%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO352^5 : 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 : n018.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 08:45:38 AM UTC 2026
% Result : Theorem 4.42s 2.42s
% Output : Refutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 21 ( 10 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 77 ( 14 ~; 5 |; 2 &; 46 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 16 !; 0 ?; 17 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(n_decl,type,
n: $i > $i ).
thf(m_decl,type,
m: $i > $i ).
thf(sk1_decl,type,
sk1: ( $i > $i ) > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( $i > $i ) > $o] :
~ ( ( A @ m )
=> ( A @ n ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i,B: $i > $o] :
( ( B @ ( m @ A ) )
=> ( B @ ( n @ A ) ) )
=> ! [A: ( $i > $i ) > $o] :
( ( A @ m )
=> ( A @ n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE5EXT) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i > $o] :
( ( B @ ( m @ A ) )
=> ( B @ ( n @ A ) ) )
=> ! [A: ( $i > $i ) > $o] :
( ( A @ m )
=> ( A @ n ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o] :
( ( B @ ( m @ A ) )
=> ( B @ ( n @ A ) ) )
=> ! [A: ( $i > $i ) > $o] :
( ( A @ m )
=> ( A @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $o,A: $i] :
( ( ~ ( B @ ( m @ A ) )
| ( B @ ( n @ A ) ) )
& ( sk1 @ m )
& ~ ( sk1 @ n ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
sk1 @ m,
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( sk1 @ n ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( ~ $true
| ( ( sk1 @ m )
!= ( sk1 @ n ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(12,plain,
( ( sk1 @ m )
!= ( sk1 @ n ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
m != n,
inference(simp,[status(thm)],[12]) ).
thf(5,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ ( m @ A ) )
| ( B @ ( n @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: $i] :
( ( ( m @ A )
!= ( m @ A ) )
| ( ( m @ A )
= ( n @ A ) ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ ( m @ A ) ))]]) ).
thf(9,plain,
! [A: $i] :
( ( ( m @ A )
!= ( m @ A ) )
| ( ( m @ A )
= ( n @ A ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
! [A: $i] :
( ( m @ A )
= ( n @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(63,plain,
n != n,
inference(rewrite,[status(thm)],[13,10]) ).
thf(64,plain,
$false,
inference(simp,[status(thm)],[63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO352^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.12/0.21 % Computer : n018.cluster.edu
% 0.12/0.21 % Model : x86_64 x86_64
% 0.12/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.21 % Memory : 8046.5625MB
% 0.12/0.21 % OS : Linux 6.8.0-71-generic
% 0.12/0.21 % CPULimit : 300
% 0.12/0.21 % WCLimit : 300
% 0.12/0.21 % DateTime : Tue Sep 29 16:50:26 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 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
% 1.05/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (175ms).
% 1.25/1.00 % [INFO] Running in sequential loop mode.
% 2.04/1.42 % [INFO] eprover registered as external prover.
% 2.04/1.43 % [INFO] Scanning for conjecture ...
% 2.20/1.52 % [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).
% 2.20/1.55 % [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 ...
% 4.42/2.41 % [INFO] Killing All external provers ...
% 4.42/2.41 % Time passed: 2056ms (effective reasoning time: 1406ms)
% 4.42/2.41 % 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)>
% 4.42/2.42 % Axioms used in derivation (0):
% 4.42/2.42 % No. of inferences in proof: 15
% 4.42/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2056 ms resp. 1406 ms w/o parsing
% 4.42/2.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.42/2.46 % [INFO] Killing All external provers ...
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