%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG259^2 : 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 07:45:04 AM UTC 2026
% Result : Theorem 6.36s 3.44s
% Output : Refutation 6.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 9 ( 8 unt; 0 typ; 5 def)
% Number of atoms : 19 ( 11 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 55 ( 6 ~; 0 |; 0 &; 45 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 23 ( 5 ^; 18 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(one_decl,type,
one: term ).
thf(ap_decl,type,
ap: term > term > 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(comp_decl,type,
comp: subst > subst > subst ).
thf(hoasap_decl,type,
hoasap: subst > term > subst > term > term ).
thf(hoaslamnotap_lthm_decl,type,
hoaslamnotap_lthm: $o ).
thf(hoaslam_decl,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(lamnotap_decl,type,
lamnotap: $o ).
thf(hoaslamnotap_decl,type,
hoaslamnotap: $o ).
thf(hoasap_def,definition,
( hoasap
= ( ^ [A: subst,B: term,C: subst] : ( ap @ ( sub @ B @ C ) ) ) ) ).
thf(hoaslamnotap_lthm_def,definition,
( hoaslamnotap_lthm
= ( lamnotap
=> hoaslamnotap ) ) ).
thf(hoaslam_def,definition,
( hoaslam
= ( ^ [A: subst,B: subst > term > term] : ( lam @ ( B @ sh @ one ) ) ) ) ).
thf(lamnotap_def,definition,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ) ).
thf(hoaslamnotap_def,definition,
( hoaslamnotap
= ( ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ! [B: term,C: term] :
( ( hoaslam @ id @ A )
!= ( hoasap @ id @ B @ id @ C ) ) ) ) ) ).
thf(1,conjecture,
hoaslamnotap_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoaslamnotap_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) )
=> ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ! [B: term,C: term] :
( ( lam @ ( A @ sh @ one ) )
!= ( ap @ ( sub @ B @ id ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG259^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.07 % 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
% 0.10/0.21 % Computer : n014.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 17:34:35 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.01/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.13/1.36 % [INFO] Parsing done (512ms).
% 2.13/1.38 % [INFO] Running in sequential loop mode.
% 3.47/1.92 % [INFO] eprover registered as external prover.
% 3.47/1.93 % [INFO] Scanning for conjecture ...
% 4.92/2.64 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 4.92/2.67 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 4.92/2.68 % [INFO] Problem is higher-order (TPTP THF).
% 4.92/2.68 % [INFO] Type checking passed.
% 4.92/2.69 % [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 ...
% 6.36/3.44 % External prover 'e' found a proof!
% 6.36/3.44 % [INFO] Killing All external provers ...
% 6.36/3.44 % Time passed: 3079ms (effective reasoning time: 2049ms)
% 6.36/3.44 % 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)>
% 6.36/3.44 % Axioms used in derivation (0):
% 6.36/3.44 % No. of inferences in proof: 4
% 6.36/3.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3079 ms resp. 2049 ms w/o parsing
% 6.36/3.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.36/3.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------