%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU779^2 : 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 08:29:17 AM UTC 2026
% Result : Theorem 37.02s 7.82s
% Output : Refutation 37.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 48 ( 4 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 170 ( 2 ~; 0 |; 4 &; 134 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 41 ( 11 ^; 28 !; 2 ?; 41 :)
% 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(dpsetconstr_decl,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(dpsetconstrI_decl,type,
dpsetconstrI: $o ).
thf(breln1_decl,type,
breln1: $i > $i > $o ).
thf(breln1compset_decl,type,
breln1compset: $i > $i > $i > $i ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(dpsetconstrI_def,definition,
( dpsetconstrI
= ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( C @ D @ E )
=> ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) ) ) ) ) ) ) ).
thf(breln1_def,definition,
( breln1
= ( ^ [A: $i] : ( breln @ A @ A ) ) ) ).
thf(breln1compset_def,definition,
( breln1compset
= ( ^ [A: $i,B: $i,C: $i] :
( dpsetconstr @ A @ A
@ ^ [D: $i,E: $i] :
? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ).
thf(1,conjecture,
( dpsetconstrI
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ A )
=> ( ( in @ ( kpair @ D @ F ) @ B )
=> ( ( in @ ( kpair @ F @ E ) @ C )
=> ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compI) ).
thf(2,negated_conjecture,
~ ( dpsetconstrI
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ A )
=> ( ( in @ ( kpair @ D @ F ) @ B )
=> ( ( in @ ( kpair @ F @ E ) @ C )
=> ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( C @ D @ E )
=> ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ 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 )
=> ! [F: $i] :
( ( in @ F @ A )
=> ( ( in @ ( kpair @ D @ F ) @ B )
=> ( ( in @ ( kpair @ F @ E ) @ C )
=> ( in @ ( kpair @ D @ E )
@ ( dpsetconstr @ A @ A
@ ^ [G: $i,H: $i] :
? [I: $i] :
( ( in @ I @ A )
& ( in @ ( kpair @ G @ I ) @ B )
& ( in @ ( kpair @ I @ H ) @ C ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7106,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU779^2 : 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
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:28:02 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.67/0.53 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.04/0.64 % [INFO] Parsing done (105ms).
% 1.04/0.64 % [INFO] Running in sequential loop mode.
% 1.42/0.84 % [INFO] eprover registered as external prover.
% 1.42/0.85 % [INFO] Scanning for conjecture ...
% 1.70/0.91 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.70/0.94 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.70/0.95 % [INFO] Problem is higher-order (TPTP THF).
% 1.70/0.95 % [INFO] Type checking passed.
% 1.70/0.96 % [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 ...
% 37.02/7.82 % External prover 'e' found a proof!
% 37.02/7.82 % [INFO] Killing All external provers ...
% 37.02/7.82 % Time passed: 7516ms (effective reasoning time: 7174ms)
% 37.02/7.82 % 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)>
% 37.02/7.82 % Axioms used in derivation (0):
% 37.02/7.82 % No. of inferences in proof: 4
% 37.02/7.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7516 ms resp. 7174 ms w/o parsing
% 37.02/7.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.02/7.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------