%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU636^2 : 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 : n020.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 2.40s 1.26s
% Output : Refutation 2.40s
% 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 : 26 ( 8 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 52 ( 2 ~; 0 |; 0 &; 37 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(setextsub_decl,type,
setextsub: $o ).
thf(setunionsingleton1_decl,type,
setunionsingleton1: $o ).
thf(setunionsingleton2_decl,type,
setunionsingleton2: $o ).
thf(setextsub_def,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ) ).
thf(setunionsingleton1_def,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
thf(setunionsingleton2_def,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
thf(1,conjecture,
( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(2,negated_conjecture,
~ ( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A )
=> ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) )
=> ! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU636^2 : 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
% 0.10/0.21 % Computer : n020.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
% 0.10/0.22 % DateTime : Tue Sep 29 14:01:34 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
% 0.65/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.88/0.60 % [INFO] Parsing done (92ms).
% 0.88/0.61 % [INFO] Running in sequential loop mode.
% 1.15/0.79 % [INFO] eprover registered as external prover.
% 1.15/0.80 % [INFO] Scanning for conjecture ...
% 1.38/0.85 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.38/0.86 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.38/0.86 % [INFO] Problem is higher-order (TPTP THF).
% 1.38/0.87 % [INFO] Type checking passed.
% 1.38/0.87 % [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 ...
% 2.40/1.25 % External prover 'e' found a proof!
% 2.40/1.25 % [INFO] Killing All external provers ...
% 2.40/1.25 % Time passed: 952ms (effective reasoning time: 645ms)
% 2.40/1.26 % 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)>
% 2.40/1.26 % Axioms used in derivation (0):
% 2.40/1.26 % No. of inferences in proof: 4
% 2.40/1.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 952 ms resp. 645 ms w/o parsing
% 2.40/1.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.40/1.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------