%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU502^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n002.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 08:28:18 AM UTC 2026
% Result : Theorem 3.26s 2.14s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 28 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 10 ~; 5 |; 1 &; 32 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 18 !; 2 ?; 21 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] : ( in @ A @ emptyset ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ! [A: $i] :
( ( in @ A @ emptyset )
=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ! [A: $i] :
( ( in @ A @ emptyset )
=> $false ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ! [A: $i] :
~ ( in @ A @ emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ~ ? [A: $i] : ( in @ A @ emptyset ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [B: $o,A: $i] :
( ( ~ ( in @ A @ emptyset )
| B )
& ( in @ sk1 @ emptyset ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
in @ sk1 @ emptyset,
inference(cnfConj,[status(thm)],[5]) ).
thf(6,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnfConj,[status(thm)],[5]) ).
thf(11,plain,
! [B: $o,A: $i] :
( ~ $true
| B
| ( ( in @ sk1 @ emptyset )
!= ( in @ A @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[7,6]) ).
thf(12,plain,
! [B: $o,A: $i] :
( B
| ( ( in @ sk1 @ emptyset )
!= ( in @ A @ emptyset ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
! [A: $o] : A,
inference(pattern_uni,[status(thm)],[12:[bind(A,$thf( sk1 ))]]) ).
thf(29,plain,
! [A: $o] : A,
inference(simp,[status(thm)],[13]) ).
thf(31,plain,
$false,
inference(prim_subst,[status(thm)],[29:[bind(A,$thf( $false ))]]) ).
thf(41,plain,
$false,
inference(simp,[status(thm)],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU502^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n002.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
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:49:22 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.96 % [INFO] Parsing done (174ms).
% 1.17/0.98 % [INFO] Running in sequential loop mode.
% 1.72/1.38 % [INFO] eprover registered as external prover.
% 1.72/1.39 % [INFO] Scanning for conjecture ...
% 1.90/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.51 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.52 % [INFO] Type checking passed.
% 2.04/1.52 % [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 ...
% 3.26/2.13 % [INFO] Killing All external provers ...
% 3.26/2.14 % Time passed: 1776ms (effective reasoning time: 1150ms)
% 3.26/2.14 % 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)>
% 3.26/2.14 % Axioms used in derivation (0):
% 3.26/2.14 % No. of inferences in proof: 13
% 3.26/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1776 ms resp. 1150 ms w/o parsing
% 3.26/2.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.26/2.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------