%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU690^2 : 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 : n019.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 08:29:02 AM UTC 2026
% Result : Theorem 4.77s 2.60s
% Output : Refutation 4.77s
% 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 : 65 ( 8 equ; 0 cnn)
% Maximal formula atoms : 21 ( 9 avg)
% Number of connectives : 200 ( 2 ~; 0 |; 0 &; 146 @)
% ( 0 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 43 ( 3 ^; 40 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(setextsub_decl,type,
setextsub: $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(cartprod_decl,type,
cartprod: $i > $i > $i ).
thf(breln_decl,type,
breln: $i > $i > $i > $o ).
thf(subbreln_decl,type,
subbreln: $o ).
thf(setextsub_def,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ) ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(subbreln_def,definition,
( subbreln
= ( ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i] :
( ( breln @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( subset @ C @ D ) ) ) ) ) ) ).
thf(1,conjecture,
( setextsub
=> ( subbreln
=> ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i] :
( ( breln @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ D )
=> ( in @ ( kpair @ E @ F ) @ C ) ) ) )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(2,negated_conjecture,
~ ( setextsub
=> ( subbreln
=> ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i] :
( ( breln @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ D )
=> ( in @ ( kpair @ E @ F ) @ C ) ) ) )
=> ( C = D ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ ( cartprod @ A @ B ) )
=> ! [D: $i] :
( ( subset @ D @ ( cartprod @ A @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( subset @ C @ D ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ ( cartprod @ A @ B ) )
=> ! [D: $i] :
( ( subset @ D @ ( cartprod @ A @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ D )
=> ( in @ ( kpair @ E @ F ) @ C ) ) ) )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU690^2 : 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
% 0.10/0.22 % Computer : n019.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 14:10:49 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
% 1.00/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.04 % [INFO] Parsing done (209ms).
% 1.51/1.06 % [INFO] Running in sequential loop mode.
% 2.18/1.57 % [INFO] eprover registered as external prover.
% 2.18/1.58 % [INFO] Scanning for conjecture ...
% 2.50/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.50/1.79 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.50/1.79 % [INFO] Problem is higher-order (TPTP THF).
% 2.70/1.80 % [INFO] Type checking passed.
% 2.70/1.81 % [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 ...
% 4.48/2.59 % External prover 'e' found a proof!
% 4.48/2.59 % [INFO] Killing All external provers ...
% 4.48/2.59 % Time passed: 2238ms (effective reasoning time: 1529ms)
% 4.48/2.59 % 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)>
% 4.77/2.60 % Axioms used in derivation (0):
% 4.77/2.60 % No. of inferences in proof: 4
% 4.77/2.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2238 ms resp. 1529 ms w/o parsing
% 4.77/2.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.77/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------