%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG262^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : n013.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 07:45:04 AM UTC 2026
% Result : Theorem 4.37s 1.69s
% Output : Refutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 5 def)
% Number of atoms : 23 ( 11 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 36 ( 6 ~; 0 |; 0 &; 30 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 3 ^; 7 !; 3 ?; 15 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(id_decl,type,
id: subst ).
thf(hoasinduction_lem0_decl,type,
hoasinduction_lem0: $o ).
thf(hoasinduction_p_and_p_prime_decl,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(hoasinduction_lem0_lthm_decl,type,
hoasinduction_lem0_lthm: $o ).
thf(sk1_decl,type,
sk1: subst > term > subst > $o ).
thf(sk2_decl,type,
sk2: ( term > $o ) > term ).
thf(hoasinduction_lem0_def,definition,
( hoasinduction_lem0
= ( ! [A: subst > term > subst > $o] :
? [B: term > $o] : ( hoasinduction_p_and_p_prime @ A @ B ) ) ) ).
thf(hoasinduction_p_and_p_prime_def,definition,
( hoasinduction_p_and_p_prime
= ( ^ [A: subst > term > subst > $o,B: term > $o] :
! [C: term] :
( ( B @ C )
= ( A @ id @ C @ id ) ) ) ) ).
thf(hoasinduction_lem0_lthm_def,definition,
hoasinduction_lem0_lthm = hoasinduction_lem0 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: subst > term > subst > $o] :
~ ? [B: term > $o] :
! [C: term] :
( ( B @ C )
= ( A @ id @ C @ id ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: term > $o] :
@+[B: term] :
( ( A @ B )
!= ( sk1 @ id @ B @ id ) ) ) ) ).
thf(1,conjecture,
hoasinduction_lem0_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoasinduction_lem0_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: subst > term > subst > $o] :
? [B: term > $o] :
! [C: term] :
( ( B @ C )
= ( A @ id @ C @ id ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: term > $o] :
( ( A @ ( sk2 @ A ) )
!= ( sk1 @ id @ ( sk2 @ A ) @ id ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: term > $o] :
( ( A @ ( sk2 @ A ) )
!= ( sk1 @ id @ ( sk2 @ A ) @ id ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
$false,
inference(pre_uni,[status(thm)],[5:[bind(A,$thf( ^ [B: term] : ( sk1 @ id @ B @ id ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG262^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.12/0.21 % Computer : n013.cluster.edu
% 0.12/0.21 % Model : x86_64 x86_64
% 0.12/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.21 % Memory : 8046.5625MB
% 0.12/0.21 % OS : Linux 6.8.0-71-generic
% 0.12/0.21 % CPULimit : 300
% 0.12/0.21 % WCLimit : 300
% 0.12/0.21 % DateTime : Tue Sep 29 17:33:21 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 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
% 0.70/0.52 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/0.75 % [INFO] Parsing done (225ms).
% 1.38/0.76 % [INFO] Running in sequential loop mode.
% 2.01/0.97 % [INFO] eprover registered as external prover.
% 2.01/0.97 % [INFO] Scanning for conjecture ...
% 3.07/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.43/1.30 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.43/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 3.43/1.30 % [INFO] Type checking passed.
% 3.43/1.31 % [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 ...
% 4.37/1.68 % [INFO] Killing All external provers ...
% 4.37/1.69 % Time passed: 1377ms (effective reasoning time: 921ms)
% 4.37/1.69 % 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)>
% 4.37/1.69 % Axioms used in derivation (0):
% 4.37/1.69 % No. of inferences in proof: 6
% 4.37/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1377 ms resp. 921 ms w/o parsing
% 4.63/1.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.63/1.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------