%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV056^5 : 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 : n016.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 08:36:46 AM UTC 2026
% Result : Theorem 6.52s 2.80s
% Output : Refutation 6.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 15 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 184 ( 17 ~; 8 |; 16 &; 130 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 5 ^; 29 !; 4 ?; 44 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > a > $o ).
thf(sk2_decl,type,
sk2: ( a > a > $o ) > a ).
thf(sk3_decl,type,
sk3: ( a > a > $o ) > a ).
thf(sk4_decl,type,
sk4: ( a > a > $o ) > a ).
thf(sk5_decl,type,
sk5: ( a > a > $o ) > a ).
thf(sk6_decl,type,
sk6: ( a > a > $o ) > a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > a > $o] :
~ ? [B: a > a > $o] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
& ! [C: a,D: a,E: a] :
( ( ( B @ C @ D )
& ( B @ D @ E ) )
=> ( B @ C @ E ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: a > a > $o] :
@+[B: a] :
~ ! [C: a] :
( ( sk1 @ B @ C )
=> ( A @ B @ C ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: a > a > $o] :
@+[B: a] :
~ ( ( sk1 @ ( sk2 @ A ) @ B )
=> ( A @ ( sk2 @ A ) @ B ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: a > a > $o] :
@+[B: a] :
~ ! [C: a,D: a] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: a > a > $o] :
@+[B: a] :
~ ! [C: a] :
( ( ( A @ ( sk4 @ A ) @ B )
& ( A @ B @ C ) )
=> ( A @ ( sk4 @ A ) @ C ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: a > a > $o] :
@+[B: a] :
~ ( ( ( A @ ( sk4 @ A ) @ ( sk5 @ A ) )
& ( A @ ( sk5 @ A ) @ B ) )
=> ( A @ ( sk4 @ A ) @ B ) ) ) ) ).
thf(1,conjecture,
! [A: a > a > $o] :
? [B: a > a > $o] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
& ! [C: a,D: a,E: a] :
( ( ( B @ C @ D )
& ( B @ D @ E ) )
=> ( B @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM275_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > $o] :
? [B: a > a > $o] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
& ! [C: a,D: a,E: a] :
( ( ( B @ C @ D )
& ( B @ D @ E ) )
=> ( B @ C @ E ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > $o] :
? [B: a > a > $o] :
( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
& ! [C: a,D: a,E: a] :
( ( ( B @ C @ D )
& ( B @ D @ E ) )
=> ( B @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: a > a > $o] :
( ( ( sk1 @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ ( sk4 @ A ) @ ( sk5 @ A ) ) )
& ( ( sk1 @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
& ( ( sk1 @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ~ ( A @ ( sk4 @ A ) @ ( sk6 @ A ) ) )
& ( ~ ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ ( sk4 @ A ) @ ( sk5 @ A ) ) )
& ( ~ ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
& ( ~ ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ~ ( A @ ( sk4 @ A ) @ ( sk6 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ~ ( A @ ( sk4 @ A ) @ ( sk6 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(80,plain,
( ~ $true
| ~ $true ),
inference(prim_subst,[status(thm)],[6:[bind(A,$thf( ^ [B: a] : ^ [C: a] : $true ))]]) ).
thf(104,plain,
$false,
inference(simp,[status(thm)],[80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV056^5 : 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
% 0.11/0.21 % Computer : n016.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 15:10:34 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (185ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.03/1.41 % [INFO] eprover registered as external prover.
% 2.03/1.42 % [INFO] Scanning for conjecture ...
% 2.22/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.55 % [INFO] Type checking passed.
% 2.22/1.56 % [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 ...
% 6.05/2.80 % [INFO] Killing All external provers ...
% 6.52/2.80 % Time passed: 2444ms (effective reasoning time: 1788ms)
% 6.52/2.80 % 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)>
% 6.52/2.80 % Axioms used in derivation (0):
% 6.52/2.80 % No. of inferences in proof: 7
% 6.52/2.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2444 ms resp. 1788 ms w/o parsing
% 6.52/2.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.52/2.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------