TSTP Solution File: LCL536+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% 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 : 600s
% DateTime : Sun Jul 17 12:52:59 EDT 2022
% Result : Theorem 0.18s 0.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 24 unt; 0 def)
% Number of atoms : 91 ( 16 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 78 ( 37 ~; 28 |; 5 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ) ).
fof(axiom_m10,axiom,
( axiom_m10
<=> ! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) ) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ) ).
fof(km5_necessitation,axiom,
necessitation ).
fof(km5_axiom_5,axiom,
axiom_5 ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies ).
fof(s1_0_m10_axiom_m10,conjecture,
axiom_m10 ).
fof(subgoal_0,plain,
axiom_m10,
inference(strip,[],[s1_0_m10_axiom_m10]) ).
fof(negate_0_0,plain,
~ axiom_m10,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ axiom_m10
<=> ? [X] : ~ is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[axiom_m10]) ).
fof(normalize_0_1,plain,
! [X] :
( ( ~ axiom_m10
| is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) )
& ( ~ is_a_theorem(strict_implies(possibly(skolemFOFtoCNF_X_34),necessarily(possibly(skolemFOFtoCNF_X_34))))
| axiom_m10 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(strict_implies(possibly(skolemFOFtoCNF_X_34),necessarily(possibly(skolemFOFtoCNF_X_34))))
| axiom_m10 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ axiom_m10,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ axiom_5
<=> ? [X] : ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_5,plain,
! [X] :
( ( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )
& ( ~ is_a_theorem(implies(possibly(skolemFOFtoCNF_X_23),necessarily(possibly(skolemFOFtoCNF_X_23))))
| axiom_5 ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
axiom_5,
inference(canonicalize,[],[km5_axiom_5]) ).
fof(normalize_0_8,plain,
( ~ necessitation
<=> ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) ) ),
inference(canonicalize,[],[necessitation]) ).
fof(normalize_0_9,plain,
! [X] :
( ( ~ is_a_theorem(necessarily(skolemFOFtoCNF_X_15))
| necessitation )
& ( is_a_theorem(skolemFOFtoCNF_X_15)
| necessitation )
& ( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
necessitation,
inference(canonicalize,[],[km5_necessitation]) ).
fof(normalize_0_12,plain,
( ~ op_strict_implies
| ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[op_strict_implies]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
op_strict_implies,
inference(canonicalize,[],[s1_0_op_strict_implies]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(strict_implies(possibly(skolemFOFtoCNF_X_34),necessarily(possibly(skolemFOFtoCNF_X_34))))
| axiom_m10 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ axiom_m10,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(strict_implies(possibly(skolemFOFtoCNF_X_34),necessarily(possibly(skolemFOFtoCNF_X_34)))),
inference(resolve,[$cnf( axiom_m10 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ axiom_5
| is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
axiom_5,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(possibly(X),necessarily(possibly(X)))),
inference(resolve,[$cnf( axiom_5 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
necessitation,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(X)
| is_a_theorem(necessarily(X)) ),
inference(resolve,[$cnf( necessitation )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| is_a_theorem(necessarily(implies(possibly(X),necessarily(possibly(X))))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(possibly(X),necessarily(possibly(X)))))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(necessarily(implies(possibly(X),necessarily(possibly(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
op_strict_implies,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
strict_implies(X,Y) = necessarily(implies(X,Y)),
inference(resolve,[$cnf( op_strict_implies )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( strict_implies(X,Y) != necessarily(implies(X,Y))
| necessarily(implies(X,Y)) = strict_implies(X,Y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(strict_implies(X,Y))),bind(Y0,$fot(necessarily(implies(X,Y))))]]) ).
cnf(refute_0_18,plain,
necessarily(implies(X,Y)) = strict_implies(X,Y),
inference(resolve,[$cnf( $equal(strict_implies(X,Y),necessarily(implies(X,Y))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
necessarily(implies(possibly(X),necessarily(possibly(X)))) = strict_implies(possibly(X),necessarily(possibly(X))),
inference(subst,[],[refute_0_18:[bind(X,$fot(possibly(X))),bind(Y,$fot(necessarily(possibly(X))))]]) ).
cnf(refute_0_20,plain,
( necessarily(implies(possibly(X),necessarily(possibly(X)))) != strict_implies(possibly(X),necessarily(possibly(X)))
| ~ is_a_theorem(necessarily(implies(possibly(X),necessarily(possibly(X)))))
| is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(implies(possibly(X),necessarily(possibly(X))))) ),[0],$fot(strict_implies(possibly(X),necessarily(possibly(X))))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(necessarily(implies(possibly(X),necessarily(possibly(X)))))
| is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) ),
inference(resolve,[$cnf( $equal(necessarily(implies(possibly(X),necessarily(possibly(X)))),strict_implies(possibly(X),necessarily(possibly(X)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))),
inference(resolve,[$cnf( is_a_theorem(necessarily(implies(possibly(X),necessarily(possibly(X))))) )],[refute_0_10,refute_0_21]) ).
cnf(refute_0_23,plain,
is_a_theorem(strict_implies(possibly(skolemFOFtoCNF_X_34),necessarily(possibly(skolemFOFtoCNF_X_34)))),
inference(subst,[],[refute_0_22:[bind(X,$fot(skolemFOFtoCNF_X_34))]]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(strict_implies(possibly(skolemFOFtoCNF_X_34),necessarily(possibly(skolemFOFtoCNF_X_34)))) )],[refute_0_23,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 15:32:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44
% 0.18/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.45
%------------------------------------------------------------------------------