%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG284^5 : 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 : n019.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 3.60s 2.15s
% Output : Refutation 3.60s
% 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 : 71 ( 2 ~; 0 |; 6 &; 60 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(cJ_decl,type,
cJ: $i > $i ).
thf(cP_decl,type,
cP: $i > $i > $i ).
thf(cE_decl,type,
cE: $i ).
thf(1,conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) )
& ! [A: $i] :
( ( cP @ cE @ A )
= A )
& ! [A: $i] :
( ( cP @ ( cJ @ A ) @ A )
= cE ) )
=> ! [A: $i,B: $i] :
( ( cJ @ ( cP @ A @ B ) )
= ( cP @ ( cJ @ B ) @ ( cJ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM18_pme) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i,C: $i] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) )
& ! [A: $i] :
( ( cP @ cE @ A )
= A )
& ! [A: $i] :
( ( cP @ ( cJ @ A ) @ A )
= cE ) )
=> ! [A: $i,B: $i] :
( ( cJ @ ( cP @ A @ B ) )
= ( cP @ ( cJ @ B ) @ ( cJ @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i,B: $i,C: $i] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) )
& ! [A: $i] :
( ( cP @ cE @ A )
= A )
& ! [A: $i] :
( ( cP @ ( cJ @ A ) @ A )
= cE ) )
=> ! [A: $i,B: $i] :
( ( cJ @ ( cP @ A @ B ) )
= ( cP @ ( cJ @ B ) @ ( cJ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG284^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.09/0.22 % Computer : n019.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 17:37:48 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.99 % [INFO] Parsing done (188ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 2.00/1.41 % [INFO] eprover registered as external prover.
% 2.00/1.42 % [INFO] Scanning for conjecture ...
% 2.20/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.20/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.20/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.56 % [INFO] Type checking passed.
% 2.20/1.56 % [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 ...
% 3.60/2.15 % External prover 'e' found a proof!
% 3.60/2.15 % [INFO] Killing All external provers ...
% 3.60/2.15 % Time passed: 1788ms (effective reasoning time: 1145ms)
% 3.60/2.15 % 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)>
% 3.60/2.15 % Axioms used in derivation (0):
% 3.60/2.15 % No. of inferences in proof: 4
% 3.60/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1788 ms resp. 1145 ms w/o parsing
% 3.60/2.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.60/2.19 % [INFO] Killing All external provers ...
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