%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG268^4 : 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 07:45:06 AM UTC 2026
% Result : Theorem 8.03s 3.28s
% Output : Refutation 8.41s
% 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 : 18 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 59 ( 7 ~; 0 |; 0 &; 52 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 2 ^; 11 !; 3 ?; 19 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(sub_decl,type,
sub: term > subst > term ).
thf(push_decl,type,
push: term > subst > subst ).
thf(hoasinduction_lem3v2_f_decl,type,
hoasinduction_lem3v2_f: $o ).
thf(hoasinduction_lem3v2_f_lthm_decl,type,
hoasinduction_lem3v2_f_lthm: $o ).
thf(sk1_decl,type,
sk1: term ).
thf(sk2_decl,type,
sk2: ( subst > term > term ) > term ).
thf(sk3_decl,type,
sk3: ( subst > term > term ) > subst ).
thf(hoasinduction_lem3v2_f_def,definition,
( hoasinduction_lem3v2_f
= ( ! [A: term] :
? [B: subst > term > term] :
! [C: term,D: subst] :
( ( B @ D @ C )
= ( sub @ A @ ( push @ C @ D ) ) ) ) ) ).
thf(hoasinduction_lem3v2_f_lthm_def,definition,
hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f ).
thf(sk1_def,definition,
( sk1
= ( @+[A: term] :
~ ? [B: subst > term > term] :
! [C: term,D: subst] :
( ( B @ D @ C )
= ( sub @ A @ ( push @ C @ D ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: subst > term > term] :
@+[B: term] :
~ ! [C: subst] :
( ( A @ C @ B )
= ( sub @ sk1 @ ( push @ B @ C ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: subst > term > term] :
@+[B: subst] :
( ( A @ B @ ( sk2 @ A ) )
!= ( sub @ sk1 @ ( push @ ( sk2 @ A ) @ B ) ) ) ) ) ).
thf(1,conjecture,
hoasinduction_lem3v2_f_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoasinduction_lem3v2_f_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: term] :
? [B: subst > term > term] :
! [C: term,D: subst] :
( ( B @ D @ C )
= ( sub @ A @ ( push @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: subst > term > term] :
( ( A @ ( sk3 @ A ) @ ( sk2 @ A ) )
!= ( sub @ sk1 @ ( push @ ( sk2 @ A ) @ ( sk3 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: subst > term > term] :
( ( A @ ( sk3 @ A ) @ ( sk2 @ A ) )
!= ( sub @ sk1 @ ( push @ ( sk2 @ A ) @ ( sk3 @ A ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
$false,
inference(pre_uni,[status(thm)],[5:[bind(A,$thf( ^ [B: subst] : ^ [C: term] : ( sub @ sk1 @ ( push @ C @ B ) ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG268^4 : 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
% 0.10/0.24 % Computer : n013.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 17:34:21 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 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
% 1.18/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.67/1.43 % [INFO] Parsing done (438ms).
% 2.67/1.44 % [INFO] Running in sequential loop mode.
% 3.97/1.89 % [INFO] eprover registered as external prover.
% 4.26/1.90 % [INFO] Scanning for conjecture ...
% 5.74/2.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 5.74/2.48 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 5.74/2.48 % [INFO] Problem is higher-order (TPTP THF).
% 5.74/2.48 % [INFO] Type checking passed.
% 5.74/2.49 % [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 ...
% 8.03/3.27 % [INFO] Killing All external provers ...
% 8.03/3.28 % Time passed: 2815ms (effective reasoning time: 1825ms)
% 8.03/3.28 % 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)>
% 8.03/3.28 % Axioms used in derivation (0):
% 8.03/3.28 % No. of inferences in proof: 6
% 8.03/3.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2815 ms resp. 1825 ms w/o parsing
% 8.41/3.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.41/3.36 % [INFO] Killing All external provers ...
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