%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU454^1 : 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 : n012.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 08:28:13 AM UTC 2026
% Result : Theorem 2.24s 1.24s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 65 ( 39 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 106 ( 24 ~; 30 |; 5 &; 47 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 23 ( 20 ^; 2 !; 0 ?; 23 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(idem_decl,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(rc_decl,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(idem_def,definition,
( idem
= ( ^ [A: ( $i > $i > $o ) > $i > $i > $o] :
! [B: $i > $i > $o] :
( ( A @ ( A @ B ) )
= ( A @ B ) ) ) ) ).
thf(rc_def,definition,
( rc
= ( ^ [A: $i > $i > $o,B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $o] :
( ( ^ [B: $i,C: $i] :
( ( B = C )
| ( B = C )
| ( A @ B @ C ) ) )
!= ( ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) ) ) ) ) ).
thf(1,conjecture,
idem @ rc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive_closure_op_is_idempotent) ).
thf(2,negated_conjecture,
~ ( idem @ rc ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ( ^ [B: $i,C: $i] :
( ( B = C )
| ( B = C )
| ( A @ B @ C ) ) )
= ( ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i,B: $i] :
( ( A = B )
| ( A = B )
| ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i,B: $i] :
( ( A = B )
| ( sk1 @ A @ B ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i,B: $i] :
( ( A = B )
| ( A = B )
| ( sk1 @ A @ B ) ) )
!= ( ^ [A: $i,B: $i] :
( ( A = B )
| ( sk1 @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk2 = sk3 )
| ( sk2 = sk3 )
| ( sk1 @ sk2 @ sk3 ) )
!= ( ( sk2 = sk3 )
| ( sk1 @ sk2 @ sk3 ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(25,plain,
( ~ ( ( sk2 = sk3 )
| ( sk2 = sk3 )
| ( sk1 @ sk2 @ sk3 ) )
| ~ ( ( sk2 = sk3 )
| ( sk1 @ sk2 @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(28,plain,
( ( ( sk2 != sk3 )
| ( sk2 != sk3 ) )
& ( ( sk2 != sk3 )
| ~ ( sk1 @ sk2 @ sk3 ) )
& ( ( sk2 != sk3 )
| ( sk2 != sk3 ) )
& ( ( sk2 != sk3 )
| ~ ( sk1 @ sk2 @ sk3 ) )
& ( ~ ( sk1 @ sk2 @ sk3 )
| ( sk2 != sk3 ) )
& ( ~ ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(31,plain,
( ~ ( sk1 @ sk2 @ sk3 )
| ~ ( sk1 @ sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(35,plain,
~ ( sk1 @ sk2 @ sk3 ),
inference(simp,[status(thm)],[31]) ).
thf(40,plain,
( ( ( sk2 = sk3 )
| ( sk2 = sk3 )
| $false )
!= ( ( sk2 = sk3 )
| $false ) ),
inference(rewrite,[status(thm)],[7,35]) ).
thf(41,plain,
$false,
inference(simp,[status(thm)],[40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU454^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % 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
% 0.00/0.12 % Computer : n012.cluster.edu
% 0.00/0.12 % Model : x86_64 x86_64
% 0.00/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.12 % Memory : 8046.5625MB
% 0.00/0.12 % OS : Linux 6.8.0-71-generic
% 0.00/0.12 % CPULimit : 300
% 0.00/0.12 % WCLimit : 300
% 0.00/0.12 % DateTime : Tue Sep 29 13:41:03 UTC 2026
% 0.00/0.12 % CPUTime :
% 0.00/0.12 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
% 0.39/0.42 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.55 % [INFO] Parsing done (136ms).
% 0.74/0.56 % [INFO] Running in sequential loop mode.
% 1.09/0.76 % [INFO] eprover registered as external prover.
% 1.09/0.77 % [INFO] Scanning for conjecture ...
% 1.29/0.85 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.29/0.87 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.29/0.87 % [INFO] Problem is higher-order (TPTP THF).
% 1.29/0.87 % [INFO] Type checking passed.
% 1.29/0.87 % [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 ...
% 2.24/1.23 % [INFO] Killing All external provers ...
% 2.24/1.24 % Time passed: 1037ms (effective reasoning time: 667ms)
% 2.24/1.24 % 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)>
% 2.24/1.24 % Axioms used in derivation (0):
% 2.24/1.24 % No. of inferences in proof: 12
% 2.24/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1037 ms resp. 667 ms w/o parsing
% 2.24/1.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.24/1.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------