%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO256^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n003.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 08:45:29 AM UTC 2026
% Result : Theorem 3.69s 2.15s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 28 ( 11 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 47 ( 7 ~; 8 |; 0 &; 32 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 22 !; 6 ?; 31 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: $o > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $o > $o] :
~ ! [B: a > $o,C: a > $o] :
? [D: $o] :
( ( A @ D )
= ( A
@ ! [E: a] :
( ( B @ E )
| ( C @ E ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
? [C: $o] :
( ( sk1 @ C )
= ( sk1
@ ! [D: a] :
( ( A @ D )
| ( B @ D ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > $o] :
~ ? [B: $o] :
( ( sk1 @ B )
= ( sk1
@ ! [C: a] :
( ( sk2 @ C )
| ( A @ C ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $o > $o,B: a > $o,C: a > $o] :
? [D: $o] :
( ( A @ D )
= ( A
@ ! [E: a] :
( ( B @ E )
| ( C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM121) ).
thf(2,negated_conjecture,
~ ! [A: $o > $o,B: a > $o,C: a > $o] :
? [D: $o] :
( ( A @ D )
= ( A
@ ! [E: a] :
( ( B @ E )
| ( C @ E ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $o > $o,B: a > $o,C: a > $o] :
? [D: $o] :
( ( A @ D )
= ( A
@ ! [E: a] :
( ( B @ E )
| ( C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $o] :
( ( sk1 @ A )
!= ( sk1
@ ! [B: a] :
( ( sk2 @ B )
| ( sk3 @ B ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: $o] :
( ( sk1 @ A )
!= ( sk1
@ ! [B: a] :
( ( sk2 @ B )
| ( sk3 @ B ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
$false,
inference(pattern_uni,[status(thm)],[5:[bind(A,$thf( ! [B: a] : ( ( sk2 @ B ) | ( sk3 @ B ) ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO256^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.22 % Computer : n003.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 16:43:28 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.00 % [INFO] Parsing done (183ms).
% 1.21/1.01 % [INFO] Running in sequential loop mode.
% 2.01/1.43 % [INFO] eprover registered as external prover.
% 2.01/1.44 % [INFO] Scanning for conjecture ...
% 2.21/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.56 % [INFO] Type checking passed.
% 2.21/1.57 % [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 ...
% 3.69/2.14 % [INFO] Killing All external provers ...
% 3.69/2.15 % Time passed: 1776ms (effective reasoning time: 1124ms)
% 3.69/2.15 % 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)>
% 3.69/2.15 % Axioms used in derivation (0):
% 3.69/2.15 % No. of inferences in proof: 6
% 3.69/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1776 ms resp. 1124 ms w/o parsing
% 3.85/2.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.85/2.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------