%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG280^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 : Wed Sep 30 07:45:08 AM UTC 2026
% Result : Theorem 3.61s 2.14s
% Output : Refutation 3.61s
% 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 : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 56 ( 2 ~; 0 |; 6 &; 45 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cE_decl,type,
cE: a ).
thf(cP_decl,type,
cP: a > a > a ).
thf(cJ_decl,type,
cJ: a > a ).
thf(1,conjecture,
( ( ! [A: a,B: a,C: a] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) )
& ! [A: a] :
( ( cP @ cE @ A )
= A )
& ! [A: a] :
( ( cP @ ( cJ @ A ) @ A )
= cE ) )
=> ! [A: a] :
( ( cP @ A @ cE )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM17_pme) ).
thf(2,negated_conjecture,
~ ( ( ! [A: a,B: a,C: a] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) )
& ! [A: a] :
( ( cP @ cE @ A )
= A )
& ! [A: a] :
( ( cP @ ( cJ @ A ) @ A )
= cE ) )
=> ! [A: a] :
( ( cP @ A @ cE )
= A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: a,B: a,C: a] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) )
& ! [A: a] :
( ( cP @ cE @ A )
= A )
& ! [A: a] :
( ( cP @ ( cJ @ A ) @ A )
= cE ) )
=> ! [A: a] :
( ( cP @ A @ cE )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG280^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.11/0.20 % Computer : n002.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 17:39:07 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (187ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 2.03/1.40 % [INFO] eprover registered as external prover.
% 2.03/1.41 % [INFO] Scanning for conjecture ...
% 2.21/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.55 % [INFO] Type checking passed.
% 2.21/1.56 % [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 ...
% 3.61/2.13 % External prover 'e' found a proof!
% 3.61/2.13 % [INFO] Killing All external provers ...
% 3.61/2.14 % Time passed: 1787ms (effective reasoning time: 1136ms)
% 3.61/2.14 % 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)>
% 3.61/2.14 % Axioms used in derivation (0):
% 3.61/2.14 % No. of inferences in proof: 4
% 3.61/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1787 ms resp. 1136 ms w/o parsing
% 3.61/2.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.61/2.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------