%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET672^3 : TPTP v9.3.1. Released v3.6.0.
% 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 08:23:06 AM UTC 2026
% Result : Theorem 4.05s 2.22s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 11 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 2 ~; 0 |; 5 &; 32 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-4 aty)
% Number of variables : 25 ( 7 ^; 18 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_rel_on_decl,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(restrict_rel_codomain_decl,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(is_rel_on_def,definition,
( is_rel_on
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
! [D: $i,E: $i] :
( ( A @ D @ E )
=> ( ( B @ D )
& ( C @ E ) ) ) ) ) ).
thf(restrict_rel_codomain_def,definition,
( restrict_rel_codomain
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i,D: $i] :
( ( B @ D )
& ( A @ C @ D ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( is_rel_on @ B @ C @ D )
=> ( is_rel_on @ ( restrict_rel_codomain @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( is_rel_on @ B @ C @ D )
=> ( is_rel_on @ ( restrict_rel_codomain @ B @ A ) @ C @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ! [E: $i,F: $i] :
( ( B @ E @ F )
=> ( ( C @ E )
& ( D @ F ) ) )
=> ! [E: $i,F: $i] :
( ( ( A @ F )
& ( B @ E @ F ) )
=> ( ( C @ E )
& ( A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET672^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % 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 : n007.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 13:38:40 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.59/1.08 % [INFO] Parsing done (275ms).
% 1.59/1.09 % [INFO] Running in sequential loop mode.
% 2.42/1.50 % [INFO] eprover registered as external prover.
% 2.42/1.51 % [INFO] Scanning for conjecture ...
% 2.63/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.86/1.70 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.86/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.86/1.71 % [INFO] Type checking passed.
% 2.86/1.71 % [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 ...
% 4.05/2.22 % External prover 'e' found a proof!
% 4.05/2.22 % [INFO] Killing All external provers ...
% 4.05/2.22 % Time passed: 1847ms (effective reasoning time: 1119ms)
% 4.05/2.22 % 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)>
% 4.05/2.22 % Axioms used in derivation (0):
% 4.05/2.22 % No. of inferences in proof: 4
% 4.05/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1847 ms resp. 1119 ms w/o parsing
% 4.05/2.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.05/2.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------