%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU743^2 : 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 08:29:12 AM UTC 2026
% Result : Theorem 6.10s 2.80s
% Output : Refutation 6.10s
% 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 : 65 ( 4 equ; 0 cnn)
% Maximal formula atoms : 22 ( 8 avg)
% Number of connectives : 231 ( 2 ~; 0 |; 0 &; 180 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(binunion_decl,type,
binunion: $i > $i > $i ).
thf(binintersect_decl,type,
binintersect: $i > $i > $i ).
thf(binintersectT_lem_decl,type,
binintersectT_lem: $o ).
thf(binunionT_lem_decl,type,
binunionT_lem: $o ).
thf(powersetTI1_decl,type,
powersetTI1: $o ).
thf(inIntersectImpInIntersectUnions_decl,type,
inIntersectImpInIntersectUnions: $o ).
thf(binintersectT_lem_def,definition,
( binintersectT_lem
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binintersect @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ).
thf(binunionT_lem_def,definition,
( binunionT_lem
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binunion @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ).
thf(powersetTI1_def,definition,
( powersetTI1
= ( ! [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 ) ) )
=> ( in @ B @ ( powerset @ C ) ) ) ) ) ) ) ).
thf(inIntersectImpInIntersectUnions_def,definition,
( inIntersectImpInIntersectUnions
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
( binintersectT_lem
=> ( binunionT_lem
=> ( powersetTI1
=> ( inIntersectImpInIntersectUnions
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ( in @ ( binintersect @ B @ C ) @ ( powerset @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(2,negated_conjecture,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetTI1
=> ( inIntersectImpInIntersectUnions
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ( in @ ( binintersect @ B @ C ) @ ( powerset @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binintersect @ B @ C ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binunion @ B @ C ) @ ( 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 ) ) )
=> ( in @ B @ ( powerset @ C ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ( in @ ( binintersect @ B @ C ) @ ( powerset @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(231,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU743^2 : 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
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:20:24 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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
% 0.87/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.98 % [INFO] Parsing done (204ms).
% 1.18/1.00 % [INFO] Running in sequential loop mode.
% 2.01/1.40 % [INFO] eprover registered as external prover.
% 2.01/1.41 % [INFO] Scanning for conjecture ...
% 2.20/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.20/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.20/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.60 % [INFO] Type checking passed.
% 2.39/1.60 % [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 ...
% 5.08/2.79 % External prover 'e' found a proof!
% 5.08/2.79 % [INFO] Killing All external provers ...
% 5.08/2.79 % Time passed: 2465ms (effective reasoning time: 1792ms)
% 5.08/2.79 % 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)>
% 5.08/2.80 % Axioms used in derivation (0):
% 5.08/2.80 % No. of inferences in proof: 4
% 6.10/2.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2465 ms resp. 1792 ms w/o parsing
% 6.10/2.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.10/2.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------