%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV409^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:37:15 AM UTC 2026
% Result : Theorem 3.53s 2.05s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 27 ( 10 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 73 ( 6 ~; 0 |; 7 &; 55 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 23 ( 3 ^; 14 !; 3 ?; 23 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk2_decl,type,
sk2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk3_decl,type,
sk3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i > $o] :
~ ! [C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ! [D: $i] :
( ( B @ D )
= ( C @ D ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i > $o] :
~ ( ( ( A @ ( sk1 @ A ) @ B )
& ( A @ B @ ( sk1 @ A ) ) )
=> ! [C: $i] :
( ( sk1 @ A @ C )
= ( B @ C ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i] :
( ( sk1 @ A @ B )
!= ( sk2 @ A @ B ) ) ) ) ).
thf(1,conjecture,
? [A: ( $i > $o ) > ( $i > $o ) > $o] :
! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ! [D: $i] :
( ( B @ D )
= ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_BUG_pme) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ! [D: $i] :
( ( B @ D )
= ( C @ D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ! [D: $i] :
( ( B @ D )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A @ ( sk1 @ A ) @ ( sk2 @ A ) )
& ( A @ ( sk2 @ A ) @ ( sk1 @ A ) )
& ( ( sk1 @ A @ ( sk3 @ A ) )
!= ( sk2 @ A @ ( sk3 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] : ( A @ ( sk1 @ A ) @ ( sk2 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
$false,
inference(prim_subst,[status(thm)],[5:[bind(A,$thf( ^ [B: $i > $o] : ^ [C: $i > $o] : $false ))]]) ).
thf(15,plain,
$false,
inference(simp,[status(thm)],[10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV409^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:47:52 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 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
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.96 % [INFO] Parsing done (181ms).
% 1.24/0.98 % [INFO] Running in sequential loop mode.
% 1.86/1.38 % [INFO] eprover registered as external prover.
% 1.86/1.38 % [INFO] Scanning for conjecture ...
% 2.07/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.51 % [INFO] Type checking passed.
% 2.23/1.51 % [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 ...
% 3.53/2.04 % [INFO] Killing All external provers ...
% 3.53/2.05 % Time passed: 1722ms (effective reasoning time: 1060ms)
% 3.53/2.05 % 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)>
% 3.53/2.05 % Axioms used in derivation (0):
% 3.53/2.05 % No. of inferences in proof: 7
% 3.53/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1722 ms resp. 1060 ms w/o parsing
% 3.53/2.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.53/2.11 % [INFO] Killing All external provers ...
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