 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.19 % [INFO] Parsing done (192ms).
% 1.40/1.20 % [INFO] Running in sequential loop mode.
% 2.05/1.60 % [INFO] eprover registered as external prover.
% 2.05/1.61 % [INFO] Scanning for conjecture ...
% 2.22/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.22/1.73 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.22/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 2.22/1.75 % [INFO] Type checking passed.
% 2.22/1.75 % [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 ...
% 3.81/2.45 % External prover 'e' found a proof!
% 3.81/2.45 % [INFO] Killing All external provers ...
% 3.81/2.45 % Time passed: 1900ms (effective reasoning time: 1239ms)
% 3.81/2.45 % Axioms used in derivation (5): associativity_of_multiply, left_cancellation, right_cancellation, commutator, nilpotency
% 3.81/2.45 % No. of inferences in proof: 13
% 3.81/2.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1900 ms resp. 1239 ms w/o parsing
% 3.81/2.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.81/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------