%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU751^2 : 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 : n001.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 08:29:13 AM UTC 2026
% Result : Theorem 3.97s 2.26s
% Output : Refutation 4.26s
% 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 : 82 ( 6 equ; 0 cnn)
% Maximal formula atoms : 26 ( 8 avg)
% Number of connectives : 262 ( 14 ~; 0 |; 0 &; 188 @)
% ( 0 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% 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(binintersectI_decl,type,
binintersectI: $o ).
thf(setminus_decl,type,
setminus: $i > $i > $i ).
thf(setminusER_decl,type,
setminusER: $o ).
thf(complementT_lem_decl,type,
complementT_lem: $o ).
thf(complementTE1_decl,type,
complementTE1: $o ).
thf(binunionTILcontra_decl,type,
binunionTILcontra: $o ).
thf(binunionTIRcontra_decl,type,
binunionTIRcontra: $o ).
thf(binintersectI_def,definition,
( binintersectI
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ( in @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
thf(setminusER_def,definition,
( setminusER
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setminus @ A @ B ) )
=> ~ ( in @ C @ B ) ) ) ) ).
thf(complementT_lem_def,definition,
( complementT_lem
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ B ) @ ( powerset @ A ) ) ) ) ) ).
thf(complementTE1_def,definition,
( complementTE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ~ ( in @ C @ ( setminus @ A @ B ) )
=> ( in @ C @ B ) ) ) ) ) ) ).
thf(binunionTILcontra_def,definition,
( binunionTILcontra
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ ( in @ D @ ( binunion @ B @ C ) )
=> ~ ( in @ D @ B ) ) ) ) ) ) ) ).
thf(binunionTIRcontra_def,definition,
( binunionTIRcontra
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ ( in @ D @ ( binunion @ B @ C ) )
=> ~ ( in @ D @ C ) ) ) ) ) ) ) ).
thf(1,conjecture,
( binintersectI
=> ( setminusER
=> ( complementT_lem
=> ( complementTE1
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) )
=> ( in @ D @ ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1a) ).
thf(2,negated_conjecture,
~ ( binintersectI
=> ( setminusER
=> ( complementT_lem
=> ( complementTE1
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) )
=> ( in @ D @ ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ( in @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setminus @ A @ B ) )
=> ~ ( in @ C @ B ) )
=> ( ! [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 @ A )
=> ( ~ ( in @ C @ ( setminus @ A @ B ) )
=> ( in @ C @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ ( in @ D @ ( binunion @ B @ C ) )
=> ~ ( in @ D @ B ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ ( in @ D @ ( binunion @ B @ C ) )
=> ~ ( in @ D @ C ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) )
=> ( in @ D @ ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU751^2 : 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
% 0.10/0.22 % Computer : n001.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 14:27:05 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.01 % [INFO] Parsing done (210ms).
% 1.23/1.02 % [INFO] Running in sequential loop mode.
% 2.16/1.43 % [INFO] eprover registered as external prover.
% 2.16/1.44 % [INFO] Scanning for conjecture ...
% 2.36/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.56/1.61 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.56/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.56/1.62 % [INFO] Type checking passed.
% 2.56/1.62 % [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 ...
% 3.97/2.25 % External prover 'e' found a proof!
% 3.97/2.25 % [INFO] Killing All external provers ...
% 3.97/2.25 % Time passed: 1897ms (effective reasoning time: 1225ms)
% 3.97/2.25 % 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)>
% 3.97/2.26 % Axioms used in derivation (0):
% 3.97/2.26 % No. of inferences in proof: 4
% 3.97/2.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1897 ms resp. 1225 ms w/o parsing
% 4.26/2.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.26/2.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------