%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU622^2 : 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 : n010.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 08:28:48 AM UTC 2026
% Result : Theorem 3.16s 2.08s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 23 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 58 ( 2 ~; 0 |; 0 &; 43 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(powersetI1_decl,type,
powersetI1: $o ).
thf(singletonsubset_decl,type,
singletonsubset: $o ).
thf(powersetI1_def,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ) ).
thf(singletonsubset_def,definition,
( singletonsubset
= ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( subset @ ( setadjoin @ B @ emptyset ) @ A ) ) ) ) ).
thf(1,conjecture,
( powersetI1
=> ( singletonsubset
=> ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(2,negated_conjecture,
~ ( powersetI1
=> ( singletonsubset
=> ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( subset @ ( setadjoin @ B @ emptyset ) @ A ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( in @ ( setadjoin @ B @ emptyset ) @ ( powerset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU622^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % 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
% 0.10/0.21 % Computer : n010.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:59:18 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
% 1.02/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.00 % [INFO] Parsing done (187ms).
% 1.19/1.02 % [INFO] Running in sequential loop mode.
% 1.96/1.41 % [INFO] eprover registered as external prover.
% 1.96/1.42 % [INFO] Scanning for conjecture ...
% 2.12/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.12/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.12/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.12/1.57 % [INFO] Type checking passed.
% 2.12/1.57 % [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 ...
% 3.16/2.08 % External prover 'e' found a proof!
% 3.16/2.08 % [INFO] Killing All external provers ...
% 3.16/2.08 % Time passed: 1716ms (effective reasoning time: 1057ms)
% 3.16/2.08 % 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)>
% 3.16/2.08 % Axioms used in derivation (0):
% 3.16/2.08 % No. of inferences in proof: 4
% 3.16/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1716 ms resp. 1057 ms w/o parsing
% 3.16/2.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.16/2.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------