%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET646^3 : TPTP v9.3.1. Released v3.6.0.
% 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 : n011.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 08:23:05 AM UTC 2026
% Result : Theorem 2.19s 1.08s
% Output : Refutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 5 unt; 0 typ; 3 def)
% Number of atoms : 20 ( 5 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 23 ( 2 ~; 1 |; 1 &; 18 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 20 ( 14 ^; 6 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(cartesian_product_decl,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(pair_rel_decl,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(sub_rel_decl,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(cartesian_product_def,definition,
( cartesian_product
= ( ^ [A: $i > $o,B: $i > $o,C: $i,D: $i] :
( ( A @ C )
& ( B @ D ) ) ) ) ).
thf(pair_rel_def,definition,
( pair_rel
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
( ( C = A )
| ( D = B ) ) ) ) ).
thf(sub_rel_def,definition,
( sub_rel
= ( ^ [A: $i > $i > $o,B: $i > $i > $o] :
! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( B @ C @ D ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( sub_rel @ ( pair_rel @ A @ B )
@ ( cartesian_product
@ ^ [C: $i] : $true
@ ^ [C: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( sub_rel @ ( pair_rel @ A @ B )
@ ( cartesian_product
@ ^ [C: $i] : $true
@ ^ [C: $i] : $true ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
$false,
inference(simp,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET646^3 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:40:31 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.64/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.06/0.66 % [INFO] Parsing done (145ms).
% 1.06/0.67 % [INFO] Running in sequential loop mode.
% 1.55/0.89 % [INFO] eprover registered as external prover.
% 1.55/0.89 % [INFO] Scanning for conjecture ...
% 1.80/0.98 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.80/1.00 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.80/1.00 % [INFO] Problem is higher-order (TPTP THF).
% 1.80/1.00 % [INFO] Type checking passed.
% 1.80/1.00 % [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 ...
% 2.19/1.08 % [INFO] Killing All external provers ...
% 2.19/1.08 % Time passed: 777ms (effective reasoning time: 409ms)
% 2.19/1.08 % 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)>
% 2.19/1.08 % Axioms used in derivation (0):
% 2.19/1.08 % No. of inferences in proof: 4
% 2.19/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 777 ms resp. 409 ms w/o parsing
% 2.19/1.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.19/1.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------