%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ109^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : n012.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 08:20:48 AM UTC 2026
% Result : Theorem 1.71s 1.07s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 2 unt; 0 typ; 1 def)
% Number of atoms : 7 ( 1 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 73 ( 2 ~; 0 |; 6 &; 56 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 2 ^; 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(c1_decl,type,
c1: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(cCKB6_BLACK_decl,type,
cCKB6_BLACK: $i > $i > $o ).
thf(cCKB6_BLACK_def,definition,
( cCKB6_BLACK
= ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( C @ c1 @ c1 )
& ! [D: $i,E: $i] :
( ( C @ D @ E )
=> ( ( C @ ( s @ ( s @ D ) ) @ E )
& ( C @ ( s @ D ) @ ( s @ E ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( cCKB6_BLACK @ A @ B )
=> ( cCKB6_BLACK @ ( s @ A ) @ ( s @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_L9000) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( cCKB6_BLACK @ A @ B )
=> ( cCKB6_BLACK @ ( s @ A ) @ ( s @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i] :
( ! [C: $i > $i > $o] :
( ( ( C @ c1 @ c1 )
& ! [D: $i,E: $i] :
( ( C @ D @ E )
=> ( ( C @ ( s @ ( s @ D ) ) @ E )
& ( C @ ( s @ D ) @ ( s @ E ) ) ) ) )
=> ( C @ A @ B ) )
=> ! [C: $i > $i > $o] :
( ( ( C @ c1 @ c1 )
& ! [D: $i,E: $i] :
( ( C @ D @ E )
=> ( ( C @ ( s @ ( s @ D ) ) @ E )
& ( C @ ( s @ D ) @ ( s @ E ) ) ) ) )
=> ( C @ ( s @ A ) @ ( s @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PUZ109^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % 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
% 0.05/0.13 % Computer : n012.cluster.edu
% 0.05/0.13 % Model : x86_64 x86_64
% 0.05/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.13 % Memory : 8046.5625MB
% 0.05/0.13 % OS : Linux 6.8.0-71-generic
% 0.05/0.13 % CPULimit : 300
% 0.05/0.13 % WCLimit : 300
% 0.05/0.13 % DateTime : Tue Sep 29 13:23:33 UTC 2026
% 0.05/0.13 % CPUTime :
% 0.05/0.13 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
% 0.39/0.41 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.54/0.50 % [INFO] Parsing done (88ms).
% 0.54/0.51 % [INFO] Running in sequential loop mode.
% 0.84/0.69 % [INFO] eprover registered as external prover.
% 0.84/0.70 % [INFO] Scanning for conjecture ...
% 0.98/0.74 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 0.98/0.76 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 0.98/0.76 % [INFO] Problem is higher-order (TPTP THF).
% 0.98/0.76 % [INFO] Type checking passed.
% 0.98/0.76 % [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 ...
% 1.71/1.07 % External prover 'e' found a proof!
% 1.71/1.07 % [INFO] Killing All external provers ...
% 1.71/1.07 % Time passed: 872ms (effective reasoning time: 564ms)
% 1.71/1.07 % 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)>
% 1.71/1.07 % Axioms used in derivation (0):
% 1.71/1.07 % No. of inferences in proof: 4
% 1.71/1.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 872 ms resp. 564 ms w/o parsing
% 1.71/1.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.71/1.09 % [INFO] Killing All external provers ...
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