TSTP Solution File: LCL542+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL542+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 12:53:01 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 25 unt; 0 def)
% Number of atoms : 92 ( 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 : 4 ( 2 avg)
% Number of predicates : 8 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 57 ( 5 sgn 19 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ) ).
fof(hilbert_and_1,axiom,
and_1 ).
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ) ).
fof(km4b_necessitation,axiom,
necessitation ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies ).
fof(s1_0_axiom_m2,conjecture,
axiom_m2 ).
fof(subgoal_0,plain,
axiom_m2,
inference(strip,[],[s1_0_axiom_m2]) ).
fof(negate_0_0,plain,
~ axiom_m2,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ axiom_m2
<=> ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),X)) ),
inference(canonicalize,[],[axiom_m2]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ axiom_m2
| is_a_theorem(strict_implies(and(X,Y),X)) )
& ( ~ is_a_theorem(strict_implies(and(skolemFOFtoCNF_X_28,skolemFOFtoCNF_Y_22),skolemFOFtoCNF_X_28))
| axiom_m2 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(strict_implies(and(skolemFOFtoCNF_X_28,skolemFOFtoCNF_Y_22),skolemFOFtoCNF_X_28))
| axiom_m2 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ axiom_m2,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ necessitation
<=> ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) ) ),
inference(canonicalize,[],[necessitation]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
necessitation,
inference(canonicalize,[],[km4b_necessitation]) ).
fof(normalize_0_8,plain,
( ~ and_1
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X)) ),
inference(canonicalize,[],[and_1]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) )
& ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_6,skolemFOFtoCNF_Y_6),skolemFOFtoCNF_X_6))
| and_1 ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
and_1,
inference(canonicalize,[],[hilbert_and_1]) ).
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(and(skolemFOFtoCNF_X_28,skolemFOFtoCNF_Y_22),skolemFOFtoCNF_X_28))
| axiom_m2 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ axiom_m2,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(strict_implies(and(skolemFOFtoCNF_X_28,skolemFOFtoCNF_Y_22),skolemFOFtoCNF_X_28)),
inference(resolve,[$cnf( axiom_m2 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
necessitation,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(X)
| is_a_theorem(necessarily(X)) ),
inference(resolve,[$cnf( necessitation )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(and(X_35,X_36),X_35))
| is_a_theorem(necessarily(implies(and(X_35,X_36),X_35))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(and(X_35,X_36),X_35)))]]) ).
cnf(refute_0_7,plain,
( ~ and_1
| is_a_theorem(implies(and(X,Y),X)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
and_1,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(and(X,Y),X)),
inference(resolve,[$cnf( and_1 )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(and(X_35,X_36),X_35)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_35)),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(necessarily(implies(and(X_35,X_36),X_35))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_35,X_36),X_35)) )],[refute_0_10,refute_0_6]) ).
cnf(refute_0_12,plain,
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_13,plain,
op_strict_implies,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_14,plain,
strict_implies(X,Y) = necessarily(implies(X,Y)),
inference(resolve,[$cnf( op_strict_implies )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_17,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( strict_implies(X,Y) != necessarily(implies(X,Y))
| necessarily(implies(X,Y)) = strict_implies(X,Y) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(strict_implies(X,Y))),bind(Y0,$fot(necessarily(implies(X,Y))))]]) ).
cnf(refute_0_19,plain,
necessarily(implies(X,Y)) = strict_implies(X,Y),
inference(resolve,[$cnf( $equal(strict_implies(X,Y),necessarily(implies(X,Y))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
necessarily(implies(and(X_35,X_36),X_35)) = strict_implies(and(X_35,X_36),X_35),
inference(subst,[],[refute_0_19:[bind(X,$fot(and(X_35,X_36))),bind(Y,$fot(X_35))]]) ).
cnf(refute_0_21,plain,
( necessarily(implies(and(X_35,X_36),X_35)) != strict_implies(and(X_35,X_36),X_35)
| ~ is_a_theorem(necessarily(implies(and(X_35,X_36),X_35)))
| is_a_theorem(strict_implies(and(X_35,X_36),X_35)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(implies(and(X_35,X_36),X_35))) ),[0],$fot(strict_implies(and(X_35,X_36),X_35))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(necessarily(implies(and(X_35,X_36),X_35)))
| is_a_theorem(strict_implies(and(X_35,X_36),X_35)) ),
inference(resolve,[$cnf( $equal(necessarily(implies(and(X_35,X_36),X_35)),strict_implies(and(X_35,X_36),X_35)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
is_a_theorem(strict_implies(and(X_35,X_36),X_35)),
inference(resolve,[$cnf( is_a_theorem(necessarily(implies(and(X_35,X_36),X_35))) )],[refute_0_11,refute_0_22]) ).
cnf(refute_0_24,plain,
is_a_theorem(strict_implies(and(skolemFOFtoCNF_X_28,skolemFOFtoCNF_Y_22),skolemFOFtoCNF_X_28)),
inference(subst,[],[refute_0_23:[bind(X_35,$fot(skolemFOFtoCNF_X_28)),bind(X_36,$fot(skolemFOFtoCNF_Y_22))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(strict_implies(and(skolemFOFtoCNF_X_28,skolemFOFtoCNF_Y_22),skolemFOFtoCNF_X_28)) )],[refute_0_24,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL542+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 16:42:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.48
%------------------------------------------------------------------------------