%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL738^5 : 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 : n026.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 08:14:14 AM UTC 2026
% Result : Theorem 4.57s 2.51s
% Output : Refutation 4.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 31 ( 21 unt; 0 typ; 18 def)
% Number of atoms : 79 ( 18 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 373 ( 27 ~; 36 |; 6 &; 281 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 189 ( 189 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 150 ( 2 ^; 69 !; 52 ?; 150 :)
% ( 0 !>; 0 ?*; 0 @-; 27 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(sk1_decl,type,
sk1: ( b > $o ) > b > b > $o ).
thf(sk2_decl,type,
sk2: ( b > $o ) > b > b > $o ).
thf(sk3_decl,type,
sk3: b > $o ).
thf(sk4_decl,type,
sk4: b > b ).
thf(sk5_decl,type,
sk5: ( b > $o ) > b > b > $o ).
thf(sk6_decl,type,
sk6: ( b > $o ) > b > b > $o ).
thf(sk7_decl,type,
sk7: ( b > $o ) > b ).
thf(sk8_decl,type,
sk8: b > $o ).
thf(sk9_decl,type,
sk9: b ).
thf(sk10_decl,type,
sk10: ( b > $o ) > b > b > $o ).
thf(sk11_decl,type,
sk11: ( b > $o ) > b > b > $o ).
thf(sk12_decl,type,
sk12: b > $o ).
thf(sk13_decl,type,
sk13: b > b ).
thf(sk14_decl,type,
sk14: ( b > $o ) > b > b > $o ).
thf(sk15_decl,type,
sk15: ( b > $o ) > b > b > $o ).
thf(sk16_decl,type,
sk16: ( b > $o ) > b ).
thf(sk17_decl,type,
sk17: b > $o ).
thf(sk18_decl,type,
sk18: 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 > $o ) > b > b > $o] :
~ ! [B: b > $o] :
? [C: b] :
! [D: b] :
( ( A @ B @ C @ D )
| ( sk1 @ B @ C @ D ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: b > $o] :
~ ? [B: b] :
! [C: b] :
( ( sk2 @ A @ B @ C )
| ( sk1 @ A @ B @ C ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: b] :
@+[B: b] :
~ ( ( sk2 @ sk3 @ A @ B )
| ( sk1 @ sk3 @ A @ B ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[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(sk6_def,definition,
( sk6
= ( @+[A: ( b > $o ) > b > b > $o] :
? [B: ( b > $o ) > b] :
! [C: b > $o,D: b] :
( ( A @ C @ ( B @ C ) @ D )
| ( sk5 @ C @ ( B @ C ) @ D ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: ( b > $o ) > b] :
! [B: b > $o,C: b] :
( ( sk6 @ B @ ( A @ B ) @ C )
| ( sk5 @ B @ ( A @ B ) @ C ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: b > $o] :
~ ( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] : ( A @ B ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: b] : ( sk8 @ A ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[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(sk11_def,definition,
( sk11
= ( @+[A: ( b > $o ) > b > b > $o] :
~ ! [B: b > $o] :
? [C: b] :
! [D: b] :
( ( A @ B @ C @ D )
| ( sk10 @ B @ C @ D ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: b > $o] :
~ ? [B: b] :
! [C: b] :
( ( sk11 @ A @ B @ C )
| ( sk10 @ A @ B @ C ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: b] :
@+[B: b] :
~ ( ( sk11 @ sk12 @ A @ B )
| ( sk10 @ sk12 @ A @ B ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[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(sk15_def,definition,
( sk15
= ( @+[A: ( b > $o ) > b > b > $o] :
? [B: ( b > $o ) > b] :
! [C: b > $o,D: b] :
( ( A @ C @ ( B @ C ) @ D )
| ( sk14 @ C @ ( B @ C ) @ D ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: ( b > $o ) > b] :
! [B: b > $o,C: b] :
( ( sk15 @ B @ ( A @ B ) @ C )
| ( sk14 @ B @ ( A @ B ) @ C ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: b > $o] :
~ ( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] :
~ ( A @ B ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: b] : ( sk17 @ A ) ) ) ).
thf(1,conjecture,
( ? [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 ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( B @ D @ ( C @ D ) @ E )
| ( A @ 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_SUB) ).
thf(2,negated_conjecture,
~ ( ? [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 ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( B @ D @ ( C @ D ) @ E )
| ( A @ 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] :
( ( B @ C @ D @ E )
| ( A @ C @ D @ E ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( B @ D @ ( C @ D ) @ E )
| ( A @ 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(5,plain,
~ ( ? [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 ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( B @ D @ ( C @ D ) @ E )
| ( A @ D @ ( C @ D ) @ E ) ) )
=> ! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] :
~ ( A @ B ) ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(12,plain,
~ ( ( ! [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 ) )
=> ? [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 ) ) )
=> ! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] :
~ ( A @ B ) ) ) ),
inference(miniscope,[status(thm)],[5]) ).
thf(13,plain,
! [C: b,B: b > $o,A: b] :
( ( ~ ( sk11 @ sk12 @ A @ ( sk13 @ A ) )
| ( sk15 @ B @ ( sk16 @ B ) @ C )
| ( sk14 @ B @ ( sk16 @ B ) @ C ) )
& ( ~ ( sk10 @ sk12 @ A @ ( sk13 @ A ) )
| ( sk15 @ B @ ( sk16 @ B ) @ C )
| ( sk14 @ B @ ( sk16 @ B ) @ C ) )
& ( sk17 @ sk18 )
& ~ ( sk17
@ @+[D: b] :
~ ( sk17 @ D ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(16,plain,
sk17 @ sk18,
inference(cnfConj,[status(thm)],[13]) ).
thf(4,plain,
~ ( ? [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 ) )
=> ? [C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( B @ D @ ( C @ D ) @ E )
| ( A @ D @ ( C @ D ) @ E ) ) )
=> ! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] : ( A @ B ) ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(6,plain,
~ ( ( ! [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 ) )
=> ? [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 ) ) )
=> ! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A
@ @+[B: b] : ( A @ B ) ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(7,plain,
! [C: b,B: b > $o,A: b] :
( ( ~ ( sk2 @ sk3 @ A @ ( sk4 @ A ) )
| ( sk6 @ B @ ( sk7 @ B ) @ C )
| ( sk5 @ B @ ( sk7 @ B ) @ C ) )
& ( ~ ( sk1 @ sk3 @ A @ ( sk4 @ A ) )
| ( sk6 @ B @ ( sk7 @ B ) @ C )
| ( sk5 @ B @ ( sk7 @ B ) @ C ) )
& ( sk8 @ sk9 )
& ~ ( sk8
@ @+[D: b] : ( sk8 @ D ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
sk8 @ sk9,
inference(cnfConj,[status(thm)],[7]) ).
thf(11,plain,
~ ( sk8
@ @+[A: b] : ( sk8 @ A ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[3,16,10,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL738^5 : 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 : n026.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 10:13:42 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
% 1.04/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.01 % [INFO] Parsing done (192ms).
% 1.45/1.03 % [INFO] Running in sequential loop mode.
% 2.00/1.44 % [INFO] eprover registered as external prover.
% 2.00/1.45 % [INFO] Scanning for conjecture ...
% 2.20/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.20/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.20/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.59 % [INFO] Type checking passed.
% 2.37/1.60 % [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 ...
% 4.57/2.50 % External prover 'e' found a proof!
% 4.57/2.50 % [INFO] Killing All external provers ...
% 4.57/2.50 % Time passed: 2131ms (effective reasoning time: 1468ms)
% 4.57/2.50 % 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)>
% 4.57/2.50 % Axioms used in derivation (0):
% 4.57/2.50 % No. of inferences in proof: 13
% 4.57/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2131 ms resp. 1468 ms w/o parsing
% 4.87/2.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.87/2.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------