TSTP Solution File: PLA053_2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---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 : 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 02:19:56 EDT 2024
% Result : Theorem 3.30s 1.84s
% Output : Refutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 23 ( 7 unt; 7 typ; 0 def)
% Number of atoms : 59 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 161 ( 2 ~; 0 |; 16 &; 116 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 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 : 39 ( 0 ^ 28 !; 11 ?; 39 :)
% 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(7,axiom,
? [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_$i\'' @ B @ C )
=> ( ( ( bomb @ B @ C )
& ( h @ B @ A ) )
=> ! [D: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ B @ D )
=> ( bomb @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(24,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_$i\'' @ B @ C )
=> ( ( ( bomb @ B @ C )
& ( h @ B @ A ) )
=> ! [D: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ B @ D )
=> ( bomb @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ( bomb @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(21,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ? [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
& ( bomb @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ( ( ( bomb @ A @ B )
& ( h @ A @ C ) )
=> ( defused @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ( ( ( bomb @ A @ B )
& ( h @ A @ C ) )
=> ( defused @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ? [C: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
& ( ( ( bomb @ A @ B )
& ( h @ A @ C ) )
=> ( defused @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
thf(17,plain,
! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: '\'$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\''] :
( ( '\'$ki_accessible\'' @ A @ D )
=> ( ( ( bomb @ D @ B )
& ( h @ D @ C ) )
=> ( defused @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(27,plain,
! [A: '\'$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\''] :
( ( '\'$ki_accessible\'' @ A @ D )
=> ( ( ( bomb @ D @ B )
& ( h @ D @ C ) )
=> ( defused @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: '\'$ki_world\''] :
? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(19,plain,
! [A: '\'$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\''] : ( '\'$ki_accessible\'' @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(15,plain,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,plain,
$false,
inference(e,[status(thm)],[24,21,9,17,27,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n002.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sat May 18 13:44:24 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.98/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.02 % [INFO] Parsing done (115ms).
% 1.29/1.03 % [INFO] Running in sequential loop mode.
% 1.83/1.31 % [INFO] eprover registered as external prover.
% 1.83/1.31 % [INFO] cvc4 registered as external prover.
% 1.83/1.32 % [INFO] Scanning for conjecture ...
% 1.97/1.39 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.97/1.42 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.97/1.44 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.97/1.44 % [INFO] Type checking passed.
% 1.97/1.44 % [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 ...
% 3.30/1.83 % External prover 'e' found a proof!
% 3.30/1.83 % [INFO] Killing All external provers ...
% 3.30/1.83 % Time passed: 1294ms (effective reasoning time: 799ms)
% 3.30/1.83 % 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)>
% 3.30/1.84 % Axioms used in derivation (6): $ki_exists_in_world_$i_nonempty, mrel_reflexive, ax1, ax2, $ki_exists_in_world_$i_const, ax3
% 3.30/1.84 % No. of inferences in proof: 16
% 3.30/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1294 ms resp. 799 ms w/o parsing
% 3.30/1.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.30/1.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------