TSTP Solution File: ALG258^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ALG258^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:14:37 EDT 2024
% Result : Theorem 4.39s 1.95s
% Output : Refutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 1 def)
% Number of atoms : 17 ( 9 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 52 ( 2 ~; 0 |; 0 &; 40 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 16 ( 0 ^ 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(one_type,type,
one: term ).
thf(lam_type,type,
lam: term > term ).
thf(sub_type,type,
sub: term > subst > term ).
thf(sh_type,type,
sh: subst ).
thf(push_type,type,
push: term > subst > subst ).
thf(comp_type,type,
comp: subst > subst > subst ).
thf(hoaslaminj_lthm_type,type,
hoaslaminj_lthm: $o ).
thf(hoaslaminj_lthm_def,definition,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ) ).
thf(1,conjecture,
hoaslaminj_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoaslaminj_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A )
=> ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B )
=> ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) )
=> ! [A: subst > term > term] :
( ! [B: subst,C: term,D: subst] :
( ( sub @ ( A @ B @ C ) @ D )
= ( A @ ( comp @ B @ D ) @ ( sub @ C @ D ) ) )
=> ! [B: subst > term > term] :
( ! [C: subst,D: term,E: subst] :
( ( sub @ ( B @ C @ D ) @ E )
= ( B @ ( comp @ C @ E ) @ ( sub @ D @ E ) ) )
=> ( ( ( lam @ ( A @ sh @ one ) )
= ( lam @ ( B @ sh @ one ) ) )
=> ! [C: subst,D: term] :
( ( A @ C @ D )
= ( B @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ALG258^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat May 18 22:54:54 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.87/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.68/1.05 % [INFO] Parsing done (215ms).
% 1.68/1.06 % [INFO] Running in sequential loop mode.
% 2.26/1.25 % [INFO] eprover registered as external prover.
% 2.26/1.26 % [INFO] cvc4 registered as external prover.
% 2.26/1.26 % [INFO] Scanning for conjecture ...
% 3.25/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.25/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.25/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 3.25/1.56 % [INFO] Type checking passed.
% 3.25/1.57 % [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 ...
% 4.39/1.94 % External prover 'e' found a proof!
% 4.39/1.94 % [INFO] Killing All external provers ...
% 4.39/1.94 % Time passed: 1439ms (effective reasoning time: 884ms)
% 4.39/1.94 % 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)>
% 4.39/1.95 % Axioms used in derivation (0):
% 4.39/1.95 % No. of inferences in proof: 4
% 4.39/1.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1439 ms resp. 884 ms w/o parsing
% 4.39/1.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.39/1.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------