TSTP Solution File: LCL602^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : LCL602^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 00:06:32 EDT 2024
% Result : Theorem 3.88s 2.08s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 15 ( 9 unt; 6 typ; 5 def)
% Number of atoms : 37 ( 8 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 87 ( 4 ~; 2 |; 8 &; 66 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 27 ( 6 ^ 21 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(mimpl_type,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimpl_def,definition,
( mimpl
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
! [D: $i] :
( ( A @ C @ D )
=> ( B @ D ) ) ) ) ).
thf(individuals_type,type,
individuals: $tType ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(reflexive_type,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(reflexive_def,definition,
( reflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(transitive_type,type,
transitive: ( $i > $i > $o ) > $o ).
thf(transitive_def,definition,
( transitive
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( ! [B: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ A @ B ) @ ( mbox @ A @ ( mbox @ A @ B ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ A @ B ) @ B ) ) ) )
= ( ( reflexive @ A )
& ( transitive @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( ! [B: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ A @ B ) @ ( mbox @ A @ ( mbox @ A @ B ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ A @ B ) @ B ) ) ) )
= ( ( reflexive @ A )
& ( transitive @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ( ! [B: $i > $o] :
( ! [C: $i] :
( ~ ! [D: $i] :
( ( A @ C @ D )
=> ( B @ D ) )
| ! [D: $i] :
( ( A @ C @ D )
=> ! [E: $i] :
( ( A @ D @ E )
=> ( B @ E ) ) ) )
& ! [C: $i] :
( ~ ! [D: $i] :
( ( A @ C @ D )
=> ( B @ D ) )
| ( B @ C ) ) ) )
= ( ! [B: $i] : ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL602^1 : TPTP v8.2.0. Released v3.6.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n010.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 20 03:32:09 EDT 2024
% 0.16/0.38 % CPUTime :
% 1.04/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/1.14 % [INFO] Parsing done (193ms).
% 1.40/1.15 % [INFO] Running in sequential loop mode.
% 2.01/1.42 % [INFO] eprover registered as external prover.
% 2.01/1.42 % [INFO] cvc4 registered as external prover.
% 2.01/1.43 % [INFO] Scanning for conjecture ...
% 2.41/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.41/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.41/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.41/1.57 % [INFO] Type checking passed.
% 2.41/1.57 % [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 ...
% 3.67/2.07 % External prover 'e' found a proof!
% 3.67/2.07 % [INFO] Killing All external provers ...
% 3.88/2.08 % Time passed: 1534ms (effective reasoning time: 921ms)
% 3.88/2.08 % 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)>
% 3.88/2.08 % Axioms used in derivation (0):
% 3.88/2.08 % No. of inferences in proof: 4
% 3.88/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1534 ms resp. 921 ms w/o parsing
% 3.97/2.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.97/2.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------