TSTP Solution File: SYO891_16 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 09:01:58 EDT 2024
% Result : Theorem 7.00s 2.93s
% Output : Refutation 7.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 7 unt; 8 typ; 0 def)
% Number of atoms : 72 ( 3 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 207 ( 27 ~; 14 |; 17 &; 135 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 41 ( 0 ^ 26 !; 15 ?; 41 :)
% 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\'' > $o ).
thf(qmltpeq_type,type,
qmltpeq: '\'$ki_world\'' > $i > $i > $o ).
thf(p_type,type,
p: '\'$ki_world\'' > $i > $o ).
thf('\'$ki_exists_in_world_$i\'_type',type,
'\'$ki_exists_in_world_$i\'': '\'$ki_world\'' > $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: '\'$ki_world\'' ).
thf(1,conjecture,
( ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ B @ C )
& ( qmltpeq @ B @ A @ C ) ) ) )
=> ( ? [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
& ? [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
& ( p @ B @ A ) ) )
=> ? [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
& ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ( p @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ B @ C )
& ( qmltpeq @ B @ A @ C ) ) ) )
=> ( ? [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
& ? [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
& ( p @ B @ A ) ) )
=> ? [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
& ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ( p @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ( ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ B @ C )
& ( qmltpeq @ B @ A @ C ) ) ) )
=> ( ? [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
& ? [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
& ( p @ B @ A ) ) )
=> ? [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
& ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ( p @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
'\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ sk2,
inference(cnf,[status(esa)],[11]) ).
thf(5,axiom,
! [A: '\'$ki_world\'',B: '\'$ki_world\'',C: $i] :
( ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ( '\'$ki_accessible\'' @ A @ B ) )
=> ( '\'$ki_exists_in_world_$i\'' @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).
thf(23,plain,
! [A: '\'$ki_world\'',B: '\'$ki_world\'',C: $i] :
( ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ( '\'$ki_accessible\'' @ A @ B ) )
=> ( '\'$ki_exists_in_world_$i\'' @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
! [C: $i,B: '\'$ki_world\'',A: '\'$ki_world\''] :
( ~ ( '\'$ki_exists_in_world_$i\'' @ A @ C )
| ~ ( '\'$ki_accessible\'' @ A @ B )
| ( '\'$ki_exists_in_world_$i\'' @ B @ C ) ),
inference(cnf,[status(esa)],[23]) ).
thf(13,plain,
p @ sk3 @ sk2,
inference(cnf,[status(esa)],[11]) ).
thf(12,plain,
! [B: $i,A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ ( '\'$ki_exists_in_world_$i\'' @ A @ B )
| ~ ( p @ A @ B ) ),
inference(cnf,[status(esa)],[11]) ).
thf(18,plain,
! [B: $i,A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ ( '\'$ki_exists_in_world_$i\'' @ A @ B )
| ~ ( p @ A @ B ) ),
inference(simp,[status(thm)],[12]) ).
thf(37,plain,
! [B: $i,A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
| ~ ( '\'$ki_exists_in_world_$i\'' @ A @ B )
| ( ( p @ sk3 @ sk2 )
!= ( p @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13,18]) ).
thf(38,plain,
( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk3 )
| ~ ( '\'$ki_exists_in_world_$i\'' @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(16,plain,
'\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk3,
inference(cnf,[status(esa)],[11]) ).
thf(45,plain,
( ~ $true
| ~ ( '\'$ki_exists_in_world_$i\'' @ sk3 @ sk2 ) ),
inference(rewrite,[status(thm)],[38,16]) ).
thf(46,plain,
~ ( '\'$ki_exists_in_world_$i\'' @ sk3 @ sk2 ),
inference(simp,[status(thm)],[45]) ).
thf(302,plain,
! [C: $i,B: '\'$ki_world\'',A: '\'$ki_world\''] :
( ~ ( '\'$ki_exists_in_world_$i\'' @ A @ C )
| ~ ( '\'$ki_accessible\'' @ A @ B )
| ( ( '\'$ki_exists_in_world_$i\'' @ B @ C )
!= ( '\'$ki_exists_in_world_$i\'' @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[24,46]) ).
thf(303,plain,
! [A: '\'$ki_world\''] :
( ~ ( '\'$ki_exists_in_world_$i\'' @ A @ sk2 )
| ~ ( '\'$ki_accessible\'' @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk2 ))]]) ).
thf(338,plain,
! [A: '\'$ki_world\''] :
( ~ ( '\'$ki_accessible\'' @ A @ sk3 )
| ( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ sk2 )
!= ( '\'$ki_exists_in_world_$i\'' @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[15,303]) ).
thf(339,plain,
~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ sk3 ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( '\'$ki_local_world\'' ))]]) ).
thf(360,plain,
~ $true,
inference(rewrite,[status(thm)],[339,16]) ).
thf(361,plain,
$false,
inference(simp,[status(thm)],[360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.11 % Command : run_Leo-III %s %d
% 0.10/0.31 % Computer : n018.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.31 % CPULimit : 300
% 0.16/0.31 % WCLimit : 300
% 0.16/0.31 % DateTime : Mon May 20 11:03:39 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.93/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.09 % [INFO] Parsing done (170ms).
% 1.30/1.10 % [INFO] Running in sequential loop mode.
% 1.94/1.46 % [INFO] nitpick registered as external prover.
% 1.95/1.46 % [INFO] Scanning for conjecture ...
% 2.11/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.11/1.61 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.34/1.63 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.34/1.64 % [INFO] Type checking passed.
% 2.34/1.64 % [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 ...
% 6.44/2.92 % [INFO] Killing All external provers ...
% 7.00/2.93 % Time passed: 2461ms (effective reasoning time: 1813ms)
% 7.00/2.93 % 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)>
% 7.00/2.93 % Axioms used in derivation (1): $ki_exists_in_world_$i_cumul
% 7.00/2.93 % No. of inferences in proof: 21
% 7.00/2.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2461 ms resp. 1813 ms w/o parsing
% 7.00/2.99 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.00/2.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------