%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% 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 : 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 06:54:21 AM UTC 2026
% Result : Unsatisfiable 3.20s 3.00s
% Output : Refutation 3.61s
% 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 : 66 ( 2 ~; 0 |; 0 &; 64 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_decl,type,
multiply: $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(b_decl,type,
b: $i ).
thf(2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( A @ multiply ) ) @ ( D @ ( C @ ( B @ ( A @ multiply ) ) @ multiply ) ) )
= ( E @ ( D @ ( C @ multiply ) ) @ ( B @ ( A @ multiply ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(10,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( A @ multiply ) ) @ ( D @ ( C @ ( B @ ( A @ multiply ) ) @ multiply ) ) )
= ( E @ ( D @ ( C @ multiply ) ) @ ( B @ ( A @ multiply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ multiply ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_2) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ multiply ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_1) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ multiply ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( b @ ( a @ inverse @ ( a @ multiply ) ) )
!= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
thf(7,plain,
( ( b @ ( a @ inverse @ ( a @ multiply ) ) )
!= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ multiply ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extra_lemma) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ multiply ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ inverse @ multiply ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ inverse @ multiply ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[10,14,12,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% 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
% 0.15/0.48 % Computer : n002.cluster.edu
% 0.15/0.48 % Model : x86_64 x86_64
% 0.15/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.48 % Memory : 8046.5625MB
% 0.15/0.48 % OS : Linux 6.8.0-71-generic
% 0.15/0.48 % CPULimit : 300
% 0.15/0.48 % WCLimit : 300
% 0.15/0.48 % DateTime : Sat Sep 26 22:35:36 UTC 2026
% 0.15/0.49 % CPUTime :
% 0.15/0.49 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
% 0.97/1.30 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.51 % [INFO] Parsing done (203ms).
% 1.29/1.53 % [INFO] Running in sequential loop mode.
% 1.76/2.04 % [INFO] eprover registered as external prover.
% 1.98/2.06 % [INFO] Scanning for conjecture ...
% 2.11/2.17 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.16/2.21 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.16/2.22 % [INFO] Problem is propositional (TPTP CNF).
% 2.16/2.23 % [INFO] Type checking passed.
% 2.16/2.24 % [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 ...
% 3.20/2.99 % External prover 'e' found a proof!
% 3.20/2.99 % [INFO] Killing All external provers ...
% 3.20/2.99 % Time passed: 2230ms (effective reasoning time: 1456ms)
% 3.20/3.00 % Axioms used in derivation (5): associativity, ternary_multiply_1, extra_lemma, ternary_multiply_2, left_inverse
% 3.20/3.00 % No. of inferences in proof: 13
% 3.20/3.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2230 ms resp. 1456 ms w/o parsing
% 3.61/3.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.61/3.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------