%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU896^5 : 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 : n005.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 08:29:33 AM UTC 2026
% Result : Theorem 3.80s 2.31s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 101 ( 100 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 166 ( 40 ~; 50 |; 12 &; 64 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 8 ^; 5 !; 7 ?; 21 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(y_decl,type,
y: b ).
thf(g_decl,type,
g: b > a ).
thf(x_decl,type,
x: b ).
thf(sk1_decl,type,
sk1: a ).
thf(sk2_decl,type,
sk2: b ).
thf(sk2_def,definition,
( sk2
= ( @+[A: b] :
( ( ( A = x )
| ( A = y ) )
& ( sk1
= ( g @ A ) ) ) ) ) ).
thf(1,conjecture,
( ( ^ [A: a] :
? [B: b] :
( ( ( B = x )
| ( B = y ) )
& ( A
= ( g @ B ) ) ) )
= ( ^ [A: a] :
( ( A
= ( g @ x ) )
| ( A
= ( g @ y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM500_pme) ).
thf(2,negated_conjecture,
( ( ^ [A: a] :
? [B: b] :
( ( ( B = x )
| ( B = y ) )
& ( A
= ( g @ B ) ) ) )
!= ( ^ [A: a] :
( ( A
= ( g @ x ) )
| ( A
= ( g @ y ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ^ [A: a] :
? [B: b] :
( ( ( B = x )
| ( B = y ) )
& ( A
= ( g @ B ) ) ) )
!= ( ^ [A: a] :
( ( A
= ( g @ x ) )
| ( A
= ( g @ y ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: a] :
? [B: b] :
( ( ( B = x )
| ( B = y ) )
& ( A
= ( g @ B ) ) ) )
!= ( ^ [A: a] :
( ( A
= ( g @ x ) )
| ( A
= ( g @ y ) ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [A: b] :
( ( ( A = x )
| ( A = y ) )
& ( sk1
= ( g @ A ) ) ) )
!= ( ( sk1
= ( g @ x ) )
| ( sk1
= ( g @ y ) ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(7,plain,
( ? [A: b] :
( ( ( A = x )
| ( A = y ) )
& ( sk1
= ( g @ A ) ) )
| ( sk1
= ( g @ x ) )
| ( sk1
= ( g @ y ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(21,plain,
( ( ( sk2 = x )
| ( sk2 = y )
| ( sk1
= ( g @ x ) )
| ( sk1
= ( g @ y ) ) )
& ( ( sk1
= ( g @ sk2 ) )
| ( sk1
= ( g @ x ) )
| ( sk1
= ( g @ y ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(22,plain,
( ( sk2 = x )
| ( sk2 = y )
| ( sk1
= ( g @ x ) )
| ( sk1
= ( g @ y ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(24,plain,
( ( sk2 = x )
| ( sk2 = y )
| ( ( g @ x )
= sk1 )
| ( ( g @ y )
= sk1 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(6,plain,
( ~ ? [A: b] :
( ( ( A = x )
| ( A = y ) )
& ( sk1
= ( g @ A ) ) )
| ~ ( ( sk1
= ( g @ x ) )
| ( sk1
= ( g @ y ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
! [A: b] :
( ( ( A != x )
| ( sk1
!= ( g @ A ) )
| ( sk1
!= ( g @ x ) ) )
& ( ( A != x )
| ( sk1
!= ( g @ A ) )
| ( sk1
!= ( g @ y ) ) )
& ( ( A != y )
| ( sk1
!= ( g @ A ) )
| ( sk1
!= ( g @ x ) ) )
& ( ( A != y )
| ( sk1
!= ( g @ A ) )
| ( sk1
!= ( g @ y ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(12,plain,
! [A: b] :
( ( A != y )
| ( sk1
!= ( g @ A ) )
| ( sk1
!= ( g @ y ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(19,plain,
! [A: b] :
( ( A != y )
| ( ( g @ A )
!= sk1 )
| ( ( g @ y )
!= sk1 ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(20,plain,
( ( g @ y )
!= sk1 ),
inference(simp,[status(thm)],[19]) ).
thf(23,plain,
( ( sk1
= ( g @ sk2 ) )
| ( sk1
= ( g @ x ) )
| ( sk1
= ( g @ y ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(25,plain,
( ( ( g @ sk2 )
= sk1 )
| ( ( g @ x )
= sk1 )
| ( ( g @ y )
= sk1 ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(9,plain,
! [A: b] :
( ( A != x )
| ( sk1
!= ( g @ A ) )
| ( sk1
!= ( g @ x ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(13,plain,
! [A: b] :
( ( A != x )
| ( ( g @ A )
!= sk1 )
| ( ( g @ x )
!= sk1 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(14,plain,
( ( g @ x )
!= sk1 ),
inference(simp,[status(thm)],[13]) ).
thf(26,plain,
( ( g @ sk2 )
= sk1 ),
inference(simplifyReflect,[status(thm)],[25,20,14]) ).
thf(31,plain,
( ( sk1 != sk1 )
| ( ( g @ sk2 )
!= ( g @ x ) ) ),
inference(paramod_ordered,[status(thm)],[26,14]) ).
thf(32,plain,
( ( g @ sk2 )
!= ( g @ x ) ),
inference(simp,[status(thm)],[31]) ).
thf(39,plain,
sk2 != x,
inference(simp,[status(thm)],[32]) ).
thf(33,plain,
( ( sk1 != sk1 )
| ( ( g @ sk2 )
!= ( g @ y ) ) ),
inference(paramod_ordered,[status(thm)],[26,20]) ).
thf(34,plain,
( ( g @ sk2 )
!= ( g @ y ) ),
inference(simp,[status(thm)],[33]) ).
thf(40,plain,
sk2 != y,
inference(simp,[status(thm)],[34]) ).
thf(57,plain,
$false,
inference(simplifyReflect,[status(thm)],[24,20,39,40,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU896^5 : 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 : n005.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 14:44:31 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
% 0.86/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (170ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.72/1.38 % [INFO] eprover registered as external prover.
% 1.72/1.39 % [INFO] Scanning for conjecture ...
% 1.91/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.05/1.51 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.05/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.52 % [INFO] Type checking passed.
% 2.05/1.53 % [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 ...
% 3.80/2.31 % [INFO] Killing All external provers ...
% 3.80/2.31 % Time passed: 1939ms (effective reasoning time: 1319ms)
% 3.80/2.31 % 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)>
% 3.80/2.31 % Axioms used in derivation (0):
% 3.80/2.31 % No. of inferences in proof: 27
% 3.80/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1939 ms resp. 1319 ms w/o parsing
% 3.80/2.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.80/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------