%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP080-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 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 : n015.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 07:19:56 AM UTC 2026
% Result : Unsatisfiable 5.13s 3.48s
% Output : Refutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of formulae : 11 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 6 ~; 4 |; 0 &; 78 @)
% ( 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 : 11 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(a1_decl,type,
a1: $i ).
thf(identity_decl,type,
identity: $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(double_divide_decl,type,
double_divide: $i > $i > $i ).
thf(1,negated_conjecture,
( ( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) )
| ( ( a2 @ ( identity @ multiply ) )
!= a2 )
| ( ( a1 @ ( a1 @ inverse @ multiply ) )
!= identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
thf(6,plain,
( ( ( c3 @ ( b3 @ ( a3 @ multiply ) @ multiply ) )
!= ( c3 @ ( b3 @ multiply ) @ ( a3 @ multiply ) ) )
| ( ( a2 @ ( identity @ multiply ) )
!= a2 )
| ( ( a1 @ ( a1 @ inverse @ multiply ) )
!= identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( identity @ ( A @ ( C @ double_divide ) @ ( B @ double_divide ) @ double_divide ) @ ( identity @ ( B @ double_divide ) @ ( A @ double_divide ) @ ( identity @ double_divide ) @ double_divide ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( identity @ ( A @ ( C @ double_divide ) @ ( B @ double_divide ) @ double_divide ) @ ( identity @ ( B @ double_divide ) @ ( A @ double_divide ) @ ( identity @ double_divide ) @ double_divide ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ inverse )
= ( identity @ ( A @ double_divide ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(13,plain,
! [A: $i] :
( ( A @ inverse )
= ( identity @ ( A @ double_divide ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( identity @ ( A @ ( B @ double_divide ) @ double_divide ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) )
= ( identity @ ( A @ ( B @ double_divide ) @ double_divide ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
( identity
= ( A @ inverse @ ( A @ double_divide ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
thf(15,plain,
! [A: $i] :
( identity
= ( A @ inverse @ ( A @ double_divide ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[6,9,13,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP080-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.11 % 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
% 0.22/0.48 % Computer : n015.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Fri Sep 25 14:24:42 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.36/1.35 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.61 % [INFO] Parsing done (256ms).
% 1.82/1.63 % [INFO] Running in sequential loop mode.
% 2.68/2.26 % [INFO] eprover registered as external prover.
% 2.68/2.28 % [INFO] Scanning for conjecture ...
% 3.00/2.41 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 3.00/2.45 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 3.00/2.47 % [INFO] Problem is propositional (TPTP CNF).
% 3.00/2.48 % [INFO] Type checking passed.
% 3.00/2.49 % [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 ...
% 5.13/3.48 % External prover 'e' found a proof!
% 5.13/3.48 % [INFO] Killing All external provers ...
% 5.13/3.48 % Time passed: 2780ms (effective reasoning time: 1837ms)
% 5.13/3.48 % Axioms used in derivation (4): single_axiom, inverse, multiply, identity
% 5.13/3.48 % No. of inferences in proof: 11
% 5.13/3.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2780 ms resp. 1837 ms w/o parsing
% 5.74/3.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.74/3.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------