%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU670^2 : 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 : 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 08:28:58 AM UTC 2026
% Result : Theorem 3.49s 1.87s
% Output : Refutation 3.81s
% 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 : 30 ( 5 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 97 ( 2 ~; 0 |; 6 &; 76 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 5 ^; 29 !; 4 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrEL_decl,type,
dsetconstrEL: $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(cartprod_decl,type,
cartprod: $i > $i > $i ).
thf(cartprodpairmemER_decl,type,
cartprodpairmemER: $o ).
thf(dpsetconstr_decl,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(dsetconstrEL_def,definition,
( dsetconstrEL
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) ) ) ) ).
thf(cartprodpairmemER_def,definition,
( cartprodpairmemER
= ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( kpair @ C @ D ) @ ( cartprod @ A @ B ) )
=> ( in @ D @ B ) ) ) ) ).
thf(dpsetconstr_def,definition,
( dpsetconstr
= ( ^ [A: $i,B: $i,C: $i > $i > $o] :
( dsetconstr @ ( cartprod @ A @ B )
@ ^ [D: $i] :
? [E: $i] :
( ( in @ E @ A )
& ? [F: $i] :
( ( in @ F @ B )
& ( C @ E @ F )
& ( D
= ( kpair @ E @ F ) ) ) ) ) ) ) ).
thf(1,conjecture,
( dsetconstrEL
=> ( cartprodpairmemER
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( in @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(2,negated_conjecture,
~ ( dsetconstrEL
=> ( cartprodpairmemER
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( in @ E @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) )
=> ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( kpair @ C @ D ) @ ( cartprod @ A @ B ) )
=> ( in @ D @ B ) )
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
( ( in @ ( kpair @ D @ E )
@ ( dsetconstr @ ( cartprod @ A @ B )
@ ^ [F: $i] :
? [G: $i] :
( ( in @ G @ A )
& ? [H: $i] :
( ( in @ H @ B )
& ( C @ G @ H )
& ( F
= ( kpair @ G @ H ) ) ) ) ) )
=> ( in @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU670^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % 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
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:09:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.88/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.05/0.87 % [INFO] Parsing done (112ms).
% 1.05/0.88 % [INFO] Running in sequential loop mode.
% 1.47/1.07 % [INFO] eprover registered as external prover.
% 1.47/1.08 % [INFO] Scanning for conjecture ...
% 1.75/1.14 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.75/1.15 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.75/1.15 % [INFO] Problem is higher-order (TPTP THF).
% 1.75/1.16 % [INFO] Type checking passed.
% 1.75/1.16 % [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 ...
% 3.49/1.86 % External prover 'e' found a proof!
% 3.49/1.86 % [INFO] Killing All external provers ...
% 3.49/1.87 % Time passed: 1537ms (effective reasoning time: 982ms)
% 3.49/1.87 % 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)>
% 3.49/1.87 % Axioms used in derivation (0):
% 3.49/1.87 % No. of inferences in proof: 4
% 3.49/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1537 ms resp. 982 ms w/o parsing
% 3.81/1.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.81/1.91 % [INFO] Killing All external provers ...
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