%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU705^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 08:29:05 AM UTC 2026
% Result : Theorem 3.82s 2.35s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 61 ( 19 equ; 0 cnn)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 139 ( 7 ~; 5 |; 13 &; 86 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 45 ( 10 ^; 32 !; 3 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subsetE_decl,type,
subsetE: $o ).
thf(sepSubset_decl,type,
sepSubset: $o ).
thf(singleton_decl,type,
singleton: $i > $o ).
thf(theprop_decl,type,
theprop: $o ).
thf(ifSingleton_decl,type,
ifSingleton: $o ).
thf(if_decl,type,
if: $i > $o > $i > $i > $i ).
thf(subsetE_def,definition,
( subsetE
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) ) ) ) ).
thf(sepSubset_def,definition,
( sepSubset
= ( ! [A: $i,B: $i > $o] : ( subset @ ( dsetconstr @ A @ B ) @ A ) ) ) ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(theprop_def,definition,
( theprop
= ( ! [A: $i] :
( ( singleton @ A )
=> ( in @ ( setunion @ A ) @ A ) ) ) ) ).
thf(ifSingleton_def,definition,
( ifSingleton
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ) ) ) ) ).
thf(if_def,definition,
( if
= ( ^ [A: $i,B: $o,C: $i,D: $i] :
( setunion
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ) ) ).
thf(1,conjecture,
( subsetE
=> ( sepSubset
=> ( theprop
=> ( ifSingleton
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( if @ A @ B @ C @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(2,negated_conjecture,
~ ( subsetE
=> ( sepSubset
=> ( theprop
=> ( ifSingleton
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( if @ A @ B @ C @ D ) @ A ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ( ! [A: $i,B: $i > $o] : ( subset @ ( dsetconstr @ A @ B ) @ A )
=> ( ! [A: $i] :
( ? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) )
=> ( in @ ( setunion @ A ) @ A ) )
=> ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ A
@ ^ [F: $i] :
( ( B
& ( F = C ) )
| ( ~ B
& ( F = D ) ) ) ) )
& ( ( dsetconstr @ A
@ ^ [F: $i] :
( ( B
& ( F = C ) )
| ( ~ B
& ( F = D ) ) ) )
= ( setadjoin @ E @ emptyset ) ) ) ) )
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) )
@ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU705^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n014.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 14:12:29 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.00 % [INFO] Parsing done (206ms).
% 1.17/1.01 % [INFO] Running in sequential loop mode.
% 2.01/1.41 % [INFO] eprover registered as external prover.
% 2.01/1.42 % [INFO] Scanning for conjecture ...
% 2.17/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.17/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.17/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.17/1.59 % [INFO] Type checking passed.
% 2.17/1.59 % [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 ...
% 3.82/2.34 % External prover 'e' found a proof!
% 3.82/2.34 % [INFO] Killing All external provers ...
% 3.82/2.34 % Time passed: 1988ms (effective reasoning time: 1323ms)
% 3.82/2.34 % 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)>
% 3.82/2.34 % Axioms used in derivation (0):
% 3.82/2.34 % No. of inferences in proof: 4
% 3.82/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1988 ms resp. 1323 ms w/o parsing
% 3.82/2.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.82/2.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------