TSTP Solution File: SYO485^6 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO485^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 08:57:07 EDT 2024
% Result : Theorem 3.63s 2.18s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 28 ( 11 unt; 10 typ; 6 def)
% Number of atoms : 47 ( 12 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 60 ( 15 ~; 4 |; 0 &; 41 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 30 ( 11 ^ 17 !; 2 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(meq_ind_type,type,
meq_ind: mu > mu > $i > $o ).
thf(meq_ind_def,definition,
( meq_ind
= ( ^ [A: mu,B: mu,C: $i] : ( A = B ) ) ) ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mforall_ind_def,definition,
( mforall_ind
= ( ^ [A: mu > $i > $o,B: $i] :
! [C: mu] : ( A @ C @ B ) ) ) ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mexists_ind_def,definition,
( mexists_ind
= ( ^ [A: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [B: mu] : ( mnot @ ( A @ B ) ) ) ) ) ) ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s5_type,type,
rel_s5: $i > $i > $o ).
thf(mdia_s5_type,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(mdia_s5_def,definition,
( mdia_s5
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ A ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: mu ).
thf(3,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(11,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(cnf,[status(esa)],[11]) ).
thf(1,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mdia_s5 @ ( mexists_ind @ ( meq_ind @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( mdia_s5 @ ( mexists_ind @ ( meq_ind @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i,B: mu] :
~ ! [C: $i] :
( ~ ( rel_s5 @ A @ C )
| ! [D: mu] : ( B != D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
~ ~ ( ~ ! [A: $i] :
? [B: $i] : ( rel_s5 @ A @ B )
| ~ ! [A: mu] :
? [B: mu] : ( A = B ) ),
inference(miniscope,[status(thm)],[6]) ).
thf(8,plain,
! [B: mu,A: $i] :
( ~ ( rel_s5 @ sk1 @ A )
| ( sk2 != B ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [B: mu,A: $i] :
( ( sk2 != B )
| ~ ( rel_s5 @ sk1 @ A ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
! [A: $i] :
~ ( rel_s5 @ sk1 @ A ),
inference(simp,[status(thm)],[9]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( rel_s5 @ A @ A )
!= ( rel_s5 @ sk1 @ B ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(18,plain,
$false,
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SYO485^6 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n012.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 10:27:39 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.91/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.13 % [INFO] Parsing done (208ms).
% 1.36/1.14 % [INFO] Running in sequential loop mode.
% 2.09/1.49 % [INFO] eprover registered as external prover.
% 2.09/1.49 % [INFO] cvc4 registered as external prover.
% 2.09/1.49 % [INFO] Scanning for conjecture ...
% 2.47/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.58/1.69 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.58/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.58/1.70 % [INFO] Type checking passed.
% 2.58/1.70 % [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 ...
% 3.63/2.18 % [INFO] Killing All external provers ...
% 3.63/2.18 % Time passed: 1718ms (effective reasoning time: 1034ms)
% 3.63/2.18 % 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)>
% 3.63/2.18 % Axioms used in derivation (1): a1
% 3.63/2.18 % No. of inferences in proof: 12
% 3.63/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1718 ms resp. 1034 ms w/o parsing
% 3.63/2.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.63/2.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------