TSTP Solution File: LCL538+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL538+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:53:00 EDT 2022
% Result : Theorem 2.15s 2.32s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 27 unt; 0 def)
% Number of atoms : 130 ( 16 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 118 ( 49 ~; 47 |; 13 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 19 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(strict_implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ) ).
fof(km4b_axiom_M,axiom,
axiom_M ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies ).
fof(s1_0_modus_ponens_strict_implies,conjecture,
modus_ponens_strict_implies ).
fof(subgoal_0,plain,
modus_ponens_strict_implies,
inference(strip,[],[s1_0_modus_ponens_strict_implies]) ).
fof(negate_0_0,plain,
~ modus_ponens_strict_implies,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ modus_ponens
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y)
| modus_ponens )
& ( is_a_theorem(implies(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| modus_ponens )
& ( is_a_theorem(skolemFOFtoCNF_X)
| modus_ponens )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_4,plain,
( ~ modus_ponens_strict_implies
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(strict_implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens_strict_implies]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies )
& ( is_a_theorem(skolemFOFtoCNF_X_16)
| modus_ponens_strict_implies )
& ( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ modus_ponens_strict_implies
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
~ modus_ponens_strict_implies,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
( ~ axiom_M
<=> ? [X] : ~ is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[axiom_M]) ).
fof(normalize_0_9,plain,
! [X] :
( ( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) )
& ( ~ is_a_theorem(implies(necessarily(skolemFOFtoCNF_X_20),skolemFOFtoCNF_X_20))
| axiom_M ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
axiom_M,
inference(canonicalize,[],[km4b_axiom_M]) ).
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]) ).
fof(normalize_0_15,plain,
( is_a_theorem(skolemFOFtoCNF_X_16)
| modus_ponens_strict_implies ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_16,plain,
( ~ is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| ~ is_a_theorem(skolemFOFtoCNF_X_16)
| is_a_theorem(skolemFOFtoCNF_Y_15) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X_16)),bind(Y,$fot(skolemFOFtoCNF_Y_15))]]) ).
cnf(refute_0_4,plain,
( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| modus_ponens_strict_implies ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
~ modus_ponens_strict_implies,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)),
inference(resolve,[$cnf( modus_ponens_strict_implies )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X),X)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
axiom_M,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(necessarily(X),X)),
inference(resolve,[$cnf( axiom_M )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(necessarily(implies(X_4,X_5)),implies(X_4,X_5))),
inference(subst,[],[refute_0_9:[bind(X,$fot(implies(X_4,X_5)))]]) ).
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,[$cnf( op_strict_implies )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
strict_implies(X_4,X_5) = necessarily(implies(X_4,X_5)),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_4)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( strict_implies(X_4,X_5) != necessarily(implies(X_4,X_5))
| necessarily(implies(X_4,X_5)) = strict_implies(X_4,X_5) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(strict_implies(X_4,X_5))),bind(Y0,$fot(necessarily(implies(X_4,X_5))))]]) ).
cnf(refute_0_19,plain,
necessarily(implies(X_4,X_5)) = strict_implies(X_4,X_5),
inference(resolve,[$cnf( $equal(strict_implies(X_4,X_5),necessarily(implies(X_4,X_5))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( necessarily(implies(X_4,X_5)) != strict_implies(X_4,X_5)
| ~ is_a_theorem(implies(necessarily(implies(X_4,X_5)),implies(X_4,X_5)))
| is_a_theorem(implies(strict_implies(X_4,X_5),implies(X_4,X_5))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(necessarily(implies(X_4,X_5)),implies(X_4,X_5))) ),[0,0],$fot(strict_implies(X_4,X_5))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(necessarily(implies(X_4,X_5)),implies(X_4,X_5)))
| is_a_theorem(implies(strict_implies(X_4,X_5),implies(X_4,X_5))) ),
inference(resolve,[$cnf( $equal(necessarily(implies(X_4,X_5)),strict_implies(X_4,X_5)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(strict_implies(X_4,X_5),implies(X_4,X_5))),
inference(resolve,[$cnf( is_a_theorem(implies(necessarily(implies(X_4,X_5)),implies(X_4,X_5))) )],[refute_0_10,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(strict_implies(X_4,X_5),implies(X_4,X_5)))
| ~ is_a_theorem(strict_implies(X_4,X_5))
| is_a_theorem(implies(X_4,X_5)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(strict_implies(X_4,X_5))),bind(Y,$fot(implies(X_4,X_5)))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(strict_implies(X_4,X_5))
| is_a_theorem(implies(X_4,X_5)) ),
inference(resolve,[$cnf( is_a_theorem(implies(strict_implies(X_4,X_5),implies(X_4,X_5))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15))
| is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)) ),
inference(subst,[],[refute_0_24:[bind(X_4,$fot(skolemFOFtoCNF_X_16)),bind(X_5,$fot(skolemFOFtoCNF_Y_15))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)),
inference(resolve,[$cnf( is_a_theorem(strict_implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)) )],[refute_0_6,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(skolemFOFtoCNF_X_16)
| is_a_theorem(skolemFOFtoCNF_Y_15) ),
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_16,skolemFOFtoCNF_Y_15)) )],[refute_0_26,refute_0_3]) ).
cnf(refute_0_28,plain,
( is_a_theorem(skolemFOFtoCNF_X_16)
| modus_ponens_strict_implies ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_29,plain,
is_a_theorem(skolemFOFtoCNF_X_16),
inference(resolve,[$cnf( modus_ponens_strict_implies )],[refute_0_28,refute_0_5]) ).
cnf(refute_0_30,plain,
is_a_theorem(skolemFOFtoCNF_Y_15),
inference(resolve,[$cnf( is_a_theorem(skolemFOFtoCNF_X_16) )],[refute_0_29,refute_0_27]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(skolemFOFtoCNF_Y_15)
| modus_ponens_strict_implies ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_32,plain,
~ is_a_theorem(skolemFOFtoCNF_Y_15),
inference(resolve,[$cnf( modus_ponens_strict_implies )],[refute_0_31,refute_0_5]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(skolemFOFtoCNF_Y_15) )],[refute_0_30,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL538+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n021.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 : Mon Jul 4 20:44:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.15/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.15/2.32
% 2.15/2.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.15/2.32
%------------------------------------------------------------------------------