%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN997^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n014.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 08:41:35 AM UTC 2026
% Result : Theorem 4.18s 2.35s
% Output : Refutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 32 ( 7 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 18 ~; 1 |; 2 &; 42 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 5 !; 10 ?; 30 :)
% ( 0 !>; 0 ?*; 0 @-; 15 @+)
% 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(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(1,conjecture,
? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ? [C: $i] : ( B @ C )
=> ( B @ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
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(5,plain,
~ ! [A: $i > $o] :
( ? [B: $i] : ( A @ B )
=> ( A
@ @+[B: $i] :
~ ( A @ B ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(9,plain,
( ( sk3 @ sk4 )
& ~ ( sk3
@ @+[A: $i] :
~ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(10,plain,
sk3 @ sk4,
inference(cnfConj,[status(thm)],[9]) ).
thf(4,plain,
~ ! [A: $i > $o] :
( ? [B: $i] : ( A @ B )
=> ( A
@ @+[B: $i] : ( A @ B ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(6,plain,
( ( sk1 @ sk2 )
& ~ ( sk1
@ @+[A: $i] : ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
sk1 @ sk2,
inference(cnfConj,[status(thm)],[6]) ).
thf(11,plain,
~ ( sk3
@ @+[A: $i] :
~ ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(8,plain,
~ ( sk1
@ @+[A: $i] : ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(15,plain,
( ~ $true
| ( ( sk1 @ sk2 )
!= ( sk1
@ @+[A: $i] : ( sk1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(16,plain,
( ( sk1 @ sk2 )
!= ( sk1
@ @+[A: $i] : ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(19,plain,
( sk2
!= ( @+[A: $i] : ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(30,plain,
$false,
inference(e,[status(thm)],[10,7,3,11,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN997^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.19 % Computer : n014.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:20:15 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 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
% 0.89/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.94 % [INFO] Parsing done (181ms).
% 1.24/0.96 % [INFO] Running in sequential loop mode.
% 1.83/1.36 % [INFO] eprover registered as external prover.
% 1.83/1.37 % [INFO] Scanning for conjecture ...
% 2.04/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.48 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.49 % [INFO] Type checking passed.
% 2.04/1.49 % [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 ...
% 4.18/2.34 % External prover 'e' found a proof!
% 4.18/2.34 % [INFO] Killing All external provers ...
% 4.18/2.34 % Time passed: 2015ms (effective reasoning time: 1382ms)
% 4.18/2.34 % 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)>
% 4.18/2.35 % Axioms used in derivation (0):
% 4.18/2.35 % No. of inferences in proof: 15
% 4.18/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2015 ms resp. 1382 ms w/o parsing
% 4.18/2.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.18/2.40 % [INFO] Killing All external provers ...
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