%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG268^2 : 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 : n014.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 8.57s 4.02s
% Output : Refutation 9.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 10 ( 9 unt; 0 typ; 6 def)
% Number of atoms : 26 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 257 ( 2 ~; 0 |; 0 &; 217 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 52 ( 2 ^; 50 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(one_decl,type,
one: term ).
thf(lam_decl,type,
lam: term > term ).
thf(sub_decl,type,
sub: term > subst > term ).
thf(id_decl,type,
id: subst ).
thf(sh_decl,type,
sh: subst ).
thf(push_decl,type,
push: term > subst > subst ).
thf(comp_decl,type,
comp: subst > subst > subst ).
thf(axvarshift_decl,type,
axvarshift: $o ).
thf(hoasinduction_lem3_decl,type,
hoasinduction_lem3: $o ).
thf(hoasinduction_lem3aa_decl,type,
hoasinduction_lem3aa: $o ).
thf(hoaslam_decl,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(hoasinduction_lem3_lthm_decl,type,
hoasinduction_lem3_lthm: $o ).
thf(axvarid_decl,type,
axvarid: $o ).
thf(axvarshift_def,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ) ).
thf(hoasinduction_lem3_def,definition,
( hoasinduction_lem3
= ( ! [A: subst > term > subst > $o] :
( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) )
=> ( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) )
=> ( ! [B: subst > term > term] :
( ! [C: subst,D: term,E: subst] :
( ( sub @ ( B @ C @ D ) @ E )
= ( B @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) )
=> ( ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( B @ id @ C ) @ id ) )
=> ( A @ id @ ( hoaslam @ id @ B ) @ id ) ) )
=> ! [B: term] :
( ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( sub @ B @ ( push @ C @ id ) ) @ id ) )
=> ( A @ id @ ( lam @ B ) @ id ) ) ) ) ) ) ) ).
thf(hoasinduction_lem3aa_def,definition,
( hoasinduction_lem3aa
= ( ! [A: subst > term > subst > $o] :
( ! [B: subst > term > term] :
( ! [C: subst,D: term,E: subst] :
( ( sub @ ( B @ C @ D ) @ E )
= ( B @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) )
=> ( ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( B @ id @ C ) @ id ) )
=> ( A @ id @ ( hoaslam @ id @ B ) @ id ) ) )
=> ! [B: term] :
( ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( sub @ B @ ( push @ C @ id ) ) @ id ) )
=> ( A @ id @ ( lam @ ( sub @ B @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
thf(hoaslam_def,definition,
( hoaslam
= ( ^ [A: subst,B: subst > term > term] : ( lam @ ( B @ sh @ one ) ) ) ) ).
thf(hoasinduction_lem3_lthm_def,definition,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ) ).
thf(axvarid_def,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf(1,conjecture,
hoasinduction_lem3_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoasinduction_lem3_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [A: subst > term > subst > $o] :
( ! [B: subst > term > term] :
( ! [C: subst,D: term,E: subst] :
( ( sub @ ( B @ C @ D ) @ E )
= ( B @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) )
=> ( ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( B @ id @ C ) @ id ) )
=> ( A @ id @ ( lam @ ( B @ sh @ one ) ) @ id ) ) )
=> ! [B: term] :
( ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( sub @ B @ ( push @ C @ id ) ) @ id ) )
=> ( A @ id @ ( lam @ ( sub @ B @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [A: subst > term > subst > $o] :
( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ B @ C @ ( comp @ E @ D ) )
=> ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D ) )
=> ( ! [B: subst,C: term,D: subst,E: subst] :
( ( A @ ( comp @ B @ E ) @ ( sub @ C @ E ) @ D )
=> ( A @ B @ C @ ( comp @ E @ D ) ) )
=> ( ! [B: subst > term > term] :
( ! [C: subst,D: term,E: subst] :
( ( sub @ ( B @ C @ D ) @ E )
= ( B @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) )
=> ( ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( B @ id @ C ) @ id ) )
=> ( A @ id @ ( lam @ ( B @ sh @ one ) ) @ id ) ) )
=> ! [B: term] :
( ! [C: term] :
( ( A @ id @ C @ id )
=> ( A @ id @ ( sub @ B @ ( push @ C @ id ) ) @ id ) )
=> ( A @ id @ ( lam @ B ) @ id ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG268^2 : 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
% 0.10/0.25 % Computer : n014.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 17:34:45 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 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
% 1.34/1.09 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.81/1.64 % [INFO] Parsing done (545ms).
% 2.81/1.66 % [INFO] Running in sequential loop mode.
% 4.18/2.22 % [INFO] eprover registered as external prover.
% 4.18/2.23 % [INFO] Scanning for conjecture ...
% 5.97/2.91 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 5.97/2.95 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 5.97/2.95 % [INFO] Problem is higher-order (TPTP THF).
% 5.97/2.95 % [INFO] Type checking passed.
% 5.97/2.96 % [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 ...
% 8.57/4.01 % External prover 'e' found a proof!
% 8.57/4.01 % [INFO] Killing All external provers ...
% 8.57/4.02 % Time passed: 3536ms (effective reasoning time: 2349ms)
% 8.57/4.02 % 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)>
% 8.57/4.02 % Axioms used in derivation (0):
% 8.57/4.02 % No. of inferences in proof: 4
% 8.57/4.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3536 ms resp. 2349 ms w/o parsing
% 9.18/4.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.18/4.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------