%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP058-1 : 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 : n008.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 07:19:53 AM UTC 2026
% Result : Unsatisfiable 4.13s 7.68s
% Output : Refutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 9 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 6 ~; 4 |; 0 &; 68 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(a1_decl,type,
a1: $i ).
thf(b1_decl,type,
b1: $i ).
thf(b2_decl,type,
b2: $i ).
thf(a2_decl,type,
a2: $i ).
thf(a3_decl,type,
a3: $i ).
thf(b3_decl,type,
b3: $i ).
thf(c3_decl,type,
c3: $i ).
thf(1,negated_conjecture,
( ( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) )
| ( ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) )
!= a2 )
| ( ( a1 @ ( a1 @ inverse @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
thf(3,plain,
( ( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) )
| ( ( a2 @ ( b2 @ ( b2 @ inverse @ multiply ) @ multiply ) )
!= a2 )
| ( ( a1 @ ( a1 @ inverse @ multiply ) )
!= ( b1 @ ( b1 @ inverse @ multiply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ multiply ) @ inverse @ ( C @ inverse @ ( C @ multiply ) @ multiply ) @ multiply ) @ ( B @ multiply ) @ inverse @ ( A @ multiply ) )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
thf(6,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ multiply ) @ inverse @ ( C @ inverse @ ( C @ multiply ) @ multiply ) @ multiply ) @ ( B @ multiply ) @ inverse @ ( A @ multiply ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,plain,
$false,
inference(e,[status(thm)],[3,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP058-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.20/5.56 % Computer : n008.cluster.edu
% 0.20/5.56 % Model : x86_64 x86_64
% 0.20/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.56 % Memory : 8046.5625MB
% 0.20/5.56 % OS : Linux 6.8.0-71-generic
% 0.20/5.56 % CPULimit : 300
% 0.20/5.56 % WCLimit : 300
% 0.20/5.56 % DateTime : Fri Sep 25 14:20:59 UTC 2026
% 0.20/5.57 % CPUTime :
% 0.20/5.57 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
% 1.05/6.16 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/6.34 % [INFO] Parsing done (179ms).
% 1.33/6.35 % [INFO] Running in sequential loop mode.
% 1.91/6.77 % [INFO] eprover registered as external prover.
% 1.91/6.78 % [INFO] Scanning for conjecture ...
% 2.11/6.87 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.30/6.90 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.30/6.91 % [INFO] Problem is propositional (TPTP CNF).
% 2.30/6.92 % [INFO] Type checking passed.
% 2.30/6.92 % [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 ...
% 4.13/7.67 % External prover 'e' found a proof!
% 4.13/7.67 % [INFO] Killing All external provers ...
% 4.13/7.67 % Time passed: 1963ms (effective reasoning time: 1313ms)
% 4.13/7.67 % Axioms used in derivation (1): single_axiom
% 4.13/7.68 % No. of inferences in proof: 5
% 4.13/7.68 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1963 ms resp. 1313 ms w/o parsing
% 4.35/7.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.35/7.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------