TSTP Solution File: NLP265_17 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : NLP265_17 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 00:59:27 EDT 2024
% Result : Theorem 4.02s 2.43s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 30 ( 9 unt; 10 typ; 0 def)
% Number of atoms : 60 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 206 ( 8 ~; 0 |; 4 &; 158 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 48 ( 0 ^ 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'$ki_world\'_type',type,
'\'$ki_world\'': $tType ).
thf('\'$ki_local_world\'_type',type,
'\'$ki_local_world\'': '\'$ki_world\'' ).
thf('\'$ki_index\'_type',type,
'\'$ki_index\'': $tType ).
thf('\'$ki_accessible\'_type',type,
'\'$ki_accessible\'': '\'$ki_index\'' > '\'$ki_world\'' > '\'$ki_world\'' > $o ).
thf('\'#idx(b_alice)\'_type',type,
'\'#idx(b_alice)\'': '\'$ki_index\'' ).
thf('\'#idx(b_bob)\'_type',type,
'\'#idx(b_bob)\'': '\'$ki_index\'' ).
thf('\'#idx(i_bob)\'_type',type,
'\'#idx(i_bob)\'': '\'$ki_index\'' ).
thf('\'#idx(i_alice)\'_type',type,
'\'#idx(i_alice)\'': '\'$ki_index\'' ).
thf(portland_type,type,
portland: $i ).
thf(bigcity_type,type,
bigcity: '\'$ki_world\'' > $i > $o ).
thf(4,axiom,
! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(b_bob)') ).
thf(17,plain,
! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ '\'$ki_local_world\'' @ A )
=> ( ( ( bigcity @ A @ portland )
& ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ B @ C )
=> ~ ( bigcity @ C @ portland ) ) ) )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(i_bob)\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ B @ C )
=> ( bigcity @ C @ portland ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_bob) ).
thf(27,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ '\'$ki_local_world\'' @ A )
=> ( ( ( bigcity @ A @ portland )
& ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ B @ C )
=> ~ ( bigcity @ C @ portland ) ) ) )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(i_bob)\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ B @ C )
=> ( bigcity @ C @ portland ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
=> ( bigcity @ A @ portland ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(31,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
=> ( bigcity @ A @ portland ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
=> ( bigcity @ B @ portland ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
=> ( bigcity @ B @ portland ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
=> ( bigcity @ B @ portland ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
=> ( ( ( bigcity @ A @ portland )
& ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ B @ C )
=> ~ ( bigcity @ C @ portland ) ) ) )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ B @ C )
=> ( bigcity @ C @ portland ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_alice) ).
thf(23,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
=> ( ( ( bigcity @ A @ portland )
& ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ B @ C )
=> ~ ( bigcity @ C @ portland ) ) ) )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ B @ C )
=> ( bigcity @ C @ portland ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(i_bob)\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(i_bob)') ).
thf(19,plain,
! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(i_bob)\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(b_alice)') ).
thf(15,plain,
! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(i_alice)') ).
thf(21,plain,
! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ '\'#idx(i_alice)\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
=> ~ ( bigcity @ B @ portland ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(33,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_alice)\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'#idx(b_bob)\'' @ A @ B )
=> ~ ( bigcity @ B @ portland ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,plain,
$false,
inference(e,[status(thm)],[17,27,31,11,23,19,15,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16 % Problem : NLP265_17 : TPTP v8.2.0. Released v8.2.0.
% 0.16/0.20 % Command : run_Leo-III %s %d
% 0.20/0.43 % Computer : n007.cluster.edu
% 0.20/0.43 % Model : x86_64 x86_64
% 0.20/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.43 % Memory : 8042.1875MB
% 0.20/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.43 % CPULimit : 300
% 0.20/0.43 % WCLimit : 300
% 0.20/0.43 % DateTime : Sun May 19 22:45:39 EDT 2024
% 0.20/0.43 % CPUTime :
% 1.27/1.10 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.60/1.29 % [INFO] Parsing done (187ms).
% 1.60/1.31 % [INFO] Running in sequential loop mode.
% 2.46/1.79 % [INFO] eprover registered as external prover.
% 2.46/1.79 % [INFO] cvc4 registered as external prover.
% 2.46/1.80 % [INFO] Scanning for conjecture ...
% 2.63/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.79/1.92 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.79/1.95 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.92/1.96 % [INFO] Type checking passed.
% 2.92/1.96 % [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 ...
% 4.02/2.42 % External prover 'e' found a proof!
% 4.02/2.42 % [INFO] Killing All external provers ...
% 4.02/2.43 % Time passed: 1802ms (effective reasoning time: 1107ms)
% 4.02/2.43 % 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)>
% 4.02/2.43 % Axioms used in derivation (8): axiom_2, axiom_3, axiom_1_bob, mrel_universal_#idx(b_alice), axiom_1_alice, mrel_universal_#idx(i_alice), mrel_universal_#idx(b_bob), mrel_universal_#idx(i_bob)
% 4.02/2.43 % No. of inferences in proof: 20
% 4.02/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1802 ms resp. 1107 ms w/o parsing
% 4.15/2.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.15/2.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------