%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET632^5 : 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 : n019.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 08:23:04 AM UTC 2026
% Result : Theorem 4.08s 2.35s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 78 ( 17 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 173 ( 37 ~; 17 |; 23 &; 78 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 8 ^; 37 !; 12 ?; 60 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a > $o ).
thf(sk4_decl,type,
sk4: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ( ? [B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
& ? [C: a > $o] :
( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ~ ? [D: a] :
( ( B @ D )
& ( C @ D ) ) ) )
=> ( A
= ( ^ [B: a] : $false ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
( ! [B: a] :
( ( sk1 @ B )
=> ( A @ B ) )
& ? [B: a > $o] :
( ! [C: a] :
( ( sk1 @ C )
=> ( B @ C ) )
& ~ ? [C: a] :
( ( A @ C )
& ( B @ C ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > $o] :
( ! [B: a] :
( ( sk1 @ B )
=> ( A @ B ) )
& ~ ? [B: a] :
( ( sk2 @ B )
& ( A @ B ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) )
& ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ~ ? [D: a] :
( ( B @ D )
& ( C @ D ) ) )
=> ( A
= ( ^ [D: a] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_114_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) )
& ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ~ ? [D: a] :
( ( B @ D )
& ( C @ D ) ) )
=> ( A
= ( ^ [D: a] : $false ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ! [D: a] :
( ( A @ D )
=> ( B @ D ) )
& ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ~ ? [D: a] :
( ( B @ D )
& ( C @ D ) ) )
=> ( A
= ( ^ [D: a] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: a > $o] :
( ? [B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
& ? [C: a > $o] :
( ! [D: a] :
( ( A @ D )
=> ( C @ D ) )
& ~ ? [D: a] :
( ( B @ D )
& ( C @ D ) ) ) )
=> ( A
= ( ^ [B: a] : $false ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [C: a,B: a,A: a] :
( ( ~ ( sk1 @ A )
| ( sk2 @ A ) )
& ( ~ ( sk1 @ B )
| ( sk3 @ B ) )
& ( ~ ( sk2 @ C )
| ~ ( sk3 @ C ) )
& ( sk1
!= ( ^ [D: a] : $false ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
( sk1
!= ( ^ [A: a] : $false ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(12,plain,
( sk1
!= ( ^ [A: a] : $false ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(13,plain,
sk1 @ sk4,
inference(func_ext,[status(esa)],[12]) ).
thf(7,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk3 @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(23,plain,
! [A: a] :
( ~ $true
| ( sk3 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13,10]) ).
thf(24,plain,
! [A: a] :
( ( sk3 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
sk3 @ sk4,
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( sk4 ))]]) ).
thf(6,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(14,plain,
! [A: a] :
( ~ $true
| ( sk2 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13,6]) ).
thf(15,plain,
! [A: a] :
( ( sk2 @ A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(16,plain,
sk2 @ sk4,
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( sk4 ))]]) ).
thf(8,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ~ ( sk3 @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(11,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ~ ( sk3 @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(20,plain,
! [A: a] :
( ~ $true
| ~ ( sk3 @ A )
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16,11]) ).
thf(21,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
~ ( sk3 @ sk4 ),
inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( sk4 ))]]) ).
thf(32,plain,
$false,
inference(rewrite,[status(thm)],[25,22]) ).
thf(33,plain,
$false,
inference(simp,[status(thm)],[32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET632^5 : 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
% 0.10/0.22 % Computer : n019.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:40:18 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.05/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (176ms).
% 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 ...
% 2.24/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.56 % [INFO] Type checking passed.
% 2.24/1.56 % [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 ...
% 4.08/2.34 % [INFO] Killing All external provers ...
% 4.08/2.34 % Time passed: 1968ms (effective reasoning time: 1330ms)
% 4.08/2.34 % 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)>
% 4.08/2.34 % Axioms used in derivation (0):
% 4.08/2.34 % No. of inferences in proof: 24
% 4.08/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1968 ms resp. 1330 ms w/o parsing
% 4.37/2.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.37/2.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------