TSTP Solution File: LCL456+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL456+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 12:52:26 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of formulae : 130 ( 66 unt; 0 def)
% Number of atoms : 214 ( 134 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 166 ( 82 ~; 74 |; 2 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 233 ( 0 sgn 34 !; 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_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(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(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
fof(hilbert_modus_tollens,axiom,
modus_tollens ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_op_and,axiom,
op_and ).
fof(principia_r3,conjecture,
r3 ).
fof(subgoal_0,plain,
r3,
inference(strip,[],[principia_r3]) ).
fof(negate_0_0,plain,
~ r3,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_1,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_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8)))
| r3 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ r3,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ modus_tollens
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[modus_tollens]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
modus_tollens,
inference(canonicalize,[],[hilbert_modus_tollens]) ).
fof(normalize_0_8,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_11,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_14,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_17,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8)))
| r3 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ r3,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8))),
inference(resolve,[$cnf( r3 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
modus_tollens,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))),
inference(resolve,[$cnf( modus_tollens )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
implies(or(X_20,not(Y)),X_27) = or(not(or(X_20,not(Y))),X_27),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_20,not(Y)))),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_10,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
op_and,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_14,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_15,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_17,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_17:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_19,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_20,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_21,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_24,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_12,refute_0_24]) ).
cnf(refute_0_26,plain,
and(not(X_20),Y) = not(implies(not(X_20),not(Y))),
inference(subst,[],[refute_0_25:[bind(X,$fot(not(X_20)))]]) ).
cnf(refute_0_27,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_28,plain,
op_or,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_29,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_31,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_32,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_34,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_34:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_36,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_37,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_29,refute_0_37]) ).
cnf(refute_0_39,plain,
or(X_20,not(Y)) = implies(not(X_20),not(Y)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_20)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_40,plain,
( or(X_20,not(Y)) != implies(not(X_20),not(Y))
| implies(not(X_20),not(Y)) = or(X_20,not(Y)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_20,not(Y)))),bind(Y0,$fot(implies(not(X_20),not(Y))))]]) ).
cnf(refute_0_41,plain,
implies(not(X_20),not(Y)) = or(X_20,not(Y)),
inference(resolve,[$cnf( $equal(or(X_20,not(Y)),implies(not(X_20),not(Y))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( and(not(X_20),Y) != not(implies(not(X_20),not(Y)))
| implies(not(X_20),not(Y)) != or(X_20,not(Y))
| and(not(X_20),Y) = not(or(X_20,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X_20),Y),not(implies(not(X_20),not(Y)))) ),[1,0],$fot(or(X_20,not(Y)))]]) ).
cnf(refute_0_43,plain,
( and(not(X_20),Y) != not(implies(not(X_20),not(Y)))
| and(not(X_20),Y) = not(or(X_20,not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_20),not(Y)),or(X_20,not(Y))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
and(not(X_20),Y) = not(or(X_20,not(Y))),
inference(resolve,[$cnf( $equal(and(not(X_20),Y),not(implies(not(X_20),not(Y)))) )],[refute_0_26,refute_0_43]) ).
cnf(refute_0_45,plain,
( and(not(X_20),Y) != not(or(X_20,not(Y)))
| not(or(X_20,not(Y))) = and(not(X_20),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(not(X_20),Y))),bind(Y0,$fot(not(or(X_20,not(Y)))))]]) ).
cnf(refute_0_46,plain,
not(or(X_20,not(Y))) = and(not(X_20),Y),
inference(resolve,[$cnf( $equal(and(not(X_20),Y),not(or(X_20,not(Y)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( implies(or(X_20,not(Y)),X_27) != or(not(or(X_20,not(Y))),X_27)
| not(or(X_20,not(Y))) != and(not(X_20),Y)
| implies(or(X_20,not(Y)),X_27) = or(and(not(X_20),Y),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_20,not(Y)),X_27),or(not(or(X_20,not(Y))),X_27)) ),[1,0],$fot(and(not(X_20),Y))]]) ).
cnf(refute_0_48,plain,
( implies(or(X_20,not(Y)),X_27) != or(not(or(X_20,not(Y))),X_27)
| implies(or(X_20,not(Y)),X_27) = or(and(not(X_20),Y),X_27) ),
inference(resolve,[$cnf( $equal(not(or(X_20,not(Y))),and(not(X_20),Y)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
implies(or(X_20,not(Y)),X_27) = or(and(not(X_20),Y),X_27),
inference(resolve,[$cnf( $equal(implies(or(X_20,not(Y)),X_27),or(not(or(X_20,not(Y))),X_27)) )],[refute_0_9,refute_0_48]) ).
cnf(refute_0_50,plain,
( implies(or(X_20,not(Y)),X_27) != or(and(not(X_20),Y),X_27)
| or(and(not(X_20),Y),X_27) = implies(or(X_20,not(Y)),X_27) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(or(X_20,not(Y)),X_27))),bind(Y0,$fot(or(and(not(X_20),Y),X_27)))]]) ).
cnf(refute_0_51,plain,
or(and(not(X_20),Y),X_27) = implies(or(X_20,not(Y)),X_27),
inference(resolve,[$cnf( $equal(implies(or(X_20,not(Y)),X_27),or(and(not(X_20),Y),X_27)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
or(and(not(Y),X),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)),
inference(subst,[],[refute_0_51:[bind(Y,$fot(X)),bind(X_20,$fot(Y)),bind(X_27,$fot(implies(X,Y)))]]) ).
cnf(refute_0_53,plain,
implies(implies(X,not(Y)),X_27) = or(not(implies(X,not(Y))),X_27),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_54,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_55,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_25,refute_0_54]) ).
cnf(refute_0_56,plain,
( implies(implies(X,not(Y)),X_27) != or(not(implies(X,not(Y))),X_27)
| not(implies(X,not(Y))) != and(X,Y)
| implies(implies(X,not(Y)),X_27) = or(and(X,Y),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(Y)),X_27),or(not(implies(X,not(Y))),X_27)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_57,plain,
( implies(implies(X,not(Y)),X_27) != or(not(implies(X,not(Y))),X_27)
| implies(implies(X,not(Y)),X_27) = or(and(X,Y),X_27) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
implies(implies(X,not(Y)),X_27) = or(and(X,Y),X_27),
inference(resolve,[$cnf( $equal(implies(implies(X,not(Y)),X_27),or(not(implies(X,not(Y))),X_27)) )],[refute_0_53,refute_0_57]) ).
cnf(refute_0_59,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = or(and(not(Y),X),implies(X,Y)),
inference(subst,[],[refute_0_58:[bind(X,$fot(not(Y))),bind(Y,$fot(X)),bind(X_27,$fot(implies(X,Y)))]]) ).
cnf(refute_0_60,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_61,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_15,refute_0_60]) ).
cnf(refute_0_62,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != or(and(not(Y),X),implies(X,Y))
| or(and(not(Y),X),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)) ),
inference(subst,[],[refute_0_61:[bind(X0,$fot(implies(implies(not(Y),not(X)),implies(X,Y)))),bind(Y0,$fot(or(and(not(Y),X),implies(X,Y)))),bind(Z,$fot(implies(or(Y,not(X)),implies(X,Y))))]]) ).
cnf(refute_0_63,plain,
( or(and(not(Y),X),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),or(and(not(Y),X),implies(X,Y))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)),
inference(resolve,[$cnf( $equal(or(and(not(Y),X),implies(X,Y)),implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_52,refute_0_63]) ).
cnf(refute_0_65,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),[0],$fot(implies(or(Y,not(X)),implies(X,Y)))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(or(Y,not(X)),implies(X,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_5,refute_0_66]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(or(X_48,not(not(X))),implies(not(X),X_48))),
inference(subst,[],[refute_0_67:[bind(X,$fot(not(X))),bind(Y,$fot(X_48))]]) ).
cnf(refute_0_69,plain,
or(X,X_48) = implies(not(X),X_48),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_48))]]) ).
cnf(refute_0_70,plain,
( or(X,X_48) != implies(not(X),X_48)
| implies(not(X),X_48) = or(X,X_48) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_48))),bind(Y0,$fot(implies(not(X),X_48)))]]) ).
cnf(refute_0_71,plain,
implies(not(X),X_48) = or(X,X_48),
inference(resolve,[$cnf( $equal(or(X,X_48),implies(not(X),X_48)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( implies(not(X),X_48) != or(X,X_48)
| ~ is_a_theorem(implies(or(X_48,not(not(X))),implies(not(X),X_48)))
| is_a_theorem(implies(or(X_48,not(not(X))),or(X,X_48))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_48,not(not(X))),implies(not(X),X_48))) ),[0,1],$fot(or(X,X_48))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(or(X_48,not(not(X))),implies(not(X),X_48)))
| is_a_theorem(implies(or(X_48,not(not(X))),or(X,X_48))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_48),or(X,X_48)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(or(X_48,not(not(X))),or(X,X_48))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_48,not(not(X))),implies(not(X),X_48))) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
or(and(X,not(Y)),X_21) = implies(not(and(X,not(Y))),X_21),
inference(subst,[],[refute_0_38:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_76,plain,
( not(and(X,not(Y))) != implies(X,Y)
| or(and(X,not(Y)),X_21) != implies(not(and(X,not(Y))),X_21)
| or(and(X,not(Y)),X_21) = implies(implies(X,Y),X_21) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),X_21),implies(not(and(X,not(Y))),X_21)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_77,plain,
( or(and(X,not(Y)),X_21) != implies(not(and(X,not(Y))),X_21)
| or(and(X,not(Y)),X_21) = implies(implies(X,Y),X_21) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_34,refute_0_76]) ).
cnf(refute_0_78,plain,
or(and(X,not(Y)),X_21) = implies(implies(X,Y),X_21),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),X_21),implies(not(and(X,not(Y))),X_21)) )],[refute_0_75,refute_0_77]) ).
cnf(refute_0_79,plain,
or(and(not(X),not(X_67)),X_68) = implies(implies(not(X),X_67),X_68),
inference(subst,[],[refute_0_78:[bind(X,$fot(not(X))),bind(Y,$fot(X_67)),bind(X_21,$fot(X_68))]]) ).
cnf(refute_0_80,plain,
or(X,X_67) = implies(not(X),X_67),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_67))]]) ).
cnf(refute_0_81,plain,
( or(X,X_67) != implies(not(X),X_67)
| implies(not(X),X_67) = or(X,X_67) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_67))),bind(Y0,$fot(implies(not(X),X_67)))]]) ).
cnf(refute_0_82,plain,
implies(not(X),X_67) = or(X,X_67),
inference(resolve,[$cnf( $equal(or(X,X_67),implies(not(X),X_67)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( implies(not(X),X_67) != or(X,X_67)
| or(and(not(X),not(X_67)),X_68) != implies(implies(not(X),X_67),X_68)
| or(and(not(X),not(X_67)),X_68) = implies(or(X,X_67),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X),not(X_67)),X_68),implies(implies(not(X),X_67),X_68)) ),[1,0],$fot(or(X,X_67))]]) ).
cnf(refute_0_84,plain,
( or(and(not(X),not(X_67)),X_68) != implies(implies(not(X),X_67),X_68)
| or(and(not(X),not(X_67)),X_68) = implies(or(X,X_67),X_68) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_67),or(X,X_67)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
or(and(not(X),not(X_67)),X_68) = implies(or(X,X_67),X_68),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_67)),X_68),implies(implies(not(X),X_67),X_68)) )],[refute_0_79,refute_0_84]) ).
cnf(refute_0_86,plain,
or(and(not(X),not(X_67)),X_68) = implies(or(X,not(not(X_67))),X_68),
inference(subst,[],[refute_0_51:[bind(Y,$fot(not(X_67))),bind(X_20,$fot(X)),bind(X_27,$fot(X_68))]]) ).
cnf(refute_0_87,plain,
( or(and(not(X),not(X_67)),X_68) != implies(or(X,X_67),X_68)
| or(and(not(X),not(X_67)),X_68) != implies(or(X,not(not(X_67))),X_68)
| implies(or(X,not(not(X_67))),X_68) = implies(or(X,X_67),X_68) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X),not(X_67)),X_68),implies(or(X,X_67),X_68)) ),[0],$fot(implies(or(X,not(not(X_67))),X_68))]]) ).
cnf(refute_0_88,plain,
( or(and(not(X),not(X_67)),X_68) != implies(or(X,X_67),X_68)
| implies(or(X,not(not(X_67))),X_68) = implies(or(X,X_67),X_68) ),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_67)),X_68),implies(or(X,not(not(X_67))),X_68)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(or(X,not(not(X_67))),X_68) = implies(or(X,X_67),X_68),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_67)),X_68),implies(or(X,X_67),X_68)) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(or(X_48,not(not(X))),or(X,X_48)) = implies(or(X_48,X),or(X,X_48)),
inference(subst,[],[refute_0_89:[bind(X,$fot(X_48)),bind(X_67,$fot(X)),bind(X_68,$fot(or(X,X_48)))]]) ).
cnf(refute_0_91,plain,
( implies(or(X_48,not(not(X))),or(X,X_48)) != implies(or(X_48,X),or(X,X_48))
| ~ is_a_theorem(implies(or(X_48,not(not(X))),or(X,X_48)))
| is_a_theorem(implies(or(X_48,X),or(X,X_48))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_48,not(not(X))),or(X,X_48))) ),[0],$fot(implies(or(X_48,X),or(X,X_48)))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(implies(or(X_48,not(not(X))),or(X,X_48)))
| is_a_theorem(implies(or(X_48,X),or(X,X_48))) ),
inference(resolve,[$cnf( $equal(implies(or(X_48,not(not(X))),or(X,X_48)),implies(or(X_48,X),or(X,X_48))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(or(X_48,X),or(X,X_48))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_48,not(not(X))),or(X,X_48))) )],[refute_0_74,refute_0_92]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8))),
inference(subst,[],[refute_0_93:[bind(X,$fot(skolemFOFtoCNF_Q_5)),bind(X_48,$fot(skolemFOFtoCNF_P_8))]]) ).
cnf(refute_0_95,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8))) )],[refute_0_94,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL456+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n012.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 19:16:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45
% 0.20/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.47
%------------------------------------------------------------------------------