%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV227^5 : 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 : n007.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 08:37:01 AM UTC 2026
% Result : Theorem 3.04s 1.37s
% Output : Refutation 3.55s
% 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 : 173 ( 33 ~; 57 |; 12 &; 71 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 8 ^; 12 !; 7 ?; 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',cX5200_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(7,plain,
( ( x @ sk1 )
| ( y @ sk1 )
| ? [A: a > $o] :
( ( ( A = x )
| ( A = y ) )
& ( A @ sk1 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(21,plain,
( ( ( x @ sk1 )
| ( y @ sk1 )
| ( sk2 = x )
| ( sk2 = y ) )
& ( ( x @ sk1 )
| ( y @ sk1 )
| ( sk2 @ sk1 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(23,plain,
( ( x @ sk1 )
| ( y @ sk1 )
| ( sk2 @ sk1 ) ),
inference(cnfConj,[status(thm)],[21]) ).
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,
! [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)],[6]) ).
thf(12,plain,
! [A: a > $o] :
( ~ ( y @ sk1 )
| ( A != y )
| ~ ( A @ sk1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(19,plain,
! [A: a > $o] :
( ( A != y )
| ~ ( y @ sk1 )
| ~ ( A @ sk1 ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(20,plain,
~ ( y @ sk1 ),
inference(simp,[status(thm)],[19]) ).
thf(9,plain,
! [A: a > $o] :
( ~ ( x @ sk1 )
| ( A != x )
| ~ ( A @ sk1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(13,plain,
! [A: a > $o] :
( ( A != x )
| ~ ( x @ sk1 )
| ~ ( A @ sk1 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(14,plain,
~ ( x @ sk1 ),
inference(simp,[status(thm)],[13]) ).
thf(31,plain,
( $false
| $false
| ( sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[23,20,14]) ).
thf(32,plain,
sk2 @ sk1,
inference(simp,[status(thm)],[31]) ).
thf(22,plain,
( ( x @ sk1 )
| ( y @ sk1 )
| ( sk2 = x )
| ( sk2 = y ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(24,plain,
( ( sk2 = x )
| ( sk2 = y )
| ( x @ sk1 )
| ( y @ sk1 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(33,plain,
( ( sk2 = x )
| ( sk2 = y )
| $false
| $false ),
inference(rewrite,[status(thm)],[24,20,14]) ).
thf(34,plain,
( ( sk2 = x )
| ( sk2 = y ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
! [B: a,A: a] :
( ( ( sk2 @ A )
= ( x @ A ) )
| ( ( sk2 @ B )
= ( y @ B ) ) ),
inference(func_ext,[status(esa)],[34]) ).
thf(50,plain,
! [B: a,A: a] :
( ( ( sk2 @ A )
= ( x @ A ) )
| ( y @ B )
| ( ( sk2 @ B )
!= ( sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[35,32]) ).
thf(51,plain,
! [A: a] :
( ( ( sk2 @ A )
= ( x @ A ) )
| ( y @ sk1 ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(61,plain,
! [A: a] :
( ( ( sk2 @ A )
= ( x @ A ) )
| $false ),
inference(rewrite,[status(thm)],[51,20]) ).
thf(62,plain,
! [A: a] :
( ( sk2 @ A )
= ( x @ A ) ),
inference(simp,[status(thm)],[61]) ).
thf(63,plain,
x @ sk1,
inference(rewrite,[status(thm)],[32,62]) ).
thf(68,plain,
$false,
inference(rewrite,[status(thm)],[63,14]) ).
thf(69,plain,
$false,
inference(simp,[status(thm)],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV227^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:20:56 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.73/0.50 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.95/0.59 % [INFO] Parsing done (91ms).
% 0.95/0.60 % [INFO] Running in sequential loop mode.
% 1.16/0.79 % [INFO] eprover registered as external prover.
% 1.16/0.79 % [INFO] Scanning for conjecture ...
% 1.37/0.83 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.37/0.84 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.37/0.84 % [INFO] Problem is higher-order (TPTP THF).
% 1.37/0.85 % [INFO] Type checking passed.
% 1.37/0.85 % [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 ...
% 3.04/1.36 % [INFO] Killing All external provers ...
% 3.04/1.37 % Time passed: 1089ms (effective reasoning time: 761ms)
% 3.04/1.37 % 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)>
% 3.04/1.37 % Axioms used in derivation (0):
% 3.04/1.37 % No. of inferences in proof: 30
% 3.04/1.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1089 ms resp. 761 ms w/o parsing
% 3.55/1.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.55/1.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------