%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG268^3 : 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 : n018.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 8.28s 3.35s
% Output : Refutation 8.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 13 ( 12 unt; 0 typ; 9 def)
% Number of atoms : 41 ( 23 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 158 ( 2 ~; 0 |; 0 &; 132 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 46 ( 4 ^; 40 !; 2 ?; 46 :)
% 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(axmap_decl,type,
axmap: $o ).
thf(hoasinduction_lem3v2_f_decl,type,
hoasinduction_lem3v2_f: $o ).
thf(axvarshift_decl,type,
axvarshift: $o ).
thf(axclos_decl,type,
axclos: $o ).
thf(hoasinduction_lem3v2a_decl,type,
hoasinduction_lem3v2a: $o ).
thf(hoaslam_decl,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(hoasinduction_lem3v2a_lthm_decl,type,
hoasinduction_lem3v2a_lthm: $o ).
thf(hoasinduction_p_and_p_prime_decl,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(axvarid_decl,type,
axvarid: $o ).
thf(axmap_def,definition,
( axmap
= ( ! [A: term,B: subst,C: subst] :
( ( comp @ ( push @ A @ B ) @ C )
= ( push @ ( sub @ A @ C ) @ ( comp @ B @ C ) ) ) ) ) ).
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(axvarshift_def,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ) ).
thf(axclos_def,definition,
( axclos
= ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) ) ) ) ).
thf(hoasinduction_lem3v2a_def,definition,
( hoasinduction_lem3v2a
= ( ! [A: subst > term > subst > $o,B: term > $o] :
( ! [C: subst > term > term] :
( ! [D: subst,E: term,F: subst] :
( ( sub @ ( C @ D @ E ) @ F )
= ( C @ ( comp @ D @ F ) @ ( sub @ E @ F ) ) )
=> ( ! [D: term] :
( ( A @ id @ D @ id )
=> ( A @ id @ ( C @ id @ D ) @ id ) )
=> ( A @ id @ ( hoaslam @ id @ C ) @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ A @ B )
=> ! [C: term] :
( ! [D: term] :
( ( B @ D )
=> ( B @ ( sub @ C @ ( push @ D @ id ) ) ) )
=> ( B @ ( lam @ C ) ) ) ) ) ) ) ).
thf(hoaslam_def,definition,
( hoaslam
= ( ^ [A: subst,B: subst > term > term] : ( lam @ ( B @ sh @ one ) ) ) ) ).
thf(hoasinduction_lem3v2a_lthm_def,definition,
( hoasinduction_lem3v2a_lthm
= ( hoasinduction_lem3v2_f
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ) ).
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(axvarid_def,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf(1,conjecture,
hoasinduction_lem3v2a_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoasinduction_lem3v2a_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 ) ) )
=> ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( comp @ ( push @ A @ B ) @ C )
= ( push @ ( sub @ A @ C ) @ ( comp @ B @ C ) ) )
=> ! [A: subst > term > subst > $o,B: term > $o] :
( ! [C: subst > term > term] :
( ! [D: subst,E: term,F: subst] :
( ( sub @ ( C @ D @ E ) @ F )
= ( C @ ( comp @ D @ F ) @ ( sub @ E @ F ) ) )
=> ( ! [D: term] :
( ( A @ id @ D @ id )
=> ( A @ id @ ( C @ id @ D ) @ id ) )
=> ( A @ id @ ( lam @ ( C @ sh @ one ) ) @ id ) ) )
=> ( ! [C: term] :
( ( B @ C )
= ( A @ id @ C @ id ) )
=> ! [C: term] :
( ! [D: term] :
( ( B @ D )
=> ( B @ ( sub @ C @ ( push @ D @ id ) ) ) )
=> ( B @ ( lam @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG268^3 : 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
% 0.09/0.21 % Computer : n018.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 17:37:26 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 1.20/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.93/1.42 % [INFO] Parsing done (510ms).
% 2.93/1.44 % [INFO] Running in sequential loop mode.
% 3.83/1.88 % [INFO] eprover registered as external prover.
% 3.83/1.89 % [INFO] Scanning for conjecture ...
% 5.49/2.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 5.80/2.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 5.80/2.52 % [INFO] Problem is higher-order (TPTP THF).
% 5.80/2.52 % [INFO] Type checking passed.
% 5.80/2.53 % [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 ...
% 8.28/3.34 % External prover 'e' found a proof!
% 8.28/3.34 % [INFO] Killing All external provers ...
% 8.28/3.34 % Time passed: 2993ms (effective reasoning time: 1897ms)
% 8.28/3.34 % 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)>
% 8.28/3.35 % Axioms used in derivation (0):
% 8.28/3.35 % No. of inferences in proof: 4
% 8.28/3.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2993 ms resp. 1897 ms w/o parsing
% 8.59/3.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.59/3.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------