%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO226^5 : 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 : n017.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 08:45:26 AM UTC 2026
% Result : Theorem 3.45s 1.92s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 21 ( 20 equ; 4 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 69 ( 12 ~; 4 |; 1 &; 42 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 1 ^; 19 !; 0 ?; 23 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: ( $i > $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) )
=> ( A = B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ! [B: $i > $i > $o] :
( ! [C: $i] : ( B @ C @ C )
=> ( B @ sk1 @ A ) )
=> ( sk1 = A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i > $i > $o] :
@+[B: $i] :
~ ( A @ B @ B ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM47B) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) )
=> ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i] :
( ! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i > $i > $o] :
( ( ~ ( A @ ( sk3 @ A ) @ ( sk3 @ A ) )
| ( A @ sk1 @ sk2 ) )
& ( sk1 != sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: $i > $i > $o] :
( ~ ( A @ ( sk3 @ A ) @ ( sk3 @ A ) )
| ( A @ sk1 @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk3 @ ( (=) @ $i ) )
!= ( sk3 @ ( (=) @ $i ) ) )
| ( sk1 = sk2 ) ),
inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ $i ))]]) ).
thf(9,plain,
( ( ( sk3 @ ( (=) @ $i ) )
!= ( sk3 @ ( (=) @ $i ) ) )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(10,plain,
sk2 = sk1,
inference(simp,[status(thm)],[9]) ).
thf(6,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
$false,
inference(simplifyReflect,[status(thm)],[10,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO226^5 : 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
% 0.09/0.22 % Computer : n017.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 16:35:37 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.96/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.88 % [INFO] Parsing done (167ms).
% 1.17/0.89 % [INFO] Running in sequential loop mode.
% 1.84/1.29 % [INFO] eprover registered as external prover.
% 2.07/1.30 % [INFO] Scanning for conjecture ...
% 2.23/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.43 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.44 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.44 % [INFO] Type checking passed.
% 2.23/1.44 % [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 ...
% 3.45/1.92 % [INFO] Killing All external provers ...
% 3.45/1.92 % Time passed: 1512ms (effective reasoning time: 1021ms)
% 3.45/1.92 % 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)>
% 3.45/1.92 % Axioms used in derivation (0):
% 3.45/1.92 % No. of inferences in proof: 11
% 3.45/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1512 ms resp. 1021 ms w/o parsing
% 3.45/1.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.45/1.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------