%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL739^5 : 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 : n011.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 3.88s 1.94s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 36 ( 24 unt; 0 typ; 15 def)
% Number of atoms : 76 ( 21 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 428 ( 39 ~; 33 |; 9 &; 329 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 195 ( 195 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 138 ( 23 ^; 62 !; 24 ?; 138 :)
% ( 0 !>; 0 ?*; 0 @-; 29 @+)
% 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(sk11_decl,type,
sk11: ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b > $o ).
thf(sk12_decl,type,
sk12: b > ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b ).
thf(sk13_decl,type,
sk13: ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > ( b > $o ) > b ).
thf(sk14_decl,type,
sk14: ( ( b > $o ) > b ) > b > $o ).
thf(sk15_decl,type,
sk15: ( ( b > $o ) > b ) > 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] :
( ( A @ C @ D @ E )
| ( B @ C @ D @ E ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: b,B: ( b > $o ) > b > b > $o,C: ( b > $o ) > b > b > $o] :
@+[D: b] :
~ ( ( B @ ( sk1 @ B @ C ) @ A @ D )
| ( C @ ( 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] :
( ( A @ D @ ( C @ D ) @ E )
| ( B @ 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] :
( ( A @ C @ D @ E )
| ( B @ C @ D @ E ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: b,B: ( b > $o ) > b > b > $o,C: ( b > $o ) > b > b > $o] :
@+[D: b] :
~ ( ( B @ ( sk6 @ B @ C ) @ A @ D )
| ( C @ ( 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] :
( ( A @ D @ ( C @ D ) @ E )
| ( B @ 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(sk11_def,definition,
( sk11
= ( ^ [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 ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: b,B: ( b > $o ) > b > b > $o,C: ( b > $o ) > b > b > $o] :
@+[D: b] :
~ ( ( B @ ( sk11 @ B @ C ) @ A @ D )
| ( C @ ( sk11 @ B @ C ) @ A @ D ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: ( b > $o ) > b > b > $o,B: ( b > $o ) > b > b > $o] :
@+[C: ( b > $o ) > b] :
! [D: b > $o,E: b] :
( ( A @ D @ ( C @ D ) @ E )
| ( B @ D @ ( C @ D ) @ E ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: ( b > $o ) > b] :
@+[B: b > $o] :
~ ( ? [C: b] : ( B @ C )
=> ( B @ ( A @ B ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: ( b > $o ) > b] :
@+[B: b] : ( sk14 @ A @ B ) ) ) ).
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/sandbox/benchmark/theBenchmark.p',cX5310_SUB2) ).
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(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,
! [E: b,D: b > $o,C: b,B: ( b > $o ) > b > b > $o,A: ( b > $o ) > b > b > $o] :
( ( ~ ( B @ ( sk1 @ B @ A ) @ C @ ( sk2 @ C @ B @ A ) )
| ( B @ D @ ( sk3 @ B @ A @ D ) @ E )
| ( A @ D @ ( sk3 @ B @ A @ D ) @ E ) )
& ( ~ ( A @ ( sk1 @ B @ A ) @ C @ ( sk2 @ C @ B @ A ) )
| ( B @ D @ ( sk3 @ B @ A @ D ) @ E )
| ( A @ D @ ( sk3 @ B @ A @ D ) @ E ) )
& ( sk4 @ sk5 )
& ~ ( sk4
@ @+[F: b] : ( sk4 @ F ) ) ),
inference(cnf,[status(esa)],[4]) ).
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] :
( ( 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(11,plain,
! [E: b,D: b > $o,C: b,B: ( b > $o ) > b > b > $o,A: ( b > $o ) > b > b > $o] :
( ( ~ ( B @ ( sk6 @ B @ A ) @ C @ ( sk7 @ C @ B @ A ) )
| ( B @ D @ ( sk8 @ B @ A @ D ) @ E )
| ( A @ D @ ( sk8 @ B @ A @ D ) @ E ) )
& ( ~ ( A @ ( sk6 @ B @ A ) @ C @ ( sk7 @ C @ B @ A ) )
| ( B @ D @ ( sk8 @ B @ A @ D ) @ E )
| ( A @ 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(9,plain,
sk4 @ sk5,
inference(cnfConj,[status(thm)],[6]) ).
thf(15,plain,
~ ( sk9
@ @+[A: b] :
~ ( sk9 @ A ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(28,plain,
( ~ $true
| ( ( sk9 @ sk10 )
!= ( sk9
@ @+[A: b] :
~ ( sk9 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,15]) ).
thf(29,plain,
( ( sk9 @ sk10 )
!= ( sk9
@ @+[A: b] :
~ ( sk9 @ A ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(31,plain,
( sk10
!= ( @+[A: b] :
~ ( sk9 @ A ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(16,plain,
! [F: ( b > $o ) > b,E: b,D: b > $o,C: b,B: ( b > $o ) > b > b > $o,A: ( b > $o ) > b > b > $o] :
( ( ~ ( B @ ( sk11 @ B @ A ) @ C @ ( sk12 @ C @ B @ A ) )
| ( B @ D @ ( sk13 @ B @ A @ D ) @ E )
| ( A @ D @ ( sk13 @ B @ A @ D ) @ E ) )
& ( ~ ( A @ ( sk11 @ B @ A ) @ C @ ( sk12 @ C @ B @ A ) )
| ( B @ D @ ( sk13 @ B @ A @ D ) @ E )
| ( A @ D @ ( sk13 @ B @ A @ D ) @ E ) )
& ( sk14 @ F @ ( sk15 @ F ) )
& ~ ( sk14 @ F @ ( F @ ( sk14 @ F ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(19,plain,
! [A: ( b > $o ) > b] : ( sk14 @ A @ ( sk15 @ A ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(22,plain,
! [A: ( b > $o ) > b] : ( sk14 @ A @ ( sk15 @ A ) ),
inference(simp,[status(thm)],[19]) ).
thf(23,plain,
( ~ $true
| ( ( sk4 @ sk5 )
!= ( sk4
@ @+[A: b] : ( sk4 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,10]) ).
thf(24,plain,
( ( sk4 @ sk5 )
!= ( sk4
@ @+[A: b] : ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(27,plain,
( sk5
!= ( @+[A: b] : ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[10,14,9,3,31,15,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL739^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.21 % Computer : n011.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 10:05:16 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.68/0.53 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.86/0.63 % [INFO] Parsing done (100ms).
% 1.01/0.64 % [INFO] Running in sequential loop mode.
% 1.30/0.87 % [INFO] eprover registered as external prover.
% 1.30/0.87 % [INFO] Scanning for conjecture ...
% 1.50/0.96 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.50/1.01 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.50/1.01 % [INFO] Problem is higher-order (TPTP THF).
% 1.50/1.01 % [INFO] Type checking passed.
% 1.50/1.02 % [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 ...
% 3.88/1.94 % External prover 'e' found a proof!
% 3.88/1.94 % [INFO] Killing All external provers ...
% 3.88/1.94 % Time passed: 1635ms (effective reasoning time: 1298ms)
% 3.88/1.94 % 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)>
% 3.88/1.94 % Axioms used in derivation (0):
% 3.88/1.94 % No. of inferences in proof: 21
% 3.88/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1635 ms resp. 1298 ms w/o parsing
% 4.32/2.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.32/2.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------