%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO516^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n006.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 08:46:03 AM UTC 2026
% Result : Theorem 4.21s 2.30s
% Output : Refutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 36 ( 20 equ; 7 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 74 ( 8 ~; 0 |; 1 &; 62 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 2 ^; 16 !; 6 ?; 26 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r_decl,type,
r: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: ( $i > $i ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i] :
@+[B: $i] :
( ( r @ A )
= ( (=) @ $i @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i > $i] :
@+[B: $i] :
~ ( r @ B @ ( A @ B ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i] :
? [B: $i] :
( ( r @ A )
= ( (=) @ $i @ B ) )
=> ? [A: $i > $i] :
! [B: $i] : ( r @ B @ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr2) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
? [B: $i] :
( ( r @ A )
= ( (=) @ $i @ B ) )
=> ? [A: $i > $i] :
! [B: $i] : ( r @ B @ ( A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
? [B: $i] :
( ( r @ A )
= ( (=) @ $i @ B ) )
=> ? [A: $i > $i] :
! [B: $i] : ( r @ B @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $i,A: $i] :
( ( ( r @ A )
= ( (=) @ $i @ ( sk1 @ A ) ) )
& ~ ( r @ ( sk2 @ B ) @ ( B @ ( sk2 @ B ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [A: $i > $i] :
~ ( r @ ( sk2 @ A ) @ ( A @ ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: $i > $i] :
~ ( r @ ( sk2 @ A ) @ ( A @ ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(5,plain,
! [A: $i] :
( ( r @ A )
= ( (=) @ $i @ ( sk1 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [A: $i] :
( ( r @ A )
= ( (=) @ $i @ ( sk1 @ A ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( r @ A @ B )
= ( ( sk1 @ A )
= B ) ),
inference(func_ext,[status(esa)],[7]) ).
thf(12,plain,
! [A: $i > $i] :
( ( sk1 @ ( sk2 @ A ) )
!= ( A @ ( sk2 @ A ) ) ),
inference(rewrite,[status(thm)],[8,9]) ).
thf(15,plain,
! [A: $i > $i] :
( ( sk1 @ ( sk2 @ A ) )
!= ( A @ ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(21,plain,
$false,
inference(pre_uni,[status(thm)],[15:[bind(A,$thf( sk1 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO516^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % 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
% 0.11/0.20 % Computer : n006.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 17:11:39 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (186ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 1.85/1.40 % [INFO] eprover registered as external prover.
% 2.05/1.40 % [INFO] Scanning for conjecture ...
% 2.05/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.53 % [INFO] Type checking passed.
% 2.23/1.53 % [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 ...
% 4.21/2.30 % [INFO] Killing All external provers ...
% 4.21/2.30 % Time passed: 1958ms (effective reasoning time: 1299ms)
% 4.21/2.30 % 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)>
% 4.21/2.30 % Axioms used in derivation (0):
% 4.21/2.30 % No. of inferences in proof: 12
% 4.21/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1958 ms resp. 1299 ms w/o parsing
% 4.21/2.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.21/2.35 % [INFO] Killing All external provers ...
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