%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV290^5 : TPTP v9.3.1. Bugfixed 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 : n018.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 08:37:07 AM UTC 2026
% Result : Theorem 6.64s 3.48s
% Output : Refutation 6.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 34 ( 9 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 99 ( 13 ~; 1 |; 17 &; 56 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 15 ^; 14 !; 8 ?; 39 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c0_decl,type,
c0: ( $i > $o ) > $o ).
thf(cSUCC_decl,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(c_less__eq__decl,type,
c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(sk1_decl,type,
sk1: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).
thf(sk2_decl,type,
sk2: ( ( ( $i > $o ) > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(cSUCC_def,definition,
( cSUCC
= ( ^ [A: ( $i > $o ) > $o,B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ) ).
thf(c_less__eq__def,definition,
( c_less__eq_
= ( ^ [A: ( $i > $o ) > $o,B: ( $i > $o ) > $o] :
! [C: ( ( $i > $o ) > $o ) > $o] :
( ( ( C @ A )
& ! [D: ( $i > $o ) > $o] :
( ( C @ D )
=> ( C @ ( cSUCC @ D ) ) ) )
=> ( C @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: ( ( $i > $o ) > $o ) > $o] :
@+[B: ( $i > $o ) > $o] :
~ ( ( A @ B )
=> ! [C: ( ( $i > $o ) > $o ) > $o] :
( ( ( C @ B )
& ! [D: ( $i > $o ) > $o] :
( ( C @ D )
=> ( C
@ ^ [E: $i > $o] :
? [F: $i] :
( ( E @ F )
& ( D
@ ^ [G: $i] :
( ( G != F )
& ( E @ G ) ) ) ) ) ) )
=> ( C @ c0 ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( ( $i > $o ) > $o ) > $o] :
@+[B: ( ( $i > $o ) > $o ) > $o] :
~ ( ( ( B @ ( sk1 @ A ) )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B
@ ^ [D: $i > $o] :
? [E: $i] :
( ( D @ E )
& ( C
@ ^ [F: $i] :
( ( F != E )
& ( D @ F ) ) ) ) ) ) )
=> ( B @ c0 ) ) ) ) ).
thf(1,conjecture,
? [A: ( ( $i > $o ) > $o ) > $o] :
! [B: ( $i > $o ) > $o] :
( ( A @ B )
=> ( c_less__eq_ @ B @ c0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE1) ).
thf(2,negated_conjecture,
~ ? [A: ( ( $i > $o ) > $o ) > $o] :
! [B: ( $i > $o ) > $o] :
( ( A @ B )
=> ( c_less__eq_ @ B @ c0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( ( $i > $o ) > $o ) > $o] :
! [B: ( $i > $o ) > $o] :
( ( A @ B )
=> ! [C: ( ( $i > $o ) > $o ) > $o] :
( ( ( C @ B )
& ! [D: ( $i > $o ) > $o] :
( ( C @ D )
=> ( C
@ ^ [E: $i > $o] :
? [F: $i] :
( ( E @ F )
& ( D
@ ^ [G: $i] :
( ( G != F )
& ( E @ G ) ) ) ) ) ) )
=> ( C @ c0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: ( $i > $o ) > $o,A: ( ( $i > $o ) > $o ) > $o] :
( ( A @ ( sk1 @ A ) )
& ( sk2 @ A @ ( sk1 @ A ) )
& ( ~ ( sk2 @ A @ B )
| ( sk2 @ A
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) ) )
& ~ ( sk2 @ A @ c0 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [A: ( ( $i > $o ) > $o ) > $o] :
~ ( sk2 @ A @ c0 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [A: ( ( $i > $o ) > $o ) > $o] : ( A @ ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
~ $true,
inference(rewrite,[status(thm)],[8,5]) ).
thf(10,plain,
$false,
inference(simp,[status(thm)],[9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV290^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.12 % 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
% 0.27/0.32 % Computer : n018.cluster.edu
% 0.27/0.32 % Model : x86_64 x86_64
% 0.27/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.32 % Memory : 8046.5625MB
% 0.27/0.32 % OS : Linux 6.8.0-71-generic
% 0.27/0.32 % CPULimit : 300
% 0.27/0.32 % WCLimit : 300
% 0.27/0.32 % DateTime : Tue Sep 29 15:33:41 UTC 2026
% 0.27/0.32 % CPUTime :
% 0.27/0.32 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
% 1.49/1.16 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.43 % [INFO] Parsing done (274ms).
% 1.94/1.45 % [INFO] Running in sequential loop mode.
% 3.00/2.06 % [INFO] eprover registered as external prover.
% 3.00/2.08 % [INFO] Scanning for conjecture ...
% 3.30/2.23 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.30/2.27 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.30/2.27 % [INFO] Problem is higher-order (TPTP THF).
% 3.30/2.28 % [INFO] Type checking passed.
% 3.30/2.29 % [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 ...
% 6.64/3.47 % [INFO] Killing All external provers ...
% 6.64/3.48 % Time passed: 2951ms (effective reasoning time: 2013ms)
% 6.64/3.48 % 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)>
% 6.64/3.48 % Axioms used in derivation (0):
% 6.64/3.48 % No. of inferences in proof: 8
% 6.64/3.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2951 ms resp. 2013 ms w/o parsing
% 6.86/3.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.86/3.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------