%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG257^2 : 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 : n008.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 07:45:03 AM UTC 2026
% Result : Theorem 5.72s 2.62s
% Output : Refutation 5.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 20 ( 12 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 35 ( 2 ~; 0 |; 0 &; 27 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 19 ( 3 ^; 16 !; 0 ?; 19 :)
% 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(hoasap_decl,type,
hoasap: subst > term > subst > term > term ).
thf(hoasapinj2_decl,type,
hoasapinj2: $o ).
thf(apinj2_decl,type,
apinj2: $o ).
thf(hoasapinj2_lthm_decl,type,
hoasapinj2_lthm: $o ).
thf(hoasap_def,definition,
( hoasap
= ( ^ [A: subst,B: term,C: subst] : ( ap @ ( sub @ B @ C ) ) ) ) ).
thf(hoasapinj2_def,definition,
( hoasapinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( C = D ) ) ) ) ).
thf(apinj2_def,definition,
( apinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) ) ) ).
thf(hoasapinj2_lthm_def,definition,
( hoasapinj2_lthm
= ( apinj2
=> hoasapinj2 ) ) ).
thf(1,conjecture,
hoasapinj2_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoasapinj2_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) )
=> ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ ( sub @ A @ id ) @ C )
= ( ap @ ( sub @ B @ id ) @ D ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG257^2 : 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
% 0.10/0.21 % Computer : n008.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
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.00/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.95/1.18 % [INFO] Parsing done (370ms).
% 1.95/1.19 % [INFO] Running in sequential loop mode.
% 2.93/1.59 % [INFO] eprover registered as external prover.
% 3.15/1.60 % [INFO] Scanning for conjecture ...
% 4.26/2.08 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 4.26/2.10 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 4.26/2.10 % [INFO] Problem is higher-order (TPTP THF).
% 4.26/2.11 % [INFO] Type checking passed.
% 4.26/2.11 % [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 ...
% 5.72/2.61 % External prover 'e' found a proof!
% 5.72/2.62 % [INFO] Killing All external provers ...
% 5.72/2.62 % Time passed: 2255ms (effective reasoning time: 1415ms)
% 5.72/2.62 % 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)>
% 5.72/2.62 % Axioms used in derivation (0):
% 5.72/2.62 % No. of inferences in proof: 4
% 5.72/2.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2255 ms resp. 1415 ms w/o parsing
% 5.72/2.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.72/2.64 % [INFO] Killing All external provers ...
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