%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO030^1 : TPTP v9.3.1. Released v3.7.0.
% 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 08:45:03 AM UTC 2026
% Result : Theorem 2.78s 1.81s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 21 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 45 ( 17 ~; 3 |; 0 &; 20 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 2 ^; 10 !; 5 ?; 18 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq_decl,type,
leibeq: $o > $o > $o ).
thf(sk3_decl,type,
sk3: $o ).
thf(leibeq_def,definition,
( leibeq
= ( ^ [A: $o,B: $o] :
! [C: $o > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $o] :
! [B: $o > $o] :
( ( B @ ~ A )
=> ( B @ A ) ) ) ) ).
thf(1,conjecture,
~ ! [A: $o > $o] :
? [B: $o] : ( leibeq @ ( A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ~ ! [A: $o > $o] :
? [B: $o] : ( leibeq @ ( A @ B ) @ B ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ! [A: $o > $o] :
? [B: $o] :
! [C: $o > $o] :
( ( C @ ( A @ B ) )
=> ( C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $o > $o] :
? [B: $o] :
! [C: $o > $o] :
( ( C @ ( A @ B ) )
=> ( C @ B ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(9,plain,
? [A: $o] :
! [B: $o > $o] :
( ( B @ ~ A )
=> ( B @ A ) ),
inference(instance,[status(thm)],[4]) ).
thf(12,plain,
! [A: $o > $o] :
( ~ ( A @ ~ sk3 )
| ( A @ sk3 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(15,plain,
( ( ( ~ sk3 ) != ( ~ sk3 ) )
| ( ( ~ sk3 ) = sk3 ) ),
inference(replace_leibeq,[status(thm)],[12:[bind(A,$thf( (=) @ $o @ ~ ( sk3 ) ))]]) ).
thf(20,plain,
( ( ( ~ sk3 ) != ( ~ sk3 ) )
| ( ( ~ sk3 ) = sk3 ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(21,plain,
$false,
inference(simp,[status(thm)],[20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO030^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.12/0.22 % Computer : n019.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 16:23:32 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 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
% 1.02/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (182ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 2.01/1.40 % [INFO] eprover registered as external prover.
% 2.01/1.41 % [INFO] Scanning for conjecture ...
% 2.19/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.19/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.19/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.53 % [INFO] Type checking passed.
% 2.19/1.54 % [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 ...
% 2.78/1.80 % [INFO] Killing All external provers ...
% 2.78/1.80 % Time passed: 1435ms (effective reasoning time: 798ms)
% 2.78/1.80 % 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)>
% 2.78/1.81 % Axioms used in derivation (0):
% 2.78/1.81 % No. of inferences in proof: 9
% 2.78/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1435 ms resp. 798 ms w/o parsing
% 2.78/1.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.78/1.87 % [INFO] Killing All external provers ...
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