TSTP Solution File: PLA053_2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 02:20:10 EDT 2024
% Result : Theorem 5.63s 2.49s
% Output : Refutation 5.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 43 ( 14 unt; 10 typ; 0 def)
% Number of atoms : 98 ( 3 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 289 ( 44 ~; 32 |; 10 &; 186 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 ^ 43 !; 5 ?; 48 :)
% 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\'' > $o ).
thf(h_type,type,
h: '\'$ki_world\'' > $i > $o ).
thf(bomb_type,type,
bomb: '\'$ki_world\'' > $i > $o ).
thf(defused_type,type,
defused: '\'$ki_world\'' > $i > $o ).
thf('\'$ki_exists_in_world_$i\'_type',type,
'\'$ki_exists_in_world_$i\'': '\'$ki_world\'' > $i > $o ).
thf(sk1_type,type,
sk1: '\'$ki_world\'' ).
thf(sk2_type,type,
sk2: $i ).
thf(sk6_type,type,
sk6: $i > '\'$ki_world\'' > $i ).
thf(1,conjecture,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ( ( ( bomb @ A @ B )
& ( h @ A @ C ) )
=> ( defused @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ( ( ( bomb @ A @ B )
& ( h @ A @ C ) )
=> ( defused @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ( ( ( bomb @ A @ B )
& ( h @ A @ C ) )
=> ( defused @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
'\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk1,
inference(cnf,[status(esa)],[9]) ).
thf(8,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ! [D: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ D )
=> ( ( ( bomb @ D @ B )
& ( h @ D @ C ) )
=> ( defused @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(27,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ! [D: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ D )
=> ( ( ( bomb @ D @ B )
& ( h @ D @ C ) )
=> ( defused @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,plain,
! [C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ ( '\'$ki_exists_in_world_$i\'' @ A @ B )
| ~ ( '\'$ki_accessible\'' @ A @ C )
| ~ ( bomb @ C @ B )
| ~ ( h @ C @ ( sk6 @ B @ A ) )
| ( defused @ C @ B ) ),
inference(cnf,[status(esa)],[27]) ).
thf(4,axiom,
! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
thf(17,plain,
! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,plain,
! [B: $i,A: '\'$ki_world\''] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
inference(cnf,[status(esa)],[17]) ).
thf(162,plain,
! [C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ $true
| ~ ( '\'$ki_accessible\'' @ A @ C )
| ~ ( bomb @ C @ B )
| ~ ( h @ C @ ( sk6 @ B @ A ) )
| ( defused @ C @ B ) ),
inference(rewrite,[status(thm)],[28,18]) ).
thf(163,plain,
! [C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ ( '\'$ki_accessible\'' @ A @ C )
| ~ ( bomb @ C @ B )
| ~ ( h @ C @ ( sk6 @ B @ A ) )
| ( defused @ C @ B ) ),
inference(simp,[status(thm)],[162]) ).
thf(10,plain,
'\'$ki_exists_in_world_$i\'' @ sk1 @ sk2,
inference(cnf,[status(esa)],[9]) ).
thf(12,plain,
! [A: $i] :
( ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A )
| ~ ( defused @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(30,plain,
! [A: $i] :
( ~ ( defused @ sk1 @ sk2 )
| ( ( '\'$ki_exists_in_world_$i\'' @ sk1 @ sk2 )
!= ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,12]) ).
thf(31,plain,
~ ( defused @ sk1 @ sk2 ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk2 ))]]) ).
thf(186,plain,
! [C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ ( '\'$ki_accessible\'' @ A @ C )
| ~ ( bomb @ C @ B )
| ~ ( h @ C @ ( sk6 @ B @ A ) )
| ( ( defused @ C @ B )
!= ( defused @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[163,31]) ).
thf(187,plain,
! [A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ ( '\'$ki_accessible\'' @ A @ sk1 )
| ~ ( bomb @ sk1 @ sk2 )
| ~ ( h @ sk1 @ ( sk6 @ sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 ))]]) ).
thf(13,plain,
! [A: $i] :
( ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A )
| ( bomb @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(38,plain,
( ~ $true
| ( bomb @ sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[13,18]) ).
thf(39,plain,
bomb @ sk1 @ sk2,
inference(simp,[status(thm)],[38]) ).
thf(14,plain,
! [A: $i] :
( ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A )
| ( h @ sk1 @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(40,plain,
! [A: $i] :
( ~ $true
| ( h @ sk1 @ A ) ),
inference(rewrite,[status(thm)],[14,18]) ).
thf(41,plain,
! [A: $i] : ( h @ sk1 @ A ),
inference(simp,[status(thm)],[40]) ).
thf(255,plain,
! [A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ ( '\'$ki_accessible\'' @ A @ sk1 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[187,39,41]) ).
thf(256,plain,
! [A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ ( '\'$ki_accessible\'' @ A @ sk1 ) ),
inference(simp,[status(thm)],[255]) ).
thf(257,plain,
! [A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ A @ sk1 )
| ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk1 )
!= ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,256]) ).
thf(258,plain,
~ ( '\'$ki_accessible\'' @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( sk1 ))]]) ).
thf(3,axiom,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(15,plain,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
inference(cnf,[status(esa)],[15]) ).
thf(269,plain,
~ $true,
inference(rewrite,[status(thm)],[258,16]) ).
thf(270,plain,
$false,
inference(simp,[status(thm)],[269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.09/0.18 % Command : run_Leo-III %s %d
% 0.19/0.40 % Computer : n012.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Sat May 18 13:44:24 EDT 2024
% 0.19/0.40 % CPUTime :
% 1.03/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/1.14 % [INFO] Parsing done (145ms).
% 1.36/1.15 % [INFO] Running in sequential loop mode.
% 1.90/1.40 % [INFO] nitpick registered as external prover.
% 1.90/1.41 % [INFO] Scanning for conjecture ...
% 2.15/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.15/1.51 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.28/1.53 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.28/1.54 % [INFO] Type checking passed.
% 2.28/1.54 % [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 ...
% 5.63/2.48 % [INFO] Killing All external provers ...
% 5.63/2.48 % Time passed: 1913ms (effective reasoning time: 1321ms)
% 5.63/2.48 % 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)>
% 5.63/2.48 % Axioms used in derivation (3): ax3, $ki_exists_in_world_$i_const, mrel_reflexive
% 5.63/2.48 % No. of inferences in proof: 33
% 5.63/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1913 ms resp. 1321 ms w/o parsing
% 5.63/2.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.63/2.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------