%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU460^1 : 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 : n020.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 08:28:14 AM UTC 2026
% Result : Theorem 4.82s 2.44s
% Output : Refutation 4.82s
% 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 : 13 ( 3 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 2 ~; 3 |; 0 &; 28 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-3 aty)
% Number of variables : 16 ( 6 ^; 10 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(subrel_decl,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(mono_decl,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(sc_decl,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(subrel_def,definition,
( subrel
= ( ^ [A: $i > $i > $o,B: $i > $i > $o] :
! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( B @ C @ D ) ) ) ) ).
thf(mono_def,definition,
( mono
= ( ^ [A: ( $i > $i > $o ) > $i > $i > $o] :
! [B: $i > $i > $o,C: $i > $i > $o] :
( ( subrel @ B @ C )
=> ( subrel @ ( A @ B ) @ ( A @ C ) ) ) ) ) ).
thf(sc_def,definition,
( sc
= ( ^ [A: $i > $i > $o,B: $i,C: $i] :
( ( A @ C @ B )
| ( A @ B @ C ) ) ) ) ).
thf(1,conjecture,
mono @ sc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_closure_op_is_monotonic) ).
thf(2,negated_conjecture,
~ ( mono @ sc ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i > $i > $o] :
( ! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ! [C: $i,D: $i] :
( ( ( A @ D @ C )
| ( A @ C @ D ) )
=> ( ( B @ D @ C )
| ( B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU460^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.10 % 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
% 0.23/0.28 % Computer : n020.cluster.edu
% 0.23/0.28 % Model : x86_64 x86_64
% 0.23/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.28 % Memory : 8046.5625MB
% 0.23/0.28 % OS : Linux 6.8.0-71-generic
% 0.23/0.28 % CPULimit : 300
% 0.23/0.28 % WCLimit : 300
% 0.23/0.28 % DateTime : Tue Sep 29 13:42:34 UTC 2026
% 0.23/0.29 % CPUTime :
% 0.23/0.29 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
% 1.20/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.88/1.25 % [INFO] Parsing done (319ms).
% 1.88/1.27 % [INFO] Running in sequential loop mode.
% 2.69/1.69 % [INFO] eprover registered as external prover.
% 2.94/1.70 % [INFO] Scanning for conjecture ...
% 3.21/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.45/1.90 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.45/1.90 % [INFO] Problem is higher-order (TPTP THF).
% 3.45/1.90 % [INFO] Type checking passed.
% 3.45/1.91 % [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 ...
% 4.82/2.43 % External prover 'e' found a proof!
% 4.82/2.44 % [INFO] Killing All external provers ...
% 4.82/2.44 % Time passed: 1949ms (effective reasoning time: 1152ms)
% 4.82/2.44 % 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)>
% 4.82/2.44 % Axioms used in derivation (0):
% 4.82/2.44 % No. of inferences in proof: 4
% 4.82/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1949 ms resp. 1152 ms w/o parsing
% 4.82/2.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.82/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------