TSTP Solution File: NLP266_4 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : NLP266_4 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 : Tue May 21 00:59:28 EDT 2024
% Result : Theorem 3.82s 2.38s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 30 ( 7 unt; 12 typ; 0 def)
% Number of atoms : 92 ( 0 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 288 ( 2 ~; 0 |; 35 &; 212 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 11 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 64 ( 0 ^ 44 !; 20 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'$ki_world\'_type',type,
'\'$ki_world\'': $tType ).
thf('\'$ki_local_world\'_type',type,
'\'$ki_local_world\'': '\'$ki_world\'' ).
thf('\'$ki_accessible\'_type',type,
'\'$ki_accessible\'': '\'$ki_world\'' > '\'$ki_world\'' > $o ).
thf(u_type,type,
u: $i ).
thf(one_type,type,
one: $i ).
thf(number_type,type,
number: '\'$ki_world\'' > $i > $i > $o ).
thf(string_type,type,
string: '\'$ki_world\'' > $i > $o ).
thf(in_type,type,
in: '\'$ki_world\'' > $i > $i > $i > $o ).
thf(do_type,type,
do: '\'$ki_world\'' > $i > $i > $i > $o ).
thf(entry_box_type,type,
entry_box: '\'$ki_world\'' > $i > $o ).
thf(userid_type,type,
userid: '\'$ki_world\'' > $i > $i > $o ).
thf('\'$ki_exists_in_world_$i\'_type',type,
'\'$ki_exists_in_world_$i\'': '\'$ki_world\'' > $i > $o ).
thf(1,conjecture,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ? [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
& ? [E: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ F )
=> ( ( userid @ F @ u @ B )
& ( entry_box @ F @ C )
& ( number @ F @ C @ one ) ) )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ( ( do @ F @ E @ D @ G )
=> ( in @ F @ B @ C @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ? [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
& ? [E: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ F )
=> ( ( userid @ F @ u @ B )
& ( entry_box @ F @ C )
& ( number @ F @ C @ one ) ) )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ( ( do @ F @ E @ D @ G )
=> ( in @ F @ B @ C @ G ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ? [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
& ? [E: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ F )
=> ( ( userid @ F @ u @ B )
& ( entry_box @ F @ C )
& ( number @ F @ C @ one ) ) )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ( ( do @ F @ E @ D @ G )
=> ( in @ F @ B @ C @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: '\'$ki_world\''] :
? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(24,plain,
! [A: '\'$ki_world\''] :
? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: '\'$ki_world\'',B: '\'$ki_world\'',C: '\'$ki_world\''] :
( ( ( '\'$ki_accessible\'' @ A @ B )
& ( '\'$ki_accessible\'' @ B @ C ) )
=> ( '\'$ki_accessible\'' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(20,plain,
! [A: '\'$ki_world\'',B: '\'$ki_world\'',C: '\'$ki_world\''] :
( ( ( '\'$ki_accessible\'' @ A @ B )
& ( '\'$ki_accessible\'' @ B @ C ) )
=> ( '\'$ki_accessible\'' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
=> ( ( ( string @ A @ C )
& ( entry_box @ A @ D ) )
=> ? [E: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ( ( do @ F @ B @ E @ G )
=> ( in @ F @ C @ D @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(34,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
=> ( ( ( string @ A @ C )
& ( entry_box @ A @ D ) )
=> ? [E: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ( ( do @ F @ B @ E @ G )
=> ( in @ F @ C @ D @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
thf(22,plain,
! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(18,plain,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ( ( userid @ C @ u @ B )
& ( string @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(26,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ( ( userid @ C @ u @ B )
& ( string @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
? [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
& ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( ( entry_box @ B @ A )
& ( number @ B @ A @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(30,plain,
? [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
& ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( ( entry_box @ B @ A )
& ( number @ B @ A @ one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[10,24,20,34,22,18,26,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.09 % Problem : NLP266_4 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 22:35:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 1.00/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.14 % [INFO] Parsing done (182ms).
% 1.30/1.16 % [INFO] Running in sequential loop mode.
% 2.05/1.53 % [INFO] eprover registered as external prover.
% 2.05/1.54 % [INFO] cvc4 registered as external prover.
% 2.05/1.54 % [INFO] Scanning for conjecture ...
% 2.23/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.41/1.71 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.41/1.74 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.41/1.75 % [INFO] Type checking passed.
% 2.41/1.75 % [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 ...
% 3.82/2.38 % External prover 'e' found a proof!
% 3.82/2.38 % [INFO] Killing All external provers ...
% 3.82/2.38 % Time passed: 1910ms (effective reasoning time: 1220ms)
% 3.82/2.38 % 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)>
% 3.82/2.38 % Axioms used in derivation (7): $ki_exists_in_world_$i_nonempty, mrel_reflexive, ax1, ax2, mrel_transitive, $ki_exists_in_world_$i_const, ax3
% 3.82/2.38 % No. of inferences in proof: 18
% 3.82/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1910 ms resp. 1220 ms w/o parsing
% 4.37/2.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.37/2.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------