%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU639^2 : 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 08:28:52 AM UTC 2026
% Result : Theorem 5.51s 2.86s
% Output : Refutation 5.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 12 ( 9 unt; 0 typ; 8 def)
% Number of atoms : 73 ( 19 equ; 0 cnn)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 162 ( 2 ~; 0 |; 2 &; 105 @)
% ( 0 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 3 ^; 46 !; 2 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrI_decl,type,
dsetconstrI: $o ).
thf(dsetconstrEL_decl,type,
dsetconstrEL: $o ).
thf(dsetconstrER_decl,type,
dsetconstrER: $o ).
thf(setext_decl,type,
setext: $o ).
thf(uniqinunit_decl,type,
uniqinunit: $o ).
thf(eqinunit_decl,type,
eqinunit: $o ).
thf(singleton_decl,type,
singleton: $i > $o ).
thf(ex1_decl,type,
ex1: $i > ( $i > $o ) > $o ).
thf(dsetconstrI_def,definition,
( dsetconstrI
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).
thf(dsetconstrEL_def,definition,
( dsetconstrEL
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) ) ) ) ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
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(uniqinunit_def,definition,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(eqinunit_def,definition,
( eqinunit
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(ex1_def,definition,
( ex1
= ( ^ [A: $i,B: $i > $o] : ( singleton @ ( dsetconstr @ A @ B ) ) ) ) ).
thf(1,conjecture,
( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( B @ D )
=> ( D = C ) ) )
=> ( ex1 @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(2,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( setext
=> ( uniqinunit
=> ( eqinunit
=> ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( B @ D )
=> ( D = C ) ) )
=> ( ex1 @ A @ B ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( in @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( B @ D )
=> ( D = C ) ) )
=> ? [D: $i] :
( ( in @ D @ ( dsetconstr @ A @ B ) )
& ( ( dsetconstr @ A @ B )
= ( setadjoin @ D @ emptyset ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU639^2 : 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
% 0.09/0.21 % Computer : n002.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 14:03:37 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.22 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
% 1.22/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.77/1.17 % [INFO] Parsing done (244ms).
% 1.77/1.19 % [INFO] Running in sequential loop mode.
% 2.62/1.67 % [INFO] eprover registered as external prover.
% 2.62/1.68 % [INFO] Scanning for conjecture ...
% 3.09/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.09/1.86 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.09/1.86 % [INFO] Problem is higher-order (TPTP THF).
% 3.09/1.87 % [INFO] Type checking passed.
% 3.09/1.87 % [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 ...
% 5.51/2.85 % External prover 'e' found a proof!
% 5.51/2.86 % [INFO] Killing All external provers ...
% 5.51/2.86 % Time passed: 2472ms (effective reasoning time: 1659ms)
% 5.51/2.86 % 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)>
% 5.51/2.86 % Axioms used in derivation (0):
% 5.51/2.86 % No. of inferences in proof: 4
% 5.51/2.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2472 ms resp. 1659 ms w/o parsing
% 5.99/2.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.99/2.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------