TSTP Solution File: LCL483+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL483+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 12:52:34 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 72 ( 36 unt; 0 def)
% Number of atoms : 117 ( 48 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 89 ( 44 ~; 36 |; 2 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_r3,axiom,
r3 ).
fof(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
fof(hilbert_modus_tollens,conjecture,
modus_tollens ).
fof(subgoal_0,plain,
modus_tollens,
inference(strip,[],[hilbert_modus_tollens]) ).
fof(negate_0_0,plain,
~ modus_tollens,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ modus_tollens
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[modus_tollens]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))
| modus_tollens )
& ( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))
| modus_tollens ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_6,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_9,plain,
~ modus_tollens,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_11,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8)))
| r3 )
& ( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [P,Q] :
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
r3,
inference(canonicalize,[],[principia_r3]) ).
fof(normalize_0_14,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))
| modus_tollens ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
op_or,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_11,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_11:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_13,plain,
( not(and(not(X),not(Y))) != implies(not(X),Y)
| or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) ),[1],$fot(implies(not(X),Y))]]) ).
cnf(refute_0_14,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_3,refute_0_14]) ).
cnf(refute_0_16,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_17,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)) = or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_Y_2)),bind(Y,$fot(not(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_0_19,plain,
implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)) = implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)),
introduced(tautology,[refl,[$fot(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))]]) ).
cnf(refute_0_20,plain,
( implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)) != implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))
| implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)) != or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2))
| implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)) = implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)),implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))) ),[1,0],$fot(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)))]]) ).
cnf(refute_0_21,plain,
( implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)) != or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2))
| implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)) = implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)),implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)) = implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)),
inference(resolve,[$cnf( $equal(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)) != implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))
| ~ is_a_theorem(implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))
| is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))) ),[0],$fot(implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))
| is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)),implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))
| modus_tollens ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))) )],[refute_0_24,refute_0_0]) ).
cnf(refute_0_26,plain,
~ modus_tollens,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_27,plain,
~ is_a_theorem(implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))),
inference(resolve,[$cnf( modus_tollens )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_29,plain,
r3,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$cnf( r3 )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(or(X_28,not(X)),or(not(X),X_28))),
inference(subst,[],[refute_0_30:[bind(P,$fot(X_28)),bind(Q,$fot(not(X)))]]) ).
cnf(refute_0_32,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_33,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_34,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
implies(X,X_28) = or(not(X),X_28),
inference(subst,[],[refute_0_34:[bind(Y,$fot(X_28))]]) ).
cnf(refute_0_36,plain,
( implies(X,X_28) != or(not(X),X_28)
| or(not(X),X_28) = implies(X,X_28) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(implies(X,X_28))),bind(Y0,$fot(or(not(X),X_28)))]]) ).
cnf(refute_0_37,plain,
or(not(X),X_28) = implies(X,X_28),
inference(resolve,[$cnf( $equal(implies(X,X_28),or(not(X),X_28)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( or(not(X),X_28) != implies(X,X_28)
| ~ is_a_theorem(implies(or(X_28,not(X)),or(not(X),X_28)))
| is_a_theorem(implies(or(X_28,not(X)),implies(X,X_28))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_28,not(X)),or(not(X),X_28))) ),[0,1],$fot(implies(X,X_28))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(or(X_28,not(X)),or(not(X),X_28)))
| is_a_theorem(implies(or(X_28,not(X)),implies(X,X_28))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_28),implies(X,X_28)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(or(X_28,not(X)),implies(X,X_28))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_28,not(X)),or(not(X),X_28))) )],[refute_0_31,refute_0_39]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))),
inference(subst,[],[refute_0_40:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(X_28,$fot(skolemFOFtoCNF_Y_2))]]) ).
cnf(refute_0_42,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(or(skolemFOFtoCNF_Y_2,not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2))) )],[refute_0_41,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL483+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n014.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 : Sun Jul 3 01:00:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.42
%------------------------------------------------------------------------------