TSTP Solution File: ALG256^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ALG256^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 18:14:36 EDT 2024
% Result : Theorem 6.52s 2.90s
% Output : Refutation 6.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 17 ( 4 unt; 12 typ; 1 def)
% Number of atoms : 74 ( 29 equ; 0 cnn)
% Maximal formula atoms : 40 ( 14 avg)
% Number of connectives : 293 ( 5 ~; 0 |; 3 &; 191 @)
% ( 0 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 34 con; 0-2 aty)
% Number of variables : 83 ( 0 ^ 83 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(one_type,type,
one: term ).
thf(ap_type,type,
ap: term > term > term ).
thf(lam_type,type,
lam: term > term ).
thf(sub_type,type,
sub: term > subst > term ).
thf(id_type,type,
id: subst ).
thf(sh_type,type,
sh: subst ).
thf(push_type,type,
push: term > subst > subst ).
thf(comp_type,type,
comp: subst > subst > subst ).
thf(var_type,type,
var: term > $o ).
thf(hoasapinj1_gthm_type,type,
hoasapinj1_gthm: $o ).
thf(hoasapinj1_gthm_def,definition,
( hoasapinj1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> hoasapinj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
hoasapinj1_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ hoasapinj1_gthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: term,B: term,C: subst] :
( ( sub @ ( ap @ A @ B ) @ C )
= ( ap @ ( sub @ A @ C ) @ ( sub @ B @ C ) ) )
=> ( ! [A: term,B: subst] :
( ( sub @ one @ ( push @ A @ B ) )
= A )
=> ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ! [A: term,B: subst] :
( ( sub @ ( lam @ A ) @ B )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ B @ sh ) ) ) ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: subst] :
( ( comp @ id @ A )
= A )
=> ( ! [A: term,B: subst] :
( ( comp @ sh @ ( push @ A @ B ) )
= B )
=> ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: term,B: subst,C: subst] :
( ( comp @ ( push @ A @ B ) @ C )
= ( push @ ( sub @ A @ C ) @ ( comp @ B @ C ) ) )
=> ( ! [A: subst] :
( ( comp @ A @ id )
= A )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [A: subst] :
( ( push @ ( sub @ one @ A ) @ ( comp @ sh @ A ) )
= A )
=> ( ( var @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) )
=> ( ! [A: term > $o] :
( ( A @ one )
=> ( ! [B: term] :
( ( var @ B )
=> ( ( A @ B )
=> ( A @ ( sub @ B @ sh ) ) ) )
=> ! [B: term] :
( ( var @ B )
=> ( A @ B ) ) ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) )
=> ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) )
=> ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) )
=> ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) )
=> ( ! [A: term] :
~ ( var @ ( lam @ A ) )
=> ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ( A @ B )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) )
=> ( ! [A: term > $o,B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( ( A @ B )
=> ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ ( push @ B @ C ) ) ) ) ) )
=> ( ! [A: term > $o] :
( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term,C: subst] :
( ! [D: term] :
( ( var @ D )
=> ( A @ ( sub @ D @ C ) ) )
=> ( A @ ( sub @ B @ C ) ) ) ) )
=> ( ! [A: term > $o] :
( ! [B: term] :
( ( var @ B )
=> ( A @ B ) )
=> ( ! [B: term,C: term] :
( ( A @ B )
=> ( ( A @ C )
=> ( A @ ( ap @ B @ C ) ) ) )
=> ( ! [B: term] :
( ! [C: term] :
( ( A @ C )
=> ( A @ ( sub @ B @ ( push @ C @ id ) ) ) )
=> ( A @ ( lam @ B ) ) )
=> ! [B: term] : ( A @ B ) ) ) )
=> ( ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
& ! [A: subst] :
( ( comp @ id @ A )
= A )
& ! [A: subst] :
( ( comp @ A @ id )
= A ) )
=> ( ( ! [A: term,B: subst,C: subst] :
( ( sub @ ( sub @ A @ B ) @ C )
= ( sub @ A @ ( comp @ B @ C ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) )
=> ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ ( sub @ A @ id ) @ C )
= ( ap @ ( sub @ B @ id ) @ D ) )
=> ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(155,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : ALG256^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.10/0.16 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 23:35:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.90/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.71/1.22 % [INFO] Parsing done (304ms).
% 1.84/1.23 % [INFO] Running in sequential loop mode.
% 2.61/1.54 % [INFO] eprover registered as external prover.
% 2.61/1.55 % [INFO] cvc4 registered as external prover.
% 2.61/1.55 % [INFO] Scanning for conjecture ...
% 3.71/1.95 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.71/1.97 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.71/1.97 % [INFO] Problem is higher-order (TPTP THF).
% 3.71/1.97 % [INFO] Type checking passed.
% 3.71/1.97 % [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 ...
% 6.52/2.89 % External prover 'e' found a proof!
% 6.52/2.89 % [INFO] Killing All external provers ...
% 6.52/2.89 % Time passed: 2383ms (effective reasoning time: 1659ms)
% 6.52/2.89 % 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)>
% 6.52/2.89 % Axioms used in derivation (0):
% 6.52/2.89 % No. of inferences in proof: 4
% 6.52/2.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2383 ms resp. 1659 ms w/o parsing
% 6.52/2.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.52/2.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------