TSTP Solution File: LCL499+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL499+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 12:52:46 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 47
% Syntax : Number of formulae : 241 ( 122 unt; 0 def)
% Number of atoms : 419 ( 227 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 344 ( 166 ~; 156 |; 9 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 12 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 321 ( 0 sgn 41 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ) ).
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(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_op_and,axiom,
op_and ).
fof(principia_modus_ponens,axiom,
modus_ponens ).
fof(principia_r1,axiom,
r1 ).
fof(principia_r3,axiom,
r3 ).
fof(rosser_op_or,axiom,
op_or ).
fof(rosser_op_implies_and,axiom,
op_implies_and ).
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,
( ~ r1
<=> ? [P] : ~ is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[r1]) ).
fof(normalize_0_5,plain,
! [P] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6))
| r1 )
& ( ~ r1
| is_a_theorem(implies(or(P,P),P)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P] :
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
r1,
inference(canonicalize,[],[principia_r1]) ).
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,[],[rosser_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,[],[rosser_op_implies_and]) ).
fof(normalize_0_20,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_21,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_20]) ).
fof(normalize_0_22,plain,
! [P,Q] :
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
r3,
inference(canonicalize,[],[principia_r3]) ).
fof(normalize_0_24,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_25,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_24]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
modus_ponens,
inference(canonicalize,[],[principia_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,[$cnf( kn1 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r1,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(or(P,P),P)),
inference(resolve,[$cnf( r1 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(or(not(X_13),not(X_13)),not(X_13))),
inference(subst,[],[refute_0_5:[bind(P,$fot(not(X_13)))]]) ).
cnf(refute_0_7,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
implies(X_13,not(X_13)) = or(not(X_13),not(X_13)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_13)),bind(Y,$fot(not(X_13)))]]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(X_13,not(X_13)) != or(not(X_13),not(X_13))
| or(not(X_13),not(X_13)) = implies(X_13,not(X_13)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X_13,not(X_13)))),bind(Y0,$fot(or(not(X_13),not(X_13))))]]) ).
cnf(refute_0_15,plain,
or(not(X_13),not(X_13)) = implies(X_13,not(X_13)),
inference(resolve,[$cnf( $equal(implies(X_13,not(X_13)),or(not(X_13),not(X_13))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( or(not(X_13),not(X_13)) != implies(X_13,not(X_13))
| ~ is_a_theorem(implies(or(not(X_13),not(X_13)),not(X_13)))
| is_a_theorem(implies(implies(X_13,not(X_13)),not(X_13))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_13),not(X_13)),not(X_13))) ),[0,0],$fot(implies(X_13,not(X_13)))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(or(not(X_13),not(X_13)),not(X_13)))
| is_a_theorem(implies(implies(X_13,not(X_13)),not(X_13))) ),
inference(resolve,[$cnf( $equal(or(not(X_13),not(X_13)),implies(X_13,not(X_13))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(X_13,not(X_13)),not(X_13))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_13),not(X_13)),not(X_13))) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(implies(X,not(Y)),X_14) = or(not(implies(X,not(Y))),X_14),
inference(subst,[],[refute_0_9:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_20,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_21,plain,
op_and,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_22,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_24,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_9,refute_0_23]) ).
cnf(refute_0_25,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_24:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_26,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_27,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_28,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_31,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_22,refute_0_31]) ).
cnf(refute_0_33,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_34,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( implies(implies(X,not(Y)),X_14) != or(not(implies(X,not(Y))),X_14)
| not(implies(X,not(Y))) != and(X,Y)
| implies(implies(X,not(Y)),X_14) = or(and(X,Y),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(Y)),X_14),or(not(implies(X,not(Y))),X_14)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_36,plain,
( implies(implies(X,not(Y)),X_14) != or(not(implies(X,not(Y))),X_14)
| implies(implies(X,not(Y)),X_14) = or(and(X,Y),X_14) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(implies(X,not(Y)),X_14) = or(and(X,Y),X_14),
inference(resolve,[$cnf( $equal(implies(implies(X,not(Y)),X_14),or(not(implies(X,not(Y))),X_14)) )],[refute_0_19,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(implies(X_13,not(X_13)),not(X_13)) = or(and(X_13,X_13),not(X_13)),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_13)),bind(Y,$fot(X_13)),bind(X_14,$fot(not(X_13)))]]) ).
cnf(refute_0_39,plain,
( implies(implies(X_13,not(X_13)),not(X_13)) != or(and(X_13,X_13),not(X_13))
| ~ is_a_theorem(implies(implies(X_13,not(X_13)),not(X_13)))
| is_a_theorem(or(and(X_13,X_13),not(X_13))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_13,not(X_13)),not(X_13))) ),[0],$fot(or(and(X_13,X_13),not(X_13)))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(X_13,not(X_13)),not(X_13)))
| is_a_theorem(or(and(X_13,X_13),not(X_13))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,not(X_13)),not(X_13)),or(and(X_13,X_13),not(X_13))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
is_a_theorem(or(and(X_13,X_13),not(X_13))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_13,not(X_13)),not(X_13))) )],[refute_0_18,refute_0_40]) ).
cnf(refute_0_42,plain,
is_a_theorem(or(and(not(not(X_44)),not(not(X_44))),not(not(not(X_44))))),
inference(subst,[],[refute_0_41:[bind(X_13,$fot(not(not(X_44))))]]) ).
cnf(refute_0_43,plain,
and(not(X_9),Y) = not(implies(not(X_9),not(Y))),
inference(subst,[],[refute_0_32:[bind(X,$fot(not(X_9)))]]) ).
cnf(refute_0_44,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_45,plain,
op_or,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_46,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_48,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_49,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_48,refute_0_47]) ).
cnf(refute_0_50,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_51,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_51:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_53,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_54,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_46,refute_0_54]) ).
cnf(refute_0_56,plain,
or(X_9,not(Y)) = implies(not(X_9),not(Y)),
inference(subst,[],[refute_0_55:[bind(X,$fot(X_9)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_57,plain,
( or(X_9,not(Y)) != implies(not(X_9),not(Y))
| implies(not(X_9),not(Y)) = or(X_9,not(Y)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X_9,not(Y)))),bind(Y0,$fot(implies(not(X_9),not(Y))))]]) ).
cnf(refute_0_58,plain,
implies(not(X_9),not(Y)) = or(X_9,not(Y)),
inference(resolve,[$cnf( $equal(or(X_9,not(Y)),implies(not(X_9),not(Y))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( and(not(X_9),Y) != not(implies(not(X_9),not(Y)))
| implies(not(X_9),not(Y)) != or(X_9,not(Y))
| and(not(X_9),Y) = not(or(X_9,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X_9),Y),not(implies(not(X_9),not(Y)))) ),[1,0],$fot(or(X_9,not(Y)))]]) ).
cnf(refute_0_60,plain,
( and(not(X_9),Y) != not(implies(not(X_9),not(Y)))
| and(not(X_9),Y) = not(or(X_9,not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_9),not(Y)),or(X_9,not(Y))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
and(not(X_9),Y) = not(or(X_9,not(Y))),
inference(resolve,[$cnf( $equal(and(not(X_9),Y),not(implies(not(X_9),not(Y)))) )],[refute_0_43,refute_0_60]) ).
cnf(refute_0_62,plain,
and(not(not(X)),X_42) = not(or(not(X),not(X_42))),
inference(subst,[],[refute_0_61:[bind(Y,$fot(X_42)),bind(X_9,$fot(not(X)))]]) ).
cnf(refute_0_63,plain,
implies(X,not(X_42)) = or(not(X),not(X_42)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(not(X_42)))]]) ).
cnf(refute_0_64,plain,
( implies(X,not(X_42)) != or(not(X),not(X_42))
| or(not(X),not(X_42)) = implies(X,not(X_42)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,not(X_42)))),bind(Y0,$fot(or(not(X),not(X_42))))]]) ).
cnf(refute_0_65,plain,
or(not(X),not(X_42)) = implies(X,not(X_42)),
inference(resolve,[$cnf( $equal(implies(X,not(X_42)),or(not(X),not(X_42))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( and(not(not(X)),X_42) != not(or(not(X),not(X_42)))
| or(not(X),not(X_42)) != implies(X,not(X_42))
| and(not(not(X)),X_42) = not(implies(X,not(X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X)),X_42),not(or(not(X),not(X_42)))) ),[1,0],$fot(implies(X,not(X_42)))]]) ).
cnf(refute_0_67,plain,
( and(not(not(X)),X_42) != not(or(not(X),not(X_42)))
| and(not(not(X)),X_42) = not(implies(X,not(X_42))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_42)),implies(X,not(X_42))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
and(not(not(X)),X_42) = not(implies(X,not(X_42))),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_42),not(or(not(X),not(X_42)))) )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
not(implies(X,not(X_42))) = and(X,X_42),
inference(subst,[],[refute_0_34:[bind(Y,$fot(X_42))]]) ).
cnf(refute_0_70,plain,
( and(not(not(X)),X_42) != not(implies(X,not(X_42)))
| not(implies(X,not(X_42))) != and(X,X_42)
| and(not(not(X)),X_42) = and(X,X_42) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(not(X)),X_42),and(X,X_42)) ),[0],$fot(not(implies(X,not(X_42))))]]) ).
cnf(refute_0_71,plain,
( and(not(not(X)),X_42) != not(implies(X,not(X_42)))
| and(not(not(X)),X_42) = and(X,X_42) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(X_42))),and(X,X_42)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
and(not(not(X)),X_42) = and(X,X_42),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_42),not(implies(X,not(X_42)))) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
and(not(not(X_44)),not(not(X_44))) = and(X_44,not(not(X_44))),
inference(subst,[],[refute_0_72:[bind(X,$fot(X_44)),bind(X_42,$fot(not(not(X_44))))]]) ).
cnf(refute_0_74,plain,
( and(not(not(X_44)),not(not(X_44))) != and(X_44,not(not(X_44)))
| ~ is_a_theorem(or(and(not(not(X_44)),not(not(X_44))),not(not(not(X_44)))))
| is_a_theorem(or(and(X_44,not(not(X_44))),not(not(not(X_44))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(X_44)),not(not(X_44))),not(not(not(X_44))))) ),[0,0],$fot(and(X_44,not(not(X_44))))]]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(or(and(not(not(X_44)),not(not(X_44))),not(not(not(X_44)))))
| is_a_theorem(or(and(X_44,not(not(X_44))),not(not(not(X_44))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X_44)),not(not(X_44))),and(X_44,not(not(X_44)))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
is_a_theorem(or(and(X_44,not(not(X_44))),not(not(not(X_44))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(X_44)),not(not(X_44))),not(not(not(X_44))))) )],[refute_0_42,refute_0_75]) ).
cnf(refute_0_77,plain,
implies(implies(X_44,not(X_44)),not(not(not(X_44)))) = or(and(X_44,X_44),not(not(not(X_44)))),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_44)),bind(Y,$fot(X_44)),bind(X_14,$fot(not(not(not(X_44)))))]]) ).
cnf(refute_0_78,plain,
or(and(X_21,not(X_22)),Y) = implies(not(and(X_21,not(X_22))),Y),
inference(subst,[],[refute_0_55:[bind(X,$fot(and(X_21,not(X_22))))]]) ).
cnf(refute_0_79,plain,
implies(X_21,X_22) = not(and(X_21,not(X_22))),
inference(subst,[],[refute_0_49:[bind(X,$fot(X_21)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_80,plain,
( implies(X_21,X_22) != not(and(X_21,not(X_22)))
| not(and(X_21,not(X_22))) = implies(X_21,X_22) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X_21,X_22))),bind(Y0,$fot(not(and(X_21,not(X_22)))))]]) ).
cnf(refute_0_81,plain,
not(and(X_21,not(X_22))) = implies(X_21,X_22),
inference(resolve,[$cnf( $equal(implies(X_21,X_22),not(and(X_21,not(X_22)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( not(and(X_21,not(X_22))) != implies(X_21,X_22)
| or(and(X_21,not(X_22)),Y) != implies(not(and(X_21,not(X_22))),Y)
| or(and(X_21,not(X_22)),Y) = implies(implies(X_21,X_22),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_21,not(X_22)),Y),implies(not(and(X_21,not(X_22))),Y)) ),[1,0],$fot(implies(X_21,X_22))]]) ).
cnf(refute_0_83,plain,
( or(and(X_21,not(X_22)),Y) != implies(not(and(X_21,not(X_22))),Y)
| or(and(X_21,not(X_22)),Y) = implies(implies(X_21,X_22),Y) ),
inference(resolve,[$cnf( $equal(not(and(X_21,not(X_22))),implies(X_21,X_22)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
or(and(X_21,not(X_22)),Y) = implies(implies(X_21,X_22),Y),
inference(resolve,[$cnf( $equal(or(and(X_21,not(X_22)),Y),implies(not(and(X_21,not(X_22))),Y)) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
or(and(X_44,not(not(X_44))),not(not(not(X_44)))) = implies(implies(X_44,not(X_44)),not(not(not(X_44)))),
inference(subst,[],[refute_0_84:[bind(Y,$fot(not(not(not(X_44))))),bind(X_21,$fot(X_44)),bind(X_22,$fot(not(X_44)))]]) ).
cnf(refute_0_86,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_87,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_13,refute_0_86]) ).
cnf(refute_0_88,plain,
( implies(implies(X_44,not(X_44)),not(not(not(X_44)))) != or(and(X_44,X_44),not(not(not(X_44))))
| or(and(X_44,not(not(X_44))),not(not(not(X_44)))) != implies(implies(X_44,not(X_44)),not(not(not(X_44))))
| or(and(X_44,not(not(X_44))),not(not(not(X_44)))) = or(and(X_44,X_44),not(not(not(X_44)))) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(or(and(X_44,not(not(X_44))),not(not(not(X_44)))))),bind(Y0,$fot(implies(implies(X_44,not(X_44)),not(not(not(X_44)))))),bind(Z,$fot(or(and(X_44,X_44),not(not(not(X_44))))))]]) ).
cnf(refute_0_89,plain,
( implies(implies(X_44,not(X_44)),not(not(not(X_44)))) != or(and(X_44,X_44),not(not(not(X_44))))
| or(and(X_44,not(not(X_44))),not(not(not(X_44)))) = or(and(X_44,X_44),not(not(not(X_44)))) ),
inference(resolve,[$cnf( $equal(or(and(X_44,not(not(X_44))),not(not(not(X_44)))),implies(implies(X_44,not(X_44)),not(not(not(X_44))))) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
or(and(X_44,not(not(X_44))),not(not(not(X_44)))) = or(and(X_44,X_44),not(not(not(X_44)))),
inference(resolve,[$cnf( $equal(implies(implies(X_44,not(X_44)),not(not(not(X_44)))),or(and(X_44,X_44),not(not(not(X_44))))) )],[refute_0_77,refute_0_89]) ).
cnf(refute_0_91,plain,
( or(and(X_44,not(not(X_44))),not(not(not(X_44)))) != or(and(X_44,X_44),not(not(not(X_44))))
| ~ is_a_theorem(or(and(X_44,not(not(X_44))),not(not(not(X_44)))))
| is_a_theorem(or(and(X_44,X_44),not(not(not(X_44))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_44,not(not(X_44))),not(not(not(X_44))))) ),[0],$fot(or(and(X_44,X_44),not(not(not(X_44)))))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(or(and(X_44,not(not(X_44))),not(not(not(X_44)))))
| is_a_theorem(or(and(X_44,X_44),not(not(not(X_44))))) ),
inference(resolve,[$cnf( $equal(or(and(X_44,not(not(X_44))),not(not(not(X_44)))),or(and(X_44,X_44),not(not(not(X_44))))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(or(and(X_44,X_44),not(not(not(X_44))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_44,not(not(X_44))),not(not(not(X_44))))) )],[refute_0_76,refute_0_92]) ).
cnf(refute_0_94,plain,
is_a_theorem(or(and(not(X_121),not(X_121)),not(not(not(not(X_121)))))),
inference(subst,[],[refute_0_93:[bind(X_44,$fot(not(X_121)))]]) ).
cnf(refute_0_95,plain,
or(and(not(X_121),not(X_121)),not(not(not(not(X_121))))) = implies(implies(not(X_121),X_121),not(not(not(not(X_121))))),
inference(subst,[],[refute_0_84:[bind(Y,$fot(not(not(not(not(X_121)))))),bind(X_21,$fot(not(X_121))),bind(X_22,$fot(X_121))]]) ).
cnf(refute_0_96,plain,
( or(and(not(X_121),not(X_121)),not(not(not(not(X_121))))) != implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))
| ~ is_a_theorem(or(and(not(X_121),not(X_121)),not(not(not(not(X_121))))))
| is_a_theorem(implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_121),not(X_121)),not(not(not(not(X_121)))))) ),[0],$fot(implies(implies(not(X_121),X_121),not(not(not(not(X_121))))))]]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(or(and(not(X_121),not(X_121)),not(not(not(not(X_121))))))
| is_a_theorem(implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_121),not(X_121)),not(not(not(not(X_121))))),implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_121),not(X_121)),not(not(not(not(X_121)))))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_100,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_55,refute_0_99]) ).
cnf(refute_0_101,plain,
implies(not(X_121),X_121) = or(X_121,X_121),
inference(subst,[],[refute_0_100:[bind(X,$fot(X_121)),bind(Y,$fot(X_121))]]) ).
cnf(refute_0_102,plain,
implies(implies(not(X_121),X_121),not(not(not(not(X_121))))) = implies(implies(not(X_121),X_121),not(not(not(not(X_121))))),
introduced(tautology,[refl,[$fot(implies(implies(not(X_121),X_121),not(not(not(not(X_121))))))]]) ).
cnf(refute_0_103,plain,
( implies(implies(not(X_121),X_121),not(not(not(not(X_121))))) != implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))
| implies(not(X_121),X_121) != or(X_121,X_121)
| implies(implies(not(X_121),X_121),not(not(not(not(X_121))))) = implies(or(X_121,X_121),not(not(not(not(X_121))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_121),X_121),not(not(not(not(X_121))))),implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))) ),[1,0],$fot(or(X_121,X_121))]]) ).
cnf(refute_0_104,plain,
( implies(not(X_121),X_121) != or(X_121,X_121)
| implies(implies(not(X_121),X_121),not(not(not(not(X_121))))) = implies(or(X_121,X_121),not(not(not(not(X_121))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_121),X_121),not(not(not(not(X_121))))),implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
implies(implies(not(X_121),X_121),not(not(not(not(X_121))))) = implies(or(X_121,X_121),not(not(not(not(X_121))))),
inference(resolve,[$cnf( $equal(implies(not(X_121),X_121),or(X_121,X_121)) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
( implies(implies(not(X_121),X_121),not(not(not(not(X_121))))) != implies(or(X_121,X_121),not(not(not(not(X_121)))))
| ~ is_a_theorem(implies(implies(not(X_121),X_121),not(not(not(not(X_121))))))
| is_a_theorem(implies(or(X_121,X_121),not(not(not(not(X_121)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))) ),[0],$fot(implies(or(X_121,X_121),not(not(not(not(X_121))))))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(implies(not(X_121),X_121),not(not(not(not(X_121))))))
| is_a_theorem(implies(or(X_121,X_121),not(not(not(not(X_121)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_121),X_121),not(not(not(not(X_121))))),implies(or(X_121,X_121),not(not(not(not(X_121)))))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(or(X_121,X_121),not(not(not(not(X_121)))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_121),X_121),not(not(not(not(X_121)))))) )],[refute_0_98,refute_0_107]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X))))))),
inference(subst,[],[refute_0_108:[bind(X_121,$fot(not(X)))]]) ).
cnf(refute_0_110,plain,
implies(X,not(X)) = or(not(X),not(X)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_111,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) = implies(X,not(X)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,not(X)))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_112,plain,
or(not(X),not(X)) = implies(X,not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X)))))))
| is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X))))))) ),[0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X)))))))
| is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(X))))))) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(implies(X,not(X)),not(not(not(not(not(X)))))) = or(and(X,X),not(not(not(not(not(X)))))),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X)),bind(X_14,$fot(not(not(not(not(not(X)))))))]]) ).
cnf(refute_0_117,plain,
( implies(implies(X,not(X)),not(not(not(not(not(X)))))) != or(and(X,X),not(not(not(not(not(X))))))
| ~ is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X)))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(X)))))))]]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X)))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(X)))))),or(and(X,X),not(not(not(not(not(X))))))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(X))))))) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_121,plain,
r3,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_122,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$cnf( r3 )],[refute_0_121,refute_0_120]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(or(not(X_13),Q),or(Q,not(X_13)))),
inference(subst,[],[refute_0_122:[bind(P,$fot(not(X_13)))]]) ).
cnf(refute_0_124,plain,
implies(X_13,Q) = or(not(X_13),Q),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_13)),bind(Y,$fot(Q))]]) ).
cnf(refute_0_125,plain,
( implies(X_13,Q) != or(not(X_13),Q)
| or(not(X_13),Q) = implies(X_13,Q) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X_13,Q))),bind(Y0,$fot(or(not(X_13),Q)))]]) ).
cnf(refute_0_126,plain,
or(not(X_13),Q) = implies(X_13,Q),
inference(resolve,[$cnf( $equal(implies(X_13,Q),or(not(X_13),Q)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( or(not(X_13),Q) != implies(X_13,Q)
| ~ is_a_theorem(implies(or(not(X_13),Q),or(Q,not(X_13))))
| is_a_theorem(implies(implies(X_13,Q),or(Q,not(X_13)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_13),Q),or(Q,not(X_13)))) ),[0,0],$fot(implies(X_13,Q))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(or(not(X_13),Q),or(Q,not(X_13))))
| is_a_theorem(implies(implies(X_13,Q),or(Q,not(X_13)))) ),
inference(resolve,[$cnf( $equal(or(not(X_13),Q),implies(X_13,Q)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(X_13,Q),or(Q,not(X_13)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_13),Q),or(Q,not(X_13)))) )],[refute_0_123,refute_0_128]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(not(X),X_66),or(X_66,not(not(X))))),
inference(subst,[],[refute_0_129:[bind(Q,$fot(X_66)),bind(X_13,$fot(not(X)))]]) ).
cnf(refute_0_131,plain,
or(X,X_66) = implies(not(X),X_66),
inference(subst,[],[refute_0_55:[bind(Y,$fot(X_66))]]) ).
cnf(refute_0_132,plain,
( or(X,X_66) != implies(not(X),X_66)
| implies(not(X),X_66) = or(X,X_66) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(or(X,X_66))),bind(Y0,$fot(implies(not(X),X_66)))]]) ).
cnf(refute_0_133,plain,
implies(not(X),X_66) = or(X,X_66),
inference(resolve,[$cnf( $equal(or(X,X_66),implies(not(X),X_66)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( implies(not(X),X_66) != or(X,X_66)
| ~ is_a_theorem(implies(implies(not(X),X_66),or(X_66,not(not(X)))))
| is_a_theorem(implies(or(X,X_66),or(X_66,not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),X_66),or(X_66,not(not(X))))) ),[0,0],$fot(or(X,X_66))]]) ).
cnf(refute_0_135,plain,
( ~ is_a_theorem(implies(implies(not(X),X_66),or(X_66,not(not(X)))))
| is_a_theorem(implies(or(X,X_66),or(X_66,not(not(X))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_66),or(X,X_66)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(or(X,X_66),or(X_66,not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_66),or(X_66,not(not(X))))) )],[refute_0_130,refute_0_135]) ).
cnf(refute_0_137,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_138,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_139,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_138,refute_0_137]) ).
cnf(refute_0_140,plain,
( ~ is_a_theorem(implies(or(X,X_66),or(X_66,not(not(X)))))
| ~ is_a_theorem(or(X,X_66))
| is_a_theorem(or(X_66,not(not(X)))) ),
inference(subst,[],[refute_0_139:[bind(X,$fot(or(X,X_66))),bind(Y,$fot(or(X_66,not(not(X)))))]]) ).
cnf(refute_0_141,plain,
( ~ is_a_theorem(or(X,X_66))
| is_a_theorem(or(X_66,not(not(X)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X,X_66),or(X_66,not(not(X))))) )],[refute_0_136,refute_0_140]) ).
cnf(refute_0_142,plain,
( ~ is_a_theorem(or(and(X,X),not(not(not(not(not(X)))))))
| is_a_theorem(or(not(not(not(not(not(X))))),not(not(and(X,X))))) ),
inference(subst,[],[refute_0_141:[bind(X,$fot(and(X,X))),bind(X_66,$fot(not(not(not(not(not(X)))))))]]) ).
cnf(refute_0_143,plain,
is_a_theorem(or(not(not(not(not(not(X))))),not(not(and(X,X))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,X),not(not(not(not(not(X))))))) )],[refute_0_119,refute_0_142]) ).
cnf(refute_0_144,plain,
or(not(X),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))),
inference(subst,[],[refute_0_24:[bind(Y,$fot(not(not(and(X,X)))))]]) ).
cnf(refute_0_145,plain,
implies(not(not(X)),not(not(and(X,X)))) = or(not(X),not(not(and(X,X)))),
inference(subst,[],[refute_0_100:[bind(X,$fot(not(X))),bind(Y,$fot(not(not(and(X,X)))))]]) ).
cnf(refute_0_146,plain,
( implies(not(not(X)),not(not(and(X,X)))) != or(not(X),not(not(and(X,X))))
| or(not(X),not(not(and(X,X)))) != implies(X,not(not(and(X,X))))
| implies(not(not(X)),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(implies(not(not(X)),not(not(and(X,X)))))),bind(Y0,$fot(or(not(X),not(not(and(X,X)))))),bind(Z,$fot(implies(X,not(not(and(X,X))))))]]) ).
cnf(refute_0_147,plain,
( or(not(X),not(not(and(X,X)))) != implies(X,not(not(and(X,X))))
| implies(not(not(X)),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))) ),
inference(resolve,[$cnf( $equal(implies(not(not(X)),not(not(and(X,X)))),or(not(X),not(not(and(X,X))))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
implies(not(not(X)),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))),
inference(resolve,[$cnf( $equal(or(not(X),not(not(and(X,X)))),implies(X,not(not(and(X,X))))) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
or(not(not(not(X))),not(not(and(X,X)))) = implies(not(not(X)),not(not(and(X,X)))),
inference(subst,[],[refute_0_24:[bind(X,$fot(not(not(X)))),bind(Y,$fot(not(not(and(X,X)))))]]) ).
cnf(refute_0_150,plain,
( implies(not(not(X)),not(not(and(X,X)))) != implies(X,not(not(and(X,X))))
| or(not(not(not(X))),not(not(and(X,X)))) != implies(not(not(X)),not(not(and(X,X))))
| or(not(not(not(X))),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(or(not(not(not(X))),not(not(and(X,X)))))),bind(Y0,$fot(implies(not(not(X)),not(not(and(X,X)))))),bind(Z,$fot(implies(X,not(not(and(X,X))))))]]) ).
cnf(refute_0_151,plain,
( implies(not(not(X)),not(not(and(X,X)))) != implies(X,not(not(and(X,X))))
| or(not(not(not(X))),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(X))),not(not(and(X,X)))),implies(not(not(X)),not(not(and(X,X))))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
or(not(not(not(X))),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))),
inference(resolve,[$cnf( $equal(implies(not(not(X)),not(not(and(X,X)))),implies(X,not(not(and(X,X))))) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
implies(not(not(not(not(X)))),not(not(and(X,X)))) = or(not(not(not(X))),not(not(and(X,X)))),
inference(subst,[],[refute_0_100:[bind(X,$fot(not(not(not(X))))),bind(Y,$fot(not(not(and(X,X)))))]]) ).
cnf(refute_0_154,plain,
( implies(not(not(not(not(X)))),not(not(and(X,X)))) != or(not(not(not(X))),not(not(and(X,X))))
| or(not(not(not(X))),not(not(and(X,X)))) != implies(X,not(not(and(X,X))))
| implies(not(not(not(not(X)))),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(implies(not(not(not(not(X)))),not(not(and(X,X)))))),bind(Y0,$fot(or(not(not(not(X))),not(not(and(X,X)))))),bind(Z,$fot(implies(X,not(not(and(X,X))))))]]) ).
cnf(refute_0_155,plain,
( or(not(not(not(X))),not(not(and(X,X)))) != implies(X,not(not(and(X,X))))
| implies(not(not(not(not(X)))),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(X)))),not(not(and(X,X)))),or(not(not(not(X))),not(not(and(X,X))))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
implies(not(not(not(not(X)))),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))),
inference(resolve,[$cnf( $equal(or(not(not(not(X))),not(not(and(X,X)))),implies(X,not(not(and(X,X))))) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
or(not(not(not(not(not(X))))),not(not(and(X,X)))) = implies(not(not(not(not(X)))),not(not(and(X,X)))),
inference(subst,[],[refute_0_24:[bind(X,$fot(not(not(not(not(X)))))),bind(Y,$fot(not(not(and(X,X)))))]]) ).
cnf(refute_0_158,plain,
( implies(not(not(not(not(X)))),not(not(and(X,X)))) != implies(X,not(not(and(X,X))))
| or(not(not(not(not(not(X))))),not(not(and(X,X)))) != implies(not(not(not(not(X)))),not(not(and(X,X))))
| or(not(not(not(not(not(X))))),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(or(not(not(not(not(not(X))))),not(not(and(X,X)))))),bind(Y0,$fot(implies(not(not(not(not(X)))),not(not(and(X,X)))))),bind(Z,$fot(implies(X,not(not(and(X,X))))))]]) ).
cnf(refute_0_159,plain,
( implies(not(not(not(not(X)))),not(not(and(X,X)))) != implies(X,not(not(and(X,X))))
| or(not(not(not(not(not(X))))),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(X))))),not(not(and(X,X)))),implies(not(not(not(not(X)))),not(not(and(X,X))))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
or(not(not(not(not(not(X))))),not(not(and(X,X)))) = implies(X,not(not(and(X,X)))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(X)))),not(not(and(X,X)))),implies(X,not(not(and(X,X))))) )],[refute_0_156,refute_0_159]) ).
cnf(refute_0_161,plain,
( or(not(not(not(not(not(X))))),not(not(and(X,X)))) != implies(X,not(not(and(X,X))))
| ~ is_a_theorem(or(not(not(not(not(not(X))))),not(not(and(X,X)))))
| is_a_theorem(implies(X,not(not(and(X,X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(not(not(not(not(X))))),not(not(and(X,X))))) ),[0],$fot(implies(X,not(not(and(X,X)))))]]) ).
cnf(refute_0_162,plain,
( ~ is_a_theorem(or(not(not(not(not(not(X))))),not(not(and(X,X)))))
| is_a_theorem(implies(X,not(not(and(X,X))))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(X))))),not(not(and(X,X)))),implies(X,not(not(and(X,X))))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
is_a_theorem(implies(X,not(not(and(X,X))))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(not(not(not(X))))),not(not(and(X,X))))) )],[refute_0_143,refute_0_162]) ).
cnf(refute_0_164,plain,
is_a_theorem(implies(not(not(X)),not(not(and(not(not(X)),not(not(X))))))),
inference(subst,[],[refute_0_163:[bind(X,$fot(not(not(X))))]]) ).
cnf(refute_0_165,plain,
and(not(not(X)),not(not(X))) = and(X,not(not(X))),
inference(subst,[],[refute_0_72:[bind(X_42,$fot(not(not(X))))]]) ).
cnf(refute_0_166,plain,
( and(not(not(X)),not(not(X))) != and(X,not(not(X)))
| ~ is_a_theorem(implies(not(not(X)),not(not(and(not(not(X)),not(not(X)))))))
| is_a_theorem(implies(not(not(X)),not(not(and(X,not(not(X))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(X)),not(not(and(not(not(X)),not(not(X))))))) ),[0,1,0,0],$fot(and(X,not(not(X))))]]) ).
cnf(refute_0_167,plain,
( ~ is_a_theorem(implies(not(not(X)),not(not(and(not(not(X)),not(not(X)))))))
| is_a_theorem(implies(not(not(X)),not(not(and(X,not(not(X))))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),not(not(X))),and(X,not(not(X)))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
is_a_theorem(implies(not(not(X)),not(not(and(X,not(not(X))))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X)),not(not(and(not(not(X)),not(not(X))))))) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
not(implies(X,not(X))) = and(X,X),
inference(subst,[],[refute_0_34:[bind(Y,$fot(X))]]) ).
cnf(refute_0_170,plain,
not(and(X,not(not(X)))) = implies(X,not(X)),
inference(subst,[],[refute_0_51:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_171,plain,
not(not(and(X,not(not(X))))) = not(not(and(X,not(not(X))))),
introduced(tautology,[refl,[$fot(not(not(and(X,not(not(X))))))]]) ).
cnf(refute_0_172,plain,
( not(and(X,not(not(X)))) != implies(X,not(X))
| not(not(and(X,not(not(X))))) != not(not(and(X,not(not(X)))))
| not(not(and(X,not(not(X))))) = not(implies(X,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(X,not(not(X))))),not(not(and(X,not(not(X)))))) ),[1,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_173,plain,
( not(and(X,not(not(X)))) != implies(X,not(X))
| not(not(and(X,not(not(X))))) = not(implies(X,not(X))) ),
inference(resolve,[$cnf( $equal(not(not(and(X,not(not(X))))),not(not(and(X,not(not(X)))))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
not(not(and(X,not(not(X))))) = not(implies(X,not(X))),
inference(resolve,[$cnf( $equal(not(and(X,not(not(X)))),implies(X,not(X))) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(and(X,not(not(X))))) != not(implies(X,not(X)))
| not(not(and(X,not(not(X))))) = and(X,X) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(not(not(and(X,not(not(X))))))),bind(Y0,$fot(not(implies(X,not(X))))),bind(Z,$fot(and(X,X)))]]) ).
cnf(refute_0_176,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(and(X,not(not(X))))) = and(X,X) ),
inference(resolve,[$cnf( $equal(not(not(and(X,not(not(X))))),not(implies(X,not(X)))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
not(not(and(X,not(not(X))))) = and(X,X),
inference(resolve,[$cnf( $equal(not(implies(X,not(X))),and(X,X)) )],[refute_0_169,refute_0_176]) ).
cnf(refute_0_178,plain,
implies(X,not(not(and(X,not(not(X)))))) = implies(X,not(not(and(X,not(not(X)))))),
introduced(tautology,[refl,[$fot(implies(X,not(not(and(X,not(not(X)))))))]]) ).
cnf(refute_0_179,plain,
( implies(X,not(not(and(X,not(not(X)))))) != implies(X,not(not(and(X,not(not(X))))))
| not(not(and(X,not(not(X))))) != and(X,X)
| implies(X,not(not(and(X,not(not(X)))))) = implies(X,and(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(not(and(X,not(not(X)))))),implies(X,not(not(and(X,not(not(X))))))) ),[1,1],$fot(and(X,X))]]) ).
cnf(refute_0_180,plain,
( not(not(and(X,not(not(X))))) != and(X,X)
| implies(X,not(not(and(X,not(not(X)))))) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(X,not(not(and(X,not(not(X)))))),implies(X,not(not(and(X,not(not(X))))))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(X,not(not(and(X,not(not(X)))))) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(not(not(and(X,not(not(X))))),and(X,X)) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
or(not(X),not(not(and(X,not(not(X)))))) = implies(X,not(not(and(X,not(not(X)))))),
inference(subst,[],[refute_0_24:[bind(Y,$fot(not(not(and(X,not(not(X)))))))]]) ).
cnf(refute_0_183,plain,
implies(not(not(X)),not(not(and(X,not(not(X)))))) = or(not(X),not(not(and(X,not(not(X)))))),
inference(subst,[],[refute_0_100:[bind(X,$fot(not(X))),bind(Y,$fot(not(not(and(X,not(not(X)))))))]]) ).
cnf(refute_0_184,plain,
( implies(not(not(X)),not(not(and(X,not(not(X)))))) != or(not(X),not(not(and(X,not(not(X))))))
| or(not(X),not(not(and(X,not(not(X)))))) != implies(X,not(not(and(X,not(not(X))))))
| implies(not(not(X)),not(not(and(X,not(not(X)))))) = implies(X,not(not(and(X,not(not(X)))))) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(implies(not(not(X)),not(not(and(X,not(not(X)))))))),bind(Y0,$fot(or(not(X),not(not(and(X,not(not(X)))))))),bind(Z,$fot(implies(X,not(not(and(X,not(not(X))))))))]]) ).
cnf(refute_0_185,plain,
( or(not(X),not(not(and(X,not(not(X)))))) != implies(X,not(not(and(X,not(not(X))))))
| implies(not(not(X)),not(not(and(X,not(not(X)))))) = implies(X,not(not(and(X,not(not(X)))))) ),
inference(resolve,[$cnf( $equal(implies(not(not(X)),not(not(and(X,not(not(X)))))),or(not(X),not(not(and(X,not(not(X))))))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(not(not(X)),not(not(and(X,not(not(X)))))) = implies(X,not(not(and(X,not(not(X)))))),
inference(resolve,[$cnf( $equal(or(not(X),not(not(and(X,not(not(X)))))),implies(X,not(not(and(X,not(not(X))))))) )],[refute_0_182,refute_0_185]) ).
cnf(refute_0_187,plain,
( implies(X,not(not(and(X,not(not(X)))))) != implies(X,and(X,X))
| implies(not(not(X)),not(not(and(X,not(not(X)))))) != implies(X,not(not(and(X,not(not(X))))))
| implies(not(not(X)),not(not(and(X,not(not(X)))))) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(implies(not(not(X)),not(not(and(X,not(not(X)))))))),bind(Y0,$fot(implies(X,not(not(and(X,not(not(X)))))))),bind(Z,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_188,plain,
( implies(X,not(not(and(X,not(not(X)))))) != implies(X,and(X,X))
| implies(not(not(X)),not(not(and(X,not(not(X)))))) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(not(not(X)),not(not(and(X,not(not(X)))))),implies(X,not(not(and(X,not(not(X))))))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
implies(not(not(X)),not(not(and(X,not(not(X)))))) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(X,not(not(and(X,not(not(X)))))),implies(X,and(X,X))) )],[refute_0_181,refute_0_188]) ).
cnf(refute_0_190,plain,
( implies(not(not(X)),not(not(and(X,not(not(X)))))) != implies(X,and(X,X))
| ~ is_a_theorem(implies(not(not(X)),not(not(and(X,not(not(X)))))))
| is_a_theorem(implies(X,and(X,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(X)),not(not(and(X,not(not(X))))))) ),[0],$fot(implies(X,and(X,X)))]]) ).
cnf(refute_0_191,plain,
( ~ is_a_theorem(implies(not(not(X)),not(not(and(X,not(not(X)))))))
| is_a_theorem(implies(X,and(X,X))) ),
inference(resolve,[$cnf( $equal(implies(not(not(X)),not(not(and(X,not(not(X)))))),implies(X,and(X,X))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
is_a_theorem(implies(X,and(X,X))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X)),not(not(and(X,not(not(X))))))) )],[refute_0_168,refute_0_191]) ).
cnf(refute_0_193,plain,
is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P))),
inference(subst,[],[refute_0_192:[bind(X,$fot(skolemFOFtoCNF_P))]]) ).
cnf(refute_0_194,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P))) )],[refute_0_193,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL499+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 : n017.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 : Sat Jul 2 21:16:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
% 0.19/0.56
%------------------------------------------------------------------------------