%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV231^5 : 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 : n009.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 08:37:02 AM UTC 2026
% Result : Theorem 4.44s 2.47s
% Output : Refutation 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 154 ( 47 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 179 ( 39 ~; 50 |; 11 &; 71 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 8 ^; 19 !; 0 ?; 28 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(y_decl,type,
y: a > $o ).
thf(x_decl,type,
x: a > $o ).
thf(sk1_decl,type,
sk1: a ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
~ ( ( ( A = x )
| ( A = y ) )
=> ( A @ sk1 ) ) ) ) ).
thf(1,conjecture,
( ( ^ [A: a] :
( ( x @ A )
& ( y @ A ) ) )
= ( ^ [A: a] :
! [B: a > $o] :
( ( ( B = x )
| ( B = y ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5201_pme) ).
thf(2,negated_conjecture,
( ( ^ [A: a] :
( ( x @ A )
& ( y @ A ) ) )
!= ( ^ [A: a] :
! [B: a > $o] :
( ( ( B = x )
| ( B = y ) )
=> ( B @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ^ [A: a] :
( ( x @ A )
& ( y @ A ) ) )
!= ( ^ [A: a] :
! [B: a > $o] :
( ( ( B = x )
| ( B = y ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: a] :
( ( x @ A )
& ( y @ A ) ) )
!= ( ^ [A: a] :
! [B: a > $o] :
( ( ( B = x )
| ( B = y ) )
=> ( B @ A ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( ( x @ sk1 )
& ( y @ sk1 ) )
!= ( ! [A: a > $o] :
( ( ( A = x )
| ( A = y ) )
=> ( A @ sk1 ) ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(6,plain,
( ~ ( ( x @ sk1 )
& ( y @ sk1 ) )
| ~ ! [A: a > $o] :
( ( ( A = x )
| ( A = y ) )
=> ( A @ sk1 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( x @ sk1 )
| ~ ( y @ sk1 )
| ( sk2 = x )
| ( sk2 = y ) )
& ( ~ ( x @ sk1 )
| ~ ( y @ sk1 )
| ~ ( sk2 @ sk1 ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
( ~ ( x @ sk1 )
| ~ ( y @ sk1 )
| ~ ( sk2 @ sk1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(7,plain,
( ( ( x @ sk1 )
& ( y @ sk1 ) )
| ! [A: a > $o] :
( ( ( A = x )
| ( A = y ) )
=> ( A @ sk1 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(12,plain,
! [A: a > $o] :
( ( ( x @ sk1 )
| ( A != x )
| ( A @ sk1 ) )
& ( ( x @ sk1 )
| ( A != y )
| ( A @ sk1 ) )
& ( ( y @ sk1 )
| ( A != x )
| ( A @ sk1 ) )
& ( ( y @ sk1 )
| ( A != y )
| ( A @ sk1 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(13,plain,
! [A: a > $o] :
( ( x @ sk1 )
| ( A != x )
| ( A @ sk1 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(17,plain,
! [A: a > $o] :
( ( A != x )
| ( x @ sk1 )
| ( A @ sk1 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(18,plain,
x @ sk1,
inference(simp,[status(thm)],[17]) ).
thf(16,plain,
! [A: a > $o] :
( ( y @ sk1 )
| ( A != y )
| ( A @ sk1 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(23,plain,
! [A: a > $o] :
( ( A != y )
| ( y @ sk1 )
| ( A @ sk1 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(24,plain,
y @ sk1,
inference(simp,[status(thm)],[23]) ).
thf(27,plain,
( ~ $true
| ~ $true
| ~ ( sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[10,18,24]) ).
thf(28,plain,
~ ( sk2 @ sk1 ),
inference(simp,[status(thm)],[27]) ).
thf(9,plain,
( ~ ( x @ sk1 )
| ~ ( y @ sk1 )
| ( sk2 = x )
| ( sk2 = y ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(11,plain,
( ( sk2 = x )
| ( sk2 = y )
| ~ ( x @ sk1 )
| ~ ( y @ sk1 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(37,plain,
( ( sk2 = x )
| ( sk2 = y )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[11,18,24]) ).
thf(38,plain,
( ( sk2 = x )
| ( sk2 = y ) ),
inference(simp,[status(thm)],[37]) ).
thf(39,plain,
! [B: a,A: a] :
( ( ( sk2 @ A )
= ( x @ A ) )
| ( ( sk2 @ B )
= ( y @ B ) ) ),
inference(func_ext,[status(esa)],[38]) ).
thf(52,plain,
! [B: a,A: a] :
( ( ( sk2 @ A )
= ( x @ A ) )
| ~ ( y @ B )
| ( ( sk2 @ B )
!= ( sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[39,28]) ).
thf(53,plain,
! [A: a] :
( ( ( sk2 @ A )
= ( x @ A ) )
| ~ ( y @ sk1 ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(56,plain,
! [A: a] :
( ( ( sk2 @ A )
= ( x @ A ) )
| ~ $true ),
inference(rewrite,[status(thm)],[53,24]) ).
thf(57,plain,
! [A: a] :
( ( sk2 @ A )
= ( x @ A ) ),
inference(simp,[status(thm)],[56]) ).
thf(58,plain,
~ ( x @ sk1 ),
inference(rewrite,[status(thm)],[28,57]) ).
thf(63,plain,
~ $true,
inference(rewrite,[status(thm)],[58,18]) ).
thf(64,plain,
$false,
inference(simp,[status(thm)],[63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV231^5 : 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
% 0.12/0.22 % Computer : n009.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 15:23:30 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 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
% 1.01/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.99 % [INFO] Parsing done (181ms).
% 1.19/1.00 % [INFO] Running in sequential loop mode.
% 1.94/1.40 % [INFO] eprover registered as external prover.
% 1.94/1.41 % [INFO] Scanning for conjecture ...
% 1.94/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.10/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.10/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.10/1.54 % [INFO] Type checking passed.
% 2.10/1.54 % [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 ...
% 4.44/2.47 % [INFO] Killing All external provers ...
% 4.44/2.47 % Time passed: 2101ms (effective reasoning time: 1462ms)
% 4.44/2.47 % 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)>
% 4.44/2.47 % Axioms used in derivation (0):
% 4.44/2.47 % No. of inferences in proof: 30
% 4.44/2.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2101 ms resp. 1462 ms w/o parsing
% 4.76/2.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.76/2.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------