TSTP Solution File: SYO891_16 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---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 : 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 08:58:43 EDT 2024
% Result : Theorem 3.70s 2.25s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 26 ( 5 unt; 6 typ; 0 def)
% Number of atoms : 81 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 240 ( 2 ~; 0 |; 23 &; 177 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 55 ( 0 ^ 38 !; 17 ?; 55 :)
% 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 > $o ).
thf(6,axiom,
! [A: '\'$ki_world\''] :
? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(25,plain,
! [A: '\'$ki_world\''] :
? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ B )
=> ( ( qmltpeq @ '\'$ki_local_world\'' @ A @ B )
=> ( qmltpeq @ '\'$ki_local_world\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(29,plain,
! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ B )
=> ( ( qmltpeq @ '\'$ki_local_world\'' @ A @ B )
=> ( qmltpeq @ '\'$ki_local_world\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( qmltpeq @ '\'$ki_local_world\'' @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(27,plain,
! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( qmltpeq @ '\'$ki_local_world\'' @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ B )
=> ! [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ C )
=> ( ( ( qmltpeq @ '\'$ki_local_world\'' @ A @ B )
& ( qmltpeq @ '\'$ki_local_world\'' @ B @ C ) )
=> ( qmltpeq @ '\'$ki_local_world\'' @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(31,plain,
! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ B )
=> ! [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ C )
=> ( ( ( qmltpeq @ '\'$ki_local_world\'' @ A @ B )
& ( qmltpeq @ '\'$ki_local_world\'' @ B @ C ) )
=> ( qmltpeq @ '\'$ki_local_world\'' @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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_$i\'' @ A @ B )
& ( p @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: '\'$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(3,axiom,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(19,plain,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
thf(21,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(10,axiom,
! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ B )
=> ( ( ( qmltpeq @ '\'$ki_local_world\'' @ A @ B )
& ( p @ '\'$ki_local_world\'' @ A ) )
=> ( p @ '\'$ki_local_world\'' @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p_substitution_1) ).
thf(33,plain,
! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ B )
=> ( ( ( qmltpeq @ '\'$ki_local_world\'' @ A @ B )
& ( p @ '\'$ki_local_world\'' @ A ) )
=> ( p @ '\'$ki_local_world\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,plain,
$false,
inference(e,[status(thm)],[25,29,27,31,11,23,19,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% 0.05/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 11:03:54 EDT 2024
% 0.12/0.32 % CPUTime :
% 1.00/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.12 % [INFO] Parsing done (174ms).
% 1.43/1.14 % [INFO] Running in sequential loop mode.
% 1.94/1.50 % [INFO] eprover registered as external prover.
% 1.94/1.51 % [INFO] cvc4 registered as external prover.
% 1.94/1.51 % [INFO] Scanning for conjecture ...
% 2.16/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.31/1.66 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.40/1.69 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.40/1.69 % [INFO] Type checking passed.
% 2.40/1.70 % [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 ...
% 3.43/2.24 % External prover 'e' found a proof!
% 3.70/2.25 % [INFO] Killing All external provers ...
% 3.70/2.25 % Time passed: 1778ms (effective reasoning time: 1103ms)
% 3.70/2.25 % 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)>
% 3.70/2.25 % Axioms used in derivation (8): $ki_exists_in_world_$i_nonempty, $ki_exists_in_world_$i_cumul, p_substitution_1, mrel_reflexive, reflexivity, mrel_transitive, transitivity, symmetry
% 3.70/2.25 % No. of inferences in proof: 20
% 3.70/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1778 ms resp. 1103 ms w/o parsing
% 3.89/2.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.89/2.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------