%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU781^2 : 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 : n018.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 08:29:17 AM UTC 2026
% Result : Theorem 3.75s 2.25s
% Output : Refutation 4.04s
% 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 : 51 ( 3 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 185 ( 2 ~; 0 |; 4 &; 139 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 37 ( 4 ^; 31 !; 2 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $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(breln1_decl,type,
breln1: $i > $i > $o ).
thf(breln1compset_decl,type,
breln1compset: $i > $i > $i > $i ).
thf(breln1compE_decl,type,
breln1compE: $o ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(breln1_def,definition,
( breln1
= ( ^ [A: $i] : ( breln @ A @ A ) ) ) ).
thf(breln1compE_def,definition,
( breln1compE
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
( breln1compE
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ! [F: $o] :
( ! [G: $i] :
( ( in @ G @ A )
=> ( ( in @ ( kpair @ D @ G ) @ B )
=> ( ( in @ ( kpair @ G @ E ) @ C )
=> F ) ) )
=> F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compEex) ).
thf(2,negated_conjecture,
~ ( breln1compE
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ! [F: $o] :
( ! [G: $i] :
( ( in @ G @ A )
=> ( ( in @ ( kpair @ D @ G ) @ B )
=> ( ( in @ ( kpair @ G @ E ) @ C )
=> F ) ) )
=> F ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( subset @ B @ ( cartprod @ A @ A ) )
=> ! [C: $i] :
( ( subset @ C @ ( cartprod @ A @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( subset @ B @ ( cartprod @ A @ A ) )
=> ! [C: $i] :
( ( subset @ C @ ( cartprod @ A @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ! [F: $o] :
( ! [G: $i] :
( ( in @ G @ A )
=> ( ( in @ ( kpair @ D @ G ) @ B )
=> ( ( in @ ( kpair @ G @ E ) @ C )
=> F ) ) )
=> F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU781^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n018.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 14:30:26 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.05/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.01 % [INFO] Parsing done (197ms).
% 1.23/1.03 % [INFO] Running in sequential loop mode.
% 2.08/1.42 % [INFO] eprover registered as external prover.
% 2.08/1.43 % [INFO] Scanning for conjecture ...
% 2.28/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.47/1.60 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.47/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.47/1.61 % [INFO] Type checking passed.
% 2.47/1.61 % [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 ...
% 3.75/2.25 % External prover 'e' found a proof!
% 3.75/2.25 % [INFO] Killing All external provers ...
% 3.75/2.25 % Time passed: 1880ms (effective reasoning time: 1216ms)
% 3.75/2.25 % 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)>
% 3.75/2.25 % Axioms used in derivation (0):
% 3.75/2.25 % No. of inferences in proof: 4
% 3.75/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1880 ms resp. 1216 ms w/o parsing
% 4.04/2.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.04/2.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------