%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU472^1 : 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 : n010.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 08:28:15 AM UTC 2026
% Result : Theorem 5.72s 3.26s
% Output : Refutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 7 def)
% Number of atoms : 28 ( 10 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 78 ( 2 ~; 5 |; 6 &; 55 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 36 ( 14 ^; 22 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(subrel_decl,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(infl_decl,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(rc_decl,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(sc_decl,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(trans_decl,type,
trans: ( $i > $i > $o ) > $o ).
thf(tc_decl,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(trsc_decl,type,
trsc: ( $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(infl_def,definition,
( infl
= ( ^ [A: ( $i > $i > $o ) > $i > $i > $o] :
! [B: $i > $i > $o] : ( subrel @ B @ ( A @ B ) ) ) ) ).
thf(rc_def,definition,
( rc
= ( ^ [A: $i > $i > $o,B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) ) ) ).
thf(sc_def,definition,
( sc
= ( ^ [A: $i > $i > $o,B: $i,C: $i] :
( ( A @ C @ B )
| ( A @ B @ C ) ) ) ) ).
thf(trans_def,definition,
( trans
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(tc_def,definition,
( tc
= ( ^ [A: $i > $i > $o,B: $i,C: $i] :
! [D: $i > $i > $o] :
( ( ( trans @ D )
& ( subrel @ A @ D ) )
=> ( D @ B @ C ) ) ) ) ).
thf(trsc_def,definition,
( trsc
= ( ^ [A: $i > $i > $o] : ( sc @ ( rc @ ( tc @ A ) ) ) ) ) ).
thf(1,conjecture,
infl @ trsc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure_op_is_inflationary) ).
thf(2,negated_conjecture,
~ ( infl @ trsc ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i,C: $i] :
( ( A @ B @ C )
=> ( ( C = B )
| ! [D: $i > $i > $o] :
( ( ! [E: $i,F: $i,G: $i] :
( ( ( D @ E @ F )
& ( D @ F @ G ) )
=> ( D @ E @ G ) )
& ! [E: $i,F: $i] :
( ( A @ E @ F )
=> ( D @ E @ F ) ) )
=> ( D @ C @ B ) )
| ( B = C )
| ! [D: $i > $i > $o] :
( ( ! [E: $i,F: $i,G: $i] :
( ( ( D @ E @ F )
& ( D @ F @ G ) )
=> ( D @ E @ G ) )
& ! [E: $i,F: $i] :
( ( A @ E @ F )
=> ( D @ E @ F ) ) )
=> ( D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU472^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.12 % 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
% 0.29/0.32 % Computer : n010.cluster.edu
% 0.29/0.32 % Model : x86_64 x86_64
% 0.29/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.32 % Memory : 8046.5625MB
% 0.29/0.32 % OS : Linux 6.8.0-71-generic
% 0.29/0.32 % CPULimit : 300
% 0.29/0.32 % WCLimit : 300
% 0.29/0.32 % DateTime : Tue Sep 29 13:43:03 UTC 2026
% 0.29/0.32 % CPUTime :
% 0.29/0.32 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
% 1.32/1.14 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.25/1.51 % [INFO] Parsing done (362ms).
% 2.25/1.53 % [INFO] Running in sequential loop mode.
% 3.12/2.12 % [INFO] eprover registered as external prover.
% 3.12/2.13 % [INFO] Scanning for conjecture ...
% 3.65/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.86/2.41 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.86/2.42 % [INFO] Problem is higher-order (TPTP THF).
% 3.86/2.42 % [INFO] Type checking passed.
% 3.86/2.43 % [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 ...
% 5.72/3.26 % External prover 'e' found a proof!
% 5.72/3.26 % [INFO] Killing All external provers ...
% 5.72/3.26 % Time passed: 2737ms (effective reasoning time: 1724ms)
% 5.72/3.26 % 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)>
% 5.72/3.26 % Axioms used in derivation (0):
% 5.72/3.26 % No. of inferences in proof: 4
% 5.72/3.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2737 ms resp. 1724 ms w/o parsing
% 6.05/3.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.05/3.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------