%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG261^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 4.84s 1.67s
% Output : Refutation 4.84s
% 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 : 24 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 40 ( 6 ~; 0 |; 0 &; 30 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 16 ( 6 ^; 10 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(ap_decl,type,
ap: term > term > term ).
thf(sub_decl,type,
sub: term > subst > term ).
thf(id_decl,type,
id: subst ).
thf(var_decl,type,
var: term > $o ).
thf(hoasap_decl,type,
hoasap: subst > term > subst > term > term ).
thf(apnotvar_decl,type,
apnotvar: $o ).
thf(hoasapnotvar_decl,type,
hoasapnotvar: $o ).
thf(hoasvar_decl,type,
hoasvar: subst > term > subst > $o ).
thf(hoasapnotvar_lthm_decl,type,
hoasapnotvar_lthm: $o ).
thf(axvarid_decl,type,
axvarid: $o ).
thf(hoasap_def,definition,
( hoasap
= ( ^ [A: subst,B: term,C: subst] : ( ap @ ( sub @ B @ C ) ) ) ) ).
thf(apnotvar_def,definition,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ) ).
thf(hoasapnotvar_def,definition,
( hoasapnotvar
= ( ! [A: term,B: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ).
thf(hoasvar_def,definition,
( hoasvar
= ( ^ [A: subst,B: term,C: subst] : ( var @ ( sub @ B @ C ) ) ) ) ).
thf(hoasapnotvar_lthm_def,definition,
( hoasapnotvar_lthm
= ( axvarid
=> ( apnotvar
=> hoasapnotvar ) ) ) ).
thf(axvarid_def,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf(1,conjecture,
hoasapnotvar_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoasapnotvar_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) )
=> ! [A: term,B: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG261^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n004.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 17:34:42 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.64/0.55 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.75/0.83 % [INFO] Parsing done (275ms).
% 1.75/0.83 % [INFO] Running in sequential loop mode.
% 2.67/1.08 % [INFO] eprover registered as external prover.
% 2.67/1.08 % [INFO] Scanning for conjecture ...
% 3.75/1.36 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.75/1.38 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.75/1.38 % [INFO] Problem is higher-order (TPTP THF).
% 3.75/1.38 % [INFO] Type checking passed.
% 3.75/1.38 % [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 ...
% 4.84/1.67 % External prover 'e' found a proof!
% 4.84/1.67 % [INFO] Killing All external provers ...
% 4.84/1.67 % Time passed: 1353ms (effective reasoning time: 832ms)
% 4.84/1.67 % 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)>
% 4.84/1.67 % Axioms used in derivation (0):
% 4.84/1.67 % No. of inferences in proof: 4
% 4.84/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1353 ms resp. 832 ms w/o parsing
% 4.84/1.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.84/1.70 % [INFO] Killing All external provers ...
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