TSTP Solution File: LCL509+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL509+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 12:52:49 EDT 2022
% Result : Theorem 238.12s 238.28s
% Output : CNFRefutation 238.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 58
% Syntax : Number of formulae : 361 ( 188 unt; 0 def)
% Number of atoms : 614 ( 175 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 489 ( 236 ~; 223 |; 13 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 13 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 637 ( 40 sgn 52 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ) ).
fof(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ) ).
fof(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ) ).
fof(kn3,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,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_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(rosser_op_or,axiom,
op_or ).
fof(rosser_op_implies_and,axiom,
op_implies_and ).
fof(rosser_op_equiv,axiom,
op_equiv ).
fof(rosser_modus_ponens,axiom,
modus_ponens ).
fof(rosser_kn1,axiom,
kn1 ).
fof(rosser_kn2,axiom,
kn2 ).
fof(rosser_kn3,axiom,
kn3 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
fof(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
fof(hilbert_op_equiv,axiom,
op_equiv ).
fof(hilbert_or_1,conjecture,
or_1 ).
fof(subgoal_0,plain,
or_1,
inference(strip,[],[hilbert_or_1]) ).
fof(negate_0_0,plain,
~ or_1,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ or_1
<=> ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) ),
inference(canonicalize,[],[or_1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9)))
| or_1 )
& ( ~ or_1
| is_a_theorem(implies(X,or(X,Y))) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9)))
| or_1 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ or_1,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,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_5,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_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
modus_ponens,
inference(canonicalize,[],[rosser_modus_ponens]) ).
fof(normalize_0_8,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_11,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_14,plain,
( ~ kn2
<=> ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[kn2]) ).
fof(normalize_0_15,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 )
& ( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [P,Q] :
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
kn2,
inference(canonicalize,[],[rosser_kn2]) ).
fof(normalize_0_18,plain,
( ~ kn1
<=> ? [P] : ~ is_a_theorem(implies(P,and(P,P))) ),
inference(canonicalize,[],[kn1]) ).
fof(normalize_0_19,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_18]) ).
fof(normalize_0_20,plain,
! [P] :
( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
kn1,
inference(canonicalize,[],[rosser_kn1]) ).
fof(normalize_0_22,plain,
( ~ kn3
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(canonicalize,[],[kn3]) ).
fof(normalize_0_23,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_2,skolemFOFtoCNF_Q_1),implies(not(and(skolemFOFtoCNF_Q_1,skolemFOFtoCNF_R)),not(and(skolemFOFtoCNF_R,skolemFOFtoCNF_P_2)))))
| kn3 )
& ( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [P,Q,R] :
( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
kn3,
inference(canonicalize,[],[rosser_kn3]) ).
fof(normalize_0_26,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ( skolemFOFtoCNF_X_1 != skolemFOFtoCNF_Y_1
| substitution_of_equivalents )
& ( is_a_theorem(equiv(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| substitution_of_equivalents )
& ( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_30,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_31,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
op_equiv,
inference(canonicalize,[],[hilbert_op_equiv]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9)))
| or_1 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ or_1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9))),
inference(resolve,[$cnf( or_1 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(not(X),X_87))
| ~ is_a_theorem(not(X))
| is_a_theorem(X_87) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(not(X))),bind(Y,$fot(X_87))]]) ).
cnf(refute_0_7,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_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( $equal(X0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_17,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_19,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_20,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
or(X,X_87) = implies(not(X),X_87),
inference(subst,[],[refute_0_21:[bind(Y,$fot(X_87))]]) ).
cnf(refute_0_23,plain,
( or(X,X_87) != implies(not(X),X_87)
| implies(not(X),X_87) = or(X,X_87) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_87))),bind(Y0,$fot(implies(not(X),X_87)))]]) ).
cnf(refute_0_24,plain,
implies(not(X),X_87) = or(X,X_87),
inference(resolve,[$cnf( $equal(or(X,X_87),implies(not(X),X_87)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( implies(not(X),X_87) != or(X,X_87)
| ~ is_a_theorem(or(X,X_87))
| is_a_theorem(implies(not(X),X_87)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(not(X),X_87)) ),[0],$fot(or(X,X_87))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(or(X,X_87))
| is_a_theorem(implies(not(X),X_87)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_87),or(X,X_87)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(not(X))
| ~ is_a_theorem(or(X,X_87))
| is_a_theorem(X_87) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),X_87)) )],[refute_0_26,refute_0_6]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(not(and(X_566,X_567)))
| ~ is_a_theorem(or(and(X_566,X_567),implies(X_567,not(X_566))))
| is_a_theorem(implies(X_567,not(X_566))) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(and(X_566,X_567))),bind(X_87,$fot(implies(X_567,not(X_566))))]]) ).
cnf(refute_0_29,plain,
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_30,plain,
kn2,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(and(P,Q),P)),
inference(resolve,[$cnf( kn2 )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(and(X_357,X_357),X_357)),
inference(subst,[],[refute_0_31:[bind(P,$fot(X_357)),bind(Q,$fot(X_357))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(and(X_325,X_325),X_324))
| ~ is_a_theorem(implies(implies(and(X_325,X_325),X_324),not(and(not(X_324),X_325))))
| is_a_theorem(not(and(not(X_324),X_325))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(and(X_325,X_325),X_324))),bind(Y,$fot(not(and(not(X_324),X_325))))]]) ).
cnf(refute_0_34,plain,
( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_35,plain,
kn1,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(P,and(P,P))),
inference(resolve,[$cnf( kn1 )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(X_308,and(X_308,X_308))),
inference(subst,[],[refute_0_36:[bind(P,$fot(X_308))]]) ).
cnf(refute_0_38,plain,
( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_39,plain,
kn3,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))),
inference(resolve,[$cnf( kn3 )],[refute_0_39,refute_0_38]) ).
cnf(refute_0_41,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_42,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_21,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(not(and(Q,R)),not(and(R,P))) = or(and(Q,R),not(and(R,P))),
inference(subst,[],[refute_0_42:[bind(X,$fot(and(Q,R))),bind(Y,$fot(not(and(R,P))))]]) ).
cnf(refute_0_44,plain,
implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),
introduced(tautology,[refl,[$fot(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))]]) ).
cnf(refute_0_45,plain,
( implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) != implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))
| implies(not(and(Q,R)),not(and(R,P))) != or(and(Q,R),not(and(R,P)))
| implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),[1,1],$fot(or(and(Q,R),not(and(R,P))))]]) ).
cnf(refute_0_46,plain,
( implies(not(and(Q,R)),not(and(R,P))) != or(and(Q,R),not(and(R,P)))
| implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))) ),
inference(resolve,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))),
inference(resolve,[$cnf( $equal(implies(not(and(Q,R)),not(and(R,P))),or(and(Q,R),not(and(R,P)))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) != implies(implies(P,Q),or(and(Q,R),not(and(R,P))))
| ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),[0],$fot(implies(implies(P,Q),or(and(Q,R),not(and(R,P)))))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) ),
inference(resolve,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )],[refute_0_40,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(P,Q))
| ~ is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P)))))
| is_a_theorem(or(and(Q,R),not(and(R,P)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(P,Q))),bind(Y,$fot(or(and(Q,R),not(and(R,P)))))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(P,Q))
| is_a_theorem(or(and(Q,R),not(and(R,P)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(implies(X_308,and(X_308,X_308)))
| is_a_theorem(or(and(and(X_308,X_308),X_310),not(and(X_310,X_308)))) ),
inference(subst,[],[refute_0_52:[bind(P,$fot(X_308)),bind(Q,$fot(and(X_308,X_308))),bind(R,$fot(X_310))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(or(and(and(X_308,X_308),X_310),not(and(X_310,X_308)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_308,and(X_308,X_308))) )],[refute_0_37,refute_0_53]) ).
cnf(refute_0_55,plain,
is_a_theorem(or(and(and(X_311,X_311),not(Y)),not(and(not(Y),X_311)))),
inference(subst,[],[refute_0_54:[bind(X_308,$fot(X_311)),bind(X_310,$fot(not(Y)))]]) ).
cnf(refute_0_56,plain,
or(and(X,not(Y)),X_19) = implies(not(and(X,not(Y))),X_19),
inference(subst,[],[refute_0_21:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_57,plain,
( not(and(X,not(Y))) != implies(X,Y)
| or(and(X,not(Y)),X_19) != implies(not(and(X,not(Y))),X_19)
| or(and(X,not(Y)),X_19) = implies(implies(X,Y),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),X_19),implies(not(and(X,not(Y))),X_19)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_58,plain,
( or(and(X,not(Y)),X_19) != implies(not(and(X,not(Y))),X_19)
| or(and(X,not(Y)),X_19) = implies(implies(X,Y),X_19) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_17,refute_0_57]) ).
cnf(refute_0_59,plain,
or(and(X,not(Y)),X_19) = implies(implies(X,Y),X_19),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),X_19),implies(not(and(X,not(Y))),X_19)) )],[refute_0_56,refute_0_58]) ).
cnf(refute_0_60,plain,
or(and(and(X_311,X_311),not(Y)),not(and(not(Y),X_311))) = implies(implies(and(X_311,X_311),Y),not(and(not(Y),X_311))),
inference(subst,[],[refute_0_59:[bind(X,$fot(and(X_311,X_311))),bind(X_19,$fot(not(and(not(Y),X_311))))]]) ).
cnf(refute_0_61,plain,
( or(and(and(X_311,X_311),not(Y)),not(and(not(Y),X_311))) != implies(implies(and(X_311,X_311),Y),not(and(not(Y),X_311)))
| ~ is_a_theorem(or(and(and(X_311,X_311),not(Y)),not(and(not(Y),X_311))))
| is_a_theorem(implies(implies(and(X_311,X_311),Y),not(and(not(Y),X_311)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(and(X_311,X_311),not(Y)),not(and(not(Y),X_311)))) ),[0],$fot(implies(implies(and(X_311,X_311),Y),not(and(not(Y),X_311))))]]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(or(and(and(X_311,X_311),not(Y)),not(and(not(Y),X_311))))
| is_a_theorem(implies(implies(and(X_311,X_311),Y),not(and(not(Y),X_311)))) ),
inference(resolve,[$cnf( $equal(or(and(and(X_311,X_311),not(Y)),not(and(not(Y),X_311))),implies(implies(and(X_311,X_311),Y),not(and(not(Y),X_311)))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(and(X_311,X_311),Y),not(and(not(Y),X_311)))),
inference(resolve,[$cnf( is_a_theorem(or(and(and(X_311,X_311),not(Y)),not(and(not(Y),X_311)))) )],[refute_0_55,refute_0_62]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(and(X_325,X_325),X_324),not(and(not(X_324),X_325)))),
inference(subst,[],[refute_0_63:[bind(Y,$fot(X_324)),bind(X_311,$fot(X_325))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(and(X_325,X_325),X_324))
| is_a_theorem(not(and(not(X_324),X_325))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_325,X_325),X_324),not(and(not(X_324),X_325)))) )],[refute_0_64,refute_0_33]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(and(X_357,X_357),X_357))
| is_a_theorem(not(and(not(X_357),X_357))) ),
inference(subst,[],[refute_0_65:[bind(X_324,$fot(X_357)),bind(X_325,$fot(X_357))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(not(and(not(X_357),X_357))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_357,X_357),X_357)) )],[refute_0_32,refute_0_66]) ).
cnf(refute_0_68,plain,
is_a_theorem(not(and(not(not(Y)),not(Y)))),
inference(subst,[],[refute_0_67:[bind(X_357,$fot(not(Y)))]]) ).
cnf(refute_0_69,plain,
implies(not(not(Y)),Y) = not(and(not(not(Y)),not(Y))),
inference(subst,[],[refute_0_12:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_70,plain,
( implies(not(not(Y)),Y) != not(and(not(not(Y)),not(Y)))
| not(and(not(not(Y)),not(Y))) = implies(not(not(Y)),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(not(not(Y)),Y))),bind(Y0,$fot(not(and(not(not(Y)),not(Y)))))]]) ).
cnf(refute_0_71,plain,
not(and(not(not(Y)),not(Y))) = implies(not(not(Y)),Y),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),not(and(not(not(Y)),not(Y)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( not(and(not(not(Y)),not(Y))) != implies(not(not(Y)),Y)
| ~ is_a_theorem(not(and(not(not(Y)),not(Y))))
| is_a_theorem(implies(not(not(Y)),Y)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(not(not(Y)),not(Y)))) ),[0],$fot(implies(not(not(Y)),Y))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(not(and(not(not(Y)),not(Y))))
| is_a_theorem(implies(not(not(Y)),Y)) ),
inference(resolve,[$cnf( $equal(not(and(not(not(Y)),not(Y))),implies(not(not(Y)),Y)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(not(not(Y)),Y)),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(Y)),not(Y)))) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
implies(not(not(Y)),Y) = or(not(Y),Y),
inference(subst,[],[refute_0_42:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_76,plain,
( implies(not(not(Y)),Y) != or(not(Y),Y)
| ~ is_a_theorem(implies(not(not(Y)),Y))
| is_a_theorem(or(not(Y),Y)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(Y)),Y)) ),[0],$fot(or(not(Y),Y))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(not(not(Y)),Y))
| is_a_theorem(or(not(Y),Y)) ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),or(not(Y),Y)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
is_a_theorem(or(not(Y),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(Y)),Y)) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
is_a_theorem(or(not(X_564),X_564)),
inference(subst,[],[refute_0_78:[bind(Y,$fot(X_564))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(or(X_116,X_117),or(and(X_117,X_118),implies(X_118,X_116))))
| ~ is_a_theorem(or(X_116,X_117))
| is_a_theorem(or(and(X_117,X_118),implies(X_118,X_116))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(or(X_116,X_117))),bind(Y,$fot(or(and(X_117,X_118),implies(X_118,X_116))))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),not(and(X_59,not(Y)))))),
inference(subst,[],[refute_0_50:[bind(P,$fot(not(Y))),bind(Q,$fot(X_58)),bind(R,$fot(X_59))]]) ).
cnf(refute_0_82,plain,
implies(X_59,Y) = not(and(X_59,not(Y))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_59))]]) ).
cnf(refute_0_83,plain,
( implies(X_59,Y) != not(and(X_59,not(Y)))
| not(and(X_59,not(Y))) = implies(X_59,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_59,Y))),bind(Y0,$fot(not(and(X_59,not(Y)))))]]) ).
cnf(refute_0_84,plain,
not(and(X_59,not(Y))) = implies(X_59,Y),
inference(resolve,[$cnf( $equal(implies(X_59,Y),not(and(X_59,not(Y)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( not(and(X_59,not(Y))) != implies(X_59,Y)
| ~ is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),not(and(X_59,not(Y))))))
| is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),not(and(X_59,not(Y)))))) ),[0,1,1],$fot(implies(X_59,Y))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),not(and(X_59,not(Y))))))
| is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y)))) ),
inference(resolve,[$cnf( $equal(not(and(X_59,not(Y))),implies(X_59,Y)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),not(and(X_59,not(Y)))))) )],[refute_0_81,refute_0_86]) ).
cnf(refute_0_88,plain,
implies(not(Y),X_58) = or(Y,X_58),
inference(subst,[],[refute_0_42:[bind(X,$fot(Y)),bind(Y,$fot(X_58))]]) ).
cnf(refute_0_89,plain,
implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))) = implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))))]]) ).
cnf(refute_0_90,plain,
( implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))) != implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y)))
| implies(not(Y),X_58) != or(Y,X_58)
| implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))) = implies(or(Y,X_58),or(and(X_58,X_59),implies(X_59,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))),implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y)))) ),[1,0],$fot(or(Y,X_58))]]) ).
cnf(refute_0_91,plain,
( implies(not(Y),X_58) != or(Y,X_58)
| implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))) = implies(or(Y,X_58),or(and(X_58,X_59),implies(X_59,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))),implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))) = implies(or(Y,X_58),or(and(X_58,X_59),implies(X_59,Y))),
inference(resolve,[$cnf( $equal(implies(not(Y),X_58),or(Y,X_58)) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
( implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))) != implies(or(Y,X_58),or(and(X_58,X_59),implies(X_59,Y)))
| ~ is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))))
| is_a_theorem(implies(or(Y,X_58),or(and(X_58,X_59),implies(X_59,Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y)))) ),[0],$fot(implies(or(Y,X_58),or(and(X_58,X_59),implies(X_59,Y))))]]) ).
cnf(refute_0_94,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))))
| is_a_theorem(implies(or(Y,X_58),or(and(X_58,X_59),implies(X_59,Y)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y))),implies(or(Y,X_58),or(and(X_58,X_59),implies(X_59,Y)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(or(Y,X_58),or(and(X_58,X_59),implies(X_59,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_58),or(and(X_58,X_59),implies(X_59,Y)))) )],[refute_0_87,refute_0_94]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(or(X_116,X_117),or(and(X_117,X_118),implies(X_118,X_116)))),
inference(subst,[],[refute_0_95:[bind(Y,$fot(X_116)),bind(X_58,$fot(X_117)),bind(X_59,$fot(X_118))]]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(or(X_116,X_117))
| is_a_theorem(or(and(X_117,X_118),implies(X_118,X_116))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_116,X_117),or(and(X_117,X_118),implies(X_118,X_116)))) )],[refute_0_96,refute_0_80]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(or(not(X_564),X_564))
| is_a_theorem(or(and(X_564,X_565),implies(X_565,not(X_564)))) ),
inference(subst,[],[refute_0_97:[bind(X_116,$fot(not(X_564))),bind(X_117,$fot(X_564)),bind(X_118,$fot(X_565))]]) ).
cnf(refute_0_99,plain,
is_a_theorem(or(and(X_564,X_565),implies(X_565,not(X_564)))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_564),X_564)) )],[refute_0_79,refute_0_98]) ).
cnf(refute_0_100,plain,
is_a_theorem(or(and(X_566,X_567),implies(X_567,not(X_566)))),
inference(subst,[],[refute_0_99:[bind(X_564,$fot(X_566)),bind(X_565,$fot(X_567))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(not(and(X_566,X_567)))
| is_a_theorem(implies(X_567,not(X_566))) ),
inference(resolve,[$cnf( is_a_theorem(or(and(X_566,X_567),implies(X_567,not(X_566)))) )],[refute_0_100,refute_0_28]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(not(and(and(not(and(X_4710,X_4710)),X_4711),X_4710)))
| is_a_theorem(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711)))) ),
inference(subst,[],[refute_0_101:[bind(X_566,$fot(and(not(and(X_4710,X_4710)),X_4711))),bind(X_567,$fot(X_4710))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(not(and(and(X_311,X_311),X_312)))
| ~ is_a_theorem(or(and(and(X_311,X_311),X_312),not(and(X_312,X_311))))
| is_a_theorem(not(and(X_312,X_311))) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(and(and(X_311,X_311),X_312))),bind(X_87,$fot(not(and(X_312,X_311))))]]) ).
cnf(refute_0_104,plain,
is_a_theorem(or(and(and(X_311,X_311),X_312),not(and(X_312,X_311)))),
inference(subst,[],[refute_0_54:[bind(X_308,$fot(X_311)),bind(X_310,$fot(X_312))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(not(and(and(X_311,X_311),X_312)))
| is_a_theorem(not(and(X_312,X_311))) ),
inference(resolve,[$cnf( is_a_theorem(or(and(and(X_311,X_311),X_312),not(and(X_312,X_311)))) )],[refute_0_104,refute_0_103]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(not(and(and(X_311,X_311),and(not(and(X_311,X_311)),X_4706))))
| is_a_theorem(not(and(and(not(and(X_311,X_311)),X_4706),X_311))) ),
inference(subst,[],[refute_0_105:[bind(X_312,$fot(and(not(and(X_311,X_311)),X_4706)))]]) ).
cnf(refute_0_107,plain,
is_a_theorem(not(and(not(X_4705),X_4705))),
inference(subst,[],[refute_0_67:[bind(X_357,$fot(X_4705))]]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(not(and(X_319,X_320)))
| ~ is_a_theorem(or(and(X_319,X_320),not(and(X_320,and(X_319,X_318)))))
| is_a_theorem(not(and(X_320,and(X_319,X_318)))) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(and(X_319,X_320))),bind(X_87,$fot(not(and(X_320,and(X_319,X_318)))))]]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(and(X_309,Q),X_309)),
inference(subst,[],[refute_0_31:[bind(P,$fot(X_309))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(and(X_309,Q),X_309))
| is_a_theorem(or(and(X_309,X_310),not(and(X_310,and(X_309,Q))))) ),
inference(subst,[],[refute_0_52:[bind(P,$fot(and(X_309,Q))),bind(Q,$fot(X_309)),bind(R,$fot(X_310))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(or(and(X_309,X_310),not(and(X_310,and(X_309,Q))))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_309,Q),X_309)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
is_a_theorem(or(and(X_319,X_320),not(and(X_320,and(X_319,X_318))))),
inference(subst,[],[refute_0_111:[bind(Q,$fot(X_318)),bind(X_309,$fot(X_319)),bind(X_310,$fot(X_320))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(not(and(X_319,X_320)))
| is_a_theorem(not(and(X_320,and(X_319,X_318)))) ),
inference(resolve,[$cnf( is_a_theorem(or(and(X_319,X_320),not(and(X_320,and(X_319,X_318))))) )],[refute_0_112,refute_0_108]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(not(and(not(X_4705),X_4705)))
| is_a_theorem(not(and(X_4705,and(not(X_4705),X_4703)))) ),
inference(subst,[],[refute_0_113:[bind(X_318,$fot(X_4703)),bind(X_319,$fot(not(X_4705))),bind(X_320,$fot(X_4705))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(not(and(X_4705,and(not(X_4705),X_4703)))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(X_4705),X_4705))) )],[refute_0_107,refute_0_114]) ).
cnf(refute_0_116,plain,
is_a_theorem(not(and(and(X_311,X_311),and(not(and(X_311,X_311)),X_4706)))),
inference(subst,[],[refute_0_115:[bind(X_4703,$fot(X_4706)),bind(X_4705,$fot(and(X_311,X_311)))]]) ).
cnf(refute_0_117,plain,
is_a_theorem(not(and(and(not(and(X_311,X_311)),X_4706),X_311))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(X_311,X_311),and(not(and(X_311,X_311)),X_4706)))) )],[refute_0_116,refute_0_106]) ).
cnf(refute_0_118,plain,
is_a_theorem(not(and(and(not(and(X_4710,X_4710)),X_4711),X_4710))),
inference(subst,[],[refute_0_117:[bind(X_311,$fot(X_4710)),bind(X_4706,$fot(X_4711))]]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711)))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(not(and(X_4710,X_4710)),X_4711),X_4710))) )],[refute_0_118,refute_0_102]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_121,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_121,refute_0_120]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(equiv(not(and(X_38210,X_38210)),not(X_38210)))
| not(and(X_38210,X_38210)) = not(X_38210) ),
inference(subst,[],[refute_0_122:[bind(X,$fot(not(and(X_38210,X_38210)))),bind(Y,$fot(not(X_38210)))]]) ).
cnf(refute_0_124,plain,
( ~ is_a_theorem(not(not(X_360)))
| ~ is_a_theorem(or(not(X_360),X_360))
| is_a_theorem(X_360) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(not(X_360))),bind(X_87,$fot(X_360))]]) ).
cnf(refute_0_125,plain,
is_a_theorem(or(not(X_360),X_360)),
inference(subst,[],[refute_0_78:[bind(Y,$fot(X_360))]]) ).
cnf(refute_0_126,plain,
( ~ is_a_theorem(not(not(X_360)))
| is_a_theorem(X_360) ),
inference(resolve,[$cnf( is_a_theorem(or(not(X_360),X_360)) )],[refute_0_125,refute_0_124]) ).
cnf(refute_0_127,plain,
( ~ is_a_theorem(not(not(equiv(not(and(X_38209,X_38209)),not(X_38209)))))
| is_a_theorem(equiv(not(and(X_38209,X_38209)),not(X_38209))) ),
inference(subst,[],[refute_0_126:[bind(X_360,$fot(equiv(not(and(X_38209,X_38209)),not(X_38209))))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(not(not(not(not(equiv(not(and(X_38208,X_38208)),not(X_38208)))))))
| is_a_theorem(not(not(equiv(not(and(X_38208,X_38208)),not(X_38208))))) ),
inference(subst,[],[refute_0_126:[bind(X_360,$fot(not(not(equiv(not(and(X_38208,X_38208)),not(X_38208))))))]]) ).
cnf(refute_0_129,plain,
( ~ is_a_theorem(not(not(not(not(not(not(equiv(not(and(X_38207,X_38207)),not(X_38207)))))))))
| is_a_theorem(not(not(not(not(equiv(not(and(X_38207,X_38207)),not(X_38207))))))) ),
inference(subst,[],[refute_0_126:[bind(X_360,$fot(not(not(not(not(equiv(not(and(X_38207,X_38207)),not(X_38207))))))))]]) ).
cnf(refute_0_130,plain,
( ~ is_a_theorem(implies(or(X_38206,not(and(X_38206,X_38206))),not(not(not(not(not(not(equiv(not(and(X_38206,X_38206)),not(X_38206))))))))))
| ~ is_a_theorem(or(X_38206,not(and(X_38206,X_38206))))
| is_a_theorem(not(not(not(not(not(not(equiv(not(and(X_38206,X_38206)),not(X_38206))))))))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(or(X_38206,not(and(X_38206,X_38206))))),bind(Y,$fot(not(not(not(not(not(not(equiv(not(and(X_38206,X_38206)),not(X_38206))))))))))]]) ).
cnf(refute_0_131,plain,
( ~ is_a_theorem(not(and(not(not(not(not(not(equiv(not(and(X_38198,X_38198)),not(X_38198))))))),or(X_38198,not(and(X_38198,X_38198))))))
| is_a_theorem(implies(or(X_38198,not(and(X_38198,X_38198))),not(not(not(not(not(not(equiv(not(and(X_38198,X_38198)),not(X_38198)))))))))) ),
inference(subst,[],[refute_0_101:[bind(X_566,$fot(not(not(not(not(not(equiv(not(and(X_38198,X_38198)),not(X_38198))))))))),bind(X_567,$fot(or(X_38198,not(and(X_38198,X_38198)))))]]) ).
cnf(refute_0_132,plain,
( ~ is_a_theorem(implies(or(not(not(not(and(X_2476,X_2476)))),X_2475),not(and(not(X_2475),X_2476))))
| ~ is_a_theorem(or(not(not(not(and(X_2476,X_2476)))),X_2475))
| is_a_theorem(not(and(not(X_2475),X_2476))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(or(not(not(not(and(X_2476,X_2476)))),X_2475))),bind(Y,$fot(not(and(not(X_2475),X_2476))))]]) ).
cnf(refute_0_133,plain,
( ~ is_a_theorem(not(and(not(not(not(and(X_1057,X_1057)))),X_1057)))
| is_a_theorem(implies(X_1057,not(not(not(not(and(X_1057,X_1057))))))) ),
inference(subst,[],[refute_0_101:[bind(X_566,$fot(not(not(not(and(X_1057,X_1057)))))),bind(X_567,$fot(X_1057))]]) ).
cnf(refute_0_134,plain,
( ~ is_a_theorem(implies(and(X_325,X_325),not(not(and(X_325,X_325)))))
| is_a_theorem(not(and(not(not(not(and(X_325,X_325)))),X_325))) ),
inference(subst,[],[refute_0_65:[bind(X_324,$fot(not(not(and(X_325,X_325)))))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(not(and(not(X_1053),X_1053))),
inference(subst,[],[refute_0_67:[bind(X_357,$fot(X_1053))]]) ).
cnf(refute_0_136,plain,
( ~ is_a_theorem(not(and(not(X_1053),X_1053)))
| is_a_theorem(implies(X_1053,not(not(X_1053)))) ),
inference(subst,[],[refute_0_101:[bind(X_566,$fot(not(X_1053))),bind(X_567,$fot(X_1053))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(X_1053,not(not(X_1053)))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(X_1053),X_1053))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(and(X_325,X_325),not(not(and(X_325,X_325))))),
inference(subst,[],[refute_0_137:[bind(X_1053,$fot(and(X_325,X_325)))]]) ).
cnf(refute_0_139,plain,
is_a_theorem(not(and(not(not(not(and(X_325,X_325)))),X_325))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_325,X_325),not(not(and(X_325,X_325))))) )],[refute_0_138,refute_0_134]) ).
cnf(refute_0_140,plain,
is_a_theorem(not(and(not(not(not(and(X_1057,X_1057)))),X_1057))),
inference(subst,[],[refute_0_139:[bind(X_325,$fot(X_1057))]]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(X_1057,not(not(not(not(and(X_1057,X_1057))))))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(not(and(X_1057,X_1057)))),X_1057))) )],[refute_0_140,refute_0_133]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(X_2464,not(not(not(not(and(X_2464,X_2464))))))),
inference(subst,[],[refute_0_141:[bind(X_1057,$fot(X_2464))]]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(implies(X_161,X_162))
| ~ is_a_theorem(implies(implies(X_161,X_162),implies(implies(X_162,X_160),not(and(not(X_160),X_161)))))
| is_a_theorem(implies(implies(X_162,X_160),not(and(not(X_160),X_161)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X_161,X_162))),bind(Y,$fot(implies(implies(X_162,X_160),not(and(not(X_160),X_161)))))]]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(implies(X_57,X_58),or(and(X_58,not(Y)),not(and(not(Y),X_57))))),
inference(subst,[],[refute_0_50:[bind(P,$fot(X_57)),bind(Q,$fot(X_58)),bind(R,$fot(not(Y)))]]) ).
cnf(refute_0_145,plain,
or(and(X_58,not(Y)),not(and(not(Y),X_57))) = implies(implies(X_58,Y),not(and(not(Y),X_57))),
inference(subst,[],[refute_0_59:[bind(X,$fot(X_58)),bind(X_19,$fot(not(and(not(Y),X_57))))]]) ).
cnf(refute_0_146,plain,
( or(and(X_58,not(Y)),not(and(not(Y),X_57))) != implies(implies(X_58,Y),not(and(not(Y),X_57)))
| ~ is_a_theorem(implies(implies(X_57,X_58),or(and(X_58,not(Y)),not(and(not(Y),X_57)))))
| is_a_theorem(implies(implies(X_57,X_58),implies(implies(X_58,Y),not(and(not(Y),X_57))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_57,X_58),or(and(X_58,not(Y)),not(and(not(Y),X_57))))) ),[0,1],$fot(implies(implies(X_58,Y),not(and(not(Y),X_57))))]]) ).
cnf(refute_0_147,plain,
( ~ is_a_theorem(implies(implies(X_57,X_58),or(and(X_58,not(Y)),not(and(not(Y),X_57)))))
| is_a_theorem(implies(implies(X_57,X_58),implies(implies(X_58,Y),not(and(not(Y),X_57))))) ),
inference(resolve,[$cnf( $equal(or(and(X_58,not(Y)),not(and(not(Y),X_57))),implies(implies(X_58,Y),not(and(not(Y),X_57)))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(implies(X_57,X_58),implies(implies(X_58,Y),not(and(not(Y),X_57))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_57,X_58),or(and(X_58,not(Y)),not(and(not(Y),X_57))))) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(implies(X_161,X_162),implies(implies(X_162,X_160),not(and(not(X_160),X_161))))),
inference(subst,[],[refute_0_148:[bind(Y,$fot(X_160)),bind(X_57,$fot(X_161)),bind(X_58,$fot(X_162))]]) ).
cnf(refute_0_150,plain,
( ~ is_a_theorem(implies(X_161,X_162))
| is_a_theorem(implies(implies(X_162,X_160),not(and(not(X_160),X_161)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_161,X_162),implies(implies(X_162,X_160),not(and(not(X_160),X_161))))) )],[refute_0_149,refute_0_143]) ).
cnf(refute_0_151,plain,
( ~ is_a_theorem(implies(X_2464,not(not(not(not(and(X_2464,X_2464)))))))
| is_a_theorem(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464)))) ),
inference(subst,[],[refute_0_150:[bind(X_160,$fot(X_2463)),bind(X_161,$fot(X_2464)),bind(X_162,$fot(not(not(not(not(and(X_2464,X_2464)))))))]]) ).
cnf(refute_0_152,plain,
is_a_theorem(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2464,not(not(not(not(and(X_2464,X_2464))))))) )],[refute_0_142,refute_0_151]) ).
cnf(refute_0_153,plain,
implies(not(not(not(not(and(X_2464,X_2464))))),X_2463) = or(not(not(not(and(X_2464,X_2464)))),X_2463),
inference(subst,[],[refute_0_42:[bind(X,$fot(not(not(not(and(X_2464,X_2464)))))),bind(Y,$fot(X_2463))]]) ).
cnf(refute_0_154,plain,
implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))) = implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))),
introduced(tautology,[refl,[$fot(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))))]]) ).
cnf(refute_0_155,plain,
( implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))) != implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464)))
| implies(not(not(not(not(and(X_2464,X_2464))))),X_2463) != or(not(not(not(and(X_2464,X_2464)))),X_2463)
| implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))) = implies(or(not(not(not(and(X_2464,X_2464)))),X_2463),not(and(not(X_2463),X_2464))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))),implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464)))) ),[1,0],$fot(or(not(not(not(and(X_2464,X_2464)))),X_2463))]]) ).
cnf(refute_0_156,plain,
( implies(not(not(not(not(and(X_2464,X_2464))))),X_2463) != or(not(not(not(and(X_2464,X_2464)))),X_2463)
| implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))) = implies(or(not(not(not(and(X_2464,X_2464)))),X_2463),not(and(not(X_2463),X_2464))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))),implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))) = implies(or(not(not(not(and(X_2464,X_2464)))),X_2463),not(and(not(X_2463),X_2464))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),or(not(not(not(and(X_2464,X_2464)))),X_2463)) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))) != implies(or(not(not(not(and(X_2464,X_2464)))),X_2463),not(and(not(X_2463),X_2464)))
| ~ is_a_theorem(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))))
| is_a_theorem(implies(or(not(not(not(and(X_2464,X_2464)))),X_2463),not(and(not(X_2463),X_2464)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464)))) ),[0],$fot(implies(or(not(not(not(and(X_2464,X_2464)))),X_2463),not(and(not(X_2463),X_2464))))]]) ).
cnf(refute_0_159,plain,
( ~ is_a_theorem(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))))
| is_a_theorem(implies(or(not(not(not(and(X_2464,X_2464)))),X_2463),not(and(not(X_2463),X_2464)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464))),implies(or(not(not(not(and(X_2464,X_2464)))),X_2463),not(and(not(X_2463),X_2464)))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
is_a_theorem(implies(or(not(not(not(and(X_2464,X_2464)))),X_2463),not(and(not(X_2463),X_2464)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(not(not(and(X_2464,X_2464))))),X_2463),not(and(not(X_2463),X_2464)))) )],[refute_0_152,refute_0_159]) ).
cnf(refute_0_161,plain,
is_a_theorem(implies(or(not(not(not(and(X_2476,X_2476)))),X_2475),not(and(not(X_2475),X_2476)))),
inference(subst,[],[refute_0_160:[bind(X_2463,$fot(X_2475)),bind(X_2464,$fot(X_2476))]]) ).
cnf(refute_0_162,plain,
( ~ is_a_theorem(or(not(not(not(and(X_2476,X_2476)))),X_2475))
| is_a_theorem(not(and(not(X_2475),X_2476))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(not(not(and(X_2476,X_2476)))),X_2475),not(and(not(X_2475),X_2476)))) )],[refute_0_161,refute_0_132]) ).
cnf(refute_0_163,plain,
( ~ is_a_theorem(or(not(not(not(and(or(X_38196,not(and(X_38196,X_38196))),or(X_38196,not(and(X_38196,X_38196))))))),not(not(not(not(equiv(not(and(X_38196,X_38196)),not(X_38196))))))))
| is_a_theorem(not(and(not(not(not(not(not(equiv(not(and(X_38196,X_38196)),not(X_38196))))))),or(X_38196,not(and(X_38196,X_38196)))))) ),
inference(subst,[],[refute_0_162:[bind(X_2475,$fot(not(not(not(not(equiv(not(and(X_38196,X_38196)),not(X_38196)))))))),bind(X_2476,$fot(or(X_38196,not(and(X_38196,X_38196)))))]]) ).
cnf(refute_0_164,plain,
( ~ is_a_theorem(implies(or(X_578,X_579),or(X_579,not(not(X_578)))))
| ~ is_a_theorem(or(X_578,X_579))
| is_a_theorem(or(X_579,not(not(X_578)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(or(X_578,X_579))),bind(Y,$fot(or(X_579,not(not(X_578)))))]]) ).
cnf(refute_0_165,plain,
is_a_theorem(or(and(X_566,not(X)),implies(not(X),not(X_566)))),
inference(subst,[],[refute_0_99:[bind(X_564,$fot(X_566)),bind(X_565,$fot(not(X)))]]) ).
cnf(refute_0_166,plain,
or(X,not(X_566)) = implies(not(X),not(X_566)),
inference(subst,[],[refute_0_21:[bind(Y,$fot(not(X_566)))]]) ).
cnf(refute_0_167,plain,
( or(X,not(X_566)) != implies(not(X),not(X_566))
| implies(not(X),not(X_566)) = or(X,not(X_566)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,not(X_566)))),bind(Y0,$fot(implies(not(X),not(X_566))))]]) ).
cnf(refute_0_168,plain,
implies(not(X),not(X_566)) = or(X,not(X_566)),
inference(resolve,[$cnf( $equal(or(X,not(X_566)),implies(not(X),not(X_566))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
( implies(not(X),not(X_566)) != or(X,not(X_566))
| ~ is_a_theorem(or(and(X_566,not(X)),implies(not(X),not(X_566))))
| is_a_theorem(or(and(X_566,not(X)),or(X,not(X_566)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_566,not(X)),implies(not(X),not(X_566)))) ),[0,1],$fot(or(X,not(X_566)))]]) ).
cnf(refute_0_170,plain,
( ~ is_a_theorem(or(and(X_566,not(X)),implies(not(X),not(X_566))))
| is_a_theorem(or(and(X_566,not(X)),or(X,not(X_566)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_566)),or(X,not(X_566))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
is_a_theorem(or(and(X_566,not(X)),or(X,not(X_566)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_566,not(X)),implies(not(X),not(X_566)))) )],[refute_0_165,refute_0_170]) ).
cnf(refute_0_172,plain,
or(and(X_566,not(X)),or(X,not(X_566))) = implies(implies(X_566,X),or(X,not(X_566))),
inference(subst,[],[refute_0_59:[bind(X,$fot(X_566)),bind(Y,$fot(X)),bind(X_19,$fot(or(X,not(X_566))))]]) ).
cnf(refute_0_173,plain,
( or(and(X_566,not(X)),or(X,not(X_566))) != implies(implies(X_566,X),or(X,not(X_566)))
| ~ is_a_theorem(or(and(X_566,not(X)),or(X,not(X_566))))
| is_a_theorem(implies(implies(X_566,X),or(X,not(X_566)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_566,not(X)),or(X,not(X_566)))) ),[0],$fot(implies(implies(X_566,X),or(X,not(X_566))))]]) ).
cnf(refute_0_174,plain,
( ~ is_a_theorem(or(and(X_566,not(X)),or(X,not(X_566))))
| is_a_theorem(implies(implies(X_566,X),or(X,not(X_566)))) ),
inference(resolve,[$cnf( $equal(or(and(X_566,not(X)),or(X,not(X_566))),implies(implies(X_566,X),or(X,not(X_566)))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
is_a_theorem(implies(implies(X_566,X),or(X,not(X_566)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_566,not(X)),or(X,not(X_566)))) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
is_a_theorem(implies(implies(not(X),X_568),or(X_568,not(not(X))))),
inference(subst,[],[refute_0_175:[bind(X,$fot(X_568)),bind(X_566,$fot(not(X)))]]) ).
cnf(refute_0_177,plain,
or(X,X_568) = implies(not(X),X_568),
inference(subst,[],[refute_0_21:[bind(Y,$fot(X_568))]]) ).
cnf(refute_0_178,plain,
( or(X,X_568) != implies(not(X),X_568)
| implies(not(X),X_568) = or(X,X_568) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_568))),bind(Y0,$fot(implies(not(X),X_568)))]]) ).
cnf(refute_0_179,plain,
implies(not(X),X_568) = or(X,X_568),
inference(resolve,[$cnf( $equal(or(X,X_568),implies(not(X),X_568)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
( implies(not(X),X_568) != or(X,X_568)
| ~ is_a_theorem(implies(implies(not(X),X_568),or(X_568,not(not(X)))))
| is_a_theorem(implies(or(X,X_568),or(X_568,not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),X_568),or(X_568,not(not(X))))) ),[0,0],$fot(or(X,X_568))]]) ).
cnf(refute_0_181,plain,
( ~ is_a_theorem(implies(implies(not(X),X_568),or(X_568,not(not(X)))))
| is_a_theorem(implies(or(X,X_568),or(X_568,not(not(X))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_568),or(X,X_568)) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
is_a_theorem(implies(or(X,X_568),or(X_568,not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_568),or(X_568,not(not(X))))) )],[refute_0_176,refute_0_181]) ).
cnf(refute_0_183,plain,
is_a_theorem(implies(or(X_578,X_579),or(X_579,not(not(X_578))))),
inference(subst,[],[refute_0_182:[bind(X,$fot(X_578)),bind(X_568,$fot(X_579))]]) ).
cnf(refute_0_184,plain,
( ~ is_a_theorem(or(X_578,X_579))
| is_a_theorem(or(X_579,not(not(X_578)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_578,X_579),or(X_579,not(not(X_578))))) )],[refute_0_183,refute_0_164]) ).
cnf(refute_0_185,plain,
( ~ is_a_theorem(or(not(not(equiv(not(and(X_37378,X_37378)),not(X_37378)))),not(not(not(and(or(X_37378,not(and(X_37378,X_37378))),X_37379))))))
| is_a_theorem(or(not(not(not(and(or(X_37378,not(and(X_37378,X_37378))),X_37379)))),not(not(not(not(equiv(not(and(X_37378,X_37378)),not(X_37378)))))))) ),
inference(subst,[],[refute_0_184:[bind(X_578,$fot(not(not(equiv(not(and(X_37378,X_37378)),not(X_37378)))))),bind(X_579,$fot(not(not(not(and(or(X_37378,not(and(X_37378,X_37378))),X_37379))))))]]) ).
cnf(refute_0_186,plain,
( ~ is_a_theorem(or(not(and(or(X_37376,not(and(X_37376,X_37376))),X_37377)),not(not(equiv(not(and(X_37376,X_37376)),not(X_37376))))))
| is_a_theorem(or(not(not(equiv(not(and(X_37376,X_37376)),not(X_37376)))),not(not(not(and(or(X_37376,not(and(X_37376,X_37376))),X_37377)))))) ),
inference(subst,[],[refute_0_184:[bind(X_578,$fot(not(and(or(X_37376,not(and(X_37376,X_37376))),X_37377)))),bind(X_579,$fot(not(not(equiv(not(and(X_37376,X_37376)),not(X_37376))))))]]) ).
cnf(refute_0_187,plain,
( ~ is_a_theorem(or(equiv(not(and(X_37060,X_37060)),not(X_37060)),not(and(or(X_37060,not(and(X_37060,X_37060))),X_37061))))
| is_a_theorem(or(not(and(or(X_37060,not(and(X_37060,X_37060))),X_37061)),not(not(equiv(not(and(X_37060,X_37060)),not(X_37060)))))) ),
inference(subst,[],[refute_0_184:[bind(X_578,$fot(equiv(not(and(X_37060,X_37060)),not(X_37060)))),bind(X_579,$fot(not(and(or(X_37060,not(and(X_37060,X_37060))),X_37061))))]]) ).
cnf(refute_0_188,plain,
( ~ is_a_theorem(not(and(and(not(or(and(X_7571,X_7571),not(X_7571))),not(or(and(X_7571,X_7571),not(X_7571)))),X_7570)))
| is_a_theorem(not(and(X_7570,not(or(and(X_7571,X_7571),not(X_7571)))))) ),
inference(subst,[],[refute_0_105:[bind(X_311,$fot(not(or(and(X_7571,X_7571),not(X_7571))))),bind(X_312,$fot(X_7570))]]) ).
cnf(refute_0_189,plain,
( ~ is_a_theorem(not(and(and(X_311,X_311),and(not(or(and(X_5635,X_5635),not(X_5635))),X_5636))))
| is_a_theorem(not(and(and(not(or(and(X_5635,X_5635),not(X_5635))),X_5636),X_311))) ),
inference(subst,[],[refute_0_105:[bind(X_312,$fot(and(not(or(and(X_5635,X_5635),not(X_5635))),X_5636)))]]) ).
cnf(refute_0_190,plain,
( ~ is_a_theorem(X_1054)
| ~ is_a_theorem(implies(X_1054,not(not(X_1054))))
| is_a_theorem(not(not(X_1054))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_1054)),bind(Y,$fot(not(not(X_1054))))]]) ).
cnf(refute_0_191,plain,
is_a_theorem(implies(X_1054,not(not(X_1054)))),
inference(subst,[],[refute_0_137:[bind(X_1053,$fot(X_1054))]]) ).
cnf(refute_0_192,plain,
( ~ is_a_theorem(X_1054)
| is_a_theorem(not(not(X_1054))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1054,not(not(X_1054)))) )],[refute_0_191,refute_0_190]) ).
cnf(refute_0_193,plain,
( ~ is_a_theorem(or(and(X_1872,X_1872),not(X_1872)))
| is_a_theorem(not(not(or(and(X_1872,X_1872),not(X_1872))))) ),
inference(subst,[],[refute_0_192:[bind(X_1054,$fot(or(and(X_1872,X_1872),not(X_1872))))]]) ).
cnf(refute_0_194,plain,
is_a_theorem(implies(X_1871,and(X_1871,X_1871))),
inference(subst,[],[refute_0_36:[bind(P,$fot(X_1871))]]) ).
cnf(refute_0_195,plain,
( ~ is_a_theorem(implies(X_569,X_568))
| ~ is_a_theorem(implies(implies(X_569,X_568),or(X_568,not(X_569))))
| is_a_theorem(or(X_568,not(X_569))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X_569,X_568))),bind(Y,$fot(or(X_568,not(X_569))))]]) ).
cnf(refute_0_196,plain,
is_a_theorem(implies(implies(X_569,X_568),or(X_568,not(X_569)))),
inference(subst,[],[refute_0_175:[bind(X,$fot(X_568)),bind(X_566,$fot(X_569))]]) ).
cnf(refute_0_197,plain,
( ~ is_a_theorem(implies(X_569,X_568))
| is_a_theorem(or(X_568,not(X_569))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_569,X_568),or(X_568,not(X_569)))) )],[refute_0_196,refute_0_195]) ).
cnf(refute_0_198,plain,
( ~ is_a_theorem(implies(X_1871,and(X_1871,X_1871)))
| is_a_theorem(or(and(X_1871,X_1871),not(X_1871))) ),
inference(subst,[],[refute_0_197:[bind(X_568,$fot(and(X_1871,X_1871))),bind(X_569,$fot(X_1871))]]) ).
cnf(refute_0_199,plain,
is_a_theorem(or(and(X_1871,X_1871),not(X_1871))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1871,and(X_1871,X_1871))) )],[refute_0_194,refute_0_198]) ).
cnf(refute_0_200,plain,
is_a_theorem(or(and(X_1872,X_1872),not(X_1872))),
inference(subst,[],[refute_0_199:[bind(X_1871,$fot(X_1872))]]) ).
cnf(refute_0_201,plain,
is_a_theorem(not(not(or(and(X_1872,X_1872),not(X_1872))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_1872,X_1872),not(X_1872))) )],[refute_0_200,refute_0_193]) ).
cnf(refute_0_202,plain,
( ~ is_a_theorem(not(X_1878))
| ~ is_a_theorem(or(X_1878,not(and(X_1878,X_1877))))
| is_a_theorem(not(and(X_1878,X_1877))) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(X_1878)),bind(X_87,$fot(not(and(X_1878,X_1877))))]]) ).
cnf(refute_0_203,plain,
is_a_theorem(implies(and(X_1870,Q),X_1870)),
inference(subst,[],[refute_0_31:[bind(P,$fot(X_1870))]]) ).
cnf(refute_0_204,plain,
( ~ is_a_theorem(implies(and(X_1870,Q),X_1870))
| is_a_theorem(or(X_1870,not(and(X_1870,Q)))) ),
inference(subst,[],[refute_0_197:[bind(X_568,$fot(X_1870)),bind(X_569,$fot(and(X_1870,Q)))]]) ).
cnf(refute_0_205,plain,
is_a_theorem(or(X_1870,not(and(X_1870,Q)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_1870,Q),X_1870)) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
is_a_theorem(or(X_1878,not(and(X_1878,X_1877)))),
inference(subst,[],[refute_0_205:[bind(Q,$fot(X_1877)),bind(X_1870,$fot(X_1878))]]) ).
cnf(refute_0_207,plain,
( ~ is_a_theorem(not(X_1878))
| is_a_theorem(not(and(X_1878,X_1877))) ),
inference(resolve,[$cnf( is_a_theorem(or(X_1878,not(and(X_1878,X_1877)))) )],[refute_0_206,refute_0_202]) ).
cnf(refute_0_208,plain,
( ~ is_a_theorem(not(not(or(and(X_1872,X_1872),not(X_1872)))))
| is_a_theorem(not(and(not(or(and(X_1872,X_1872),not(X_1872))),X_2168))) ),
inference(subst,[],[refute_0_207:[bind(X_1877,$fot(X_2168)),bind(X_1878,$fot(not(or(and(X_1872,X_1872),not(X_1872)))))]]) ).
cnf(refute_0_209,plain,
is_a_theorem(not(and(not(or(and(X_1872,X_1872),not(X_1872))),X_2168))),
inference(resolve,[$cnf( is_a_theorem(not(not(or(and(X_1872,X_1872),not(X_1872))))) )],[refute_0_201,refute_0_208]) ).
cnf(refute_0_210,plain,
is_a_theorem(not(and(not(or(and(X_1872,X_1872),not(X_1872))),X_4705))),
inference(subst,[],[refute_0_209:[bind(X_2168,$fot(X_4705))]]) ).
cnf(refute_0_211,plain,
( ~ is_a_theorem(not(and(not(or(and(X_1872,X_1872),not(X_1872))),X_4705)))
| is_a_theorem(not(and(X_4705,and(not(or(and(X_1872,X_1872),not(X_1872))),X_4703)))) ),
inference(subst,[],[refute_0_113:[bind(X_318,$fot(X_4703)),bind(X_319,$fot(not(or(and(X_1872,X_1872),not(X_1872))))),bind(X_320,$fot(X_4705))]]) ).
cnf(refute_0_212,plain,
is_a_theorem(not(and(X_4705,and(not(or(and(X_1872,X_1872),not(X_1872))),X_4703)))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(or(and(X_1872,X_1872),not(X_1872))),X_4705))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
is_a_theorem(not(and(and(X_311,X_311),and(not(or(and(X_5635,X_5635),not(X_5635))),X_5636)))),
inference(subst,[],[refute_0_212:[bind(X_1872,$fot(X_5635)),bind(X_4703,$fot(X_5636)),bind(X_4705,$fot(and(X_311,X_311)))]]) ).
cnf(refute_0_214,plain,
is_a_theorem(not(and(and(not(or(and(X_5635,X_5635),not(X_5635))),X_5636),X_311))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(X_311,X_311),and(not(or(and(X_5635,X_5635),not(X_5635))),X_5636)))) )],[refute_0_213,refute_0_189]) ).
cnf(refute_0_215,plain,
is_a_theorem(not(and(and(not(or(and(X_7571,X_7571),not(X_7571))),not(or(and(X_7571,X_7571),not(X_7571)))),X_7570))),
inference(subst,[],[refute_0_214:[bind(X_311,$fot(X_7570)),bind(X_5635,$fot(X_7571)),bind(X_5636,$fot(not(or(and(X_7571,X_7571),not(X_7571)))))]]) ).
cnf(refute_0_216,plain,
is_a_theorem(not(and(X_7570,not(or(and(X_7571,X_7571),not(X_7571)))))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(not(or(and(X_7571,X_7571),not(X_7571))),not(or(and(X_7571,X_7571),not(X_7571)))),X_7570))) )],[refute_0_215,refute_0_188]) ).
cnf(refute_0_217,plain,
not(and(X_7570,not(or(and(X_7571,X_7571),not(X_7571))))) = implies(X_7570,or(and(X_7571,X_7571),not(X_7571))),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_7570)),bind(Y,$fot(or(and(X_7571,X_7571),not(X_7571))))]]) ).
cnf(refute_0_218,plain,
( not(and(X_7570,not(or(and(X_7571,X_7571),not(X_7571))))) != implies(X_7570,or(and(X_7571,X_7571),not(X_7571)))
| ~ is_a_theorem(not(and(X_7570,not(or(and(X_7571,X_7571),not(X_7571))))))
| is_a_theorem(implies(X_7570,or(and(X_7571,X_7571),not(X_7571)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(X_7570,not(or(and(X_7571,X_7571),not(X_7571)))))) ),[0],$fot(implies(X_7570,or(and(X_7571,X_7571),not(X_7571))))]]) ).
cnf(refute_0_219,plain,
( ~ is_a_theorem(not(and(X_7570,not(or(and(X_7571,X_7571),not(X_7571))))))
| is_a_theorem(implies(X_7570,or(and(X_7571,X_7571),not(X_7571)))) ),
inference(resolve,[$cnf( $equal(not(and(X_7570,not(or(and(X_7571,X_7571),not(X_7571))))),implies(X_7570,or(and(X_7571,X_7571),not(X_7571)))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
is_a_theorem(implies(X_7570,or(and(X_7571,X_7571),not(X_7571)))),
inference(resolve,[$cnf( is_a_theorem(not(and(X_7570,not(or(and(X_7571,X_7571),not(X_7571)))))) )],[refute_0_216,refute_0_219]) ).
cnf(refute_0_221,plain,
is_a_theorem(implies(X_37031,or(and(X_37029,X_37029),not(X_37029)))),
inference(subst,[],[refute_0_220:[bind(X_7570,$fot(X_37031)),bind(X_7571,$fot(X_37029))]]) ).
cnf(refute_0_222,plain,
( ~ is_a_theorem(implies(X_214,or(X_213,not(X_212))))
| ~ is_a_theorem(implies(implies(X_214,or(X_213,not(X_212))),or(equiv(not(X_213),not(X_212)),not(and(or(X_212,not(X_213)),X_214)))))
| is_a_theorem(or(equiv(not(X_213),not(X_212)),not(and(or(X_212,not(X_213)),X_214)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X_214,or(X_213,not(X_212))))),bind(Y,$fot(or(equiv(not(X_213),not(X_212)),not(and(or(X_212,not(X_213)),X_214)))))]]) ).
cnf(refute_0_223,plain,
is_a_theorem(implies(implies(X_57,or(X_23,not(X))),or(and(or(X_23,not(X)),or(X,not(X_23))),not(and(or(X,not(X_23)),X_57))))),
inference(subst,[],[refute_0_50:[bind(P,$fot(X_57)),bind(Q,$fot(or(X_23,not(X)))),bind(R,$fot(or(X,not(X_23))))]]) ).
cnf(refute_0_224,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_225,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_226,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_225,refute_0_224]) ).
cnf(refute_0_227,plain,
equiv(not(X_18),Y) = and(implies(not(X_18),Y),implies(Y,not(X_18))),
inference(subst,[],[refute_0_226:[bind(X,$fot(not(X_18)))]]) ).
cnf(refute_0_228,plain,
or(X_18,Y) = implies(not(X_18),Y),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_229,plain,
( or(X_18,Y) != implies(not(X_18),Y)
| implies(not(X_18),Y) = or(X_18,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_18,Y))),bind(Y0,$fot(implies(not(X_18),Y)))]]) ).
cnf(refute_0_230,plain,
implies(not(X_18),Y) = or(X_18,Y),
inference(resolve,[$cnf( $equal(or(X_18,Y),implies(not(X_18),Y)) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
( equiv(not(X_18),Y) != and(implies(not(X_18),Y),implies(Y,not(X_18)))
| implies(not(X_18),Y) != or(X_18,Y)
| equiv(not(X_18),Y) = and(or(X_18,Y),implies(Y,not(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_18),Y),and(implies(not(X_18),Y),implies(Y,not(X_18)))) ),[1,0],$fot(or(X_18,Y))]]) ).
cnf(refute_0_232,plain,
( equiv(not(X_18),Y) != and(implies(not(X_18),Y),implies(Y,not(X_18)))
| equiv(not(X_18),Y) = and(or(X_18,Y),implies(Y,not(X_18))) ),
inference(resolve,[$cnf( $equal(implies(not(X_18),Y),or(X_18,Y)) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
equiv(not(X_18),Y) = and(or(X_18,Y),implies(Y,not(X_18))),
inference(resolve,[$cnf( $equal(equiv(not(X_18),Y),and(implies(not(X_18),Y),implies(Y,not(X_18)))) )],[refute_0_227,refute_0_232]) ).
cnf(refute_0_234,plain,
equiv(not(X_23),not(X)) = and(or(X_23,not(X)),implies(not(X),not(X_23))),
inference(subst,[],[refute_0_233:[bind(Y,$fot(not(X))),bind(X_18,$fot(X_23))]]) ).
cnf(refute_0_235,plain,
or(X,not(X_23)) = implies(not(X),not(X_23)),
inference(subst,[],[refute_0_21:[bind(Y,$fot(not(X_23)))]]) ).
cnf(refute_0_236,plain,
( or(X,not(X_23)) != implies(not(X),not(X_23))
| implies(not(X),not(X_23)) = or(X,not(X_23)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,not(X_23)))),bind(Y0,$fot(implies(not(X),not(X_23))))]]) ).
cnf(refute_0_237,plain,
implies(not(X),not(X_23)) = or(X,not(X_23)),
inference(resolve,[$cnf( $equal(or(X,not(X_23)),implies(not(X),not(X_23))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
( equiv(not(X_23),not(X)) != and(or(X_23,not(X)),implies(not(X),not(X_23)))
| implies(not(X),not(X_23)) != or(X,not(X_23))
| equiv(not(X_23),not(X)) = and(or(X_23,not(X)),or(X,not(X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_23),not(X)),and(or(X_23,not(X)),implies(not(X),not(X_23)))) ),[1,1],$fot(or(X,not(X_23)))]]) ).
cnf(refute_0_239,plain,
( equiv(not(X_23),not(X)) != and(or(X_23,not(X)),implies(not(X),not(X_23)))
| equiv(not(X_23),not(X)) = and(or(X_23,not(X)),or(X,not(X_23))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_23)),or(X,not(X_23))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
equiv(not(X_23),not(X)) = and(or(X_23,not(X)),or(X,not(X_23))),
inference(resolve,[$cnf( $equal(equiv(not(X_23),not(X)),and(or(X_23,not(X)),implies(not(X),not(X_23)))) )],[refute_0_234,refute_0_239]) ).
cnf(refute_0_241,plain,
( equiv(not(X_23),not(X)) != and(or(X_23,not(X)),or(X,not(X_23)))
| and(or(X_23,not(X)),or(X,not(X_23))) = equiv(not(X_23),not(X)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(equiv(not(X_23),not(X)))),bind(Y0,$fot(and(or(X_23,not(X)),or(X,not(X_23)))))]]) ).
cnf(refute_0_242,plain,
and(or(X_23,not(X)),or(X,not(X_23))) = equiv(not(X_23),not(X)),
inference(resolve,[$cnf( $equal(equiv(not(X_23),not(X)),and(or(X_23,not(X)),or(X,not(X_23)))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
( and(or(X_23,not(X)),or(X,not(X_23))) != equiv(not(X_23),not(X))
| ~ is_a_theorem(implies(implies(X_57,or(X_23,not(X))),or(and(or(X_23,not(X)),or(X,not(X_23))),not(and(or(X,not(X_23)),X_57)))))
| is_a_theorem(implies(implies(X_57,or(X_23,not(X))),or(equiv(not(X_23),not(X)),not(and(or(X,not(X_23)),X_57))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_57,or(X_23,not(X))),or(and(or(X_23,not(X)),or(X,not(X_23))),not(and(or(X,not(X_23)),X_57))))) ),[0,1,0],$fot(equiv(not(X_23),not(X)))]]) ).
cnf(refute_0_244,plain,
( ~ is_a_theorem(implies(implies(X_57,or(X_23,not(X))),or(and(or(X_23,not(X)),or(X,not(X_23))),not(and(or(X,not(X_23)),X_57)))))
| is_a_theorem(implies(implies(X_57,or(X_23,not(X))),or(equiv(not(X_23),not(X)),not(and(or(X,not(X_23)),X_57))))) ),
inference(resolve,[$cnf( $equal(and(or(X_23,not(X)),or(X,not(X_23))),equiv(not(X_23),not(X))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
is_a_theorem(implies(implies(X_57,or(X_23,not(X))),or(equiv(not(X_23),not(X)),not(and(or(X,not(X_23)),X_57))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_57,or(X_23,not(X))),or(and(or(X_23,not(X)),or(X,not(X_23))),not(and(or(X,not(X_23)),X_57))))) )],[refute_0_223,refute_0_244]) ).
cnf(refute_0_246,plain,
is_a_theorem(implies(implies(X_214,or(X_213,not(X_212))),or(equiv(not(X_213),not(X_212)),not(and(or(X_212,not(X_213)),X_214))))),
inference(subst,[],[refute_0_245:[bind(X,$fot(X_212)),bind(X_23,$fot(X_213)),bind(X_57,$fot(X_214))]]) ).
cnf(refute_0_247,plain,
( ~ is_a_theorem(implies(X_214,or(X_213,not(X_212))))
| is_a_theorem(or(equiv(not(X_213),not(X_212)),not(and(or(X_212,not(X_213)),X_214)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_214,or(X_213,not(X_212))),or(equiv(not(X_213),not(X_212)),not(and(or(X_212,not(X_213)),X_214))))) )],[refute_0_246,refute_0_222]) ).
cnf(refute_0_248,plain,
( ~ is_a_theorem(implies(X_37031,or(and(X_37029,X_37029),not(X_37029))))
| is_a_theorem(or(equiv(not(and(X_37029,X_37029)),not(X_37029)),not(and(or(X_37029,not(and(X_37029,X_37029))),X_37031)))) ),
inference(subst,[],[refute_0_247:[bind(X_212,$fot(X_37029)),bind(X_213,$fot(and(X_37029,X_37029))),bind(X_214,$fot(X_37031))]]) ).
cnf(refute_0_249,plain,
is_a_theorem(or(equiv(not(and(X_37029,X_37029)),not(X_37029)),not(and(or(X_37029,not(and(X_37029,X_37029))),X_37031)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_37031,or(and(X_37029,X_37029),not(X_37029)))) )],[refute_0_221,refute_0_248]) ).
cnf(refute_0_250,plain,
is_a_theorem(or(equiv(not(and(X_37060,X_37060)),not(X_37060)),not(and(or(X_37060,not(and(X_37060,X_37060))),X_37061)))),
inference(subst,[],[refute_0_249:[bind(X_37029,$fot(X_37060)),bind(X_37031,$fot(X_37061))]]) ).
cnf(refute_0_251,plain,
is_a_theorem(or(not(and(or(X_37060,not(and(X_37060,X_37060))),X_37061)),not(not(equiv(not(and(X_37060,X_37060)),not(X_37060)))))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(not(and(X_37060,X_37060)),not(X_37060)),not(and(or(X_37060,not(and(X_37060,X_37060))),X_37061)))) )],[refute_0_250,refute_0_187]) ).
cnf(refute_0_252,plain,
is_a_theorem(or(not(and(or(X_37376,not(and(X_37376,X_37376))),X_37377)),not(not(equiv(not(and(X_37376,X_37376)),not(X_37376)))))),
inference(subst,[],[refute_0_251:[bind(X_37060,$fot(X_37376)),bind(X_37061,$fot(X_37377))]]) ).
cnf(refute_0_253,plain,
is_a_theorem(or(not(not(equiv(not(and(X_37376,X_37376)),not(X_37376)))),not(not(not(and(or(X_37376,not(and(X_37376,X_37376))),X_37377)))))),
inference(resolve,[$cnf( is_a_theorem(or(not(and(or(X_37376,not(and(X_37376,X_37376))),X_37377)),not(not(equiv(not(and(X_37376,X_37376)),not(X_37376)))))) )],[refute_0_252,refute_0_186]) ).
cnf(refute_0_254,plain,
is_a_theorem(or(not(not(equiv(not(and(X_37378,X_37378)),not(X_37378)))),not(not(not(and(or(X_37378,not(and(X_37378,X_37378))),X_37379)))))),
inference(subst,[],[refute_0_253:[bind(X_37376,$fot(X_37378)),bind(X_37377,$fot(X_37379))]]) ).
cnf(refute_0_255,plain,
is_a_theorem(or(not(not(not(and(or(X_37378,not(and(X_37378,X_37378))),X_37379)))),not(not(not(not(equiv(not(and(X_37378,X_37378)),not(X_37378)))))))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(equiv(not(and(X_37378,X_37378)),not(X_37378)))),not(not(not(and(or(X_37378,not(and(X_37378,X_37378))),X_37379)))))) )],[refute_0_254,refute_0_185]) ).
cnf(refute_0_256,plain,
is_a_theorem(or(not(not(not(and(or(X_38196,not(and(X_38196,X_38196))),or(X_38196,not(and(X_38196,X_38196))))))),not(not(not(not(equiv(not(and(X_38196,X_38196)),not(X_38196)))))))),
inference(subst,[],[refute_0_255:[bind(X_37378,$fot(X_38196)),bind(X_37379,$fot(or(X_38196,not(and(X_38196,X_38196)))))]]) ).
cnf(refute_0_257,plain,
is_a_theorem(not(and(not(not(not(not(not(equiv(not(and(X_38196,X_38196)),not(X_38196))))))),or(X_38196,not(and(X_38196,X_38196)))))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(not(and(or(X_38196,not(and(X_38196,X_38196))),or(X_38196,not(and(X_38196,X_38196))))))),not(not(not(not(equiv(not(and(X_38196,X_38196)),not(X_38196)))))))) )],[refute_0_256,refute_0_163]) ).
cnf(refute_0_258,plain,
is_a_theorem(not(and(not(not(not(not(not(equiv(not(and(X_38198,X_38198)),not(X_38198))))))),or(X_38198,not(and(X_38198,X_38198)))))),
inference(subst,[],[refute_0_257:[bind(X_38196,$fot(X_38198))]]) ).
cnf(refute_0_259,plain,
is_a_theorem(implies(or(X_38198,not(and(X_38198,X_38198))),not(not(not(not(not(not(equiv(not(and(X_38198,X_38198)),not(X_38198)))))))))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(not(not(not(equiv(not(and(X_38198,X_38198)),not(X_38198))))))),or(X_38198,not(and(X_38198,X_38198)))))) )],[refute_0_258,refute_0_131]) ).
cnf(refute_0_260,plain,
is_a_theorem(implies(or(X_38206,not(and(X_38206,X_38206))),not(not(not(not(not(not(equiv(not(and(X_38206,X_38206)),not(X_38206)))))))))),
inference(subst,[],[refute_0_259:[bind(X_38198,$fot(X_38206))]]) ).
cnf(refute_0_261,plain,
( ~ is_a_theorem(or(X_38206,not(and(X_38206,X_38206))))
| is_a_theorem(not(not(not(not(not(not(equiv(not(and(X_38206,X_38206)),not(X_38206))))))))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_38206,not(and(X_38206,X_38206))),not(not(not(not(not(not(equiv(not(and(X_38206,X_38206)),not(X_38206)))))))))) )],[refute_0_260,refute_0_130]) ).
cnf(refute_0_262,plain,
is_a_theorem(or(X_38206,not(and(X_38206,X_38206)))),
inference(subst,[],[refute_0_205:[bind(Q,$fot(X_38206)),bind(X_1870,$fot(X_38206))]]) ).
cnf(refute_0_263,plain,
is_a_theorem(not(not(not(not(not(not(equiv(not(and(X_38206,X_38206)),not(X_38206))))))))),
inference(resolve,[$cnf( is_a_theorem(or(X_38206,not(and(X_38206,X_38206)))) )],[refute_0_262,refute_0_261]) ).
cnf(refute_0_264,plain,
is_a_theorem(not(not(not(not(not(not(equiv(not(and(X_38207,X_38207)),not(X_38207))))))))),
inference(subst,[],[refute_0_263:[bind(X_38206,$fot(X_38207))]]) ).
cnf(refute_0_265,plain,
is_a_theorem(not(not(not(not(equiv(not(and(X_38207,X_38207)),not(X_38207))))))),
inference(resolve,[$cnf( is_a_theorem(not(not(not(not(not(not(equiv(not(and(X_38207,X_38207)),not(X_38207))))))))) )],[refute_0_264,refute_0_129]) ).
cnf(refute_0_266,plain,
is_a_theorem(not(not(not(not(equiv(not(and(X_38208,X_38208)),not(X_38208))))))),
inference(subst,[],[refute_0_265:[bind(X_38207,$fot(X_38208))]]) ).
cnf(refute_0_267,plain,
is_a_theorem(not(not(equiv(not(and(X_38208,X_38208)),not(X_38208))))),
inference(resolve,[$cnf( is_a_theorem(not(not(not(not(equiv(not(and(X_38208,X_38208)),not(X_38208))))))) )],[refute_0_266,refute_0_128]) ).
cnf(refute_0_268,plain,
is_a_theorem(not(not(equiv(not(and(X_38209,X_38209)),not(X_38209))))),
inference(subst,[],[refute_0_267:[bind(X_38208,$fot(X_38209))]]) ).
cnf(refute_0_269,plain,
is_a_theorem(equiv(not(and(X_38209,X_38209)),not(X_38209))),
inference(resolve,[$cnf( is_a_theorem(not(not(equiv(not(and(X_38209,X_38209)),not(X_38209))))) )],[refute_0_268,refute_0_127]) ).
cnf(refute_0_270,plain,
is_a_theorem(equiv(not(and(X_38210,X_38210)),not(X_38210))),
inference(subst,[],[refute_0_269:[bind(X_38209,$fot(X_38210))]]) ).
cnf(refute_0_271,plain,
not(and(X_38210,X_38210)) = not(X_38210),
inference(resolve,[$cnf( is_a_theorem(equiv(not(and(X_38210,X_38210)),not(X_38210))) )],[refute_0_270,refute_0_123]) ).
cnf(refute_0_272,plain,
not(and(X_4710,X_4710)) = not(X_4710),
inference(subst,[],[refute_0_271:[bind(X_38210,$fot(X_4710))]]) ).
cnf(refute_0_273,plain,
and(not(and(X_4710,X_4710)),X_4711) = and(not(and(X_4710,X_4710)),X_4711),
introduced(tautology,[refl,[$fot(and(not(and(X_4710,X_4710)),X_4711))]]) ).
cnf(refute_0_274,plain,
( and(not(and(X_4710,X_4710)),X_4711) != and(not(and(X_4710,X_4710)),X_4711)
| not(and(X_4710,X_4710)) != not(X_4710)
| and(not(and(X_4710,X_4710)),X_4711) = and(not(X_4710),X_4711) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_4710,X_4710)),X_4711),and(not(and(X_4710,X_4710)),X_4711)) ),[1,0],$fot(not(X_4710))]]) ).
cnf(refute_0_275,plain,
( not(and(X_4710,X_4710)) != not(X_4710)
| and(not(and(X_4710,X_4710)),X_4711) = and(not(X_4710),X_4711) ),
inference(resolve,[$cnf( $equal(and(not(and(X_4710,X_4710)),X_4711),and(not(and(X_4710,X_4710)),X_4711)) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
and(not(and(X_4710,X_4710)),X_4711) = and(not(X_4710),X_4711),
inference(resolve,[$cnf( $equal(not(and(X_4710,X_4710)),not(X_4710)) )],[refute_0_272,refute_0_275]) ).
cnf(refute_0_277,plain,
not(and(not(and(X_4710,X_4710)),X_4711)) = not(and(not(and(X_4710,X_4710)),X_4711)),
introduced(tautology,[refl,[$fot(not(and(not(and(X_4710,X_4710)),X_4711)))]]) ).
cnf(refute_0_278,plain,
( and(not(and(X_4710,X_4710)),X_4711) != and(not(X_4710),X_4711)
| not(and(not(and(X_4710,X_4710)),X_4711)) != not(and(not(and(X_4710,X_4710)),X_4711))
| not(and(not(and(X_4710,X_4710)),X_4711)) = not(and(not(X_4710),X_4711)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(not(and(X_4710,X_4710)),X_4711)),not(and(not(and(X_4710,X_4710)),X_4711))) ),[1,0],$fot(and(not(X_4710),X_4711))]]) ).
cnf(refute_0_279,plain,
( and(not(and(X_4710,X_4710)),X_4711) != and(not(X_4710),X_4711)
| not(and(not(and(X_4710,X_4710)),X_4711)) = not(and(not(X_4710),X_4711)) ),
inference(resolve,[$cnf( $equal(not(and(not(and(X_4710,X_4710)),X_4711)),not(and(not(and(X_4710,X_4710)),X_4711))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
not(and(not(and(X_4710,X_4710)),X_4711)) = not(and(not(X_4710),X_4711)),
inference(resolve,[$cnf( $equal(and(not(and(X_4710,X_4710)),X_4711),and(not(X_4710),X_4711)) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))) = implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))),
introduced(tautology,[refl,[$fot(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))))]]) ).
cnf(refute_0_282,plain,
( implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))) != implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711)))
| not(and(not(and(X_4710,X_4710)),X_4711)) != not(and(not(X_4710),X_4711))
| implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))) = implies(X_4710,not(and(not(X_4710),X_4711))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))),implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711)))) ),[1,1],$fot(not(and(not(X_4710),X_4711)))]]) ).
cnf(refute_0_283,plain,
( not(and(not(and(X_4710,X_4710)),X_4711)) != not(and(not(X_4710),X_4711))
| implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))) = implies(X_4710,not(and(not(X_4710),X_4711))) ),
inference(resolve,[$cnf( $equal(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))),implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711)))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))) = implies(X_4710,not(and(not(X_4710),X_4711))),
inference(resolve,[$cnf( $equal(not(and(not(and(X_4710,X_4710)),X_4711)),not(and(not(X_4710),X_4711))) )],[refute_0_280,refute_0_283]) ).
cnf(refute_0_285,plain,
( implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))) != implies(X_4710,not(and(not(X_4710),X_4711)))
| ~ is_a_theorem(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))))
| is_a_theorem(implies(X_4710,not(and(not(X_4710),X_4711)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711)))) ),[0],$fot(implies(X_4710,not(and(not(X_4710),X_4711))))]]) ).
cnf(refute_0_286,plain,
( ~ is_a_theorem(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))))
| is_a_theorem(implies(X_4710,not(and(not(X_4710),X_4711)))) ),
inference(resolve,[$cnf( $equal(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711))),implies(X_4710,not(and(not(X_4710),X_4711)))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
is_a_theorem(implies(X_4710,not(and(not(X_4710),X_4711)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_4710,not(and(not(and(X_4710,X_4710)),X_4711)))) )],[refute_0_119,refute_0_286]) ).
cnf(refute_0_288,plain,
is_a_theorem(implies(X_38330,not(and(not(X_38330),not(Y))))),
inference(subst,[],[refute_0_287:[bind(X_4710,$fot(X_38330)),bind(X_4711,$fot(not(Y)))]]) ).
cnf(refute_0_289,plain,
implies(not(X_38330),Y) = not(and(not(X_38330),not(Y))),
inference(subst,[],[refute_0_12:[bind(X,$fot(not(X_38330)))]]) ).
cnf(refute_0_290,plain,
( implies(not(X_38330),Y) != not(and(not(X_38330),not(Y)))
| not(and(not(X_38330),not(Y))) = implies(not(X_38330),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(not(X_38330),Y))),bind(Y0,$fot(not(and(not(X_38330),not(Y)))))]]) ).
cnf(refute_0_291,plain,
not(and(not(X_38330),not(Y))) = implies(not(X_38330),Y),
inference(resolve,[$cnf( $equal(implies(not(X_38330),Y),not(and(not(X_38330),not(Y)))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
( not(and(not(X_38330),not(Y))) != implies(not(X_38330),Y)
| ~ is_a_theorem(implies(X_38330,not(and(not(X_38330),not(Y)))))
| is_a_theorem(implies(X_38330,implies(not(X_38330),Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_38330,not(and(not(X_38330),not(Y))))) ),[0,1],$fot(implies(not(X_38330),Y))]]) ).
cnf(refute_0_293,plain,
( ~ is_a_theorem(implies(X_38330,not(and(not(X_38330),not(Y)))))
| is_a_theorem(implies(X_38330,implies(not(X_38330),Y))) ),
inference(resolve,[$cnf( $equal(not(and(not(X_38330),not(Y))),implies(not(X_38330),Y)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
is_a_theorem(implies(X_38330,implies(not(X_38330),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(X_38330,not(and(not(X_38330),not(Y))))) )],[refute_0_288,refute_0_293]) ).
cnf(refute_0_295,plain,
implies(not(X_38330),Y) = or(X_38330,Y),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_38330))]]) ).
cnf(refute_0_296,plain,
implies(X_38330,implies(not(X_38330),Y)) = implies(X_38330,implies(not(X_38330),Y)),
introduced(tautology,[refl,[$fot(implies(X_38330,implies(not(X_38330),Y)))]]) ).
cnf(refute_0_297,plain,
( implies(X_38330,implies(not(X_38330),Y)) != implies(X_38330,implies(not(X_38330),Y))
| implies(not(X_38330),Y) != or(X_38330,Y)
| implies(X_38330,implies(not(X_38330),Y)) = implies(X_38330,or(X_38330,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_38330,implies(not(X_38330),Y)),implies(X_38330,implies(not(X_38330),Y))) ),[1,1],$fot(or(X_38330,Y))]]) ).
cnf(refute_0_298,plain,
( implies(not(X_38330),Y) != or(X_38330,Y)
| implies(X_38330,implies(not(X_38330),Y)) = implies(X_38330,or(X_38330,Y)) ),
inference(resolve,[$cnf( $equal(implies(X_38330,implies(not(X_38330),Y)),implies(X_38330,implies(not(X_38330),Y))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
implies(X_38330,implies(not(X_38330),Y)) = implies(X_38330,or(X_38330,Y)),
inference(resolve,[$cnf( $equal(implies(not(X_38330),Y),or(X_38330,Y)) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
( implies(X_38330,implies(not(X_38330),Y)) != implies(X_38330,or(X_38330,Y))
| ~ is_a_theorem(implies(X_38330,implies(not(X_38330),Y)))
| is_a_theorem(implies(X_38330,or(X_38330,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_38330,implies(not(X_38330),Y))) ),[0],$fot(implies(X_38330,or(X_38330,Y)))]]) ).
cnf(refute_0_301,plain,
( ~ is_a_theorem(implies(X_38330,implies(not(X_38330),Y)))
| is_a_theorem(implies(X_38330,or(X_38330,Y))) ),
inference(resolve,[$cnf( $equal(implies(X_38330,implies(not(X_38330),Y)),implies(X_38330,or(X_38330,Y))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
is_a_theorem(implies(X_38330,or(X_38330,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(X_38330,implies(not(X_38330),Y))) )],[refute_0_294,refute_0_301]) ).
cnf(refute_0_303,plain,
is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9))),
inference(subst,[],[refute_0_302:[bind(Y,$fot(skolemFOFtoCNF_Y_9)),bind(X_38330,$fot(skolemFOFtoCNF_X_9))]]) ).
cnf(refute_0_304,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(skolemFOFtoCNF_X_9,or(skolemFOFtoCNF_X_9,skolemFOFtoCNF_Y_9))) )],[refute_0_303,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL509+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n004.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 00:30:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 238.12/238.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 238.12/238.28
% 238.12/238.28 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 238.12/238.32
%------------------------------------------------------------------------------