%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU820^2 : 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 : n011.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 08:29:25 AM UTC 2026
% Result : Theorem 4.29s 1.70s
% Output : Refutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 35 ( 21 unt; 0 typ; 17 def)
% Number of atoms : 254 ( 42 equ; 0 cnn)
% Maximal formula atoms : 101 ( 7 avg)
% Number of connectives : 527 ( 71 ~; 102 |; 41 &; 258 @)
% ( 0 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 16 con; 0-2 aty)
% Number of variables : 64 ( 6 ^; 46 !; 3 ?; 64 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(nonempty_decl,type,
nonempty: $i > $o ).
thf(vacuousDall_decl,type,
vacuousDall: $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subsetemptysetimpeq_decl,type,
subsetemptysetimpeq: $o ).
thf(powersetE1_decl,type,
powersetE1: $o ).
thf(transitiveset_decl,type,
transitiveset: $i > $o ).
thf(stricttotalorderedByIn_decl,type,
stricttotalorderedByIn: $i > $o ).
thf(wellorderedByIn_decl,type,
wellorderedByIn: $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $o ).
thf(sk4_decl,type,
sk4: $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(nonempty_def,definition,
( nonempty
= ( ^ [A: $i] : ( A != emptyset ) ) ) ).
thf(vacuousDall_def,definition,
( vacuousDall
= ( ! [A: $i > $o,B: $i] :
( ( in @ B @ emptyset )
=> ( A @ B ) ) ) ) ).
thf(subsetemptysetimpeq_def,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ) ).
thf(powersetE1_def,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ) ).
thf(transitiveset_def,definition,
( transitiveset
= ( ^ [A: $i] :
! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) ) ).
thf(stricttotalorderedByIn_def,definition,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( ( in @ B @ C )
& ( in @ C @ D ) )
=> ( in @ B @ D ) ) ) ) )
& ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( B = C )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ A )
=> ~ ( in @ B @ B ) ) ) ) ) ).
thf(wellorderedByIn_def,definition,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( nonempty @ B )
=> ? [C: $i] :
( ( in @ C @ B )
& ! [D: $i] :
( ( in @ D @ B )
=> ( ( C = D )
| ( in @ C @ D ) ) ) ) ) ) ) ) ) ).
thf(ordinal_def,definition,
( ordinal
= ( ^ [A: $i] :
( ( transitiveset @ A )
& ( wellorderedByIn @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( in @ A @ emptyset )
=> ( subset @ A @ emptyset ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( in @ A @ emptyset )
=> ! [B: $i] :
( ( in @ B @ emptyset )
=> ! [C: $i] :
( ( in @ C @ emptyset )
=> ( ( ( in @ A @ B )
& ( in @ B @ C ) )
=> ( in @ A @ C ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( in @ A @ emptyset )
=> ! [B: $i] :
( ( in @ B @ emptyset )
=> ( ( ( in @ sk5 @ A )
& ( in @ A @ B ) )
=> ( in @ sk5 @ B ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( in @ A @ emptyset )
=> ( ( ( in @ sk5 @ sk6 )
& ( in @ sk6 @ A ) )
=> ( in @ sk5 @ A ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( in @ A @ emptyset )
=> ! [B: $i] :
( ( in @ B @ emptyset )
=> ( ( A = B )
| ( in @ A @ B )
| ( in @ B @ A ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ( in @ A @ emptyset )
=> ( ( sk8 = A )
| ( in @ sk8 @ A )
| ( in @ A @ sk8 ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ( in @ A @ emptyset )
=> ~ ( in @ A @ A ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( ( in @ A @ ( powerset @ emptyset ) )
=> ( ( A != emptyset )
=> ? [B: $i] :
( ( in @ B @ A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( B = C )
| ( in @ B @ C ) ) ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( in @ B @ sk11 )
=> ( ( A = B )
| ( in @ A @ B ) ) ) ) ) ).
thf(1,conjecture,
( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetOrdinal) ).
thf(2,negated_conjecture,
~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o,B: $i] :
( ( in @ B @ emptyset )
=> ( A @ B ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ( subset @ A @ emptyset ) )
& ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $i] :
( ( in @ B @ emptyset )
=> ! [C: $i] :
( ( in @ C @ emptyset )
=> ( ( ( in @ A @ B )
& ( in @ B @ C ) )
=> ( in @ A @ C ) ) ) ) )
& ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $i] :
( ( in @ B @ emptyset )
=> ( ( A = B )
| ( in @ A @ B )
| ( in @ B @ A ) ) ) )
& ! [A: $i] :
( ( in @ A @ emptyset )
=> ~ ( in @ A @ A ) )
& ! [A: $i] :
( ( in @ A @ ( powerset @ emptyset ) )
=> ( ( A != emptyset )
=> ? [B: $i] :
( ( in @ B @ A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( B = C )
| ( in @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i > $o] :
( ( ~ ( in @ B @ emptyset )
| ( A @ B ) )
& ( ~ ( subset @ C @ emptyset )
| ( C = emptyset ) )
& ( ~ ( in @ E @ ( powerset @ D ) )
| ( subset @ E @ D ) )
& ( ( in @ sk2 @ emptyset )
| ~ sk1 )
& ( ~ ( subset @ sk2 @ emptyset )
| ~ sk1 )
& ( sk1
| ( in @ sk5 @ emptyset )
| ~ sk4
| ~ sk3 )
& ( sk1
| ( in @ sk6 @ emptyset )
| ~ sk4
| ~ sk3 )
& ( sk1
| ( in @ sk7 @ emptyset )
| ~ sk4
| ~ sk3 )
& ( sk1
| ( in @ sk5 @ sk6 )
| ~ sk4
| ~ sk3 )
& ( sk1
| ( in @ sk6 @ sk7 )
| ~ sk4
| ~ sk3 )
& ( sk1
| ~ ( in @ sk5 @ sk7 )
| ~ sk4
| ~ sk3 )
& ( sk1
| sk4
| ( in @ sk8 @ emptyset )
| ( in @ sk10 @ emptyset )
| ~ sk3 )
& ( sk1
| sk4
| ( in @ sk8 @ emptyset )
| ( in @ sk10 @ sk10 )
| ~ sk3 )
& ( sk1
| sk4
| ( in @ sk9 @ emptyset )
| ( in @ sk10 @ emptyset )
| ~ sk3 )
& ( sk1
| sk4
| ( in @ sk9 @ emptyset )
| ( in @ sk10 @ sk10 )
| ~ sk3 )
& ( sk1
| sk4
| ( sk8 != sk9 )
| ( in @ sk10 @ emptyset )
| ~ sk3 )
& ( sk1
| sk4
| ( sk8 != sk9 )
| ( in @ sk10 @ sk10 )
| ~ sk3 )
& ( sk1
| sk4
| ~ ( in @ sk8 @ sk9 )
| ( in @ sk10 @ emptyset )
| ~ sk3 )
& ( sk1
| sk4
| ~ ( in @ sk8 @ sk9 )
| ( in @ sk10 @ sk10 )
| ~ sk3 )
& ( sk1
| sk4
| ~ ( in @ sk9 @ sk8 )
| ( in @ sk10 @ emptyset )
| ~ sk3 )
& ( sk1
| sk4
| ~ ( in @ sk9 @ sk8 )
| ( in @ sk10 @ sk10 )
| ~ sk3 )
& ( sk1
| sk3
| ( in @ sk11 @ ( powerset @ emptyset ) ) )
& ( sk1
| sk3
| ( sk11 != emptyset ) )
& ( sk1
| sk3
| ~ ( in @ F @ sk11 )
| ( in @ ( sk12 @ F ) @ sk11 ) )
& ( sk1
| sk3
| ~ ( in @ F @ sk11 )
| ( F
!= ( sk12 @ F ) ) )
& ( sk1
| sk3
| ~ ( in @ F @ sk11 )
| ~ ( in @ F @ ( sk12 @ F ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(24,plain,
! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(36,plain,
! [A: $i] :
( ( A = emptyset )
| ~ ( subset @ A @ emptyset ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(37,plain,
! [A: $i] :
( ( A = emptyset )
| ~ ( subset @ A @ emptyset ) ),
inference(simp,[status(thm)],[36]) ).
thf(26,plain,
! [B: $i,A: $i > $o] :
( ~ ( in @ B @ emptyset )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(79,plain,
! [A: $i] :
( ~ ( in @ A @ emptyset )
| $false ),
inference(prim_subst,[status(thm)],[26:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).
thf(104,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(simp,[status(thm)],[79]) ).
thf(17,plain,
( ( in @ sk2 @ emptyset )
| ~ sk1 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(182,plain,
( $false
| ~ sk1 ),
inference(rewrite,[status(thm)],[17,104]) ).
thf(183,plain,
~ sk1,
inference(simp,[status(thm)],[182]) ).
thf(6,plain,
( sk1
| sk3
| ( sk11 != emptyset ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(32,plain,
( ( sk11 != emptyset )
| sk1
| sk3 ),
inference(lifteq,[status(thm)],[6]) ).
thf(199,plain,
( ( sk11 != emptyset )
| $false
| sk3 ),
inference(rewrite,[status(thm)],[32,183]) ).
thf(200,plain,
( ( sk11 != emptyset )
| sk3 ),
inference(simp,[status(thm)],[199]) ).
thf(266,plain,
$false,
inference(e,[status(thm)],[37,3,104,183,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU820^2 : 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
% 0.13/0.20 % Computer : n011.cluster.edu
% 0.13/0.20 % Model : x86_64 x86_64
% 0.13/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.20 % Memory : 8046.5625MB
% 0.13/0.20 % OS : Linux 6.8.0-71-generic
% 0.13/0.20 % CPULimit : 300
% 0.13/0.20 % WCLimit : 300
% 0.13/0.20 % DateTime : Tue Sep 29 14:34:31 UTC 2026
% 0.13/0.21 % CPUTime :
% 0.13/0.21 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
% 0.64/0.51 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.86/0.62 % [INFO] Parsing done (106ms).
% 0.86/0.63 % [INFO] Running in sequential loop mode.
% 1.45/0.81 % [INFO] eprover registered as external prover.
% 1.45/0.82 % [INFO] Scanning for conjecture ...
% 1.45/0.89 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.72/0.90 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.72/0.90 % [INFO] Problem is higher-order (TPTP THF).
% 1.72/0.90 % [INFO] Type checking passed.
% 1.72/0.90 % [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 ...
% 4.29/1.69 % External prover 'e' found a proof!
% 4.29/1.69 % [INFO] Killing All external provers ...
% 4.29/1.69 % Time passed: 1393ms (effective reasoning time: 1065ms)
% 4.29/1.69 % 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)>
% 4.29/1.69 % Axioms used in derivation (0):
% 4.29/1.69 % No. of inferences in proof: 18
% 4.29/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1393 ms resp. 1065 ms w/o parsing
% 4.83/1.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.83/1.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------