%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO307^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n009.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 08:45:34 AM UTC 2026
% Result : Theorem 3.56s 2.27s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 34 ( 3 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 124 ( 9 ~; 18 |; 21 &; 70 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 23 ( 3 ^; 14 !; 3 ?; 23 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cT_decl,type,
cT: $i > $o ).
thf(q_decl,type,
q: $i > $o ).
thf(cR_decl,type,
cR: $i > $o ).
thf(p_decl,type,
p: $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: ( $i > $o ) > $i ).
thf(sk3_decl,type,
sk3: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ! [C: $i,D: $i] :
( ( ( A @ B )
| ( ( A @ C )
& ( A @ D ) ) )
=> ( ( ( p @ B )
& ( cR @ C ) )
| ( ( q @ B )
& ( cT @ D ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ! [C: $i] :
( ( ( A @ ( sk1 @ A ) )
| ( ( A @ B )
& ( A @ C ) ) )
=> ( ( ( p @ ( sk1 @ A ) )
& ( cR @ B ) )
| ( ( q @ ( sk1 @ A ) )
& ( cT @ C ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( ( A @ ( sk1 @ A ) )
| ( ( A @ ( sk2 @ A ) )
& ( A @ B ) ) )
=> ( ( ( p @ ( sk1 @ A ) )
& ( cR @ ( sk2 @ A ) ) )
| ( ( q @ ( sk1 @ A ) )
& ( cT @ B ) ) ) ) ) ) ).
thf(1,conjecture,
? [A: $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B )
| ( ( A @ C )
& ( A @ D ) ) )
=> ( ( ( p @ B )
& ( cR @ C ) )
| ( ( q @ B )
& ( cT @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE5F) ).
thf(2,negated_conjecture,
~ ? [A: $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B )
| ( ( A @ C )
& ( A @ D ) ) )
=> ( ( ( p @ B )
& ( cR @ C ) )
| ( ( q @ B )
& ( cT @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B )
| ( ( A @ C )
& ( A @ D ) ) )
=> ( ( ( p @ B )
& ( cR @ C ) )
| ( ( q @ B )
& ( cT @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i > $o] :
( ( ( A @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) ) )
& ( ( A @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) ) )
& ( ~ ( p @ ( sk1 @ A ) )
| ~ ( cR @ ( sk2 @ A ) ) )
& ( ~ ( q @ ( sk1 @ A ) )
| ~ ( cT @ ( sk3 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: $i > $o] :
( ( A @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(23,plain,
( $false
| $false ),
inference(prim_subst,[status(thm)],[5:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(46,plain,
$false,
inference(simp,[status(thm)],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO307^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.09/0.21 % Computer : n009.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 16:44:45 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.84/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.97 % [INFO] Parsing done (179ms).
% 1.16/0.98 % [INFO] Running in sequential loop mode.
% 1.71/1.38 % [INFO] eprover registered as external prover.
% 1.71/1.39 % [INFO] Scanning for conjecture ...
% 1.89/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.52 % [INFO] Type checking passed.
% 2.04/1.53 % [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 ...
% 3.56/2.26 % [INFO] Killing All external provers ...
% 3.56/2.27 % Time passed: 1903ms (effective reasoning time: 1273ms)
% 3.56/2.27 % 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)>
% 3.56/2.27 % Axioms used in derivation (0):
% 3.56/2.27 % No. of inferences in proof: 7
% 3.56/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1903 ms resp. 1273 ms w/o parsing
% 3.81/2.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.81/2.33 % [INFO] Killing All external provers ...
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