%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL735^5 : 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 : 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 08:14:13 AM UTC 2026
% Result : Theorem 5.07s 2.51s
% Output : Refutation 5.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 10 def)
% Number of atoms : 35 ( 10 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 298 ( 20 ~; 24 |; 6 &; 231 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 147 ( 147 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 104 ( 14 ^; 51 !; 22 ?; 104 :)
% ( 0 !>; 0 ?*; 0 @-; 17 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(sk1_decl,type,
sk1: ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b > $o ).
thf(sk2_decl,type,
sk2: b > ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b ).
thf(sk3_decl,type,
sk3: ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > ( b > $o ) > b ).
thf(sk4_decl,type,
sk4: b > $o ).
thf(sk5_decl,type,
sk5: b ).
thf(sk6_decl,type,
sk6: ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b > $o ).
thf(sk7_decl,type,
sk7: b > ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b ).
thf(sk8_decl,type,
sk8: ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > ( b > $o ) > b ).
thf(sk9_decl,type,
sk9: b > $o ).
thf(sk10_decl,type,
sk10: b ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
@+[C: b > $o] :
~ ? [D: b] :
! [E: b] :
( ( B @ C @ D @ E )
| ( A @ C @ D @ E ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: b,B: ( b > $o ) > b > b > $o,C: ( b > $o ) > b > b > $o] :
@+[D: b] :
~ ( ( C @ ( sk1 @ B @ C ) @ A @ D )
| ( B @ ( sk1 @ B @ C ) @ A @ D ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
@+[C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( B @ D @ ( C @ D ) @ E )
| ( A @ D @ ( C @ D ) @ E ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: b > $o] :
~ ( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] : ( A @ B ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: b] : ( sk4 @ A ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
@+[C: b > $o] :
~ ? [D: b] :
! [E: b] :
( ( B @ C @ D @ E )
| ( A @ C @ D @ E ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: b,B: ( b > $o ) > b > b > $o,C: ( b > $o ) > b > b > $o] :
@+[D: b] :
~ ( ( C @ ( sk6 @ B @ C ) @ A @ D )
| ( B @ ( sk6 @ B @ C ) @ A @ D ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
@+[C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( B @ D @ ( C @ D ) @ E )
| ( A @ D @ ( C @ D ) @ E ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: b > $o] :
~ ( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] :
~ ( A @ B ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: b] : ( sk9 @ A ) ) ) ).
thf(1,conjecture,
( ! [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
( ! [C: b > $o] :
? [D: b] :
! [E: b] :
( ( A @ C @ D @ E )
| ( B @ C @ D @ E ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( A @ D @ ( C @ D ) @ E )
| ( B @ D @ ( C @ D ) @ E ) ) )
=> ? [A: ( b > $o ) > b] :
! [B: b > $o] :
( ? [C: b] : ( B @ C )
=> ( B @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5310_SUB5) ).
thf(2,negated_conjecture,
~ ( ! [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
( ! [C: b > $o] :
? [D: b] :
! [E: b] :
( ( A @ C @ D @ E )
| ( B @ C @ D @ E ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( A @ D @ ( C @ D ) @ E )
| ( B @ D @ ( C @ D ) @ E ) ) )
=> ? [A: ( b > $o ) > b] :
! [B: b > $o] :
( ? [C: b] : ( B @ C )
=> ( B @ ( A @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
( ! [C: b > $o] :
? [D: b] :
! [E: b] :
( ( A @ C @ D @ E )
| ( B @ C @ D @ E ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( A @ D @ ( C @ D ) @ E )
| ( B @ D @ ( C @ D ) @ E ) ) )
=> ? [A: ( b > $o ) > b] :
! [B: b > $o] :
( ? [C: b] : ( B @ C )
=> ( B @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
( ! [C: b > $o] :
? [D: b] :
! [E: b] :
( ( A @ C @ D @ E )
| ( B @ C @ D @ E ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( A @ D @ ( C @ D ) @ E )
| ( B @ D @ ( C @ D ) @ E ) ) )
=> ! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] : ( A @ B ) ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(6,plain,
! [E: b,D: b > $o,C: b,B: ( b > $o ) > b > b > $o,A: ( b > $o ) > b > b > $o] :
( ( ~ ( A @ ( sk1 @ B @ A ) @ C @ ( sk2 @ C @ B @ A ) )
| ( A @ D @ ( sk3 @ B @ A @ D ) @ E )
| ( B @ D @ ( sk3 @ B @ A @ D ) @ E ) )
& ( ~ ( B @ ( sk1 @ B @ A ) @ C @ ( sk2 @ C @ B @ A ) )
| ( A @ D @ ( sk3 @ B @ A @ D ) @ E )
| ( B @ D @ ( sk3 @ B @ A @ D ) @ E ) )
& ( sk4 @ sk5 )
& ~ ( sk4
@ @+[F: b] : ( sk4 @ F ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
sk4 @ sk5,
inference(cnfConj,[status(thm)],[6]) ).
thf(10,plain,
~ ( sk4
@ @+[A: b] : ( sk4 @ A ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(5,plain,
~ ( ! [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
( ! [C: b > $o] :
? [D: b] :
! [E: b] :
( ( A @ C @ D @ E )
| ( B @ C @ D @ E ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( A @ D @ ( C @ D ) @ E )
| ( B @ D @ ( C @ D ) @ E ) ) )
=> ! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] :
~ ( A @ B ) ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(11,plain,
! [E: b,D: b > $o,C: b,B: ( b > $o ) > b > b > $o,A: ( b > $o ) > b > b > $o] :
( ( ~ ( A @ ( sk6 @ B @ A ) @ C @ ( sk7 @ C @ B @ A ) )
| ( A @ D @ ( sk8 @ B @ A @ D ) @ E )
| ( B @ D @ ( sk8 @ B @ A @ D ) @ E ) )
& ( ~ ( B @ ( sk6 @ B @ A ) @ C @ ( sk7 @ C @ B @ A ) )
| ( A @ D @ ( sk8 @ B @ A @ D ) @ E )
| ( B @ D @ ( sk8 @ B @ A @ D ) @ E ) )
& ( sk9 @ sk10 )
& ~ ( sk9
@ @+[F: b] :
~ ( sk9 @ F ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(14,plain,
sk9 @ sk10,
inference(cnfConj,[status(thm)],[11]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[3,9,10,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL735^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.23 % Computer : n002.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 10:10:07 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.06/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.00 % [INFO] Parsing done (201ms).
% 1.27/1.02 % [INFO] Running in sequential loop mode.
% 2.14/1.41 % [INFO] eprover registered as external prover.
% 2.14/1.42 % [INFO] Scanning for conjecture ...
% 2.34/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.34/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.34/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.34/1.56 % [INFO] Type checking passed.
% 2.34/1.56 % [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 ...
% 5.07/2.51 % External prover 'e' found a proof!
% 5.07/2.51 % [INFO] Killing All external provers ...
% 5.07/2.51 % Time passed: 2137ms (effective reasoning time: 1481ms)
% 5.07/2.51 % 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)>
% 5.07/2.51 % Axioms used in derivation (0):
% 5.07/2.51 % No. of inferences in proof: 11
% 5.07/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2137 ms resp. 1481 ms w/o parsing
% 5.37/2.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.37/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------