TSTP Solution File: LCL459+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL459+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:52:27 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 21 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 88 ( 40 ~; 30 |; 9 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-1 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 20 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ) ).
fof(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens ).
fof(hilbert_implies_2,axiom,
implies_2 ).
fof(hilbert_and_3,axiom,
and_3 ).
fof(rosser_kn1,conjecture,
kn1 ).
fof(subgoal_0,plain,
kn1,
inference(strip,[],[rosser_kn1]) ).
fof(negate_0_0,plain,
~ kn1,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ kn1
<=> ? [P] : ~ is_a_theorem(implies(P,and(P,P))) ),
inference(canonicalize,[],[kn1]) ).
fof(normalize_0_1,plain,
! [P] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P)))
| kn1 )
& ( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P)))
| kn1 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ kn1,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) )
& ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_8,implies(skolemFOFtoCNF_Y_8,and(skolemFOFtoCNF_X_8,skolemFOFtoCNF_Y_8))))
| and_3 ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_8,plain,
( ~ implies_2
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[implies_2]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)))
| implies_2 ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
implies_2,
inference(canonicalize,[],[hilbert_implies_2]) ).
fof(normalize_0_12,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_13,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_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P)))
| kn1 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ kn1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P))),
inference(resolve,[$cnf( kn1 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
and_3,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(X_315,implies(X_315,and(X_315,X_315)))),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_315)),bind(Y,$fot(X_315))]]) ).
cnf(refute_0_7,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
implies_2,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))),
inference(resolve,[$cnf( implies_2 )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_11,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(implies(X,implies(X,Y)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(X_315,implies(X_315,and(X_315,X_315))))
| is_a_theorem(implies(X_315,and(X_315,X_315))) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_315)),bind(Y,$fot(and(X_315,X_315)))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_315,and(X_315,X_315))),
inference(resolve,[$cnf( is_a_theorem(implies(X_315,implies(X_315,and(X_315,X_315)))) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P))),
inference(subst,[],[refute_0_16:[bind(X_315,$fot(skolemFOFtoCNF_P))]]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P))) )],[refute_0_17,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL459+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 16:44:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.53
% 0.19/0.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.53
%------------------------------------------------------------------------------