%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU634^2 : 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 08:28:51 AM UTC 2026
% Result : Theorem 5.32s 3.30s
% Output : Refutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 32 ( 5 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 70 ( 2 ~; 0 |; 2 &; 49 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 19 ( 0 ^; 17 !; 2 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(uniqinunit_decl,type,
uniqinunit: $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subsetI2_decl,type,
subsetI2: $o ).
thf(setunionE2_decl,type,
setunionE2: $o ).
thf(uniqinunit_def,definition,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(subsetI2_def,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf(setunionE2_def,definition,
( setunionE2
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) ) ) ) ).
thf(1,conjecture,
( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(2,negated_conjecture,
~ ( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) )
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU634^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.12 % 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
% 0.28/0.33 % Computer : n002.cluster.edu
% 0.28/0.33 % Model : x86_64 x86_64
% 0.28/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.33 % Memory : 8046.5625MB
% 0.28/0.33 % OS : Linux 6.8.0-71-generic
% 0.28/0.33 % CPULimit : 300
% 0.28/0.33 % WCLimit : 300
% 0.28/0.33 % DateTime : Tue Sep 29 14:03:07 UTC 2026
% 0.28/0.33 % CPUTime :
% 0.28/0.33 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
% 1.44/1.16 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.43 % [INFO] Parsing done (265ms).
% 1.85/1.45 % [INFO] Running in sequential loop mode.
% 2.86/2.05 % [INFO] eprover registered as external prover.
% 2.86/2.06 % [INFO] Scanning for conjecture ...
% 3.12/2.22 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.12/2.27 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.12/2.27 % [INFO] Problem is higher-order (TPTP THF).
% 3.12/2.28 % [INFO] Type checking passed.
% 3.12/2.28 % [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 ...
% 5.32/3.29 % External prover 'e' found a proof!
% 5.32/3.29 % [INFO] Killing All external provers ...
% 5.32/3.29 % Time passed: 2761ms (effective reasoning time: 1833ms)
% 5.32/3.29 % 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)>
% 5.32/3.29 % Axioms used in derivation (0):
% 5.32/3.29 % No. of inferences in proof: 4
% 5.32/3.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2761 ms resp. 1833 ms w/o parsing
% 5.56/3.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.56/3.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------