%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n001.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 4.26s 7.87s
% Output : Refutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 78 ( 2 ~; 0 |; 0 &; 76 @)
% ( 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 : 12 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(d_decl,type,
d: $i ).
thf(h_decl,type,
h: $i ).
thf(j_decl,type,
j: $i ).
thf(k_decl,type,
k: $i ).
thf(identity_decl,type,
identity: $i ).
thf(1,negated_conjecture,
( ( b @ ( a @ multiply ) )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
thf(14,plain,
( ( b @ ( a @ multiply ) )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,negated_conjecture,
( ( h @ inverse @ ( j @ multiply ) )
= k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
thf(13,plain,
( ( h @ inverse @ ( j @ multiply ) )
= k ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,negated_conjecture,
( ( b @ ( h @ multiply ) )
= j ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_b_is_j) ).
thf(18,plain,
( ( b @ ( h @ multiply ) )
= j ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
( ( a @ inverse @ ( c @ multiply ) )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
thf(16,plain,
( ( a @ inverse @ ( c @ multiply ) )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,negated_conjecture,
( ( b @ inverse @ ( k @ multiply ) )
!= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
thf(15,plain,
( ( b @ inverse @ ( k @ multiply ) )
!= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,negated_conjecture,
( ( b @ inverse @ ( d @ multiply ) )
= h ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
thf(17,plain,
( ( b @ inverse @ ( d @ multiply ) )
= h ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i] :
( ( identity @ ( A @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(32,plain,
! [A: $i] :
( ( identity @ ( A @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(34,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( A @ multiply ) @ ( A @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( A @ multiply ) @ ( A @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,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(30,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)],[9]) ).
thf(44,plain,
$false,
inference(e,[status(thm)],[14,28,13,18,16,26,15,17,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.22/5.48 % Computer : n001.cluster.edu
% 0.22/5.48 % Model : x86_64 x86_64
% 0.22/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/5.48 % Memory : 8046.5625MB
% 0.22/5.48 % OS : Linux 6.8.0-71-generic
% 0.22/5.48 % CPULimit : 300
% 0.22/5.48 % WCLimit : 300
% 0.22/5.48 % DateTime : Fri Sep 25 14:21:16 UTC 2026
% 0.22/5.48 % CPUTime :
% 0.22/5.48 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
% 1.42/6.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/6.56 % [INFO] Parsing done (219ms).
% 1.74/6.58 % [INFO] Running in sequential loop mode.
% 2.42/7.02 % [INFO] eprover registered as external prover.
% 2.42/7.03 % [INFO] Scanning for conjecture ...
% 2.69/7.15 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.85/7.18 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.85/7.20 % [INFO] Problem is propositional (TPTP CNF).
% 2.96/7.20 % [INFO] Type checking passed.
% 2.96/7.21 % [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 ...
% 4.26/7.86 % External prover 'e' found a proof!
% 4.26/7.87 % [INFO] Killing All external provers ...
% 4.26/7.87 % Time passed: 2175ms (effective reasoning time: 1279ms)
% 4.26/7.87 % Axioms used in derivation (6): associativity, left_identity, left_inverse, right_identity, right_inverse, x_cubed_is_identity
% 4.26/7.87 % No. of inferences in proof: 25
% 4.26/7.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2175 ms resp. 1279 ms w/o parsing
% 4.64/7.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.64/7.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------