%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU526^2 : 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 : n026.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 08:28:24 AM UTC 2026
% Result : Theorem 4.52s 2.54s
% Output : Refutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 13 unt; 0 typ; 6 def)
% Number of atoms : 86 ( 25 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 211 ( 28 ~; 19 |; 8 &; 126 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 57 ( 5 ^; 43 !; 6 ?; 57 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(setext_decl,type,
setext: $o ).
thf(nonempty_decl,type,
nonempty: $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(setext_def,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( A = B ) ) ) ) ) ).
thf(nonempty_def,definition,
( nonempty
= ( ^ [A: $i] : ( A != emptyset ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( in @ C @ B )
=> ( in @ C @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( in @ C @ A )
=> ( in @ C @ B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A != emptyset )
=> ? [B: $i] : ( in @ B @ A ) ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ( setext
=> ! [A: $i] :
( ( nonempty @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( setext
=> ! [A: $i] :
( ( nonempty @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& $true ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( A = B ) ) )
=> ! [A: $i] :
( ( A != emptyset )
=> ? [B: $i] : ( in @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( A = B ) ) )
=> ! [A: $i] :
( ( A != emptyset )
=> ? [B: $i] : ( in @ B @ A ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [E: $i,D: $i,C: $i,B: $o,A: $i] :
( ( ~ ( in @ A @ emptyset )
| B )
& ( ( in @ ( sk1 @ D @ C ) @ C )
| ( in @ ( sk2 @ D @ C ) @ D )
| ( C = D ) )
& ( ( in @ ( sk1 @ D @ C ) @ C )
| ~ ( in @ ( sk2 @ D @ C ) @ C )
| ( C = D ) )
& ( ~ ( in @ ( sk1 @ D @ C ) @ D )
| ( in @ ( sk2 @ D @ C ) @ D )
| ( C = D ) )
& ( ~ ( in @ ( sk1 @ D @ C ) @ D )
| ~ ( in @ ( sk2 @ D @ C ) @ C )
| ( C = D ) )
& ( sk3 != emptyset )
& ~ ( in @ E @ sk3 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
! [A: $i] :
~ ( in @ A @ sk3 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(22,plain,
! [A: $i] :
~ ( in @ A @ sk3 ),
inference(simp,[status(thm)],[8]) ).
thf(23,plain,
! [C: $i,B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ~ $true
| ( B
!= ( in @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[7,22]) ).
thf(24,plain,
! [C: $i,B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ( B
!= ( in @ C @ sk3 ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( A )),bind(B,$thf( in @ D @ sk3 )),bind(C,$thf( D ))]]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( in @ ( sk1 @ B @ A ) @ A )
| ( in @ ( sk2 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[13]) ).
thf(11,plain,
sk3 != emptyset,
inference(cnfConj,[status(thm)],[5]) ).
thf(21,plain,
sk3 != emptyset,
inference(lifteq,[status(thm)],[11]) ).
thf(123,plain,
$false,
inference(e,[status(thm)],[25,14,21,22,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU526^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.10/0.21 % Computer : n026.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
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:50:57 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.00 % [INFO] Parsing done (190ms).
% 1.20/1.01 % [INFO] Running in sequential loop mode.
% 1.96/1.40 % [INFO] eprover registered as external prover.
% 1.96/1.41 % [INFO] Scanning for conjecture ...
% 2.14/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.14/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.14/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.56 % [INFO] Type checking passed.
% 2.14/1.57 % [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 ...
% 4.52/2.53 % External prover 'e' found a proof!
% 4.52/2.53 % [INFO] Killing All external provers ...
% 4.52/2.53 % Time passed: 2179ms (effective reasoning time: 1515ms)
% 4.52/2.53 % 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)>
% 4.52/2.54 % Axioms used in derivation (0):
% 4.52/2.54 % No. of inferences in proof: 17
% 4.52/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2179 ms resp. 1515 ms w/o parsing
% 4.52/2.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.52/2.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------