%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO548^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n017.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 08:46:06 AM UTC 2026
% Result : Theorem 5.06s 2.56s
% Output : Refutation 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 40 ( 9 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 131 ( 50 ~; 1 |; 3 &; 66 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 2 ^; 16 !; 9 ?; 46 :)
% ( 0 !>; 0 ?*; 0 @-; 19 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: ( ( $i > $o ) > $i ) > $i > $o ).
thf(sk6_decl,type,
sk6: ( ( $i > $o ) > $i ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ( ~ ! [B: $i] : ( A @ B )
=> ~ ( A
@ @+[B: $i] : ( A @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( sk1 @ A ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $o] :
~ ( ~ ! [B: $i] : ( A @ B )
=> ~ ( A
@ @+[B: $i] :
~ ( A @ B ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( sk3 @ A ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: ( $i > $o ) > $i] :
@+[B: $i > $o] :
~ ( ~ ! [C: $i] : ( B @ C )
=> ~ ( B @ ( A @ B ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: ( $i > $o ) > $i] :
@+[B: $i] :
~ ( sk5 @ A @ B ) ) ) ).
thf(1,conjecture,
? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ? [C: $i] :
~ ( B @ C )
=> ~ ( B @ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choicecomp) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ? [C: $i] :
~ ( B @ C )
=> ~ ( B @ ( A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ? [C: $i] :
~ ( B @ C )
=> ~ ( B @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: $i > $o] :
( ? [B: $i] :
~ ( A @ B )
=> ~ ( A
@ @+[B: $i] : ( A @ B ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(6,plain,
~ ! [A: $i > $o] :
( ~ ! [B: $i] : ( A @ B )
=> ~ ( A
@ @+[B: $i] : ( A @ B ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(7,plain,
( ~ ( sk1 @ sk2 )
& ( sk1
@ @+[A: $i] : ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(9,plain,
( sk1
@ @+[A: $i] : ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(5,plain,
~ ! [A: $i > $o] :
( ? [B: $i] :
~ ( A @ B )
=> ~ ( A
@ @+[B: $i] :
~ ( A @ B ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(10,plain,
~ ! [A: $i > $o] :
( ~ ! [B: $i] : ( A @ B )
=> ~ ( A
@ @+[B: $i] :
~ ( A @ B ) ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(11,plain,
( ~ ( sk3 @ sk4 )
& ( sk3
@ @+[A: $i] :
~ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(13,plain,
( sk3
@ @+[A: $i] :
~ ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(8,plain,
~ ( sk1 @ sk2 ),
inference(cnfConj,[status(thm)],[7]) ).
thf(18,plain,
( ~ $true
| ( ( sk1
@ @+[A: $i] : ( sk1 @ A ) )
!= ( sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[9,8]) ).
thf(19,plain,
( ( sk1
@ @+[A: $i] : ( sk1 @ A ) )
!= ( sk1 @ sk2 ) ),
inference(simp,[status(thm)],[18]) ).
thf(22,plain,
( ( @+[A: $i] : ( sk1 @ A ) )
!= sk2 ),
inference(simp,[status(thm)],[19]) ).
thf(12,plain,
~ ( sk3 @ sk4 ),
inference(cnfConj,[status(thm)],[11]) ).
thf(14,plain,
~ ? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ~ ! [C: $i] : ( B @ C )
=> ~ ( B @ ( A @ B ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(15,plain,
! [A: ( $i > $o ) > $i] :
( ~ ( sk5 @ A @ ( sk6 @ A ) )
& ( sk5 @ A @ ( A @ ( sk5 @ A ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [A: ( $i > $o ) > $i] :
~ ( sk5 @ A @ ( sk6 @ A ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(34,plain,
$false,
inference(e,[status(thm)],[9,13,22,12,3,16,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO548^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:09:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.91/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/0.96 % [INFO] Parsing done (175ms).
% 1.27/0.97 % [INFO] Running in sequential loop mode.
% 1.88/1.37 % [INFO] eprover registered as external prover.
% 1.88/1.38 % [INFO] Scanning for conjecture ...
% 2.12/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.12/1.49 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.12/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 2.12/1.49 % [INFO] Type checking passed.
% 2.28/1.50 % [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 ...
% 5.06/2.56 % External prover 'e' found a proof!
% 5.06/2.56 % [INFO] Killing All external provers ...
% 5.06/2.56 % Time passed: 2211ms (effective reasoning time: 1583ms)
% 5.06/2.56 % 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)>
% 5.06/2.56 % Axioms used in derivation (0):
% 5.06/2.56 % No. of inferences in proof: 20
% 5.06/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2211 ms resp. 1583 ms w/o parsing
% 5.33/2.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.33/2.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------