TSTP Solution File: SYO888_10 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO888_10 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 08:58:42 EDT 2024
% Result : Theorem 2.55s 1.60s
% Output : Refutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 17 ( 5 unt; 7 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 131 ( 2 ~; 0 |; 5 &; 92 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 ^ 28 !; 2 ?; 30 :)
% 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\'' > $o ).
thf(f_type,type,
f: '\'$ki_world\'' > $i > $o ).
thf(g_type,type,
g: '\'$ki_world\'' > $i > $o ).
thf(h_type,type,
h: '\'$ki_world\'' > $i > $o ).
thf('\'$ki_exists_in_world_$i\'_type',type,
'\'$ki_exists_in_world_$i\'': '\'$ki_world\'' > $i > $o ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( ( f @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( g @ B @ A ) ) ) )
& ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( ( g @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( h @ B @ A ) ) ) ) )
=> ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( ( f @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( h @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( ( f @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( g @ B @ A ) ) ) )
& ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( ( g @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( h @ B @ A ) ) ) ) )
=> ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( ( f @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( h @ B @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ( ( ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( ( f @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( g @ B @ A ) ) ) )
& ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( ( g @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( h @ B @ A ) ) ) ) )
=> ! [A: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
=> ( ( f @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
=> ( h @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(14,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(16,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(5,axiom,
! [A: '\'$ki_world\''] :
? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(18,plain,
! [A: '\'$ki_world\''] :
? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[6,14,16,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO888_10 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 10:46:39 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.94 % [INFO] Parsing done (113ms).
% 1.20/0.95 % [INFO] Running in sequential loop mode.
% 1.65/1.18 % [INFO] eprover registered as external prover.
% 1.65/1.18 % [INFO] cvc4 registered as external prover.
% 1.65/1.18 % [INFO] Scanning for conjecture ...
% 1.80/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.84/1.28 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.84/1.29 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.84/1.29 % [INFO] Type checking passed.
% 1.84/1.29 % [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 ...
% 2.55/1.59 % External prover 'e' found a proof!
% 2.55/1.59 % [INFO] Killing All external provers ...
% 2.55/1.60 % Time passed: 1082ms (effective reasoning time: 642ms)
% 2.55/1.60 % 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)>
% 2.55/1.60 % Axioms used in derivation (3): mrel_reflexive, mrel_transitive, $ki_exists_in_world_$i_nonempty
% 2.55/1.60 % No. of inferences in proof: 10
% 2.55/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1082 ms resp. 642 ms w/o parsing
% 2.93/1.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.93/1.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------