%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV239^5 : 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 : n003.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 08:37:03 AM UTC 2026
% Result : Theorem 4.91s 2.50s
% Output : Refutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 113 ( 51 equ; 16 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 164 ( 31 ~; 27 |; 19 &; 87 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 4 ^; 8 !; 15 ?; 29 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(y_decl,type,
y: a > $o ).
thf(sk1_decl,type,
sk1: a ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
( ? [B: a] :
( ( y @ B )
& ( A
= ( (=) @ a @ B ) ) )
& ( A @ sk1 ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a] :
( ( y @ A )
& ( sk2
= ( (=) @ a @ A ) ) ) ) ) ).
thf(1,conjecture,
( y
= ( ^ [A: a] :
? [B: a > $o] :
( ? [C: a] :
( ( y @ C )
& ( B
= ( (=) @ a @ C ) ) )
& ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5211_pme) ).
thf(2,negated_conjecture,
( y
!= ( ^ [A: a] :
? [B: a > $o] :
( ? [C: a] :
( ( y @ C )
& ( B
= ( (=) @ a @ C ) ) )
& ( B @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( y
!= ( ^ [A: a] :
? [B: a > $o] :
( ? [C: a] :
( ( y @ C )
& ( B
= ( (=) @ a @ C ) ) )
& ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( y
!= ( ^ [A: a] :
? [B: a > $o] :
( ? [C: a] :
( ( y @ C )
& ( B
= ( (=) @ a @ C ) ) )
& ( B @ A ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( y @ sk1 )
!= ( ? [A: a > $o] :
( ? [B: a] :
( ( y @ B )
& ( A
= ( (=) @ a @ B ) ) )
& ( A @ sk1 ) ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(7,plain,
( ( y @ sk1 )
| ? [A: a > $o] :
( ? [B: a] :
( ( y @ B )
& ( A
= ( (=) @ a @ B ) ) )
& ( A @ sk1 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(11,plain,
( ( ( y @ sk1 )
| ( y @ sk3 ) )
& ( ( y @ sk1 )
| ( sk2
= ( (=) @ a @ sk3 ) ) )
& ( ( y @ sk1 )
| ( sk2 @ sk1 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(14,plain,
( ( y @ sk1 )
| ( sk2 @ sk1 ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(6,plain,
( ~ ( y @ sk1 )
| ~ ? [A: a > $o] :
( ? [B: a] :
( ( y @ B )
& ( A
= ( (=) @ a @ B ) ) )
& ( A @ sk1 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
! [B: a,A: a > $o] :
( ~ ( y @ sk1 )
| ~ ( y @ B )
| ( A
!= ( (=) @ a @ B ) )
| ~ ( A @ sk1 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(9,plain,
! [B: a,A: a > $o] :
( ( A
!= ( (=) @ a @ B ) )
| ~ ( y @ sk1 )
| ~ ( y @ B )
| ~ ( A @ sk1 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
! [A: a] :
( ~ ( y @ sk1 )
| ~ ( y @ A )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[9]) ).
thf(24,plain,
! [A: a] :
( ( A != sk1 )
| ~ ( y @ sk1 )
| ~ ( y @ A ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(32,plain,
! [A: a] :
( ( A != sk1 )
| ~ ( y @ sk1 )
| ( ( y @ A )
!= ( y @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[24]) ).
thf(35,plain,
( ( sk1 != sk1 )
| ~ ( y @ sk1 ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk1 ))]]) ).
thf(36,plain,
~ ( y @ sk1 ),
inference(pattern_uni,[status(thm)],[35:[]]) ).
thf(42,plain,
( $false
| ( sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[14,36]) ).
thf(43,plain,
sk2 @ sk1,
inference(simp,[status(thm)],[42]) ).
thf(13,plain,
( ( y @ sk1 )
| ( sk2
= ( (=) @ a @ sk3 ) ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(15,plain,
( ( sk2
= ( (=) @ a @ sk3 ) )
| ( y @ sk1 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(54,plain,
( ( sk2
= ( (=) @ a @ sk3 ) )
| $false ),
inference(rewrite,[status(thm)],[15,36]) ).
thf(55,plain,
( sk2
= ( (=) @ a @ sk3 ) ),
inference(simp,[status(thm)],[54]) ).
thf(56,plain,
! [A: a] :
( ( sk2 @ A )
= ( sk3 = A ) ),
inference(func_ext,[status(esa)],[55]) ).
thf(68,plain,
sk3 = sk1,
inference(rewrite,[status(thm)],[43,56]) ).
thf(73,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[68]) ).
thf(12,plain,
( ( y @ sk1 )
| ( y @ sk3 ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(40,plain,
( $false
| ( y @ sk3 ) ),
inference(rewrite,[status(thm)],[12,36]) ).
thf(41,plain,
y @ sk3,
inference(simp,[status(thm)],[40]) ).
thf(49,plain,
( ~ $true
| ( ( y @ sk3 )
!= ( y @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[41,36]) ).
thf(50,plain,
( ( y @ sk3 )
!= ( y @ sk1 ) ),
inference(simp,[status(thm)],[49]) ).
thf(51,plain,
sk3 != sk1,
inference(simp,[status(thm)],[50]) ).
thf(77,plain,
$false,
inference(simplifyReflect,[status(thm)],[73,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV239^5 : 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
% 0.10/0.21 % Computer : n003.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 15:28:28 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
% 0.97/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.14/0.98 % [INFO] Parsing done (178ms).
% 1.14/0.99 % [INFO] Running in sequential loop mode.
% 1.70/1.39 % [INFO] eprover registered as external prover.
% 1.88/1.40 % [INFO] Scanning for conjecture ...
% 1.88/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.03/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.03/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.03/1.53 % [INFO] Type checking passed.
% 2.03/1.53 % [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 ...
% 4.52/2.49 % [INFO] Killing All external provers ...
% 4.52/2.50 % Time passed: 2138ms (effective reasoning time: 1498ms)
% 4.52/2.50 % 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)>
% 4.91/2.50 % Axioms used in derivation (0):
% 4.91/2.50 % No. of inferences in proof: 32
% 4.91/2.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2138 ms resp. 1498 ms w/o parsing
% 4.91/2.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.91/2.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------