TSTP Solution File: SYO478^6 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO478^6 : 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 09:00:39 EDT 2024
% Result : Theorem 3.40s 2.11s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 26 ( 10 unt; 10 typ; 4 def)
% Number of atoms : 51 ( 5 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 90 ( 21 ~; 9 |; 0 &; 60 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 23 ( 7 ^ 14 !; 2 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
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(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s5_type,type,
rel_s5: $i > $i > $o ).
thf(mbox_s5_type,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(mbox_s5_def,definition,
( mbox_s5
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(f_type,type,
f: mu > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: mu ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( mvalid
@ ( mimplies
@ ( mexists_ind
@ ^ [A: mu] : ( mbox_s5 @ ( f @ A ) ) )
@ ( mbox_s5 @ ( mexists_ind @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mexists_ind
@ ^ [A: mu] : ( mbox_s5 @ ( f @ A ) ) )
@ ( mbox_s5 @ ( mexists_ind @ f ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ! [B: mu] :
~ ! [C: $i] :
( ~ ( rel_s5 @ A @ C )
| ( f @ B @ C ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: mu] :
~ ( f @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
~ ! [A: $i] :
( ~ ? [B: mu] :
! [C: $i] :
( ~ ( rel_s5 @ A @ C )
| ( f @ B @ C ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ~ ? [C: mu] : ( f @ C @ B ) ) ),
inference(miniscope,[status(thm)],[6]) ).
thf(10,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk1 @ A )
| ( f @ sk2 @ A ) ),
inference(cnf,[status(esa)],[7]) ).
thf(8,plain,
! [A: mu] :
~ ( f @ A @ sk3 ),
inference(cnf,[status(esa)],[7]) ).
thf(11,plain,
! [A: mu] :
~ ( f @ A @ sk3 ),
inference(simp,[status(thm)],[8]) ).
thf(20,plain,
! [B: mu,A: $i] :
( ~ ( rel_s5 @ sk1 @ A )
| ( ( f @ sk2 @ A )
!= ( f @ B @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[10,11]) ).
thf(21,plain,
~ ( rel_s5 @ sk1 @ sk3 ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(9,plain,
rel_s5 @ sk1 @ sk3,
inference(cnf,[status(esa)],[7]) ).
thf(24,plain,
~ $true,
inference(rewrite,[status(thm)],[21,9]) ).
thf(25,plain,
$false,
inference(simp,[status(thm)],[24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO478^6 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.12 % Command : run_Leo-III %s %d
% 0.12/0.31 % Computer : n016.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.31 % CPULimit : 300
% 0.17/0.31 % WCLimit : 300
% 0.17/0.31 % DateTime : Mon May 20 09:48:39 EDT 2024
% 0.17/0.31 % CPUTime :
% 0.92/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/1.08 % [INFO] Parsing done (217ms).
% 1.42/1.10 % [INFO] Running in sequential loop mode.
% 1.96/1.44 % [INFO] nitpick registered as external prover.
% 2.07/1.45 % [INFO] Scanning for conjecture ...
% 2.32/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.32/1.61 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.32/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.32/1.62 % [INFO] Type checking passed.
% 2.32/1.62 % [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 ...
% 3.40/2.11 % [INFO] Killing All external provers ...
% 3.40/2.11 % Time passed: 1646ms (effective reasoning time: 1007ms)
% 3.40/2.11 % 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)>
% 3.40/2.11 % Axioms used in derivation (0):
% 3.40/2.11 % No. of inferences in proof: 12
% 3.40/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1646 ms resp. 1007 ms w/o parsing
% 3.56/2.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.56/2.17 % [INFO] Killing All external provers ...
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