%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU828^1 : 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 : n013.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 08:29:26 AM UTC 2026
% Result : Theorem 4.76s 2.23s
% Output : Refutation 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 10 unt; 0 typ; 6 def)
% Number of atoms : 79 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 69 ( 25 ~; 11 |; 0 &; 32 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 19 ^; 12 !; 0 ?; 33 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(seteq_decl,type,
seteq: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(subseteq_decl,type,
subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(powerset_decl,type,
powerset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(emptyset_decl,type,
emptyset: $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(seteq_def,definition,
( seteq
= ( ^ [A: ( $i > $o ) > $o,B: ( $i > $o ) > $o] :
! [C: $i > $o] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(subseteq_def,definition,
( subseteq
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(powerset_def,definition,
( powerset
= ( ^ [A: $i > $o,B: $i > $o] : ( subseteq @ B @ A ) ) ) ).
thf(emptyset_def,definition,
( emptyset
= ( ^ [A: $i] : $false ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
( ( ! [B: $i] :
~ ( A @ B ) )
!= ( A
= ( ^ [B: $i] : $false ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ~ ( sk1 @ A ) ) ) ).
thf(1,conjecture,
( seteq @ ( powerset @ emptyset )
@ ^ [A: $i > $o] : ( A = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( seteq @ ( powerset @ emptyset )
@ ^ [A: $i > $o] : ( A = emptyset ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o] :
( ( ! [B: $i] :
~ ( A @ B ) )
= ( A
= ( ^ [B: $i] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: $i] :
~ ( sk1 @ A ) )
!= ( sk1
= ( ^ [A: $i] : $false ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [A: $i] :
~ ( sk1 @ A ) )
!= ( sk1
= ( ^ [A: $i] : $false ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ~ ! [A: $i] :
~ ( sk1 @ A )
| ( sk1
!= ( ^ [A: $i] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( sk1
!= ( ^ [A: $i] : $false ) )
| ~ ! [A: $i] :
~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
( ( sk1
!= ( ^ [A: $i] : $false ) )
| ( sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(12,plain,
( ( sk1 @ sk3 )
| ( sk1 @ sk2 ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(13,plain,
( ( sk1 @ sk2 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(14,plain,
( ( sk1 @ sk2 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(7,plain,
( ! [A: $i] :
~ ( sk1 @ A )
| ( sk1
= ( ^ [A: $i] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( sk1
= ( ^ [A: $i] : $false ) )
| ! [A: $i] :
~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(11,plain,
! [A: $i] :
( ( sk1
= ( ^ [B: $i] : $false ) )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(15,plain,
( ( sk1 @ sk2 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[13]) ).
thf(85,plain,
$false,
inference(e,[status(thm)],[5,10,14,12,3,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU828^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.10 % 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
% 0.21/0.31 % Computer : n013.cluster.edu
% 0.21/0.31 % Model : x86_64 x86_64
% 0.21/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.31 % Memory : 8046.5625MB
% 0.21/0.31 % OS : Linux 6.8.0-71-generic
% 0.21/0.31 % CPULimit : 300
% 0.21/0.31 % WCLimit : 300
% 0.21/0.31 % DateTime : Tue Sep 29 14:34:51 UTC 2026
% 0.21/0.31 % CPUTime :
% 0.21/0.31 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
% 0.96/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.89 % [INFO] Parsing done (112ms).
% 1.16/0.90 % [INFO] Running in sequential loop mode.
% 1.72/1.15 % [INFO] eprover registered as external prover.
% 1.95/1.16 % [INFO] Scanning for conjecture ...
% 2.05/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.05/1.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.05/1.26 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.27 % [INFO] Type checking passed.
% 2.05/1.27 % [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 ...
% 4.76/2.23 % External prover 'e' found a proof!
% 4.76/2.23 % [INFO] Killing All external provers ...
% 4.76/2.23 % Time passed: 1788ms (effective reasoning time: 1330ms)
% 4.76/2.23 % 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)>
% 4.76/2.23 % Axioms used in derivation (0):
% 4.76/2.23 % No. of inferences in proof: 16
% 4.76/2.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1788 ms resp. 1330 ms w/o parsing
% 4.76/2.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.76/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------