%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG270^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n017.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 : Wed Sep 30 07:45:06 AM UTC 2026
% Result : Theorem 2.45s 1.16s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 65 ( 2 ~; 0 |; 0 &; 60 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(c_star_decl,type,
c_star: a > a > a ).
thf(1,conjecture,
( ! [A: a,B: a,C: a] :
( ( c_star @ ( c_star @ A @ B ) @ C )
= ( c_star @ A @ ( c_star @ B @ C ) ) )
=> ! [A: a,B: a,C: a,D: a] :
( ( c_star @ ( c_star @ ( c_star @ A @ B ) @ C ) @ D )
= ( c_star @ A @ ( c_star @ B @ ( c_star @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM23_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a,B: a,C: a] :
( ( c_star @ ( c_star @ A @ B ) @ C )
= ( c_star @ A @ ( c_star @ B @ C ) ) )
=> ! [A: a,B: a,C: a,D: a] :
( ( c_star @ ( c_star @ ( c_star @ A @ B ) @ C ) @ D )
= ( c_star @ A @ ( c_star @ B @ ( c_star @ C @ D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a,B: a,C: a] :
( ( c_star @ ( c_star @ A @ B ) @ C )
= ( c_star @ A @ ( c_star @ B @ C ) ) )
=> ! [A: a,B: a,C: a,D: a] :
( ( c_star @ ( c_star @ ( c_star @ A @ B ) @ C ) @ D )
= ( c_star @ A @ ( c_star @ B @ ( c_star @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG270^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.10/0.19 % Computer : n017.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:31:07 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.64/0.49 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.87/0.58 % [INFO] Parsing done (88ms).
% 0.87/0.59 % [INFO] Running in sequential loop mode.
% 1.15/0.77 % [INFO] eprover registered as external prover.
% 1.15/0.78 % [INFO] Scanning for conjecture ...
% 1.38/0.82 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.38/0.84 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.38/0.84 % [INFO] Problem is higher-order (TPTP THF).
% 1.38/0.84 % [INFO] Type checking passed.
% 1.38/0.84 % [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 ...
% 2.45/1.15 % External prover 'e' found a proof!
% 2.45/1.15 % [INFO] Killing All external provers ...
% 2.45/1.15 % Time passed: 864ms (effective reasoning time: 561ms)
% 2.45/1.15 % Solved by 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)>
% 2.45/1.15 % Axioms used in derivation (0):
% 2.45/1.15 % No. of inferences in proof: 4
% 2.45/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 864 ms resp. 561 ms w/o parsing
% 2.45/1.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.45/1.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------