TSTP Solution File: SYO414^1 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO414^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 08:56:42 EDT 2024
% Result : Theorem 3.80s 2.36s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 19 ( 6 unt; 10 typ; 5 def)
% Number of atoms : 72 ( 5 equ; 0 cnn)
% Maximal formula atoms : 19 ( 8 avg)
% Number of connectives : 101 ( 22 ~; 12 |; 0 &; 67 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 6 ^ 7 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_k_type,type,
rel_k: $i > $i > $o ).
thf(mbox_k_type,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(mbox_k_def,definition,
( mbox_k
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_k @ B @ C )
| ( A @ C ) ) ) ) ).
thf(mdia_k_type,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(mdia_k_def,definition,
( mdia_k
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ A ) ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(r_type,type,
r: $i > $o ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mdia_k @ ( mimplies @ p @ ( mand @ q @ r ) ) ) @ ( mand @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ q ) ) @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_k @ ( mimplies @ p @ ( mand @ q @ r ) ) ) @ ( mand @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ q ) ) @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ r ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( ~ ( p @ B )
| ~ ( ~ ( q @ B )
| ~ ( r @ B ) ) ) )
| ~ ( ~ ( ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( q @ B ) ) )
| ~ ( ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( r @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO414^1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 09:59:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 1.09/1.03 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.26 % [INFO] Parsing done (230ms).
% 1.61/1.28 % [INFO] Running in sequential loop mode.
% 2.31/1.66 % [INFO] eprover registered as external prover.
% 2.31/1.66 % [INFO] cvc4 registered as external prover.
% 2.31/1.67 % [INFO] Scanning for conjecture ...
% 2.75/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.75/1.88 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.75/1.89 % [INFO] Problem is higher-order (TPTP THF).
% 2.75/1.89 % [INFO] Type checking passed.
% 2.75/1.89 % [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 ...
% 3.80/2.35 % External prover 'e' found a proof!
% 3.80/2.35 % [INFO] Killing All external provers ...
% 3.80/2.36 % Time passed: 1853ms (effective reasoning time: 1073ms)
% 3.80/2.36 % 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)>
% 3.80/2.36 % Axioms used in derivation (0):
% 3.80/2.36 % No. of inferences in proof: 4
% 3.80/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1853 ms resp. 1073 ms w/o parsing
% 4.03/2.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.03/2.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------