%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO006^1 : 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 : n013.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 08:45:00 AM UTC 2026
% Result : Theorem 3.09s 2.01s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 44 ( 16 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 41 ( 11 ~; 4 |; 1 &; 16 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 2 ^; 13 !; 0 ?; 17 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq_decl,type,
leibeq: $o > $o > $o ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $o ).
thf(leibeq_def,definition,
( leibeq
= ( ^ [A: $o,B: $o] :
! [C: $o > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $o] :
~ ! [B: $o] :
( ! [C: $o > $o] :
( ( C @ A )
=> ( C @ B ) )
=> ( A = B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $o] :
~ ( ! [B: $o > $o] :
( ( B @ sk1 )
=> ( B @ A ) )
=> ( sk1 = A ) ) ) ) ).
thf(1,conjecture,
! [A: $o,B: $o] :
( ( leibeq @ A @ B )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $o,B: $o] :
( ( leibeq @ A @ B )
=> ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $o,B: $o] :
( ! [C: $o > $o] :
( ( C @ A )
=> ( C @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $o > $o] :
( ( ~ ( A @ sk1 )
| ( A @ sk2 ) )
& ( sk1 != sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: $o > $o] :
( ~ ( A @ sk1 )
| ( A @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ( sk1 != sk1 )
| ( sk1 = sk2 ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( (=) @ $o @ sk1 ))]]) ).
thf(9,plain,
( ( sk1 != sk1 )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(10,plain,
sk2 = sk1,
inference(simp,[status(thm)],[9]) ).
thf(6,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[6]) ).
thf(13,plain,
$false,
inference(simplifyReflect,[status(thm)],[10,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO006^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:20:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.96 % [INFO] Parsing done (180ms).
% 1.26/0.97 % [INFO] Running in sequential loop mode.
% 1.86/1.38 % [INFO] eprover registered as external prover.
% 1.86/1.38 % [INFO] Scanning for conjecture ...
% 2.06/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.51 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.51 % [INFO] Type checking passed.
% 2.24/1.52 % [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 ...
% 3.09/2.00 % [INFO] Killing All external provers ...
% 3.09/2.01 % Time passed: 1672ms (effective reasoning time: 1023ms)
% 3.09/2.01 % 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)>
% 3.09/2.01 % Axioms used in derivation (0):
% 3.09/2.01 % No. of inferences in proof: 11
% 3.09/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1672 ms resp. 1023 ms w/o parsing
% 3.41/2.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.41/2.06 % [INFO] Killing All external provers ...
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