%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU789^2 : 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 : n007.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 08:29:19 AM UTC 2026
% Result : Theorem 4.20s 2.30s
% Output : Refutation 4.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 9 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 71 ( 10 equ; 0 cnn)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 192 ( 2 ~; 0 |; 0 &; 138 @)
% ( 0 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% 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(breln1_decl,type,
breln1: $i > $i > $o ).
thf(subbreln1_decl,type,
subbreln1: $o ).
thf(breln1invset_decl,type,
breln1invset: $i > $i > $i ).
thf(breln1invprop_decl,type,
breln1invprop: $o ).
thf(breln1invI_decl,type,
breln1invI: $o ).
thf(breln1invE_decl,type,
breln1invE: $o ).
thf(setextsub_def,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ) ).
thf(subbreln1_def,definition,
( subbreln1
= ( ! [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 ) @ B )
=> ( in @ ( kpair @ D @ E ) @ C ) ) ) )
=> ( subset @ B @ C ) ) ) ) ) ) ).
thf(breln1invprop_def,definition,
( breln1invprop
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ( breln1 @ A @ ( breln1invset @ A @ B ) ) ) ) ) ).
thf(breln1invI_def,definition,
( breln1invI
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ ( kpair @ C @ D ) @ B )
=> ( in @ ( kpair @ D @ C ) @ ( breln1invset @ A @ B ) ) ) ) ) ) ) ) ).
thf(breln1invE_def,definition,
( breln1invE
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ ( kpair @ D @ C ) @ ( breln1invset @ A @ B ) )
=> ( in @ ( kpair @ C @ D ) @ B ) ) ) ) ) ) ) ).
thf(1,conjecture,
( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ( B
= ( breln1invset @ A @ ( breln1invset @ A @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz2Ex) ).
thf(2,negated_conjecture,
~ ( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ( B
= ( breln1invset @ A @ ( breln1invset @ A @ B ) ) ) ) ) ) ) ) ),
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] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ B )
=> ( in @ ( kpair @ D @ E ) @ C ) ) ) )
=> ( subset @ B @ C ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ( breln1 @ A @ ( breln1invset @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ ( kpair @ C @ D ) @ B )
=> ( in @ ( kpair @ D @ C ) @ ( breln1invset @ A @ B ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ ( kpair @ D @ C ) @ ( breln1invset @ A @ B ) )
=> ( in @ ( kpair @ C @ D ) @ B ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ( B
= ( breln1invset @ A @ ( breln1invset @ A @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU789^2 : 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
% 0.10/0.23 % Computer : n007.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 14:26:55 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.05/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.01 % [INFO] Parsing done (196ms).
% 1.24/1.03 % [INFO] Running in sequential loop mode.
% 2.16/1.47 % [INFO] eprover registered as external prover.
% 2.16/1.48 % [INFO] Scanning for conjecture ...
% 2.55/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.55/1.65 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.55/1.65 % [INFO] Problem is higher-order (TPTP THF).
% 2.55/1.65 % [INFO] Type checking passed.
% 2.55/1.66 % [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 ...
% 4.20/2.30 % External prover 'e' found a proof!
% 4.20/2.30 % [INFO] Killing All external provers ...
% 4.20/2.30 % Time passed: 1925ms (effective reasoning time: 1266ms)
% 4.20/2.30 % 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)>
% 4.20/2.30 % Axioms used in derivation (0):
% 4.20/2.30 % No. of inferences in proof: 4
% 4.20/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1925 ms resp. 1266 ms w/o parsing
% 4.20/2.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.20/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------