%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU731^2 : 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 : n008.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 08:29:09 AM UTC 2026
% Result : Theorem 3.58s 2.27s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 61 ( 9 equ; 0 cnn)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 172 ( 2 ~; 0 |; 0 &; 125 @)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(setminus_decl,type,
setminus: $i > $i > $i ).
thf(complementT_lem_decl,type,
complementT_lem: $o ).
thf(setextT_decl,type,
setextT: $o ).
thf(doubleComplementI1_decl,type,
doubleComplementI1: $o ).
thf(doubleComplementE1_decl,type,
doubleComplementE1: $o ).
thf(complementT_lem_def,definition,
( complementT_lem
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ B ) @ ( powerset @ A ) ) ) ) ) ).
thf(setextT_def,definition,
( setextT
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ B )
=> ( in @ D @ C ) ) )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ C )
=> ( in @ D @ B ) ) )
=> ( B = C ) ) ) ) ) ) ) ).
thf(doubleComplementI1_def,definition,
( doubleComplementI1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ( in @ C @ ( setminus @ A @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ).
thf(doubleComplementE1_def,definition,
( doubleComplementE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ ( setminus @ A @ ( setminus @ A @ B ) ) )
=> ( in @ C @ B ) ) ) ) ) ) ).
thf(1,conjecture,
( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( B
= ( setminus @ A @ ( setminus @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(2,negated_conjecture,
~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( B
= ( setminus @ A @ ( setminus @ A @ B ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ B ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ B )
=> ( in @ D @ C ) ) )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ C )
=> ( in @ D @ B ) ) )
=> ( B = C ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ( in @ C @ ( setminus @ A @ ( setminus @ A @ B ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ ( setminus @ A @ ( setminus @ A @ B ) ) )
=> ( in @ C @ B ) ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( B
= ( setminus @ A @ ( setminus @ A @ B ) ) ) ) ) ) ) ),
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 : SEU731^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % 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
% 0.11/0.23 % Computer : n008.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 14:18:39 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 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
% 1.01/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/1.02 % [INFO] Parsing done (189ms).
% 1.43/1.03 % [INFO] Running in sequential loop mode.
% 1.97/1.43 % [INFO] eprover registered as external prover.
% 1.97/1.44 % [INFO] Scanning for conjecture ...
% 2.14/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.33/1.62 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.33/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.33/1.62 % [INFO] Type checking passed.
% 2.33/1.63 % [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 ...
% 3.58/2.27 % External prover 'e' found a proof!
% 3.58/2.27 % [INFO] Killing All external provers ...
% 3.58/2.27 % Time passed: 1884ms (effective reasoning time: 1228ms)
% 3.58/2.27 % 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)>
% 3.58/2.27 % Axioms used in derivation (0):
% 3.58/2.27 % No. of inferences in proof: 4
% 3.58/2.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1884 ms resp. 1228 ms w/o parsing
% 3.88/2.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.88/2.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------