TSTP Solution File: LCL531+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:52:57 EDT 2022
% Result : Theorem 0.48s 0.65s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 34 unt; 0 def)
% Number of atoms : 149 ( 16 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 136 ( 61 ~; 50 |; 12 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 29 !; 8 ?)
% 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(hilbert_modus_ponens,axiom,
modus_ponens ).
fof(hilbert_implies_2,axiom,
implies_2 ).
fof(hilbert_and_3,axiom,
and_3 ).
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,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(s1_0_op_strict_implies,axiom,
op_strict_implies ).
fof(s1_0_axiom_m4,conjecture,
axiom_m4 ).
fof(subgoal_0,plain,
axiom_m4,
inference(strip,[],[s1_0_axiom_m4]) ).
fof(negate_0_0,plain,
~ axiom_m4,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ axiom_m4
<=> ? [X] : ~ is_a_theorem(strict_implies(X,and(X,X))) ),
inference(canonicalize,[],[axiom_m4]) ).
fof(normalize_0_1,plain,
! [X] :
( ( ~ axiom_m4
| is_a_theorem(strict_implies(X,and(X,X))) )
& ( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_30,and(skolemFOFtoCNF_X_30,skolemFOFtoCNF_X_30)))
| axiom_m4 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_30,and(skolemFOFtoCNF_X_30,skolemFOFtoCNF_X_30)))
| axiom_m4 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ axiom_m4,
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,[],[km5_necessitation]) ).
fof(normalize_0_8,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_12,plain,
( ~ implies_2
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[implies_2]) ).
fof(normalize_0_13,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_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
implies_2,
inference(canonicalize,[],[hilbert_implies_2]) ).
fof(normalize_0_16,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_17,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_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_20,plain,
( ~ op_strict_implies
| ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[op_strict_implies]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
op_strict_implies,
inference(canonicalize,[],[s1_0_op_strict_implies]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_30,and(skolemFOFtoCNF_X_30,skolemFOFtoCNF_X_30)))
| axiom_m4 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ axiom_m4,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(strict_implies(skolemFOFtoCNF_X_30,and(skolemFOFtoCNF_X_30,skolemFOFtoCNF_X_30))),
inference(resolve,[$cnf( axiom_m4 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X)
| ~ necessitation
| is_a_theorem(necessarily(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
necessitation,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(X)
| is_a_theorem(necessarily(X)) ),
inference(resolve,[$cnf( necessitation )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(X_397,and(X_397,X_397)))
| is_a_theorem(necessarily(implies(X_397,and(X_397,X_397)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X_397,and(X_397,X_397))))]]) ).
cnf(refute_0_7,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
and_3,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(X_392,implies(X_392,and(X_392,X_392)))),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_392)),bind(Y,$fot(X_392))]]) ).
cnf(refute_0_11,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
implies_2,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))),
inference(resolve,[$cnf( implies_2 )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_15,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,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_16:[bind(X,$fot(implies(X,implies(X,Y)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(X_392,implies(X_392,and(X_392,X_392))))
| is_a_theorem(implies(X_392,and(X_392,X_392))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_392)),bind(Y,$fot(and(X_392,X_392)))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(X_392,and(X_392,X_392))),
inference(resolve,[$cnf( is_a_theorem(implies(X_392,implies(X_392,and(X_392,X_392)))) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(X_397,and(X_397,X_397))),
inference(subst,[],[refute_0_20:[bind(X_392,$fot(X_397))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(necessarily(implies(X_397,and(X_397,X_397)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_397,and(X_397,X_397))) )],[refute_0_21,refute_0_6]) ).
cnf(refute_0_23,plain,
( ~ op_strict_implies
| strict_implies(X,Y) = necessarily(implies(X,Y)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_24,plain,
op_strict_implies,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_25,plain,
strict_implies(X,Y) = necessarily(implies(X,Y)),
inference(resolve,[$cnf( op_strict_implies )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_28,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( strict_implies(X,Y) != necessarily(implies(X,Y))
| necessarily(implies(X,Y)) = strict_implies(X,Y) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(strict_implies(X,Y))),bind(Y0,$fot(necessarily(implies(X,Y))))]]) ).
cnf(refute_0_30,plain,
necessarily(implies(X,Y)) = strict_implies(X,Y),
inference(resolve,[$cnf( $equal(strict_implies(X,Y),necessarily(implies(X,Y))) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
necessarily(implies(X_397,and(X_397,X_397))) = strict_implies(X_397,and(X_397,X_397)),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_397)),bind(Y,$fot(and(X_397,X_397)))]]) ).
cnf(refute_0_32,plain,
( necessarily(implies(X_397,and(X_397,X_397))) != strict_implies(X_397,and(X_397,X_397))
| ~ is_a_theorem(necessarily(implies(X_397,and(X_397,X_397))))
| is_a_theorem(strict_implies(X_397,and(X_397,X_397))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(necessarily(implies(X_397,and(X_397,X_397)))) ),[0],$fot(strict_implies(X_397,and(X_397,X_397)))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(necessarily(implies(X_397,and(X_397,X_397))))
| is_a_theorem(strict_implies(X_397,and(X_397,X_397))) ),
inference(resolve,[$cnf( $equal(necessarily(implies(X_397,and(X_397,X_397))),strict_implies(X_397,and(X_397,X_397))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(strict_implies(X_397,and(X_397,X_397))),
inference(resolve,[$cnf( is_a_theorem(necessarily(implies(X_397,and(X_397,X_397)))) )],[refute_0_22,refute_0_33]) ).
cnf(refute_0_35,plain,
is_a_theorem(strict_implies(skolemFOFtoCNF_X_30,and(skolemFOFtoCNF_X_30,skolemFOFtoCNF_X_30))),
inference(subst,[],[refute_0_34:[bind(X_397,$fot(skolemFOFtoCNF_X_30))]]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(strict_implies(skolemFOFtoCNF_X_30,and(skolemFOFtoCNF_X_30,skolemFOFtoCNF_X_30))) )],[refute_0_35,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Sun Jul 3 18:35:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.65
% 0.48/0.65 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.48/0.65
%------------------------------------------------------------------------------