%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ100^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 08:20:47 AM UTC 2026
% Result : Theorem 3.37s 2.03s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 15 ( 3 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 8 ~; 1 |; 6 &; 36 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 2 ^; 11 !; 0 ?; 15 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(s_decl,type,
s: $i > $i ).
thf(cCKB_E2_decl,type,
cCKB_E2: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(cCKB_E2_def,definition,
( cCKB_E2
= ( ^ [A: $i,B: $i] :
! [C: $i > $o] :
( ( ( C @ A )
& ! [D: $i] :
( ( C @ D )
=> ( C @ ( s @ ( s @ D ) ) ) ) )
=> ( C @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i > $o] :
( ( ( B @ A )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( s @ ( s @ C ) ) ) ) )
=> ( B @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
~ ( ( ( A @ sk1 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( s @ ( s @ B ) ) ) ) )
=> ( A @ sk1 ) ) ) ) ).
thf(1,conjecture,
! [A: $i] : ( cCKB_E2 @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_L32000) ).
thf(2,negated_conjecture,
~ ! [A: $i] : ( cCKB_E2 @ A @ A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i > $o] :
( ( ( B @ A )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( s @ ( s @ C ) ) ) ) )
=> ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i] :
( ( sk2 @ sk1 )
& ( ~ ( sk2 @ A )
| ( sk2 @ ( s @ ( s @ A ) ) ) )
& ~ ( sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
~ ( sk2 @ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
sk2 @ sk1,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
~ $true,
inference(rewrite,[status(thm)],[7,5]) ).
thf(9,plain,
$false,
inference(simp,[status(thm)],[8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ100^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.11/0.22 % Computer : n002.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 13:25:54 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (180ms).
% 1.25/1.00 % [INFO] Running in sequential loop mode.
% 1.98/1.45 % [INFO] eprover registered as external prover.
% 1.98/1.46 % [INFO] Scanning for conjecture ...
% 2.21/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.59 % [INFO] Type checking passed.
% 2.38/1.60 % [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 ...
% 3.00/2.02 % [INFO] Killing All external provers ...
% 3.37/2.03 % Time passed: 1654ms (effective reasoning time: 1020ms)
% 3.37/2.03 % 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)>
% 3.37/2.03 % Axioms used in derivation (0):
% 3.37/2.03 % No. of inferences in proof: 8
% 3.37/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1654 ms resp. 1020 ms w/o parsing
% 3.37/2.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.37/2.08 % [INFO] Killing All external provers ...
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