%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU604^2 : 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 08:28:43 AM UTC 2026
% Result : Theorem 4.04s 2.27s
% Output : Refutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 9 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 51 ( 10 equ; 0 cnn)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 100 ( 4 ~; 0 |; 0 &; 64 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subsetI2_decl,type,
subsetI2: $o ).
thf(subsetE_decl,type,
subsetE: $o ).
thf(subsetemptysetimpeq_decl,type,
subsetemptysetimpeq: $o ).
thf(setminus_decl,type,
setminus: $i > $i > $i ).
thf(setminusEL_decl,type,
setminusEL: $o ).
thf(setminusER_decl,type,
setminusER: $o ).
thf(subsetI2_def,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf(subsetE_def,definition,
( subsetE
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) ) ) ) ).
thf(subsetemptysetimpeq_def,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ) ).
thf(setminusEL_def,definition,
( setminusEL
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setminus @ A @ B ) )
=> ( in @ C @ A ) ) ) ) ).
thf(setminusER_def,definition,
( setminusER
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setminus @ A @ B ) )
=> ~ ( in @ C @ B ) ) ) ) ).
thf(1,conjecture,
( subsetI2
=> ( subsetE
=> ( subsetemptysetimpeq
=> ( setminusEL
=> ( setminusER
=> ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(2,negated_conjecture,
~ ( subsetI2
=> ( subsetE
=> ( subsetemptysetimpeq
=> ( setminusEL
=> ( setminusER
=> ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setminus @ A @ B ) )
=> ( in @ C @ A ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setminus @ A @ B ) )
=> ~ ( in @ C @ B ) )
=> ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(40,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU604^2 : 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
% 0.10/0.22 % Computer : n002.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:59:52 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.06/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.00 % [INFO] Parsing done (201ms).
% 1.26/1.02 % [INFO] Running in sequential loop mode.
% 2.14/1.43 % [INFO] eprover registered as external prover.
% 2.14/1.44 % [INFO] Scanning for conjecture ...
% 2.35/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.54/1.60 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.54/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.54/1.60 % [INFO] Type checking passed.
% 2.54/1.61 % [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 ...
% 4.04/2.27 % External prover 'e' found a proof!
% 4.04/2.27 % [INFO] Killing All external provers ...
% 4.04/2.27 % Time passed: 1898ms (effective reasoning time: 1247ms)
% 4.04/2.27 % 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)>
% 4.04/2.27 % Axioms used in derivation (0):
% 4.04/2.27 % No. of inferences in proof: 4
% 4.04/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1898 ms resp. 1247 ms w/o parsing
% 4.31/2.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.31/2.31 % [INFO] Killing All external provers ...
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