TSTP Solution File: SYO458^5 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO458^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 09:00:25 EDT 2024
% Result : Theorem 3.95s 1.86s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 32 ( 11 unt; 11 typ; 5 def)
% Number of atoms : 76 ( 7 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 115 ( 23 ~; 16 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 17 ( 7 ^ 10 !; 0 ?; 17 :)
% 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(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ A ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(mbox_s4_def,definition,
( mbox_s4
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mequiv @ p @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mequiv @ p @ q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ( q @ B ) )
| ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( ~ ( ~ ( p @ B )
| ( q @ B ) )
| ~ ( ~ ( q @ B )
| ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
rel_s4 @ sk1 @ sk2,
inference(cnf,[status(esa)],[5]) ).
thf(12,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ( q @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(13,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[12]) ).
thf(100,plain,
! [A: $i] :
( ( q @ A )
| ( ( rel_s4 @ sk1 @ sk2 )
!= ( rel_s4 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,13]) ).
thf(101,plain,
q @ sk2,
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( sk2 ))]]) ).
thf(7,plain,
( ~ ( q @ sk2 )
| ~ ( p @ sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(8,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ( p @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(89,plain,
! [A: $i] :
( ( p @ A )
| ( ( rel_s4 @ sk1 @ sk2 )
!= ( rel_s4 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(90,plain,
p @ sk2,
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( sk2 ))]]) ).
thf(96,plain,
( ~ ( q @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[7,90]) ).
thf(97,plain,
~ ( q @ sk2 ),
inference(simp,[status(thm)],[96]) ).
thf(107,plain,
$false,
inference(rewrite,[status(thm)],[101,97]) ).
thf(108,plain,
$false,
inference(simp,[status(thm)],[107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO458^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n005.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 09:03:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.02 % [INFO] Parsing done (141ms).
% 1.38/1.02 % [INFO] Running in sequential loop mode.
% 1.86/1.22 % [INFO] nitpick registered as external prover.
% 1.86/1.22 % [INFO] Scanning for conjecture ...
% 1.96/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.24/1.34 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.24/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.34 % [INFO] Type checking passed.
% 2.24/1.35 % [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 ...
% 3.95/1.85 % [INFO] Killing All external provers ...
% 3.95/1.86 % Time passed: 1315ms (effective reasoning time: 828ms)
% 3.95/1.86 % 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)>
% 3.95/1.86 % Axioms used in derivation (0):
% 3.95/1.86 % No. of inferences in proof: 16
% 3.95/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1315 ms resp. 828 ms w/o parsing
% 3.95/1.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.95/1.89 % [INFO] Killing All external provers ...
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