TSTP Solution File: LCL498+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL498+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:52:45 EDT 2022
% Result : Theorem 22.78s 22.99s
% Output : CNFRefutation 22.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 121
% Syntax : Number of formulae : 583 ( 297 unt; 0 def)
% Number of atoms : 1006 ( 550 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 826 ( 403 ~; 386 |; 15 &)
% ( 16 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 16 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 16 con; 0-2 aty)
% Number of variables : 1007 ( 26 sgn 71 !; 16 ?)
% 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(cn3,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ) ).
fof(r4,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ).
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_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_op_and,axiom,
op_and ).
fof(principia_op_equiv,axiom,
op_equiv ).
fof(principia_modus_ponens,axiom,
modus_ponens ).
fof(principia_r1,axiom,
r1 ).
fof(principia_r2,axiom,
r2 ).
fof(principia_r3,axiom,
r3 ).
fof(principia_r4,axiom,
r4 ).
fof(principia_r5,axiom,
r5 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
fof(luka_op_or,axiom,
op_or ).
fof(luka_op_equiv,axiom,
op_equiv ).
fof(luka_cn3,conjecture,
cn3 ).
fof(subgoal_0,plain,
cn3,
inference(strip,[],[luka_cn3]) ).
fof(negate_0_0,plain,
~ cn3,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ cn3
<=> ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P)) ),
inference(canonicalize,[],[cn3]) ).
fof(normalize_0_1,plain,
! [P] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(P),P),P)) )
& ( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ cn3,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [P,Q] :
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
r3,
inference(canonicalize,[],[principia_r3]) ).
fof(normalize_0_8,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_9,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_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
modus_ponens,
inference(canonicalize,[],[principia_modus_ponens]) ).
fof(normalize_0_12,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_15,plain,
( ~ r1
<=> ? [P] : ~ is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[r1]) ).
fof(normalize_0_16,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_15]) ).
fof(normalize_0_17,plain,
! [P] :
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
r1,
inference(canonicalize,[],[principia_r1]) ).
fof(normalize_0_19,plain,
( ~ r2
<=> ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[r2]) ).
fof(normalize_0_20,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_Q_4,or(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_4)))
| r2 )
& ( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [P,Q] :
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
r2,
inference(canonicalize,[],[principia_r2]) ).
fof(normalize_0_23,plain,
( ~ r4
<=> ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[r4]) ).
fof(normalize_0_24,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_9,or(skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_2)),or(skolemFOFtoCNF_Q_6,or(skolemFOFtoCNF_P_9,skolemFOFtoCNF_R_2))))
| r4 )
& ( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [P,Q,R] :
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
r4,
inference(canonicalize,[],[principia_r4]) ).
fof(normalize_0_27,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_28,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
op_or,
inference(canonicalize,[],[luka_op_or]) ).
fof(normalize_0_30,plain,
( ~ r5
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[r5]) ).
fof(normalize_0_31,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3))))
| r5 )
& ( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ),
inference(clausify,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [P,Q,R] :
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(conjunct,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
r5,
inference(canonicalize,[],[principia_r5]) ).
fof(normalize_0_34,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_37,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_38,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_37]) ).
fof(normalize_0_39,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_41,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_42,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
op_equiv,
inference(canonicalize,[],[luka_op_equiv]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ cn3,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)),
inference(resolve,[$cnf( cn3 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r3,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$cnf( r3 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(P,Q))),bind(Y,$fot(or(Q,P)))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,Q),or(Q,P))) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(or(X_7480,not(implies(not(X_7480),X_7480))))
| is_a_theorem(or(not(implies(not(X_7480),X_7480)),X_7480)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_7480)),bind(Q,$fot(not(implies(not(X_7480),X_7480))))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(not(equiv(X_7479,not(X_7479))),or(X_7479,not(implies(not(X_7479),X_7479)))))
| ~ is_a_theorem(not(equiv(X_7479,not(X_7479))))
| is_a_theorem(or(X_7479,not(implies(not(X_7479),X_7479)))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(not(equiv(X_7479,not(X_7479))))),bind(Y,$fot(or(X_7479,not(implies(not(X_7479),X_7479)))))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7)))),
inference(subst,[],[refute_0_5:[bind(P,$fot(not(X_7)))]]) ).
cnf(refute_0_14,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_16,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
implies(X_7,Q) = or(not(X_7),Q),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_7)),bind(Y,$fot(Q))]]) ).
cnf(refute_0_18,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_19,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_20,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( implies(X_7,Q) != or(not(X_7),Q)
| or(not(X_7),Q) = implies(X_7,Q) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(implies(X_7,Q))),bind(Y0,$fot(or(not(X_7),Q)))]]) ).
cnf(refute_0_22,plain,
or(not(X_7),Q) = implies(X_7,Q),
inference(resolve,[$cnf( $equal(implies(X_7,Q),or(not(X_7),Q)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( or(not(X_7),Q) != implies(X_7,Q)
| ~ is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7))))
| is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7)))) ),[0,0],$fot(implies(X_7,Q))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7))))
| is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7)))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),Q),implies(X_7,Q)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7)))) )],[refute_0_13,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(X_7,Q))
| ~ is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7))))
| is_a_theorem(or(Q,not(X_7))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_7,Q))),bind(Y,$fot(or(Q,not(X_7))))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(X_7,Q))
| is_a_theorem(or(Q,not(X_7))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(X_1668,X_1668))
| is_a_theorem(or(X_1668,not(X_1668))) ),
inference(subst,[],[refute_0_27:[bind(Q,$fot(X_1668)),bind(X_7,$fot(X_1668))]]) ).
cnf(refute_0_29,plain,
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_30,plain,
r1,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(or(P,P),P)),
inference(resolve,[$cnf( r1 )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(or(X_171,X_171),X_171)),
inference(subst,[],[refute_0_31:[bind(P,$fot(X_171))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(or(X_171,X_171),X_171))
| ~ is_a_theorem(or(X_171,X_171))
| is_a_theorem(X_171) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_171,X_171))),bind(Y,$fot(X_171))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(or(X_171,X_171))
| is_a_theorem(X_171) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_171,X_171),X_171)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(or(implies(X_1667,X_1667),implies(X_1667,X_1667)))
| is_a_theorem(implies(X_1667,X_1667)) ),
inference(subst,[],[refute_0_34:[bind(X_171,$fot(implies(X_1667,X_1667)))]]) ).
cnf(refute_0_36,plain,
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_37,plain,
r2,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(Q,or(P,Q))),
inference(resolve,[$cnf( r2 )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(Q,or(not(X_7),Q))),
inference(subst,[],[refute_0_38:[bind(P,$fot(not(X_7)))]]) ).
cnf(refute_0_40,plain,
( or(not(X_7),Q) != implies(X_7,Q)
| ~ is_a_theorem(implies(Q,or(not(X_7),Q)))
| is_a_theorem(implies(Q,implies(X_7,Q))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(Q,or(not(X_7),Q))) ),[0,1],$fot(implies(X_7,Q))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(Q,or(not(X_7),Q)))
| is_a_theorem(implies(Q,implies(X_7,Q))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),Q),implies(X_7,Q)) )],[refute_0_22,refute_0_40]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(Q,implies(X_7,Q))),
inference(resolve,[$cnf( is_a_theorem(implies(Q,or(not(X_7),Q))) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(X_1594,implies(X_1593,X_1594))),
inference(subst,[],[refute_0_42:[bind(Q,$fot(X_1594)),bind(X_7,$fot(X_1593))]]) ).
cnf(refute_0_44,plain,
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_45,plain,
r4,
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))),
inference(resolve,[$cnf( r4 )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(or(X_72,or(not(X),X_74)),or(not(X),or(X_72,X_74)))),
inference(subst,[],[refute_0_46:[bind(P,$fot(X_72)),bind(Q,$fot(not(X))),bind(R,$fot(X_74))]]) ).
cnf(refute_0_48,plain,
implies(X,or(X_72,X_74)) = or(not(X),or(X_72,X_74)),
inference(subst,[],[refute_0_16:[bind(Y,$fot(or(X_72,X_74)))]]) ).
cnf(refute_0_49,plain,
( implies(X,or(X_72,X_74)) != or(not(X),or(X_72,X_74))
| or(not(X),or(X_72,X_74)) = implies(X,or(X_72,X_74)) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(implies(X,or(X_72,X_74)))),bind(Y0,$fot(or(not(X),or(X_72,X_74))))]]) ).
cnf(refute_0_50,plain,
or(not(X),or(X_72,X_74)) = implies(X,or(X_72,X_74)),
inference(resolve,[$cnf( $equal(implies(X,or(X_72,X_74)),or(not(X),or(X_72,X_74))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( or(not(X),or(X_72,X_74)) != implies(X,or(X_72,X_74))
| ~ is_a_theorem(implies(or(X_72,or(not(X),X_74)),or(not(X),or(X_72,X_74))))
| is_a_theorem(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_72,or(not(X),X_74)),or(not(X),or(X_72,X_74)))) ),[0,1],$fot(implies(X,or(X_72,X_74)))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(or(X_72,or(not(X),X_74)),or(not(X),or(X_72,X_74))))
| is_a_theorem(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_72,X_74)),implies(X,or(X_72,X_74))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_72,or(not(X),X_74)),or(not(X),or(X_72,X_74)))) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_55,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_16,refute_0_54]) ).
cnf(refute_0_56,plain,
or(not(X),X_74) = implies(X,X_74),
inference(subst,[],[refute_0_55:[bind(Y,$fot(X_74))]]) ).
cnf(refute_0_57,plain,
or(X_72,or(not(X),X_74)) = or(X_72,or(not(X),X_74)),
introduced(tautology,[refl,[$fot(or(X_72,or(not(X),X_74)))]]) ).
cnf(refute_0_58,plain,
( or(X_72,or(not(X),X_74)) != or(X_72,or(not(X),X_74))
| or(not(X),X_74) != implies(X,X_74)
| or(X_72,or(not(X),X_74)) = or(X_72,implies(X,X_74)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_72,or(not(X),X_74)),or(X_72,or(not(X),X_74))) ),[1,1],$fot(implies(X,X_74))]]) ).
cnf(refute_0_59,plain,
( or(not(X),X_74) != implies(X,X_74)
| or(X_72,or(not(X),X_74)) = or(X_72,implies(X,X_74)) ),
inference(resolve,[$cnf( $equal(or(X_72,or(not(X),X_74)),or(X_72,or(not(X),X_74))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
or(X_72,or(not(X),X_74)) = or(X_72,implies(X,X_74)),
inference(resolve,[$cnf( $equal(or(not(X),X_74),implies(X,X_74)) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))) = implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))),
introduced(tautology,[refl,[$fot(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))))]]) ).
cnf(refute_0_62,plain,
( implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))) != implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74)))
| or(X_72,or(not(X),X_74)) != or(X_72,implies(X,X_74))
| implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))) = implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))),implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74)))) ),[1,0],$fot(or(X_72,implies(X,X_74)))]]) ).
cnf(refute_0_63,plain,
( or(X_72,or(not(X),X_74)) != or(X_72,implies(X,X_74))
| implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))) = implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74))) ),
inference(resolve,[$cnf( $equal(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))),implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74)))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))) = implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74))),
inference(resolve,[$cnf( $equal(or(X_72,or(not(X),X_74)),or(X_72,implies(X,X_74))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))) != implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74)))
| ~ is_a_theorem(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))))
| is_a_theorem(implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74)))) ),[0],$fot(implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74))))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))))
| is_a_theorem(implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74))),implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_72,or(not(X),X_74)),implies(X,or(X_72,X_74)))) )],[refute_0_53,refute_0_66]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77)))),
inference(subst,[],[refute_0_67:[bind(X,$fot(X_75)),bind(X_72,$fot(not(X))),bind(X_74,$fot(X_77))]]) ).
cnf(refute_0_69,plain,
implies(X,X_77) = or(not(X),X_77),
inference(subst,[],[refute_0_16:[bind(Y,$fot(X_77))]]) ).
cnf(refute_0_70,plain,
( implies(X,X_77) != or(not(X),X_77)
| or(not(X),X_77) = implies(X,X_77) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(implies(X,X_77))),bind(Y0,$fot(or(not(X),X_77)))]]) ).
cnf(refute_0_71,plain,
or(not(X),X_77) = implies(X,X_77),
inference(resolve,[$cnf( $equal(implies(X,X_77),or(not(X),X_77)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( or(not(X),X_77) != implies(X,X_77)
| ~ is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77))))
| is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77)))) ),[0,1,1],$fot(implies(X,X_77))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77))))
| is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_77),implies(X,X_77)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,or(not(X),X_77)))) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
or(not(X),implies(X_75,X_77)) = implies(X,implies(X_75,X_77)),
inference(subst,[],[refute_0_55:[bind(Y,$fot(implies(X_75,X_77)))]]) ).
cnf(refute_0_76,plain,
implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) = implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))))]]) ).
cnf(refute_0_77,plain,
( implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) != implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))
| or(not(X),implies(X_75,X_77)) != implies(X,implies(X_75,X_77))
| implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) = implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))),implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) ),[1,0],$fot(implies(X,implies(X_75,X_77)))]]) ).
cnf(refute_0_78,plain,
( or(not(X),implies(X_75,X_77)) != implies(X,implies(X_75,X_77))
| implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) = implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))),implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) = implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_75,X_77)),implies(X,implies(X_75,X_77))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))) != implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))
| ~ is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))))
| is_a_theorem(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) ),[0],$fot(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))))
| is_a_theorem(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77))),implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) )],[refute_0_74,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(implies(X,implies(X_75,X_77)))
| ~ is_a_theorem(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77))))
| is_a_theorem(implies(X_75,implies(X,X_77))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X,implies(X_75,X_77)))),bind(Y,$fot(implies(X_75,implies(X,X_77))))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(X,implies(X_75,X_77)))
| is_a_theorem(implies(X_75,implies(X,X_77))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X_75,X_77)),implies(X_75,implies(X,X_77)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(X_1594,implies(X_1593,X_1594)))
| is_a_theorem(implies(X_1593,implies(X_1594,X_1594))) ),
inference(subst,[],[refute_0_84:[bind(X,$fot(X_1594)),bind(X_75,$fot(X_1593)),bind(X_77,$fot(X_1594))]]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(X_1593,implies(X_1594,X_1594))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1594,implies(X_1593,X_1594))) )],[refute_0_43,refute_0_85]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(and(not(X_12),not(X_13)),implies(X_1606,X_1606))),
inference(subst,[],[refute_0_86:[bind(X_1593,$fot(and(not(X_12),not(X_13)))),bind(X_1594,$fot(X_1606))]]) ).
cnf(refute_0_88,plain,
implies(and(not(X_12),not(X_13)),Y) = or(not(and(not(X_12),not(X_13))),Y),
inference(subst,[],[refute_0_16:[bind(X,$fot(and(not(X_12),not(X_13))))]]) ).
cnf(refute_0_89,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_90,plain,
op_or,
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_91,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_90,refute_0_89]) ).
cnf(refute_0_92,plain,
or(X_12,X_13) = not(and(not(X_12),not(X_13))),
inference(subst,[],[refute_0_91:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_93,plain,
( or(X_12,X_13) != not(and(not(X_12),not(X_13)))
| not(and(not(X_12),not(X_13))) = or(X_12,X_13) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(or(X_12,X_13))),bind(Y0,$fot(not(and(not(X_12),not(X_13)))))]]) ).
cnf(refute_0_94,plain,
not(and(not(X_12),not(X_13))) = or(X_12,X_13),
inference(resolve,[$cnf( $equal(or(X_12,X_13),not(and(not(X_12),not(X_13)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( implies(and(not(X_12),not(X_13)),Y) != or(not(and(not(X_12),not(X_13))),Y)
| not(and(not(X_12),not(X_13))) != or(X_12,X_13)
| implies(and(not(X_12),not(X_13)),Y) = or(or(X_12,X_13),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(X_12),not(X_13)),Y),or(not(and(not(X_12),not(X_13))),Y)) ),[1,0],$fot(or(X_12,X_13))]]) ).
cnf(refute_0_96,plain,
( implies(and(not(X_12),not(X_13)),Y) != or(not(and(not(X_12),not(X_13))),Y)
| implies(and(not(X_12),not(X_13)),Y) = or(or(X_12,X_13),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X_12),not(X_13))),or(X_12,X_13)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
implies(and(not(X_12),not(X_13)),Y) = or(or(X_12,X_13),Y),
inference(resolve,[$cnf( $equal(implies(and(not(X_12),not(X_13)),Y),or(not(and(not(X_12),not(X_13))),Y)) )],[refute_0_88,refute_0_96]) ).
cnf(refute_0_98,plain,
implies(and(not(X_12),not(X_13)),implies(X_1606,X_1606)) = or(or(X_12,X_13),implies(X_1606,X_1606)),
inference(subst,[],[refute_0_97:[bind(Y,$fot(implies(X_1606,X_1606)))]]) ).
cnf(refute_0_99,plain,
( implies(and(not(X_12),not(X_13)),implies(X_1606,X_1606)) != or(or(X_12,X_13),implies(X_1606,X_1606))
| ~ is_a_theorem(implies(and(not(X_12),not(X_13)),implies(X_1606,X_1606)))
| is_a_theorem(or(or(X_12,X_13),implies(X_1606,X_1606))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(X_12),not(X_13)),implies(X_1606,X_1606))) ),[0],$fot(or(or(X_12,X_13),implies(X_1606,X_1606)))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(and(not(X_12),not(X_13)),implies(X_1606,X_1606)))
| is_a_theorem(or(or(X_12,X_13),implies(X_1606,X_1606))) ),
inference(resolve,[$cnf( $equal(implies(and(not(X_12),not(X_13)),implies(X_1606,X_1606)),or(or(X_12,X_13),implies(X_1606,X_1606))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
is_a_theorem(or(or(X_12,X_13),implies(X_1606,X_1606))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(X_12),not(X_13)),implies(X_1606,X_1606))) )],[refute_0_87,refute_0_100]) ).
cnf(refute_0_102,plain,
is_a_theorem(or(or(not(X),X_1663),implies(X_1664,X_1664))),
inference(subst,[],[refute_0_101:[bind(X_12,$fot(not(X))),bind(X_13,$fot(X_1663)),bind(X_1606,$fot(X_1664))]]) ).
cnf(refute_0_103,plain,
implies(X,X_1663) = or(not(X),X_1663),
inference(subst,[],[refute_0_16:[bind(Y,$fot(X_1663))]]) ).
cnf(refute_0_104,plain,
( implies(X,X_1663) != or(not(X),X_1663)
| or(not(X),X_1663) = implies(X,X_1663) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(implies(X,X_1663))),bind(Y0,$fot(or(not(X),X_1663)))]]) ).
cnf(refute_0_105,plain,
or(not(X),X_1663) = implies(X,X_1663),
inference(resolve,[$cnf( $equal(implies(X,X_1663),or(not(X),X_1663)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( or(not(X),X_1663) != implies(X,X_1663)
| ~ is_a_theorem(or(or(not(X),X_1663),implies(X_1664,X_1664)))
| is_a_theorem(or(implies(X,X_1663),implies(X_1664,X_1664))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(not(X),X_1663),implies(X_1664,X_1664))) ),[0,0],$fot(implies(X,X_1663))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(or(or(not(X),X_1663),implies(X_1664,X_1664)))
| is_a_theorem(or(implies(X,X_1663),implies(X_1664,X_1664))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_1663),implies(X,X_1663)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
is_a_theorem(or(implies(X,X_1663),implies(X_1664,X_1664))),
inference(resolve,[$cnf( is_a_theorem(or(or(not(X),X_1663),implies(X_1664,X_1664))) )],[refute_0_102,refute_0_107]) ).
cnf(refute_0_109,plain,
is_a_theorem(or(implies(X_1667,X_1667),implies(X_1667,X_1667))),
inference(subst,[],[refute_0_108:[bind(X,$fot(X_1667)),bind(X_1663,$fot(X_1667)),bind(X_1664,$fot(X_1667))]]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(X_1667,X_1667)),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_1667,X_1667),implies(X_1667,X_1667))) )],[refute_0_109,refute_0_35]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(X_1668,X_1668)),
inference(subst,[],[refute_0_110:[bind(X_1667,$fot(X_1668))]]) ).
cnf(refute_0_112,plain,
is_a_theorem(or(X_1668,not(X_1668))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1668,X_1668)) )],[refute_0_111,refute_0_28]) ).
cnf(refute_0_113,plain,
is_a_theorem(or(not(X),not(not(X)))),
inference(subst,[],[refute_0_112:[bind(X_1668,$fot(not(X)))]]) ).
cnf(refute_0_114,plain,
implies(X,not(not(X))) = or(not(X),not(not(X))),
inference(subst,[],[refute_0_16:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_115,plain,
( implies(X,not(not(X))) != or(not(X),not(not(X)))
| or(not(X),not(not(X))) = implies(X,not(not(X))) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(implies(X,not(not(X))))),bind(Y0,$fot(or(not(X),not(not(X)))))]]) ).
cnf(refute_0_116,plain,
or(not(X),not(not(X))) = implies(X,not(not(X))),
inference(resolve,[$cnf( $equal(implies(X,not(not(X))),or(not(X),not(not(X)))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( or(not(X),not(not(X))) != implies(X,not(not(X)))
| ~ is_a_theorem(or(not(X),not(not(X))))
| is_a_theorem(implies(X,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),not(not(X)))) ),[0],$fot(implies(X,not(not(X))))]]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(or(not(X),not(not(X))))
| is_a_theorem(implies(X,not(not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(X))),implies(X,not(not(X)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(not(X)))) )],[refute_0_113,refute_0_118]) ).
cnf(refute_0_120,plain,
is_a_theorem(implies(X_2148,not(not(X_2148)))),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_2148))]]) ).
cnf(refute_0_121,plain,
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_122,plain,
r5,
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))),
inference(resolve,[$cnf( r5 )],[refute_0_122,refute_0_121]) ).
cnf(refute_0_124,plain,
( ~ is_a_theorem(implies(Q,R))
| ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| is_a_theorem(implies(or(P,Q),or(P,R))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(Q,R))),bind(Y,$fot(implies(or(P,Q),or(P,R))))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(Q,R))
| is_a_theorem(implies(or(P,Q),or(P,R))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
( ~ is_a_theorem(implies(X_2148,not(not(X_2148))))
| is_a_theorem(implies(or(X_2147,X_2148),or(X_2147,not(not(X_2148))))) ),
inference(subst,[],[refute_0_125:[bind(P,$fot(X_2147)),bind(Q,$fot(X_2148)),bind(R,$fot(not(not(X_2148))))]]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(or(X_2147,X_2148),or(X_2147,not(not(X_2148))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2148,not(not(X_2148)))) )],[refute_0_120,refute_0_126]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(or(X_2157,implies(not(X_52),not(not(X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))),
inference(subst,[],[refute_0_127:[bind(X_2147,$fot(X_2157)),bind(X_2148,$fot(implies(not(X_52),not(not(X_53)))))]]) ).
cnf(refute_0_129,plain,
or(X,implies(X_14,not(X_15))) = not(and(not(X),not(implies(X_14,not(X_15))))),
inference(subst,[],[refute_0_91:[bind(Y,$fot(implies(X_14,not(X_15))))]]) ).
cnf(refute_0_130,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_131,plain,
op_and,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_132,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_131,refute_0_130]) ).
cnf(refute_0_133,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_55:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_134,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_135,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_136,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_139,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_132,refute_0_139]) ).
cnf(refute_0_141,plain,
and(X_14,X_15) = not(implies(X_14,not(X_15))),
inference(subst,[],[refute_0_140:[bind(X,$fot(X_14)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_142,plain,
( and(X_14,X_15) != not(implies(X_14,not(X_15)))
| not(implies(X_14,not(X_15))) = and(X_14,X_15) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(and(X_14,X_15))),bind(Y0,$fot(not(implies(X_14,not(X_15)))))]]) ).
cnf(refute_0_143,plain,
not(implies(X_14,not(X_15))) = and(X_14,X_15),
inference(resolve,[$cnf( $equal(and(X_14,X_15),not(implies(X_14,not(X_15)))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( not(implies(X_14,not(X_15))) != and(X_14,X_15)
| or(X,implies(X_14,not(X_15))) != not(and(not(X),not(implies(X_14,not(X_15)))))
| or(X,implies(X_14,not(X_15))) = not(and(not(X),and(X_14,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,implies(X_14,not(X_15))),not(and(not(X),not(implies(X_14,not(X_15)))))) ),[1,0,1],$fot(and(X_14,X_15))]]) ).
cnf(refute_0_145,plain,
( or(X,implies(X_14,not(X_15))) != not(and(not(X),not(implies(X_14,not(X_15)))))
| or(X,implies(X_14,not(X_15))) = not(and(not(X),and(X_14,X_15))) ),
inference(resolve,[$cnf( $equal(not(implies(X_14,not(X_15))),and(X_14,X_15)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
or(X,implies(X_14,not(X_15))) = not(and(not(X),and(X_14,X_15))),
inference(resolve,[$cnf( $equal(or(X,implies(X_14,not(X_15))),not(and(not(X),not(implies(X_14,not(X_15)))))) )],[refute_0_129,refute_0_145]) ).
cnf(refute_0_147,plain,
or(X,implies(not(X_52),not(not(X_53)))) = not(and(not(X),and(not(X_52),not(X_53)))),
inference(subst,[],[refute_0_146:[bind(X_14,$fot(not(X_52))),bind(X_15,$fot(not(X_53)))]]) ).
cnf(refute_0_148,plain,
and(X_14,and(not(X),not(Y))) = not(implies(X_14,not(and(not(X),not(Y))))),
inference(subst,[],[refute_0_140:[bind(X,$fot(X_14)),bind(Y,$fot(and(not(X),not(Y))))]]) ).
cnf(refute_0_149,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| not(and(not(X),not(Y))) = or(X,Y) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(not(and(not(X),not(Y)))))]]) ).
cnf(refute_0_150,plain,
not(and(not(X),not(Y))) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_91,refute_0_149]) ).
cnf(refute_0_151,plain,
( and(X_14,and(not(X),not(Y))) != not(implies(X_14,not(and(not(X),not(Y)))))
| not(and(not(X),not(Y))) != or(X,Y)
| and(X_14,and(not(X),not(Y))) = not(implies(X_14,or(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_14,and(not(X),not(Y))),not(implies(X_14,not(and(not(X),not(Y)))))) ),[1,0,1],$fot(or(X,Y))]]) ).
cnf(refute_0_152,plain,
( and(X_14,and(not(X),not(Y))) != not(implies(X_14,not(and(not(X),not(Y)))))
| and(X_14,and(not(X),not(Y))) = not(implies(X_14,or(X,Y))) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),or(X,Y)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
and(X_14,and(not(X),not(Y))) = not(implies(X_14,or(X,Y))),
inference(resolve,[$cnf( $equal(and(X_14,and(not(X),not(Y))),not(implies(X_14,not(and(not(X),not(Y)))))) )],[refute_0_148,refute_0_152]) ).
cnf(refute_0_154,plain,
and(not(X),and(not(X_52),not(X_53))) = not(implies(not(X),or(X_52,X_53))),
inference(subst,[],[refute_0_153:[bind(X,$fot(X_52)),bind(Y,$fot(X_53)),bind(X_14,$fot(not(X)))]]) ).
cnf(refute_0_155,plain,
( and(not(X),and(not(X_52),not(X_53))) != not(implies(not(X),or(X_52,X_53)))
| or(X,implies(not(X_52),not(not(X_53)))) != not(and(not(X),and(not(X_52),not(X_53))))
| or(X,implies(not(X_52),not(not(X_53)))) = not(not(implies(not(X),or(X_52,X_53)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,implies(not(X_52),not(not(X_53)))),not(and(not(X),and(not(X_52),not(X_53))))) ),[1,0],$fot(not(implies(not(X),or(X_52,X_53))))]]) ).
cnf(refute_0_156,plain,
( or(X,implies(not(X_52),not(not(X_53)))) != not(and(not(X),and(not(X_52),not(X_53))))
| or(X,implies(not(X_52),not(not(X_53)))) = not(not(implies(not(X),or(X_52,X_53)))) ),
inference(resolve,[$cnf( $equal(and(not(X),and(not(X_52),not(X_53))),not(implies(not(X),or(X_52,X_53)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
or(X,implies(not(X_52),not(not(X_53)))) = not(not(implies(not(X),or(X_52,X_53)))),
inference(resolve,[$cnf( $equal(or(X,implies(not(X_52),not(not(X_53)))),not(and(not(X),and(not(X_52),not(X_53))))) )],[refute_0_147,refute_0_156]) ).
cnf(refute_0_158,plain,
or(X_2157,implies(not(X_52),not(not(X_53)))) = not(not(implies(not(X_2157),or(X_52,X_53)))),
inference(subst,[],[refute_0_157:[bind(X,$fot(X_2157))]]) ).
cnf(refute_0_159,plain,
( or(X_2157,implies(not(X_52),not(not(X_53)))) != not(not(implies(not(X_2157),or(X_52,X_53))))
| ~ is_a_theorem(implies(or(X_2157,implies(not(X_52),not(not(X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))))
| is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_2157,implies(not(X_52),not(not(X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))) ),[0,0],$fot(not(not(implies(not(X_2157),or(X_52,X_53)))))]]) ).
cnf(refute_0_160,plain,
( ~ is_a_theorem(implies(or(X_2157,implies(not(X_52),not(not(X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))))
| is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))) ),
inference(resolve,[$cnf( $equal(or(X_2157,implies(not(X_52),not(not(X_53)))),not(not(implies(not(X_2157),or(X_52,X_53))))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_2157,implies(not(X_52),not(not(X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))) )],[refute_0_128,refute_0_160]) ).
cnf(refute_0_162,plain,
not(and(not(X_52),not(X_53))) = or(X_52,X_53),
inference(subst,[],[refute_0_150:[bind(X,$fot(X_52)),bind(Y,$fot(X_53))]]) ).
cnf(refute_0_163,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_164,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_140,refute_0_163]) ).
cnf(refute_0_165,plain,
not(implies(not(X_52),not(not(X_53)))) = and(not(X_52),not(X_53)),
inference(subst,[],[refute_0_164:[bind(X,$fot(not(X_52))),bind(Y,$fot(not(X_53)))]]) ).
cnf(refute_0_166,plain,
not(not(implies(not(X_52),not(not(X_53))))) = not(not(implies(not(X_52),not(not(X_53))))),
introduced(tautology,[refl,[$fot(not(not(implies(not(X_52),not(not(X_53))))))]]) ).
cnf(refute_0_167,plain,
( not(implies(not(X_52),not(not(X_53)))) != and(not(X_52),not(X_53))
| not(not(implies(not(X_52),not(not(X_53))))) != not(not(implies(not(X_52),not(not(X_53)))))
| not(not(implies(not(X_52),not(not(X_53))))) = not(and(not(X_52),not(X_53))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(not(X_52),not(not(X_53))))),not(not(implies(not(X_52),not(not(X_53)))))) ),[1,0],$fot(and(not(X_52),not(X_53)))]]) ).
cnf(refute_0_168,plain,
( not(implies(not(X_52),not(not(X_53)))) != and(not(X_52),not(X_53))
| not(not(implies(not(X_52),not(not(X_53))))) = not(and(not(X_52),not(X_53))) ),
inference(resolve,[$cnf( $equal(not(not(implies(not(X_52),not(not(X_53))))),not(not(implies(not(X_52),not(not(X_53)))))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
not(not(implies(not(X_52),not(not(X_53))))) = not(and(not(X_52),not(X_53))),
inference(resolve,[$cnf( $equal(not(implies(not(X_52),not(not(X_53)))),and(not(X_52),not(X_53))) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_171,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_20,refute_0_170]) ).
cnf(refute_0_172,plain,
( not(and(not(X_52),not(X_53))) != or(X_52,X_53)
| not(not(implies(not(X_52),not(not(X_53))))) != not(and(not(X_52),not(X_53)))
| not(not(implies(not(X_52),not(not(X_53))))) = or(X_52,X_53) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(not(not(implies(not(X_52),not(not(X_53))))))),bind(Y0,$fot(not(and(not(X_52),not(X_53))))),bind(Z,$fot(or(X_52,X_53)))]]) ).
cnf(refute_0_173,plain,
( not(and(not(X_52),not(X_53))) != or(X_52,X_53)
| not(not(implies(not(X_52),not(not(X_53))))) = or(X_52,X_53) ),
inference(resolve,[$cnf( $equal(not(not(implies(not(X_52),not(not(X_53))))),not(and(not(X_52),not(X_53)))) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
not(not(implies(not(X_52),not(not(X_53))))) = or(X_52,X_53),
inference(resolve,[$cnf( $equal(not(and(not(X_52),not(X_53))),or(X_52,X_53)) )],[refute_0_162,refute_0_173]) ).
cnf(refute_0_175,plain,
or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))) = or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))),
introduced(tautology,[refl,[$fot(or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))]]) ).
cnf(refute_0_176,plain,
( not(not(implies(not(X_52),not(not(X_53))))) != or(X_52,X_53)
| or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))) != or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))
| or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))) = or(X_2157,or(X_52,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))) ),[1,1],$fot(or(X_52,X_53))]]) ).
cnf(refute_0_177,plain,
( not(not(implies(not(X_52),not(not(X_53))))) != or(X_52,X_53)
| or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))) = or(X_2157,or(X_52,X_53)) ),
inference(resolve,[$cnf( $equal(or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))) = or(X_2157,or(X_52,X_53)),
inference(resolve,[$cnf( $equal(not(not(implies(not(X_52),not(not(X_53))))),or(X_52,X_53)) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))) = implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))),
introduced(tautology,[refl,[$fot(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))))]]) ).
cnf(refute_0_180,plain,
( implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))) != implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))
| or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))) != or(X_2157,or(X_52,X_53))
| implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))) = implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))),implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))) ),[1,1],$fot(or(X_2157,or(X_52,X_53)))]]) ).
cnf(refute_0_181,plain,
( or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))) != or(X_2157,or(X_52,X_53))
| implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))) = implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53))) ),
inference(resolve,[$cnf( $equal(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))),implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))) = implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53))),
inference(resolve,[$cnf( $equal(or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))),or(X_2157,or(X_52,X_53))) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
( implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))) != implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53)))
| ~ is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))))
| is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))) ),[0],$fot(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53))))]]) ).
cnf(refute_0_184,plain,
( ~ is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))))
| is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53)))) ),
inference(resolve,[$cnf( $equal(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53))))))),implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53)))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,not(not(implies(not(X_52),not(not(X_53)))))))) )],[refute_0_161,refute_0_184]) ).
cnf(refute_0_186,plain,
or(and(not(X_12),not(X_13)),Y) = not(and(not(and(not(X_12),not(X_13))),not(Y))),
inference(subst,[],[refute_0_91:[bind(X,$fot(and(not(X_12),not(X_13))))]]) ).
cnf(refute_0_187,plain,
( not(and(not(X_12),not(X_13))) != or(X_12,X_13)
| or(and(not(X_12),not(X_13)),Y) != not(and(not(and(not(X_12),not(X_13))),not(Y)))
| or(and(not(X_12),not(X_13)),Y) = not(and(or(X_12,X_13),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_12),not(X_13)),Y),not(and(not(and(not(X_12),not(X_13))),not(Y)))) ),[1,0,0],$fot(or(X_12,X_13))]]) ).
cnf(refute_0_188,plain,
( or(and(not(X_12),not(X_13)),Y) != not(and(not(and(not(X_12),not(X_13))),not(Y)))
| or(and(not(X_12),not(X_13)),Y) = not(and(or(X_12,X_13),not(Y))) ),
inference(resolve,[$cnf( $equal(not(and(not(X_12),not(X_13))),or(X_12,X_13)) )],[refute_0_94,refute_0_187]) ).
cnf(refute_0_189,plain,
or(and(not(X_12),not(X_13)),Y) = not(and(or(X_12,X_13),not(Y))),
inference(resolve,[$cnf( $equal(or(and(not(X_12),not(X_13)),Y),not(and(not(and(not(X_12),not(X_13))),not(Y)))) )],[refute_0_186,refute_0_188]) ).
cnf(refute_0_190,plain,
or(and(not(X_13),not(X_13)),Y) = not(and(or(X_13,X_13),not(Y))),
inference(subst,[],[refute_0_189:[bind(X_12,$fot(X_13))]]) ).
cnf(refute_0_191,plain,
and(Y,Y) = not(implies(Y,not(Y))),
inference(subst,[],[refute_0_140:[bind(X,$fot(Y))]]) ).
cnf(refute_0_192,plain,
implies(X,not(X)) = or(not(X),not(X)),
inference(subst,[],[refute_0_16:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_193,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_194,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_195,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_194,refute_0_193]) ).
cnf(refute_0_196,plain,
( ~ is_a_theorem(equiv(or(X_5268,X_5268),X_5268))
| or(X_5268,X_5268) = X_5268 ),
inference(subst,[],[refute_0_195:[bind(X,$fot(or(X_5268,X_5268))),bind(Y,$fot(X_5268))]]) ).
cnf(refute_0_197,plain,
( ~ is_a_theorem(implies(not(not(implies(X_5267,or(X_5267,X_5267)))),equiv(or(X_5267,X_5267),X_5267)))
| ~ is_a_theorem(not(not(implies(X_5267,or(X_5267,X_5267)))))
| is_a_theorem(equiv(or(X_5267,X_5267),X_5267)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(not(not(implies(X_5267,or(X_5267,X_5267)))))),bind(Y,$fot(equiv(or(X_5267,X_5267),X_5267)))]]) ).
cnf(refute_0_198,plain,
( ~ is_a_theorem(or(equiv(or(X_3117,X_3117),X_3117),not(not(not(implies(X_3117,or(X_3117,X_3117)))))))
| is_a_theorem(or(not(not(not(implies(X_3117,or(X_3117,X_3117))))),equiv(or(X_3117,X_3117),X_3117))) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(equiv(or(X_3117,X_3117),X_3117))),bind(Q,$fot(not(not(not(implies(X_3117,or(X_3117,X_3117)))))))]]) ).
cnf(refute_0_199,plain,
( ~ is_a_theorem(X_2482)
| ~ is_a_theorem(implies(X_2482,or(and(X_2482,X_2481),not(not(not(X_2481))))))
| is_a_theorem(or(and(X_2482,X_2481),not(not(not(X_2481))))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_2482)),bind(Y,$fot(or(and(X_2482,X_2481),not(not(not(X_2481))))))]]) ).
cnf(refute_0_200,plain,
is_a_theorem(implies(or(not(X),X_2158),or(not(X),not(not(X_2158))))),
inference(subst,[],[refute_0_127:[bind(X_2147,$fot(not(X))),bind(X_2148,$fot(X_2158))]]) ).
cnf(refute_0_201,plain,
implies(X,not(not(X_2158))) = or(not(X),not(not(X_2158))),
inference(subst,[],[refute_0_16:[bind(Y,$fot(not(not(X_2158))))]]) ).
cnf(refute_0_202,plain,
( implies(X,not(not(X_2158))) != or(not(X),not(not(X_2158)))
| or(not(X),not(not(X_2158))) = implies(X,not(not(X_2158))) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(implies(X,not(not(X_2158))))),bind(Y0,$fot(or(not(X),not(not(X_2158)))))]]) ).
cnf(refute_0_203,plain,
or(not(X),not(not(X_2158))) = implies(X,not(not(X_2158))),
inference(resolve,[$cnf( $equal(implies(X,not(not(X_2158))),or(not(X),not(not(X_2158)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
( or(not(X),not(not(X_2158))) != implies(X,not(not(X_2158)))
| ~ is_a_theorem(implies(or(not(X),X_2158),or(not(X),not(not(X_2158)))))
| is_a_theorem(implies(or(not(X),X_2158),implies(X,not(not(X_2158))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),X_2158),or(not(X),not(not(X_2158))))) ),[0,1],$fot(implies(X,not(not(X_2158))))]]) ).
cnf(refute_0_205,plain,
( ~ is_a_theorem(implies(or(not(X),X_2158),or(not(X),not(not(X_2158)))))
| is_a_theorem(implies(or(not(X),X_2158),implies(X,not(not(X_2158))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(X_2158))),implies(X,not(not(X_2158)))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
is_a_theorem(implies(or(not(X),X_2158),implies(X,not(not(X_2158))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),X_2158),or(not(X),not(not(X_2158))))) )],[refute_0_200,refute_0_205]) ).
cnf(refute_0_207,plain,
or(not(X),X_2158) = implies(X,X_2158),
inference(subst,[],[refute_0_55:[bind(Y,$fot(X_2158))]]) ).
cnf(refute_0_208,plain,
implies(or(not(X),X_2158),implies(X,not(not(X_2158)))) = implies(or(not(X),X_2158),implies(X,not(not(X_2158)))),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_2158),implies(X,not(not(X_2158)))))]]) ).
cnf(refute_0_209,plain,
( implies(or(not(X),X_2158),implies(X,not(not(X_2158)))) != implies(or(not(X),X_2158),implies(X,not(not(X_2158))))
| or(not(X),X_2158) != implies(X,X_2158)
| implies(or(not(X),X_2158),implies(X,not(not(X_2158)))) = implies(implies(X,X_2158),implies(X,not(not(X_2158)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_2158),implies(X,not(not(X_2158)))),implies(or(not(X),X_2158),implies(X,not(not(X_2158))))) ),[1,0],$fot(implies(X,X_2158))]]) ).
cnf(refute_0_210,plain,
( or(not(X),X_2158) != implies(X,X_2158)
| implies(or(not(X),X_2158),implies(X,not(not(X_2158)))) = implies(implies(X,X_2158),implies(X,not(not(X_2158)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_2158),implies(X,not(not(X_2158)))),implies(or(not(X),X_2158),implies(X,not(not(X_2158))))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
implies(or(not(X),X_2158),implies(X,not(not(X_2158)))) = implies(implies(X,X_2158),implies(X,not(not(X_2158)))),
inference(resolve,[$cnf( $equal(or(not(X),X_2158),implies(X,X_2158)) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
( implies(or(not(X),X_2158),implies(X,not(not(X_2158)))) != implies(implies(X,X_2158),implies(X,not(not(X_2158))))
| ~ is_a_theorem(implies(or(not(X),X_2158),implies(X,not(not(X_2158)))))
| is_a_theorem(implies(implies(X,X_2158),implies(X,not(not(X_2158))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),X_2158),implies(X,not(not(X_2158))))) ),[0],$fot(implies(implies(X,X_2158),implies(X,not(not(X_2158)))))]]) ).
cnf(refute_0_213,plain,
( ~ is_a_theorem(implies(or(not(X),X_2158),implies(X,not(not(X_2158)))))
| is_a_theorem(implies(implies(X,X_2158),implies(X,not(not(X_2158))))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_2158),implies(X,not(not(X_2158)))),implies(implies(X,X_2158),implies(X,not(not(X_2158))))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
is_a_theorem(implies(implies(X,X_2158),implies(X,not(not(X_2158))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),X_2158),implies(X,not(not(X_2158))))) )],[refute_0_206,refute_0_213]) ).
cnf(refute_0_215,plain,
is_a_theorem(implies(implies(X_2171,not(X_15)),implies(X_2171,not(not(not(X_15)))))),
inference(subst,[],[refute_0_214:[bind(X,$fot(X_2171)),bind(X_2158,$fot(not(X_15)))]]) ).
cnf(refute_0_216,plain,
implies(implies(X_14,not(X_15)),Y) = or(not(implies(X_14,not(X_15))),Y),
inference(subst,[],[refute_0_16:[bind(X,$fot(implies(X_14,not(X_15))))]]) ).
cnf(refute_0_217,plain,
( implies(implies(X_14,not(X_15)),Y) != or(not(implies(X_14,not(X_15))),Y)
| not(implies(X_14,not(X_15))) != and(X_14,X_15)
| implies(implies(X_14,not(X_15)),Y) = or(and(X_14,X_15),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,not(X_15)),Y),or(not(implies(X_14,not(X_15))),Y)) ),[1,0],$fot(and(X_14,X_15))]]) ).
cnf(refute_0_218,plain,
( implies(implies(X_14,not(X_15)),Y) != or(not(implies(X_14,not(X_15))),Y)
| implies(implies(X_14,not(X_15)),Y) = or(and(X_14,X_15),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_14,not(X_15))),and(X_14,X_15)) )],[refute_0_143,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(implies(X_14,not(X_15)),Y) = or(and(X_14,X_15),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_14,not(X_15)),Y),or(not(implies(X_14,not(X_15))),Y)) )],[refute_0_216,refute_0_218]) ).
cnf(refute_0_220,plain,
implies(implies(X_2171,not(X_15)),implies(X_2171,not(not(not(X_15))))) = or(and(X_2171,X_15),implies(X_2171,not(not(not(X_15))))),
inference(subst,[],[refute_0_219:[bind(Y,$fot(implies(X_2171,not(not(not(X_15)))))),bind(X_14,$fot(X_2171))]]) ).
cnf(refute_0_221,plain,
( implies(implies(X_2171,not(X_15)),implies(X_2171,not(not(not(X_15))))) != or(and(X_2171,X_15),implies(X_2171,not(not(not(X_15)))))
| ~ is_a_theorem(implies(implies(X_2171,not(X_15)),implies(X_2171,not(not(not(X_15))))))
| is_a_theorem(or(and(X_2171,X_15),implies(X_2171,not(not(not(X_15)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_2171,not(X_15)),implies(X_2171,not(not(not(X_15)))))) ),[0],$fot(or(and(X_2171,X_15),implies(X_2171,not(not(not(X_15))))))]]) ).
cnf(refute_0_222,plain,
( ~ is_a_theorem(implies(implies(X_2171,not(X_15)),implies(X_2171,not(not(not(X_15))))))
| is_a_theorem(or(and(X_2171,X_15),implies(X_2171,not(not(not(X_15)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_2171,not(X_15)),implies(X_2171,not(not(not(X_15))))),or(and(X_2171,X_15),implies(X_2171,not(not(not(X_15)))))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
is_a_theorem(or(and(X_2171,X_15),implies(X_2171,not(not(not(X_15)))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2171,not(X_15)),implies(X_2171,not(not(not(X_15)))))) )],[refute_0_215,refute_0_222]) ).
cnf(refute_0_224,plain,
is_a_theorem(or(and(X_2346,X_15),implies(X_2346,not(not(not(X_15)))))),
inference(subst,[],[refute_0_223:[bind(X_2171,$fot(X_2346))]]) ).
cnf(refute_0_225,plain,
( ~ is_a_theorem(implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74))))
| ~ is_a_theorem(or(X_72,implies(X,X_74)))
| is_a_theorem(implies(X,or(X_72,X_74))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_72,implies(X,X_74)))),bind(Y,$fot(implies(X,or(X_72,X_74))))]]) ).
cnf(refute_0_226,plain,
( ~ is_a_theorem(or(X_72,implies(X,X_74)))
| is_a_theorem(implies(X,or(X_72,X_74))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_72,implies(X,X_74)),implies(X,or(X_72,X_74)))) )],[refute_0_67,refute_0_225]) ).
cnf(refute_0_227,plain,
( ~ is_a_theorem(or(and(X_2346,X_15),implies(X_2346,not(not(not(X_15))))))
| is_a_theorem(implies(X_2346,or(and(X_2346,X_15),not(not(not(X_15)))))) ),
inference(subst,[],[refute_0_226:[bind(X,$fot(X_2346)),bind(X_72,$fot(and(X_2346,X_15))),bind(X_74,$fot(not(not(not(X_15)))))]]) ).
cnf(refute_0_228,plain,
is_a_theorem(implies(X_2346,or(and(X_2346,X_15),not(not(not(X_15)))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_2346,X_15),implies(X_2346,not(not(not(X_15)))))) )],[refute_0_224,refute_0_227]) ).
cnf(refute_0_229,plain,
is_a_theorem(implies(X_2482,or(and(X_2482,X_2481),not(not(not(X_2481)))))),
inference(subst,[],[refute_0_228:[bind(X_15,$fot(X_2481)),bind(X_2346,$fot(X_2482))]]) ).
cnf(refute_0_230,plain,
( ~ is_a_theorem(X_2482)
| is_a_theorem(or(and(X_2482,X_2481),not(not(not(X_2481))))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_2482,or(and(X_2482,X_2481),not(not(not(X_2481)))))) )],[refute_0_229,refute_0_199]) ).
cnf(refute_0_231,plain,
( ~ is_a_theorem(implies(or(P,P),P))
| is_a_theorem(or(and(implies(or(P,P),P),X_2737),not(not(not(X_2737))))) ),
inference(subst,[],[refute_0_230:[bind(X_2481,$fot(X_2737)),bind(X_2482,$fot(implies(or(P,P),P)))]]) ).
cnf(refute_0_232,plain,
is_a_theorem(or(and(implies(or(P,P),P),X_2737),not(not(not(X_2737))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,P),P)) )],[refute_0_31,refute_0_231]) ).
cnf(refute_0_233,plain,
is_a_theorem(or(and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))),not(not(not(implies(X_2739,or(X_2739,X_2739))))))),
inference(subst,[],[refute_0_232:[bind(P,$fot(X_2739)),bind(X_2737,$fot(implies(X_2739,or(X_2739,X_2739))))]]) ).
cnf(refute_0_234,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_235,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_236,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_235,refute_0_234]) ).
cnf(refute_0_237,plain,
equiv(or(X_2739,X_2739),X_2739) = and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))),
inference(subst,[],[refute_0_236:[bind(X,$fot(or(X_2739,X_2739))),bind(Y,$fot(X_2739))]]) ).
cnf(refute_0_238,plain,
( equiv(or(X_2739,X_2739),X_2739) != and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739)))
| and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))) = equiv(or(X_2739,X_2739),X_2739) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(equiv(or(X_2739,X_2739),X_2739))),bind(Y0,$fot(and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739)))))]]) ).
cnf(refute_0_239,plain,
and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))) = equiv(or(X_2739,X_2739),X_2739),
inference(resolve,[$cnf( $equal(equiv(or(X_2739,X_2739),X_2739),and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739)))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
( and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))) != equiv(or(X_2739,X_2739),X_2739)
| ~ is_a_theorem(or(and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))),not(not(not(implies(X_2739,or(X_2739,X_2739)))))))
| is_a_theorem(or(equiv(or(X_2739,X_2739),X_2739),not(not(not(implies(X_2739,or(X_2739,X_2739))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))),not(not(not(implies(X_2739,or(X_2739,X_2739))))))) ),[0,0],$fot(equiv(or(X_2739,X_2739),X_2739))]]) ).
cnf(refute_0_241,plain,
( ~ is_a_theorem(or(and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))),not(not(not(implies(X_2739,or(X_2739,X_2739)))))))
| is_a_theorem(or(equiv(or(X_2739,X_2739),X_2739),not(not(not(implies(X_2739,or(X_2739,X_2739))))))) ),
inference(resolve,[$cnf( $equal(and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))),equiv(or(X_2739,X_2739),X_2739)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
is_a_theorem(or(equiv(or(X_2739,X_2739),X_2739),not(not(not(implies(X_2739,or(X_2739,X_2739))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(or(X_2739,X_2739),X_2739),implies(X_2739,or(X_2739,X_2739))),not(not(not(implies(X_2739,or(X_2739,X_2739))))))) )],[refute_0_233,refute_0_241]) ).
cnf(refute_0_243,plain,
is_a_theorem(or(equiv(or(X_3117,X_3117),X_3117),not(not(not(implies(X_3117,or(X_3117,X_3117))))))),
inference(subst,[],[refute_0_242:[bind(X_2739,$fot(X_3117))]]) ).
cnf(refute_0_244,plain,
is_a_theorem(or(not(not(not(implies(X_3117,or(X_3117,X_3117))))),equiv(or(X_3117,X_3117),X_3117))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(or(X_3117,X_3117),X_3117),not(not(not(implies(X_3117,or(X_3117,X_3117))))))) )],[refute_0_243,refute_0_198]) ).
cnf(refute_0_245,plain,
or(not(not(not(implies(X_3117,or(X_3117,X_3117))))),equiv(or(X_3117,X_3117),X_3117)) = implies(not(not(implies(X_3117,or(X_3117,X_3117)))),equiv(or(X_3117,X_3117),X_3117)),
inference(subst,[],[refute_0_55:[bind(X,$fot(not(not(implies(X_3117,or(X_3117,X_3117)))))),bind(Y,$fot(equiv(or(X_3117,X_3117),X_3117)))]]) ).
cnf(refute_0_246,plain,
( or(not(not(not(implies(X_3117,or(X_3117,X_3117))))),equiv(or(X_3117,X_3117),X_3117)) != implies(not(not(implies(X_3117,or(X_3117,X_3117)))),equiv(or(X_3117,X_3117),X_3117))
| ~ is_a_theorem(or(not(not(not(implies(X_3117,or(X_3117,X_3117))))),equiv(or(X_3117,X_3117),X_3117)))
| is_a_theorem(implies(not(not(implies(X_3117,or(X_3117,X_3117)))),equiv(or(X_3117,X_3117),X_3117))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(not(not(implies(X_3117,or(X_3117,X_3117))))),equiv(or(X_3117,X_3117),X_3117))) ),[0],$fot(implies(not(not(implies(X_3117,or(X_3117,X_3117)))),equiv(or(X_3117,X_3117),X_3117)))]]) ).
cnf(refute_0_247,plain,
( ~ is_a_theorem(or(not(not(not(implies(X_3117,or(X_3117,X_3117))))),equiv(or(X_3117,X_3117),X_3117)))
| is_a_theorem(implies(not(not(implies(X_3117,or(X_3117,X_3117)))),equiv(or(X_3117,X_3117),X_3117))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(implies(X_3117,or(X_3117,X_3117))))),equiv(or(X_3117,X_3117),X_3117)),implies(not(not(implies(X_3117,or(X_3117,X_3117)))),equiv(or(X_3117,X_3117),X_3117))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
is_a_theorem(implies(not(not(implies(X_3117,or(X_3117,X_3117)))),equiv(or(X_3117,X_3117),X_3117))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(not(implies(X_3117,or(X_3117,X_3117))))),equiv(or(X_3117,X_3117),X_3117))) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
is_a_theorem(implies(not(not(implies(X_5267,or(X_5267,X_5267)))),equiv(or(X_5267,X_5267),X_5267))),
inference(subst,[],[refute_0_248:[bind(X_3117,$fot(X_5267))]]) ).
cnf(refute_0_250,plain,
( ~ is_a_theorem(not(not(implies(X_5267,or(X_5267,X_5267)))))
| is_a_theorem(equiv(or(X_5267,X_5267),X_5267)) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(X_5267,or(X_5267,X_5267)))),equiv(or(X_5267,X_5267),X_5267))) )],[refute_0_249,refute_0_197]) ).
cnf(refute_0_251,plain,
( ~ is_a_theorem(or(not(not(implies(X_3996,or(X_3995,X_3996)))),not(not(implies(X_3996,or(X_3995,X_3996))))))
| is_a_theorem(not(not(implies(X_3996,or(X_3995,X_3996))))) ),
inference(subst,[],[refute_0_34:[bind(X_171,$fot(not(not(implies(X_3996,or(X_3995,X_3996))))))]]) ).
cnf(refute_0_252,plain,
( ~ is_a_theorem(X_2357)
| ~ is_a_theorem(implies(X_2357,or(X_2358,not(not(X_2357)))))
| is_a_theorem(or(X_2358,not(not(X_2357)))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_2357)),bind(Y,$fot(or(X_2358,not(not(X_2357)))))]]) ).
cnf(refute_0_253,plain,
is_a_theorem(implies(X_170,or(P,X_170))),
inference(subst,[],[refute_0_38:[bind(Q,$fot(X_170))]]) ).
cnf(refute_0_254,plain,
( ~ is_a_theorem(X_170)
| ~ is_a_theorem(implies(X_170,or(P,X_170)))
| is_a_theorem(or(P,X_170)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_170)),bind(Y,$fot(or(P,X_170)))]]) ).
cnf(refute_0_255,plain,
( ~ is_a_theorem(X_170)
| is_a_theorem(or(P,X_170)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_170,or(P,X_170))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
( ~ is_a_theorem(implies(X_1673,not(not(X_1673))))
| is_a_theorem(or(P,implies(X_1673,not(not(X_1673))))) ),
inference(subst,[],[refute_0_255:[bind(X_170,$fot(implies(X_1673,not(not(X_1673)))))]]) ).
cnf(refute_0_257,plain,
is_a_theorem(implies(X_1673,not(not(X_1673)))),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_1673))]]) ).
cnf(refute_0_258,plain,
is_a_theorem(or(P,implies(X_1673,not(not(X_1673))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1673,not(not(X_1673)))) )],[refute_0_257,refute_0_256]) ).
cnf(refute_0_259,plain,
is_a_theorem(or(X_2347,implies(X_2346,not(not(X_2346))))),
inference(subst,[],[refute_0_258:[bind(P,$fot(X_2347)),bind(X_1673,$fot(X_2346))]]) ).
cnf(refute_0_260,plain,
( ~ is_a_theorem(or(X_2347,implies(X_2346,not(not(X_2346)))))
| is_a_theorem(implies(X_2346,or(X_2347,not(not(X_2346))))) ),
inference(subst,[],[refute_0_226:[bind(X,$fot(X_2346)),bind(X_72,$fot(X_2347)),bind(X_74,$fot(not(not(X_2346))))]]) ).
cnf(refute_0_261,plain,
is_a_theorem(implies(X_2346,or(X_2347,not(not(X_2346))))),
inference(resolve,[$cnf( is_a_theorem(or(X_2347,implies(X_2346,not(not(X_2346))))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
is_a_theorem(implies(X_2357,or(X_2358,not(not(X_2357))))),
inference(subst,[],[refute_0_261:[bind(X_2346,$fot(X_2357)),bind(X_2347,$fot(X_2358))]]) ).
cnf(refute_0_263,plain,
( ~ is_a_theorem(X_2357)
| is_a_theorem(or(X_2358,not(not(X_2357)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_2357,or(X_2358,not(not(X_2357))))) )],[refute_0_262,refute_0_252]) ).
cnf(refute_0_264,plain,
( ~ is_a_theorem(implies(Q,or(P,Q)))
| is_a_theorem(or(X_3693,not(not(implies(Q,or(P,Q)))))) ),
inference(subst,[],[refute_0_263:[bind(X_2357,$fot(implies(Q,or(P,Q)))),bind(X_2358,$fot(X_3693))]]) ).
cnf(refute_0_265,plain,
is_a_theorem(or(X_3693,not(not(implies(Q,or(P,Q)))))),
inference(resolve,[$cnf( is_a_theorem(implies(Q,or(P,Q))) )],[refute_0_38,refute_0_264]) ).
cnf(refute_0_266,plain,
is_a_theorem(or(not(not(implies(X_3996,or(X_3995,X_3996)))),not(not(implies(X_3996,or(X_3995,X_3996)))))),
inference(subst,[],[refute_0_265:[bind(P,$fot(X_3995)),bind(Q,$fot(X_3996)),bind(X_3693,$fot(not(not(implies(X_3996,or(X_3995,X_3996))))))]]) ).
cnf(refute_0_267,plain,
is_a_theorem(not(not(implies(X_3996,or(X_3995,X_3996))))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(implies(X_3996,or(X_3995,X_3996)))),not(not(implies(X_3996,or(X_3995,X_3996)))))) )],[refute_0_266,refute_0_251]) ).
cnf(refute_0_268,plain,
is_a_theorem(not(not(implies(X_5267,or(X_5267,X_5267))))),
inference(subst,[],[refute_0_267:[bind(X_3995,$fot(X_5267)),bind(X_3996,$fot(X_5267))]]) ).
cnf(refute_0_269,plain,
is_a_theorem(equiv(or(X_5267,X_5267),X_5267)),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(X_5267,or(X_5267,X_5267))))) )],[refute_0_268,refute_0_250]) ).
cnf(refute_0_270,plain,
is_a_theorem(equiv(or(X_5268,X_5268),X_5268)),
inference(subst,[],[refute_0_269:[bind(X_5267,$fot(X_5268))]]) ).
cnf(refute_0_271,plain,
or(X_5268,X_5268) = X_5268,
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_5268,X_5268),X_5268)) )],[refute_0_270,refute_0_196]) ).
cnf(refute_0_272,plain,
or(not(X),not(X)) = not(X),
inference(subst,[],[refute_0_271:[bind(X_5268,$fot(not(X)))]]) ).
cnf(refute_0_273,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) != not(X)
| implies(X,not(X)) = not(X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(X)),not(X)) ),[0],$fot(or(not(X),not(X)))]]) ).
cnf(refute_0_274,plain,
( implies(X,not(X)) != or(not(X),not(X))
| implies(X,not(X)) = not(X) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(X)) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
implies(X,not(X)) = not(X),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_192,refute_0_274]) ).
cnf(refute_0_276,plain,
implies(Y,not(Y)) = not(Y),
inference(subst,[],[refute_0_275:[bind(X,$fot(Y))]]) ).
cnf(refute_0_277,plain,
( and(Y,Y) != not(implies(Y,not(Y)))
| implies(Y,not(Y)) != not(Y)
| and(Y,Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(Y,Y),not(implies(Y,not(Y)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_278,plain,
( and(Y,Y) != not(implies(Y,not(Y)))
| and(Y,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(Y,not(Y)),not(Y)) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
and(Y,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(and(Y,Y),not(implies(Y,not(Y)))) )],[refute_0_191,refute_0_278]) ).
cnf(refute_0_280,plain,
and(not(X_13),not(X_13)) = not(not(not(X_13))),
inference(subst,[],[refute_0_279:[bind(Y,$fot(not(X_13)))]]) ).
cnf(refute_0_281,plain,
( and(not(X_13),not(X_13)) != not(not(not(X_13)))
| or(and(not(X_13),not(X_13)),Y) != not(and(or(X_13,X_13),not(Y)))
| or(not(not(not(X_13))),Y) = not(and(or(X_13,X_13),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_13),not(X_13)),Y),not(and(or(X_13,X_13),not(Y)))) ),[0,0],$fot(not(not(not(X_13))))]]) ).
cnf(refute_0_282,plain,
( or(and(not(X_13),not(X_13)),Y) != not(and(or(X_13,X_13),not(Y)))
| or(not(not(not(X_13))),Y) = not(and(or(X_13,X_13),not(Y))) ),
inference(resolve,[$cnf( $equal(and(not(X_13),not(X_13)),not(not(not(X_13)))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
or(not(not(not(X_13))),Y) = not(and(or(X_13,X_13),not(Y))),
inference(resolve,[$cnf( $equal(or(and(not(X_13),not(X_13)),Y),not(and(or(X_13,X_13),not(Y)))) )],[refute_0_190,refute_0_282]) ).
cnf(refute_0_284,plain,
or(not(not(not(X_13))),Y) = implies(not(not(X_13)),Y),
inference(subst,[],[refute_0_55:[bind(X,$fot(not(not(X_13))))]]) ).
cnf(refute_0_285,plain,
( or(not(not(not(X_13))),Y) != implies(not(not(X_13)),Y)
| or(not(not(not(X_13))),Y) != not(and(or(X_13,X_13),not(Y)))
| implies(not(not(X_13)),Y) = not(and(or(X_13,X_13),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(not(not(X_13))),Y),not(and(or(X_13,X_13),not(Y)))) ),[0],$fot(implies(not(not(X_13)),Y))]]) ).
cnf(refute_0_286,plain,
( or(not(not(not(X_13))),Y) != not(and(or(X_13,X_13),not(Y)))
| implies(not(not(X_13)),Y) = not(and(or(X_13,X_13),not(Y))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(X_13))),Y),implies(not(not(X_13)),Y)) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
or(X_13,X_13) = X_13,
inference(subst,[],[refute_0_271:[bind(X_5268,$fot(X_13))]]) ).
cnf(refute_0_288,plain,
and(or(X_13,X_13),not(Y)) = and(or(X_13,X_13),not(Y)),
introduced(tautology,[refl,[$fot(and(or(X_13,X_13),not(Y)))]]) ).
cnf(refute_0_289,plain,
( and(or(X_13,X_13),not(Y)) != and(or(X_13,X_13),not(Y))
| or(X_13,X_13) != X_13
| and(or(X_13,X_13),not(Y)) = and(X_13,not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(X_13,X_13),not(Y)),and(or(X_13,X_13),not(Y))) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_290,plain,
( or(X_13,X_13) != X_13
| and(or(X_13,X_13),not(Y)) = and(X_13,not(Y)) ),
inference(resolve,[$cnf( $equal(and(or(X_13,X_13),not(Y)),and(or(X_13,X_13),not(Y))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
and(or(X_13,X_13),not(Y)) = and(X_13,not(Y)),
inference(resolve,[$cnf( $equal(or(X_13,X_13),X_13) )],[refute_0_287,refute_0_290]) ).
cnf(refute_0_292,plain,
not(and(or(X_13,X_13),not(Y))) = not(and(or(X_13,X_13),not(Y))),
introduced(tautology,[refl,[$fot(not(and(or(X_13,X_13),not(Y))))]]) ).
cnf(refute_0_293,plain,
( and(or(X_13,X_13),not(Y)) != and(X_13,not(Y))
| not(and(or(X_13,X_13),not(Y))) != not(and(or(X_13,X_13),not(Y)))
| not(and(or(X_13,X_13),not(Y))) = not(and(X_13,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(X_13,X_13),not(Y))),not(and(or(X_13,X_13),not(Y)))) ),[1,0],$fot(and(X_13,not(Y)))]]) ).
cnf(refute_0_294,plain,
( and(or(X_13,X_13),not(Y)) != and(X_13,not(Y))
| not(and(or(X_13,X_13),not(Y))) = not(and(X_13,not(Y))) ),
inference(resolve,[$cnf( $equal(not(and(or(X_13,X_13),not(Y))),not(and(or(X_13,X_13),not(Y)))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
not(and(or(X_13,X_13),not(Y))) = not(and(X_13,not(Y))),
inference(resolve,[$cnf( $equal(and(or(X_13,X_13),not(Y)),and(X_13,not(Y))) )],[refute_0_291,refute_0_294]) ).
cnf(refute_0_296,plain,
( implies(not(not(X_13)),Y) != not(and(or(X_13,X_13),not(Y)))
| not(and(or(X_13,X_13),not(Y))) != not(and(X_13,not(Y)))
| implies(not(not(X_13)),Y) = not(and(X_13,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(X_13)),Y),not(and(X_13,not(Y)))) ),[0],$fot(not(and(or(X_13,X_13),not(Y))))]]) ).
cnf(refute_0_297,plain,
( implies(not(not(X_13)),Y) != not(and(or(X_13,X_13),not(Y)))
| implies(not(not(X_13)),Y) = not(and(X_13,not(Y))) ),
inference(resolve,[$cnf( $equal(not(and(or(X_13,X_13),not(Y))),not(and(X_13,not(Y)))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
( or(not(not(not(X_13))),Y) != not(and(or(X_13,X_13),not(Y)))
| implies(not(not(X_13)),Y) = not(and(X_13,not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_13)),Y),not(and(or(X_13,X_13),not(Y)))) )],[refute_0_286,refute_0_297]) ).
cnf(refute_0_299,plain,
implies(not(not(X_13)),Y) = not(and(X_13,not(Y))),
inference(resolve,[$cnf( $equal(or(not(not(not(X_13))),Y),not(and(or(X_13,X_13),not(Y)))) )],[refute_0_283,refute_0_298]) ).
cnf(refute_0_300,plain,
implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53))) = not(and(implies(not(X_2157),or(X_52,X_53)),not(or(X_2157,or(X_52,X_53))))),
inference(subst,[],[refute_0_299:[bind(Y,$fot(or(X_2157,or(X_52,X_53)))),bind(X_13,$fot(implies(not(X_2157),or(X_52,X_53))))]]) ).
cnf(refute_0_301,plain,
( implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53))) != not(and(implies(not(X_2157),or(X_52,X_53)),not(or(X_2157,or(X_52,X_53)))))
| ~ is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53))))
| is_a_theorem(not(and(implies(not(X_2157),or(X_52,X_53)),not(or(X_2157,or(X_52,X_53)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53)))) ),[0],$fot(not(and(implies(not(X_2157),or(X_52,X_53)),not(or(X_2157,or(X_52,X_53))))))]]) ).
cnf(refute_0_302,plain,
( ~ is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53))))
| is_a_theorem(not(and(implies(not(X_2157),or(X_52,X_53)),not(or(X_2157,or(X_52,X_53)))))) ),
inference(resolve,[$cnf( $equal(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53))),not(and(implies(not(X_2157),or(X_52,X_53)),not(or(X_2157,or(X_52,X_53)))))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
is_a_theorem(not(and(implies(not(X_2157),or(X_52,X_53)),not(or(X_2157,or(X_52,X_53)))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(X_2157),or(X_52,X_53)))),or(X_2157,or(X_52,X_53)))) )],[refute_0_185,refute_0_302]) ).
cnf(refute_0_304,plain,
is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,or(X_6301,X_6301)))))),
inference(subst,[],[refute_0_303:[bind(X_2157,$fot(X_6299)),bind(X_52,$fot(X_6301)),bind(X_53,$fot(X_6301))]]) ).
cnf(refute_0_305,plain,
or(X_6301,X_6301) = X_6301,
inference(subst,[],[refute_0_271:[bind(X_5268,$fot(X_6301))]]) ).
cnf(refute_0_306,plain,
( or(X_6301,X_6301) != X_6301
| ~ is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,or(X_6301,X_6301))))))
| is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,or(X_6301,X_6301)))))) ),[0,0,1,0,1],$fot(X_6301)]]) ).
cnf(refute_0_307,plain,
( ~ is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,or(X_6301,X_6301))))))
| is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))))) ),
inference(resolve,[$cnf( $equal(or(X_6301,X_6301),X_6301) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,or(X_6301,X_6301)))))) )],[refute_0_304,refute_0_307]) ).
cnf(refute_0_309,plain,
implies(not(X_6299),or(X_6301,X_6301)) = implies(not(X_6299),or(X_6301,X_6301)),
introduced(tautology,[refl,[$fot(implies(not(X_6299),or(X_6301,X_6301)))]]) ).
cnf(refute_0_310,plain,
( implies(not(X_6299),or(X_6301,X_6301)) != implies(not(X_6299),or(X_6301,X_6301))
| or(X_6301,X_6301) != X_6301
| implies(not(X_6299),or(X_6301,X_6301)) = implies(not(X_6299),X_6301) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_6299),or(X_6301,X_6301)),implies(not(X_6299),or(X_6301,X_6301))) ),[1,1],$fot(X_6301)]]) ).
cnf(refute_0_311,plain,
( or(X_6301,X_6301) != X_6301
| implies(not(X_6299),or(X_6301,X_6301)) = implies(not(X_6299),X_6301) ),
inference(resolve,[$cnf( $equal(implies(not(X_6299),or(X_6301,X_6301)),implies(not(X_6299),or(X_6301,X_6301))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
implies(not(X_6299),or(X_6301,X_6301)) = implies(not(X_6299),X_6301),
inference(resolve,[$cnf( $equal(or(X_6301,X_6301),X_6301) )],[refute_0_305,refute_0_311]) ).
cnf(refute_0_313,plain,
and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))) = and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))),
introduced(tautology,[refl,[$fot(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))))]]) ).
cnf(refute_0_314,plain,
( and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))) != and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))
| implies(not(X_6299),or(X_6301,X_6301)) != implies(not(X_6299),X_6301)
| and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))) = and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301))) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))),and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))) ),[1,0],$fot(implies(not(X_6299),X_6301))]]) ).
cnf(refute_0_315,plain,
( implies(not(X_6299),or(X_6301,X_6301)) != implies(not(X_6299),X_6301)
| and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))) = and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301))) ),
inference(resolve,[$cnf( $equal(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))),and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))) = and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301))),
inference(resolve,[$cnf( $equal(implies(not(X_6299),or(X_6301,X_6301)),implies(not(X_6299),X_6301)) )],[refute_0_312,refute_0_315]) ).
cnf(refute_0_317,plain,
not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))) = not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))),
introduced(tautology,[refl,[$fot(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))))]]) ).
cnf(refute_0_318,plain,
( and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))) != and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301)))
| not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))) != not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))))
| not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))) = not(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))),not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))))) ),[1,0],$fot(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301))))]]) ).
cnf(refute_0_319,plain,
( and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))) != and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301)))
| not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))) = not(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301)))) ),
inference(resolve,[$cnf( $equal(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))),not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))) = not(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301)))),
inference(resolve,[$cnf( $equal(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))),and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301)))) )],[refute_0_316,refute_0_319]) ).
cnf(refute_0_321,plain,
( not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))) != not(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301))))
| ~ is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))))
| is_a_theorem(not(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))))) ),[0],$fot(not(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301)))))]]) ).
cnf(refute_0_322,plain,
( ~ is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))))
| is_a_theorem(not(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301))))) ),
inference(resolve,[$cnf( $equal(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301)))),not(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301))))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
is_a_theorem(not(and(implies(not(X_6299),X_6301),not(or(X_6299,X_6301))))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(not(X_6299),or(X_6301,X_6301)),not(or(X_6299,X_6301))))) )],[refute_0_308,refute_0_322]) ).
cnf(refute_0_324,plain,
is_a_theorem(not(and(implies(not(X_6302),not(implies(not(X_6302),X_6302))),not(or(X_6302,not(implies(not(X_6302),X_6302))))))),
inference(subst,[],[refute_0_323:[bind(X_6299,$fot(X_6302)),bind(X_6301,$fot(not(implies(not(X_6302),X_6302))))]]) ).
cnf(refute_0_325,plain,
or(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) = or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),
inference(subst,[],[refute_0_271:[bind(X_5268,$fot(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))]]) ).
cnf(refute_0_326,plain,
or(implies(X_14,not(X_15)),Y) = not(and(not(implies(X_14,not(X_15))),not(Y))),
inference(subst,[],[refute_0_91:[bind(X,$fot(implies(X_14,not(X_15))))]]) ).
cnf(refute_0_327,plain,
( not(implies(X_14,not(X_15))) != and(X_14,X_15)
| or(implies(X_14,not(X_15)),Y) != not(and(not(implies(X_14,not(X_15))),not(Y)))
| or(implies(X_14,not(X_15)),Y) = not(and(and(X_14,X_15),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_14,not(X_15)),Y),not(and(not(implies(X_14,not(X_15))),not(Y)))) ),[1,0,0],$fot(and(X_14,X_15))]]) ).
cnf(refute_0_328,plain,
( or(implies(X_14,not(X_15)),Y) != not(and(not(implies(X_14,not(X_15))),not(Y)))
| or(implies(X_14,not(X_15)),Y) = not(and(and(X_14,X_15),not(Y))) ),
inference(resolve,[$cnf( $equal(not(implies(X_14,not(X_15))),and(X_14,X_15)) )],[refute_0_143,refute_0_327]) ).
cnf(refute_0_329,plain,
or(implies(X_14,not(X_15)),Y) = not(and(and(X_14,X_15),not(Y))),
inference(resolve,[$cnf( $equal(or(implies(X_14,not(X_15)),Y),not(and(not(implies(X_14,not(X_15))),not(Y)))) )],[refute_0_326,refute_0_328]) ).
cnf(refute_0_330,plain,
or(implies(implies(X,Y),not(implies(Y,X))),X_127) = not(and(and(implies(X,Y),implies(Y,X)),not(X_127))),
inference(subst,[],[refute_0_329:[bind(Y,$fot(X_127)),bind(X_14,$fot(implies(X,Y))),bind(X_15,$fot(implies(Y,X)))]]) ).
cnf(refute_0_331,plain,
( equiv(X,Y) != and(implies(X,Y),implies(Y,X))
| and(implies(X,Y),implies(Y,X)) = equiv(X,Y) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_332,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_236,refute_0_331]) ).
cnf(refute_0_333,plain,
( and(implies(X,Y),implies(Y,X)) != equiv(X,Y)
| or(implies(implies(X,Y),not(implies(Y,X))),X_127) != not(and(and(implies(X,Y),implies(Y,X)),not(X_127)))
| or(implies(implies(X,Y),not(implies(Y,X))),X_127) = not(and(equiv(X,Y),not(X_127))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(implies(X,Y),not(implies(Y,X))),X_127),not(and(and(implies(X,Y),implies(Y,X)),not(X_127)))) ),[1,0,0],$fot(equiv(X,Y))]]) ).
cnf(refute_0_334,plain,
( or(implies(implies(X,Y),not(implies(Y,X))),X_127) != not(and(and(implies(X,Y),implies(Y,X)),not(X_127)))
| or(implies(implies(X,Y),not(implies(Y,X))),X_127) = not(and(equiv(X,Y),not(X_127))) ),
inference(resolve,[$cnf( $equal(and(implies(X,Y),implies(Y,X)),equiv(X,Y)) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
or(implies(implies(X,Y),not(implies(Y,X))),X_127) = not(and(equiv(X,Y),not(X_127))),
inference(resolve,[$cnf( $equal(or(implies(implies(X,Y),not(implies(Y,X))),X_127),not(and(and(implies(X,Y),implies(Y,X)),not(X_127)))) )],[refute_0_330,refute_0_334]) ).
cnf(refute_0_336,plain,
or(implies(implies(X_1004,not(X_15)),not(implies(not(X_15),X_1004))),X_1006) = not(and(equiv(X_1004,not(X_15)),not(X_1006))),
inference(subst,[],[refute_0_335:[bind(X,$fot(X_1004)),bind(Y,$fot(not(X_15))),bind(X_127,$fot(X_1006))]]) ).
cnf(refute_0_337,plain,
implies(implies(X_1004,not(X_15)),not(implies(not(X_15),X_1004))) = or(and(X_1004,X_15),not(implies(not(X_15),X_1004))),
inference(subst,[],[refute_0_219:[bind(Y,$fot(not(implies(not(X_15),X_1004)))),bind(X_14,$fot(X_1004))]]) ).
cnf(refute_0_338,plain,
( implies(implies(X_1004,not(X_15)),not(implies(not(X_15),X_1004))) != or(and(X_1004,X_15),not(implies(not(X_15),X_1004)))
| or(implies(implies(X_1004,not(X_15)),not(implies(not(X_15),X_1004))),X_1006) != not(and(equiv(X_1004,not(X_15)),not(X_1006)))
| or(or(and(X_1004,X_15),not(implies(not(X_15),X_1004))),X_1006) = not(and(equiv(X_1004,not(X_15)),not(X_1006))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(implies(X_1004,not(X_15)),not(implies(not(X_15),X_1004))),X_1006),not(and(equiv(X_1004,not(X_15)),not(X_1006)))) ),[0,0],$fot(or(and(X_1004,X_15),not(implies(not(X_15),X_1004))))]]) ).
cnf(refute_0_339,plain,
( or(implies(implies(X_1004,not(X_15)),not(implies(not(X_15),X_1004))),X_1006) != not(and(equiv(X_1004,not(X_15)),not(X_1006)))
| or(or(and(X_1004,X_15),not(implies(not(X_15),X_1004))),X_1006) = not(and(equiv(X_1004,not(X_15)),not(X_1006))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_1004,not(X_15)),not(implies(not(X_15),X_1004))),or(and(X_1004,X_15),not(implies(not(X_15),X_1004)))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
or(or(and(X_1004,X_15),not(implies(not(X_15),X_1004))),X_1006) = not(and(equiv(X_1004,not(X_15)),not(X_1006))),
inference(resolve,[$cnf( $equal(or(implies(implies(X_1004,not(X_15)),not(implies(not(X_15),X_1004))),X_1006),not(and(equiv(X_1004,not(X_15)),not(X_1006)))) )],[refute_0_336,refute_0_339]) ).
cnf(refute_0_341,plain,
or(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) = not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))),
inference(subst,[],[refute_0_340:[bind(X_1004,$fot(X_5912)),bind(X_1006,$fot(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))),bind(X_15,$fot(X_5914))]]) ).
cnf(refute_0_342,plain,
( or(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) != not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))))
| or(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) != or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))
| not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) = or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) ),[0],$fot(not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))))]]) ).
cnf(refute_0_343,plain,
( or(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) != or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))
| not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) = or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))) ),
inference(resolve,[$cnf( $equal(or(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))),not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) = or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),
inference(resolve,[$cnf( $equal(or(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) )],[refute_0_325,refute_0_343]) ).
cnf(refute_0_345,plain,
and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914))) = not(not(equiv(X_5912,not(X_5914)))),
inference(subst,[],[refute_0_279:[bind(Y,$fot(equiv(X_5912,not(X_5914))))]]) ).
cnf(refute_0_346,plain,
and(implies(X_5912,not(X_5914)),implies(not(X_5914),X_5912)) = equiv(X_5912,not(X_5914)),
inference(subst,[],[refute_0_332:[bind(X,$fot(X_5912)),bind(Y,$fot(not(X_5914)))]]) ).
cnf(refute_0_347,plain,
and(implies(X_32,not(X_33)),Y) = not(implies(implies(X_32,not(X_33)),not(Y))),
inference(subst,[],[refute_0_140:[bind(X,$fot(implies(X_32,not(X_33))))]]) ).
cnf(refute_0_348,plain,
implies(implies(X_32,not(X_33)),not(Y)) = or(and(X_32,X_33),not(Y)),
inference(subst,[],[refute_0_219:[bind(Y,$fot(not(Y))),bind(X_14,$fot(X_32)),bind(X_15,$fot(X_33))]]) ).
cnf(refute_0_349,plain,
( and(implies(X_32,not(X_33)),Y) != not(implies(implies(X_32,not(X_33)),not(Y)))
| implies(implies(X_32,not(X_33)),not(Y)) != or(and(X_32,X_33),not(Y))
| and(implies(X_32,not(X_33)),Y) = not(or(and(X_32,X_33),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_32,not(X_33)),Y),not(implies(implies(X_32,not(X_33)),not(Y)))) ),[1,0],$fot(or(and(X_32,X_33),not(Y)))]]) ).
cnf(refute_0_350,plain,
( and(implies(X_32,not(X_33)),Y) != not(implies(implies(X_32,not(X_33)),not(Y)))
| and(implies(X_32,not(X_33)),Y) = not(or(and(X_32,X_33),not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_32,not(X_33)),not(Y)),or(and(X_32,X_33),not(Y))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
and(implies(X_32,not(X_33)),Y) = not(or(and(X_32,X_33),not(Y))),
inference(resolve,[$cnf( $equal(and(implies(X_32,not(X_33)),Y),not(implies(implies(X_32,not(X_33)),not(Y)))) )],[refute_0_347,refute_0_350]) ).
cnf(refute_0_352,plain,
( and(implies(X_32,not(X_33)),Y) != not(or(and(X_32,X_33),not(Y)))
| not(or(and(X_32,X_33),not(Y))) = and(implies(X_32,not(X_33)),Y) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(and(implies(X_32,not(X_33)),Y))),bind(Y0,$fot(not(or(and(X_32,X_33),not(Y)))))]]) ).
cnf(refute_0_353,plain,
not(or(and(X_32,X_33),not(Y))) = and(implies(X_32,not(X_33)),Y),
inference(resolve,[$cnf( $equal(and(implies(X_32,not(X_33)),Y),not(or(and(X_32,X_33),not(Y)))) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) = and(implies(X_5912,not(X_5914)),implies(not(X_5914),X_5912)),
inference(subst,[],[refute_0_353:[bind(Y,$fot(implies(not(X_5914),X_5912))),bind(X_32,$fot(X_5912)),bind(X_33,$fot(X_5914))]]) ).
cnf(refute_0_355,plain,
( and(implies(X_5912,not(X_5914)),implies(not(X_5914),X_5912)) != equiv(X_5912,not(X_5914))
| not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) != and(implies(X_5912,not(X_5914)),implies(not(X_5914),X_5912))
| not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) = equiv(X_5912,not(X_5914)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))),bind(Y0,$fot(and(implies(X_5912,not(X_5914)),implies(not(X_5914),X_5912)))),bind(Z,$fot(equiv(X_5912,not(X_5914))))]]) ).
cnf(refute_0_356,plain,
( and(implies(X_5912,not(X_5914)),implies(not(X_5914),X_5912)) != equiv(X_5912,not(X_5914))
| not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) = equiv(X_5912,not(X_5914)) ),
inference(resolve,[$cnf( $equal(not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))),and(implies(X_5912,not(X_5914)),implies(not(X_5914),X_5912))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) = equiv(X_5912,not(X_5914)),
inference(resolve,[$cnf( $equal(and(implies(X_5912,not(X_5914)),implies(not(X_5914),X_5912)),equiv(X_5912,not(X_5914))) )],[refute_0_346,refute_0_356]) ).
cnf(refute_0_358,plain,
and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) = and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))),
introduced(tautology,[refl,[$fot(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))))]]) ).
cnf(refute_0_359,plain,
( and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) != and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))
| not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) != equiv(X_5912,not(X_5914))
| and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) = and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914))) ),
introduced(tautology,[equality,[$cnf( $equal(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))),and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) ),[1,1],$fot(equiv(X_5912,not(X_5914)))]]) ).
cnf(refute_0_360,plain,
( not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) != equiv(X_5912,not(X_5914))
| and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) = and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914))) ),
inference(resolve,[$cnf( $equal(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))),and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) = and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914))),
inference(resolve,[$cnf( $equal(not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))),equiv(X_5912,not(X_5914))) )],[refute_0_357,refute_0_360]) ).
cnf(refute_0_362,plain,
( and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914))) != not(not(equiv(X_5912,not(X_5914))))
| and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) != and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914)))
| and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) = not(not(equiv(X_5912,not(X_5914)))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))))),bind(Y0,$fot(and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914))))),bind(Z,$fot(not(not(equiv(X_5912,not(X_5914))))))]]) ).
cnf(refute_0_363,plain,
( and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914))) != not(not(equiv(X_5912,not(X_5914))))
| and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) = not(not(equiv(X_5912,not(X_5914)))) ),
inference(resolve,[$cnf( $equal(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))),and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914)))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) = not(not(equiv(X_5912,not(X_5914)))),
inference(resolve,[$cnf( $equal(and(equiv(X_5912,not(X_5914)),equiv(X_5912,not(X_5914))),not(not(equiv(X_5912,not(X_5914))))) )],[refute_0_345,refute_0_363]) ).
cnf(refute_0_365,plain,
not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) = not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))),
introduced(tautology,[refl,[$fot(not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))))]]) ).
cnf(refute_0_366,plain,
( and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) != not(not(equiv(X_5912,not(X_5914))))
| not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) != not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))))
| not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) = not(not(not(equiv(X_5912,not(X_5914))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))),not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))))) ),[1,0],$fot(not(not(equiv(X_5912,not(X_5914)))))]]) ).
cnf(refute_0_367,plain,
( and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))) != not(not(equiv(X_5912,not(X_5914))))
| not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) = not(not(not(equiv(X_5912,not(X_5914))))) ),
inference(resolve,[$cnf( $equal(not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))),not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) = not(not(not(equiv(X_5912,not(X_5914))))),
inference(resolve,[$cnf( $equal(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))))),not(not(equiv(X_5912,not(X_5914))))) )],[refute_0_364,refute_0_367]) ).
cnf(refute_0_369,plain,
( not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) != not(not(not(equiv(X_5912,not(X_5914)))))
| not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) != or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))
| not(not(not(equiv(X_5912,not(X_5914))))) = or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) ),[0],$fot(not(not(not(equiv(X_5912,not(X_5914))))))]]) ).
cnf(refute_0_370,plain,
( not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))) != or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))
| not(not(not(equiv(X_5912,not(X_5914))))) = or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))) ),
inference(resolve,[$cnf( $equal(not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))),not(not(not(equiv(X_5912,not(X_5914)))))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
not(not(not(equiv(X_5912,not(X_5914))))) = or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912))),
inference(resolve,[$cnf( $equal(not(and(equiv(X_5912,not(X_5914)),not(or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))))),or(and(X_5912,X_5914),not(implies(not(X_5914),X_5912)))) )],[refute_0_344,refute_0_370]) ).
cnf(refute_0_372,plain,
not(not(not(equiv(X_5916,not(X_5916))))) = or(and(X_5916,X_5916),not(implies(not(X_5916),X_5916))),
inference(subst,[],[refute_0_371:[bind(X_5912,$fot(X_5916)),bind(X_5914,$fot(X_5916))]]) ).
cnf(refute_0_373,plain,
and(X_5916,X_5916) = not(not(X_5916)),
inference(subst,[],[refute_0_279:[bind(Y,$fot(X_5916))]]) ).
cnf(refute_0_374,plain,
( and(X_5916,X_5916) != not(not(X_5916))
| not(not(not(equiv(X_5916,not(X_5916))))) != or(and(X_5916,X_5916),not(implies(not(X_5916),X_5916)))
| not(not(not(equiv(X_5916,not(X_5916))))) = or(not(not(X_5916)),not(implies(not(X_5916),X_5916))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(equiv(X_5916,not(X_5916))))),or(and(X_5916,X_5916),not(implies(not(X_5916),X_5916)))) ),[1,0],$fot(not(not(X_5916)))]]) ).
cnf(refute_0_375,plain,
( not(not(not(equiv(X_5916,not(X_5916))))) != or(and(X_5916,X_5916),not(implies(not(X_5916),X_5916)))
| not(not(not(equiv(X_5916,not(X_5916))))) = or(not(not(X_5916)),not(implies(not(X_5916),X_5916))) ),
inference(resolve,[$cnf( $equal(and(X_5916,X_5916),not(not(X_5916))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
not(not(not(equiv(X_5916,not(X_5916))))) = or(not(not(X_5916)),not(implies(not(X_5916),X_5916))),
inference(resolve,[$cnf( $equal(not(not(not(equiv(X_5916,not(X_5916))))),or(and(X_5916,X_5916),not(implies(not(X_5916),X_5916)))) )],[refute_0_372,refute_0_375]) ).
cnf(refute_0_377,plain,
or(not(not(X_5916)),not(implies(not(X_5916),X_5916))) = implies(not(X_5916),not(implies(not(X_5916),X_5916))),
inference(subst,[],[refute_0_55:[bind(X,$fot(not(X_5916))),bind(Y,$fot(not(implies(not(X_5916),X_5916))))]]) ).
cnf(refute_0_378,plain,
( not(not(not(equiv(X_5916,not(X_5916))))) != or(not(not(X_5916)),not(implies(not(X_5916),X_5916)))
| or(not(not(X_5916)),not(implies(not(X_5916),X_5916))) != implies(not(X_5916),not(implies(not(X_5916),X_5916)))
| not(not(not(equiv(X_5916,not(X_5916))))) = implies(not(X_5916),not(implies(not(X_5916),X_5916))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(not(not(equiv(X_5916,not(X_5916))))),implies(not(X_5916),not(implies(not(X_5916),X_5916)))) ),[0],$fot(or(not(not(X_5916)),not(implies(not(X_5916),X_5916))))]]) ).
cnf(refute_0_379,plain,
( not(not(not(equiv(X_5916,not(X_5916))))) != or(not(not(X_5916)),not(implies(not(X_5916),X_5916)))
| not(not(not(equiv(X_5916,not(X_5916))))) = implies(not(X_5916),not(implies(not(X_5916),X_5916))) ),
inference(resolve,[$cnf( $equal(or(not(not(X_5916)),not(implies(not(X_5916),X_5916))),implies(not(X_5916),not(implies(not(X_5916),X_5916)))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
not(not(not(equiv(X_5916,not(X_5916))))) = implies(not(X_5916),not(implies(not(X_5916),X_5916))),
inference(resolve,[$cnf( $equal(not(not(not(equiv(X_5916,not(X_5916))))),or(not(not(X_5916)),not(implies(not(X_5916),X_5916)))) )],[refute_0_376,refute_0_379]) ).
cnf(refute_0_381,plain,
not(not(not(equiv(X_6302,not(X_6302))))) = implies(not(X_6302),not(implies(not(X_6302),X_6302))),
inference(subst,[],[refute_0_380:[bind(X_5916,$fot(X_6302))]]) ).
cnf(refute_0_382,plain,
( not(not(not(equiv(X_6302,not(X_6302))))) != implies(not(X_6302),not(implies(not(X_6302),X_6302)))
| implies(not(X_6302),not(implies(not(X_6302),X_6302))) = not(not(not(equiv(X_6302,not(X_6302))))) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(not(not(not(equiv(X_6302,not(X_6302))))))),bind(Y0,$fot(implies(not(X_6302),not(implies(not(X_6302),X_6302)))))]]) ).
cnf(refute_0_383,plain,
implies(not(X_6302),not(implies(not(X_6302),X_6302))) = not(not(not(equiv(X_6302,not(X_6302))))),
inference(resolve,[$cnf( $equal(not(not(not(equiv(X_6302,not(X_6302))))),implies(not(X_6302),not(implies(not(X_6302),X_6302)))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
( implies(not(X_6302),not(implies(not(X_6302),X_6302))) != not(not(not(equiv(X_6302,not(X_6302)))))
| ~ is_a_theorem(not(and(implies(not(X_6302),not(implies(not(X_6302),X_6302))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))))
| is_a_theorem(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(implies(not(X_6302),not(implies(not(X_6302),X_6302))),not(or(X_6302,not(implies(not(X_6302),X_6302))))))) ),[0,0,0],$fot(not(not(not(equiv(X_6302,not(X_6302))))))]]) ).
cnf(refute_0_385,plain,
( ~ is_a_theorem(not(and(implies(not(X_6302),not(implies(not(X_6302),X_6302))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))))
| is_a_theorem(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302))))))) ),
inference(resolve,[$cnf( $equal(implies(not(X_6302),not(implies(not(X_6302),X_6302))),not(not(not(equiv(X_6302,not(X_6302)))))) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
is_a_theorem(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302))))))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(not(X_6302),not(implies(not(X_6302),X_6302))),not(or(X_6302,not(implies(not(X_6302),X_6302))))))) )],[refute_0_324,refute_0_385]) ).
cnf(refute_0_387,plain,
or(not(not(equiv(X_6302,not(X_6302)))),or(X_6302,not(implies(not(X_6302),X_6302)))) = implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302)))),
inference(subst,[],[refute_0_55:[bind(X,$fot(not(equiv(X_6302,not(X_6302))))),bind(Y,$fot(or(X_6302,not(implies(not(X_6302),X_6302)))))]]) ).
cnf(refute_0_388,plain,
not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))) = or(not(not(equiv(X_6302,not(X_6302)))),or(X_6302,not(implies(not(X_6302),X_6302)))),
inference(subst,[],[refute_0_150:[bind(X,$fot(not(not(equiv(X_6302,not(X_6302)))))),bind(Y,$fot(or(X_6302,not(implies(not(X_6302),X_6302)))))]]) ).
cnf(refute_0_389,plain,
( not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))) != or(not(not(equiv(X_6302,not(X_6302)))),or(X_6302,not(implies(not(X_6302),X_6302))))
| or(not(not(equiv(X_6302,not(X_6302)))),or(X_6302,not(implies(not(X_6302),X_6302)))) != implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302))))
| not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))) = implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302)))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))))),bind(Y0,$fot(or(not(not(equiv(X_6302,not(X_6302)))),or(X_6302,not(implies(not(X_6302),X_6302)))))),bind(Z,$fot(implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302))))))]]) ).
cnf(refute_0_390,plain,
( or(not(not(equiv(X_6302,not(X_6302)))),or(X_6302,not(implies(not(X_6302),X_6302)))) != implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302))))
| not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))) = implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302)))) ),
inference(resolve,[$cnf( $equal(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))),or(not(not(equiv(X_6302,not(X_6302)))),or(X_6302,not(implies(not(X_6302),X_6302))))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))) = implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302)))),
inference(resolve,[$cnf( $equal(or(not(not(equiv(X_6302,not(X_6302)))),or(X_6302,not(implies(not(X_6302),X_6302)))),implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302))))) )],[refute_0_387,refute_0_390]) ).
cnf(refute_0_392,plain,
( not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))) != implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302))))
| ~ is_a_theorem(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))))
| is_a_theorem(implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302))))))) ),[0],$fot(implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302)))))]]) ).
cnf(refute_0_393,plain,
( ~ is_a_theorem(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))))
| is_a_theorem(implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302))))) ),
inference(resolve,[$cnf( $equal(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302)))))),implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302))))) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
is_a_theorem(implies(not(equiv(X_6302,not(X_6302))),or(X_6302,not(implies(not(X_6302),X_6302))))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(not(equiv(X_6302,not(X_6302))))),not(or(X_6302,not(implies(not(X_6302),X_6302))))))) )],[refute_0_386,refute_0_393]) ).
cnf(refute_0_395,plain,
is_a_theorem(implies(not(equiv(X_7479,not(X_7479))),or(X_7479,not(implies(not(X_7479),X_7479))))),
inference(subst,[],[refute_0_394:[bind(X_6302,$fot(X_7479))]]) ).
cnf(refute_0_396,plain,
( ~ is_a_theorem(not(equiv(X_7479,not(X_7479))))
| is_a_theorem(or(X_7479,not(implies(not(X_7479),X_7479)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(equiv(X_7479,not(X_7479))),or(X_7479,not(implies(not(X_7479),X_7479))))) )],[refute_0_395,refute_0_12]) ).
cnf(refute_0_397,plain,
( ~ is_a_theorem(or(and(X_5277,not(not(X_5277))),not(X_5277)))
| is_a_theorem(or(not(X_5277),and(X_5277,not(not(X_5277))))) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(and(X_5277,not(not(X_5277))))),bind(Q,$fot(not(X_5277)))]]) ).
cnf(refute_0_398,plain,
is_a_theorem(implies(or(not(not(X_2148)),X_2148),or(not(not(X_2148)),not(not(X_2148))))),
inference(subst,[],[refute_0_127:[bind(X_2147,$fot(not(not(X_2148))))]]) ).
cnf(refute_0_399,plain,
or(not(not(X_2148)),not(not(X_2148))) = not(not(X_2148)),
inference(subst,[],[refute_0_271:[bind(X_5268,$fot(not(not(X_2148))))]]) ).
cnf(refute_0_400,plain,
( or(not(not(X_2148)),not(not(X_2148))) != not(not(X_2148))
| ~ is_a_theorem(implies(or(not(not(X_2148)),X_2148),or(not(not(X_2148)),not(not(X_2148)))))
| is_a_theorem(implies(or(not(not(X_2148)),X_2148),not(not(X_2148)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(not(X_2148)),X_2148),or(not(not(X_2148)),not(not(X_2148))))) ),[0,1],$fot(not(not(X_2148)))]]) ).
cnf(refute_0_401,plain,
( ~ is_a_theorem(implies(or(not(not(X_2148)),X_2148),or(not(not(X_2148)),not(not(X_2148)))))
| is_a_theorem(implies(or(not(not(X_2148)),X_2148),not(not(X_2148)))) ),
inference(resolve,[$cnf( $equal(or(not(not(X_2148)),not(not(X_2148))),not(not(X_2148))) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
is_a_theorem(implies(or(not(not(X_2148)),X_2148),not(not(X_2148)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(not(X_2148)),X_2148),or(not(not(X_2148)),not(not(X_2148))))) )],[refute_0_398,refute_0_401]) ).
cnf(refute_0_403,plain,
or(not(not(X_2148)),X_2148) = implies(not(X_2148),X_2148),
inference(subst,[],[refute_0_55:[bind(X,$fot(not(X_2148))),bind(Y,$fot(X_2148))]]) ).
cnf(refute_0_404,plain,
implies(or(not(not(X_2148)),X_2148),not(not(X_2148))) = implies(or(not(not(X_2148)),X_2148),not(not(X_2148))),
introduced(tautology,[refl,[$fot(implies(or(not(not(X_2148)),X_2148),not(not(X_2148))))]]) ).
cnf(refute_0_405,plain,
( implies(or(not(not(X_2148)),X_2148),not(not(X_2148))) != implies(or(not(not(X_2148)),X_2148),not(not(X_2148)))
| or(not(not(X_2148)),X_2148) != implies(not(X_2148),X_2148)
| implies(or(not(not(X_2148)),X_2148),not(not(X_2148))) = implies(implies(not(X_2148),X_2148),not(not(X_2148))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(not(X_2148)),X_2148),not(not(X_2148))),implies(or(not(not(X_2148)),X_2148),not(not(X_2148)))) ),[1,0],$fot(implies(not(X_2148),X_2148))]]) ).
cnf(refute_0_406,plain,
( or(not(not(X_2148)),X_2148) != implies(not(X_2148),X_2148)
| implies(or(not(not(X_2148)),X_2148),not(not(X_2148))) = implies(implies(not(X_2148),X_2148),not(not(X_2148))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(X_2148)),X_2148),not(not(X_2148))),implies(or(not(not(X_2148)),X_2148),not(not(X_2148)))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
implies(or(not(not(X_2148)),X_2148),not(not(X_2148))) = implies(implies(not(X_2148),X_2148),not(not(X_2148))),
inference(resolve,[$cnf( $equal(or(not(not(X_2148)),X_2148),implies(not(X_2148),X_2148)) )],[refute_0_403,refute_0_406]) ).
cnf(refute_0_408,plain,
( implies(or(not(not(X_2148)),X_2148),not(not(X_2148))) != implies(implies(not(X_2148),X_2148),not(not(X_2148)))
| ~ is_a_theorem(implies(or(not(not(X_2148)),X_2148),not(not(X_2148))))
| is_a_theorem(implies(implies(not(X_2148),X_2148),not(not(X_2148)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(not(X_2148)),X_2148),not(not(X_2148)))) ),[0],$fot(implies(implies(not(X_2148),X_2148),not(not(X_2148))))]]) ).
cnf(refute_0_409,plain,
( ~ is_a_theorem(implies(or(not(not(X_2148)),X_2148),not(not(X_2148))))
| is_a_theorem(implies(implies(not(X_2148),X_2148),not(not(X_2148)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(X_2148)),X_2148),not(not(X_2148))),implies(implies(not(X_2148),X_2148),not(not(X_2148)))) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
is_a_theorem(implies(implies(not(X_2148),X_2148),not(not(X_2148)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(not(X_2148)),X_2148),not(not(X_2148)))) )],[refute_0_402,refute_0_409]) ).
cnf(refute_0_411,plain,
is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(not(not(not(not(Y))))))),
inference(subst,[],[refute_0_410:[bind(X_2148,$fot(not(not(not(Y)))))]]) ).
cnf(refute_0_412,plain,
or(Y,Y) = not(and(not(Y),not(Y))),
inference(subst,[],[refute_0_91:[bind(X,$fot(Y))]]) ).
cnf(refute_0_413,plain,
and(not(Y),not(Y)) = not(not(not(Y))),
inference(subst,[],[refute_0_279:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_414,plain,
( and(not(Y),not(Y)) != not(not(not(Y)))
| or(Y,Y) != not(and(not(Y),not(Y)))
| or(Y,Y) = not(not(not(not(Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,Y),not(and(not(Y),not(Y)))) ),[1,0],$fot(not(not(not(Y))))]]) ).
cnf(refute_0_415,plain,
( or(Y,Y) != not(and(not(Y),not(Y)))
| or(Y,Y) = not(not(not(not(Y)))) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(not(not(Y)))) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
or(Y,Y) = not(not(not(not(Y)))),
inference(resolve,[$cnf( $equal(or(Y,Y),not(and(not(Y),not(Y)))) )],[refute_0_412,refute_0_415]) ).
cnf(refute_0_417,plain,
or(Y,Y) = Y,
inference(subst,[],[refute_0_271:[bind(X_5268,$fot(Y))]]) ).
cnf(refute_0_418,plain,
( or(Y,Y) != Y
| or(Y,Y) != not(not(not(not(Y))))
| Y = not(not(not(not(Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,Y),not(not(not(not(Y))))) ),[0],$fot(Y)]]) ).
cnf(refute_0_419,plain,
( or(Y,Y) != not(not(not(not(Y))))
| Y = not(not(not(not(Y)))) ),
inference(resolve,[$cnf( $equal(or(Y,Y),Y) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
Y = not(not(not(not(Y)))),
inference(resolve,[$cnf( $equal(or(Y,Y),not(not(not(not(Y))))) )],[refute_0_416,refute_0_419]) ).
cnf(refute_0_421,plain,
( Y != not(not(not(not(Y))))
| not(not(not(not(Y)))) = Y ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(Y)),bind(Y0,$fot(not(not(not(not(Y))))))]]) ).
cnf(refute_0_422,plain,
not(not(not(not(Y)))) = Y,
inference(resolve,[$cnf( $equal(Y,not(not(not(not(Y))))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
( not(not(not(not(Y)))) != Y
| ~ is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(not(not(not(not(Y)))))))
| is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(not(not(not(not(Y))))))) ),[0,1,0],$fot(Y)]]) ).
cnf(refute_0_424,plain,
( ~ is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(not(not(not(not(Y)))))))
| is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y))) ),
inference(resolve,[$cnf( $equal(not(not(not(not(Y)))),Y) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(not(not(not(not(Y))))))) )],[refute_0_411,refute_0_424]) ).
cnf(refute_0_426,plain,
not(and(not(and(Y,not(not(Y)))),not(not(Y)))) = or(and(Y,not(not(Y))),not(Y)),
inference(subst,[],[refute_0_150:[bind(X,$fot(and(Y,not(not(Y))))),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_427,plain,
implies(not(not(Y)),not(Y)) = not(and(Y,not(not(Y)))),
inference(subst,[],[refute_0_299:[bind(Y,$fot(not(Y))),bind(X_13,$fot(Y))]]) ).
cnf(refute_0_428,plain,
or(not(not(not(Y))),not(Y)) = implies(not(not(Y)),not(Y)),
inference(subst,[],[refute_0_55:[bind(X,$fot(not(not(Y)))),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_429,plain,
( implies(not(not(Y)),not(Y)) != not(and(Y,not(not(Y))))
| or(not(not(not(Y))),not(Y)) != implies(not(not(Y)),not(Y))
| or(not(not(not(Y))),not(Y)) = not(and(Y,not(not(Y)))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(or(not(not(not(Y))),not(Y)))),bind(Y0,$fot(implies(not(not(Y)),not(Y)))),bind(Z,$fot(not(and(Y,not(not(Y))))))]]) ).
cnf(refute_0_430,plain,
( implies(not(not(Y)),not(Y)) != not(and(Y,not(not(Y))))
| or(not(not(not(Y))),not(Y)) = not(and(Y,not(not(Y)))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(Y))),not(Y)),implies(not(not(Y)),not(Y))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
or(not(not(not(Y))),not(Y)) = not(and(Y,not(not(Y)))),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),not(Y)),not(and(Y,not(not(Y))))) )],[refute_0_427,refute_0_430]) ).
cnf(refute_0_432,plain,
and(or(not(not(not(Y))),not(Y)),not(not(Y))) = and(or(not(not(not(Y))),not(Y)),not(not(Y))),
introduced(tautology,[refl,[$fot(and(or(not(not(not(Y))),not(Y)),not(not(Y))))]]) ).
cnf(refute_0_433,plain,
( and(or(not(not(not(Y))),not(Y)),not(not(Y))) != and(or(not(not(not(Y))),not(Y)),not(not(Y)))
| or(not(not(not(Y))),not(Y)) != not(and(Y,not(not(Y))))
| and(or(not(not(not(Y))),not(Y)),not(not(Y))) = and(not(and(Y,not(not(Y)))),not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(not(not(not(Y))),not(Y)),not(not(Y))),and(or(not(not(not(Y))),not(Y)),not(not(Y)))) ),[1,0],$fot(not(and(Y,not(not(Y)))))]]) ).
cnf(refute_0_434,plain,
( or(not(not(not(Y))),not(Y)) != not(and(Y,not(not(Y))))
| and(or(not(not(not(Y))),not(Y)),not(not(Y))) = and(not(and(Y,not(not(Y)))),not(not(Y))) ),
inference(resolve,[$cnf( $equal(and(or(not(not(not(Y))),not(Y)),not(not(Y))),and(or(not(not(not(Y))),not(Y)),not(not(Y)))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
and(or(not(not(not(Y))),not(Y)),not(not(Y))) = and(not(and(Y,not(not(Y)))),not(not(Y))),
inference(resolve,[$cnf( $equal(or(not(not(not(Y))),not(Y)),not(and(Y,not(not(Y))))) )],[refute_0_431,refute_0_434]) ).
cnf(refute_0_436,plain,
not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) = not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))),
introduced(tautology,[refl,[$fot(not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))))]]) ).
cnf(refute_0_437,plain,
( and(or(not(not(not(Y))),not(Y)),not(not(Y))) != and(not(and(Y,not(not(Y)))),not(not(Y)))
| not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) != not(and(or(not(not(not(Y))),not(Y)),not(not(Y))))
| not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) = not(and(not(and(Y,not(not(Y)))),not(not(Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))),not(and(or(not(not(not(Y))),not(Y)),not(not(Y))))) ),[1,0],$fot(and(not(and(Y,not(not(Y)))),not(not(Y))))]]) ).
cnf(refute_0_438,plain,
( and(or(not(not(not(Y))),not(Y)),not(not(Y))) != and(not(and(Y,not(not(Y)))),not(not(Y)))
| not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) = not(and(not(and(Y,not(not(Y)))),not(not(Y)))) ),
inference(resolve,[$cnf( $equal(not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))),not(and(or(not(not(not(Y))),not(Y)),not(not(Y))))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) = not(and(not(and(Y,not(not(Y)))),not(not(Y)))),
inference(resolve,[$cnf( $equal(and(or(not(not(not(Y))),not(Y)),not(not(Y))),and(not(and(Y,not(not(Y)))),not(not(Y)))) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
( not(and(not(and(Y,not(not(Y)))),not(not(Y)))) != or(and(Y,not(not(Y))),not(Y))
| not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) != not(and(not(and(Y,not(not(Y)))),not(not(Y))))
| not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) = or(and(Y,not(not(Y))),not(Y)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))))),bind(Y0,$fot(not(and(not(and(Y,not(not(Y)))),not(not(Y)))))),bind(Z,$fot(or(and(Y,not(not(Y))),not(Y))))]]) ).
cnf(refute_0_441,plain,
( not(and(not(and(Y,not(not(Y)))),not(not(Y)))) != or(and(Y,not(not(Y))),not(Y))
| not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) = or(and(Y,not(not(Y))),not(Y)) ),
inference(resolve,[$cnf( $equal(not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))),not(and(not(and(Y,not(not(Y)))),not(not(Y))))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) = or(and(Y,not(not(Y))),not(Y)),
inference(resolve,[$cnf( $equal(not(and(not(and(Y,not(not(Y)))),not(not(Y)))),or(and(Y,not(not(Y))),not(Y))) )],[refute_0_426,refute_0_441]) ).
cnf(refute_0_443,plain,
or(and(not(not(not(not(Y)))),not(not(Y))),not(Y)) = not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))),
inference(subst,[],[refute_0_189:[bind(Y,$fot(not(Y))),bind(X_12,$fot(not(not(not(Y))))),bind(X_13,$fot(not(Y)))]]) ).
cnf(refute_0_444,plain,
implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) = or(and(not(not(not(not(Y)))),not(not(Y))),not(Y)),
inference(subst,[],[refute_0_219:[bind(Y,$fot(not(Y))),bind(X_14,$fot(not(not(not(not(Y)))))),bind(X_15,$fot(not(not(Y))))]]) ).
cnf(refute_0_445,plain,
( implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) != or(and(not(not(not(not(Y)))),not(not(Y))),not(Y))
| or(and(not(not(not(not(Y)))),not(not(Y))),not(Y)) != not(and(or(not(not(not(Y))),not(Y)),not(not(Y))))
| implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) = not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)))),bind(Y0,$fot(or(and(not(not(not(not(Y)))),not(not(Y))),not(Y)))),bind(Z,$fot(not(and(or(not(not(not(Y))),not(Y)),not(not(Y))))))]]) ).
cnf(refute_0_446,plain,
( or(and(not(not(not(not(Y)))),not(not(Y))),not(Y)) != not(and(or(not(not(not(Y))),not(Y)),not(not(Y))))
| implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) = not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)),or(and(not(not(not(not(Y)))),not(not(Y))),not(Y))) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) = not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))),
inference(resolve,[$cnf( $equal(or(and(not(not(not(not(Y)))),not(not(Y))),not(Y)),not(and(or(not(not(not(Y))),not(Y)),not(not(Y))))) )],[refute_0_443,refute_0_446]) ).
cnf(refute_0_448,plain,
( implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) != not(and(or(not(not(not(Y))),not(Y)),not(not(Y))))
| not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) != or(and(Y,not(not(Y))),not(Y))
| implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) = or(and(Y,not(not(Y))),not(Y)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)))),bind(Y0,$fot(not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))))),bind(Z,$fot(or(and(Y,not(not(Y))),not(Y))))]]) ).
cnf(refute_0_449,plain,
( not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))) != or(and(Y,not(not(Y))),not(Y))
| implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) = or(and(Y,not(not(Y))),not(Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)),not(and(or(not(not(not(Y))),not(Y)),not(not(Y))))) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) = or(and(Y,not(not(Y))),not(Y)),
inference(resolve,[$cnf( $equal(not(and(or(not(not(not(Y))),not(Y)),not(not(Y)))),or(and(Y,not(not(Y))),not(Y))) )],[refute_0_442,refute_0_449]) ).
cnf(refute_0_451,plain,
( implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)) != or(and(Y,not(not(Y))),not(Y))
| ~ is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)))
| is_a_theorem(or(and(Y,not(not(Y))),not(Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y))) ),[0],$fot(or(and(Y,not(not(Y))),not(Y)))]]) ).
cnf(refute_0_452,plain,
( ~ is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)))
| is_a_theorem(or(and(Y,not(not(Y))),not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y)),or(and(Y,not(not(Y))),not(Y))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
is_a_theorem(or(and(Y,not(not(Y))),not(Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(not(not(Y)))),not(not(not(Y)))),not(Y))) )],[refute_0_425,refute_0_452]) ).
cnf(refute_0_454,plain,
is_a_theorem(or(and(X_5277,not(not(X_5277))),not(X_5277))),
inference(subst,[],[refute_0_453:[bind(Y,$fot(X_5277))]]) ).
cnf(refute_0_455,plain,
is_a_theorem(or(not(X_5277),and(X_5277,not(not(X_5277))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_5277,not(not(X_5277))),not(X_5277))) )],[refute_0_454,refute_0_397]) ).
cnf(refute_0_456,plain,
or(not(X_5277),and(X_5277,not(not(X_5277)))) = implies(X_5277,and(X_5277,not(not(X_5277)))),
inference(subst,[],[refute_0_55:[bind(X,$fot(X_5277)),bind(Y,$fot(and(X_5277,not(not(X_5277)))))]]) ).
cnf(refute_0_457,plain,
( or(not(X_5277),and(X_5277,not(not(X_5277)))) != implies(X_5277,and(X_5277,not(not(X_5277))))
| ~ is_a_theorem(or(not(X_5277),and(X_5277,not(not(X_5277)))))
| is_a_theorem(implies(X_5277,and(X_5277,not(not(X_5277))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X_5277),and(X_5277,not(not(X_5277))))) ),[0],$fot(implies(X_5277,and(X_5277,not(not(X_5277)))))]]) ).
cnf(refute_0_458,plain,
( ~ is_a_theorem(or(not(X_5277),and(X_5277,not(not(X_5277)))))
| is_a_theorem(implies(X_5277,and(X_5277,not(not(X_5277))))) ),
inference(resolve,[$cnf( $equal(or(not(X_5277),and(X_5277,not(not(X_5277)))),implies(X_5277,and(X_5277,not(not(X_5277))))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
is_a_theorem(implies(X_5277,and(X_5277,not(not(X_5277))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_5277),and(X_5277,not(not(X_5277))))) )],[refute_0_455,refute_0_458]) ).
cnf(refute_0_460,plain,
is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(not(not(not(not(Y)))))))),
inference(subst,[],[refute_0_459:[bind(X_5277,$fot(not(not(not(Y)))))]]) ).
cnf(refute_0_461,plain,
( not(not(not(not(Y)))) != Y
| ~ is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(not(not(not(not(Y))))))))
| is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(not(not(not(not(Y)))))))) ),[0,1,1,0],$fot(Y)]]) ).
cnf(refute_0_462,plain,
( ~ is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(not(not(not(not(Y))))))))
| is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y)))) ),
inference(resolve,[$cnf( $equal(not(not(not(not(Y)))),Y) )],[refute_0_422,refute_0_461]) ).
cnf(refute_0_463,plain,
is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(not(not(not(not(Y)))))))) )],[refute_0_460,refute_0_462]) ).
cnf(refute_0_464,plain,
equiv(X,not(X)) = and(implies(X,not(X)),implies(not(X),X)),
inference(subst,[],[refute_0_236:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_465,plain,
( equiv(X,not(X)) != and(implies(X,not(X)),implies(not(X),X))
| implies(X,not(X)) != not(X)
| equiv(X,not(X)) = and(not(X),implies(not(X),X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,not(X)),and(implies(X,not(X)),implies(not(X),X))) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_466,plain,
( equiv(X,not(X)) != and(implies(X,not(X)),implies(not(X),X))
| equiv(X,not(X)) = and(not(X),implies(not(X),X)) ),
inference(resolve,[$cnf( $equal(implies(X,not(X)),not(X)) )],[refute_0_275,refute_0_465]) ).
cnf(refute_0_467,plain,
equiv(X,not(X)) = and(not(X),implies(not(X),X)),
inference(resolve,[$cnf( $equal(equiv(X,not(X)),and(implies(X,not(X)),implies(not(X),X))) )],[refute_0_464,refute_0_466]) ).
cnf(refute_0_468,plain,
( equiv(X,not(X)) != and(not(X),implies(not(X),X))
| and(not(X),implies(not(X),X)) = equiv(X,not(X)) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(equiv(X,not(X)))),bind(Y0,$fot(and(not(X),implies(not(X),X))))]]) ).
cnf(refute_0_469,plain,
and(not(X),implies(not(X),X)) = equiv(X,not(X)),
inference(resolve,[$cnf( $equal(equiv(X,not(X)),and(not(X),implies(not(X),X))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
and(not(Y),implies(not(Y),Y)) = equiv(Y,not(Y)),
inference(subst,[],[refute_0_469:[bind(X,$fot(Y))]]) ).
cnf(refute_0_471,plain,
or(not(not(Y)),Y) = implies(not(Y),Y),
inference(subst,[],[refute_0_55:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_472,plain,
and(not(Y),or(not(not(Y)),Y)) = and(not(Y),or(not(not(Y)),Y)),
introduced(tautology,[refl,[$fot(and(not(Y),or(not(not(Y)),Y)))]]) ).
cnf(refute_0_473,plain,
( and(not(Y),or(not(not(Y)),Y)) != and(not(Y),or(not(not(Y)),Y))
| or(not(not(Y)),Y) != implies(not(Y),Y)
| and(not(Y),or(not(not(Y)),Y)) = and(not(Y),implies(not(Y),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(Y),or(not(not(Y)),Y)),and(not(Y),or(not(not(Y)),Y))) ),[1,1],$fot(implies(not(Y),Y))]]) ).
cnf(refute_0_474,plain,
( or(not(not(Y)),Y) != implies(not(Y),Y)
| and(not(Y),or(not(not(Y)),Y)) = and(not(Y),implies(not(Y),Y)) ),
inference(resolve,[$cnf( $equal(and(not(Y),or(not(not(Y)),Y)),and(not(Y),or(not(not(Y)),Y))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
and(not(Y),or(not(not(Y)),Y)) = and(not(Y),implies(not(Y),Y)),
inference(resolve,[$cnf( $equal(or(not(not(Y)),Y),implies(not(Y),Y)) )],[refute_0_471,refute_0_474]) ).
cnf(refute_0_476,plain,
( and(not(Y),implies(not(Y),Y)) != equiv(Y,not(Y))
| and(not(Y),or(not(not(Y)),Y)) != and(not(Y),implies(not(Y),Y))
| and(not(Y),or(not(not(Y)),Y)) = equiv(Y,not(Y)) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(and(not(Y),or(not(not(Y)),Y)))),bind(Y0,$fot(and(not(Y),implies(not(Y),Y)))),bind(Z,$fot(equiv(Y,not(Y))))]]) ).
cnf(refute_0_477,plain,
( and(not(Y),implies(not(Y),Y)) != equiv(Y,not(Y))
| and(not(Y),or(not(not(Y)),Y)) = equiv(Y,not(Y)) ),
inference(resolve,[$cnf( $equal(and(not(Y),or(not(not(Y)),Y)),and(not(Y),implies(not(Y),Y))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
and(not(Y),or(not(not(Y)),Y)) = equiv(Y,not(Y)),
inference(resolve,[$cnf( $equal(and(not(Y),implies(not(Y),Y)),equiv(Y,not(Y))) )],[refute_0_470,refute_0_477]) ).
cnf(refute_0_479,plain,
not(and(not(Y),or(not(not(Y)),Y))) = not(and(not(Y),or(not(not(Y)),Y))),
introduced(tautology,[refl,[$fot(not(and(not(Y),or(not(not(Y)),Y))))]]) ).
cnf(refute_0_480,plain,
( and(not(Y),or(not(not(Y)),Y)) != equiv(Y,not(Y))
| not(and(not(Y),or(not(not(Y)),Y))) != not(and(not(Y),or(not(not(Y)),Y)))
| not(and(not(Y),or(not(not(Y)),Y))) = not(equiv(Y,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(not(Y),or(not(not(Y)),Y))),not(and(not(Y),or(not(not(Y)),Y)))) ),[1,0],$fot(equiv(Y,not(Y)))]]) ).
cnf(refute_0_481,plain,
( and(not(Y),or(not(not(Y)),Y)) != equiv(Y,not(Y))
| not(and(not(Y),or(not(not(Y)),Y))) = not(equiv(Y,not(Y))) ),
inference(resolve,[$cnf( $equal(not(and(not(Y),or(not(not(Y)),Y))),not(and(not(Y),or(not(not(Y)),Y)))) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
not(and(not(Y),or(not(not(Y)),Y))) = not(equiv(Y,not(Y))),
inference(resolve,[$cnf( $equal(and(not(Y),or(not(not(Y)),Y)),equiv(Y,not(Y))) )],[refute_0_478,refute_0_481]) ).
cnf(refute_0_483,plain,
or(X,and(not(X_12),not(X_13))) = not(and(not(X),not(and(not(X_12),not(X_13))))),
inference(subst,[],[refute_0_91:[bind(Y,$fot(and(not(X_12),not(X_13))))]]) ).
cnf(refute_0_484,plain,
( not(and(not(X_12),not(X_13))) != or(X_12,X_13)
| or(X,and(not(X_12),not(X_13))) != not(and(not(X),not(and(not(X_12),not(X_13)))))
| or(X,and(not(X_12),not(X_13))) = not(and(not(X),or(X_12,X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,and(not(X_12),not(X_13))),not(and(not(X),not(and(not(X_12),not(X_13)))))) ),[1,0,1],$fot(or(X_12,X_13))]]) ).
cnf(refute_0_485,plain,
( or(X,and(not(X_12),not(X_13))) != not(and(not(X),not(and(not(X_12),not(X_13)))))
| or(X,and(not(X_12),not(X_13))) = not(and(not(X),or(X_12,X_13))) ),
inference(resolve,[$cnf( $equal(not(and(not(X_12),not(X_13))),or(X_12,X_13)) )],[refute_0_94,refute_0_484]) ).
cnf(refute_0_486,plain,
or(X,and(not(X_12),not(X_13))) = not(and(not(X),or(X_12,X_13))),
inference(resolve,[$cnf( $equal(or(X,and(not(X_12),not(X_13))),not(and(not(X),not(and(not(X_12),not(X_13)))))) )],[refute_0_483,refute_0_485]) ).
cnf(refute_0_487,plain,
or(Y,and(not(not(not(Y))),not(Y))) = not(and(not(Y),or(not(not(Y)),Y))),
inference(subst,[],[refute_0_486:[bind(X,$fot(Y)),bind(X_12,$fot(not(not(Y)))),bind(X_13,$fot(Y))]]) ).
cnf(refute_0_488,plain,
not(and(not(Y),not(and(not(not(not(Y))),not(Y))))) = or(Y,and(not(not(not(Y))),not(Y))),
inference(subst,[],[refute_0_150:[bind(X,$fot(Y)),bind(Y,$fot(and(not(not(not(Y))),not(Y))))]]) ).
cnf(refute_0_489,plain,
( not(and(not(Y),not(and(not(not(not(Y))),not(Y))))) != or(Y,and(not(not(not(Y))),not(Y)))
| or(Y,and(not(not(not(Y))),not(Y))) != not(and(not(Y),or(not(not(Y)),Y)))
| not(and(not(Y),not(and(not(not(not(Y))),not(Y))))) = not(and(not(Y),or(not(not(Y)),Y))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(not(and(not(Y),not(and(not(not(not(Y))),not(Y))))))),bind(Y0,$fot(or(Y,and(not(not(not(Y))),not(Y))))),bind(Z,$fot(not(and(not(Y),or(not(not(Y)),Y)))))]]) ).
cnf(refute_0_490,plain,
( or(Y,and(not(not(not(Y))),not(Y))) != not(and(not(Y),or(not(not(Y)),Y)))
| not(and(not(Y),not(and(not(not(not(Y))),not(Y))))) = not(and(not(Y),or(not(not(Y)),Y))) ),
inference(resolve,[$cnf( $equal(not(and(not(Y),not(and(not(not(not(Y))),not(Y))))),or(Y,and(not(not(not(Y))),not(Y)))) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
not(and(not(Y),not(and(not(not(not(Y))),not(Y))))) = not(and(not(Y),or(not(not(Y)),Y))),
inference(resolve,[$cnf( $equal(or(Y,and(not(not(not(Y))),not(Y))),not(and(not(Y),or(not(not(Y)),Y)))) )],[refute_0_487,refute_0_490]) ).
cnf(refute_0_492,plain,
implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) = not(and(not(Y),not(and(not(not(not(Y))),not(Y))))),
inference(subst,[],[refute_0_299:[bind(Y,$fot(and(not(not(not(Y))),not(Y)))),bind(X_13,$fot(not(Y)))]]) ).
cnf(refute_0_493,plain,
( implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) != not(and(not(Y),not(and(not(not(not(Y))),not(Y)))))
| not(and(not(Y),not(and(not(not(not(Y))),not(Y))))) != not(and(not(Y),or(not(not(Y)),Y)))
| implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) = not(and(not(Y),or(not(not(Y)),Y))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))))),bind(Y0,$fot(not(and(not(Y),not(and(not(not(not(Y))),not(Y))))))),bind(Z,$fot(not(and(not(Y),or(not(not(Y)),Y)))))]]) ).
cnf(refute_0_494,plain,
( not(and(not(Y),not(and(not(not(not(Y))),not(Y))))) != not(and(not(Y),or(not(not(Y)),Y)))
| implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) = not(and(not(Y),or(not(not(Y)),Y))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))),not(and(not(Y),not(and(not(not(not(Y))),not(Y)))))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) = not(and(not(Y),or(not(not(Y)),Y))),
inference(resolve,[$cnf( $equal(not(and(not(Y),not(and(not(not(not(Y))),not(Y))))),not(and(not(Y),or(not(not(Y)),Y)))) )],[refute_0_491,refute_0_494]) ).
cnf(refute_0_496,plain,
( implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) != not(and(not(Y),or(not(not(Y)),Y)))
| not(and(not(Y),or(not(not(Y)),Y))) != not(equiv(Y,not(Y)))
| implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) = not(equiv(Y,not(Y))) ),
inference(subst,[],[refute_0_171:[bind(X0,$fot(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))))),bind(Y0,$fot(not(and(not(Y),or(not(not(Y)),Y))))),bind(Z,$fot(not(equiv(Y,not(Y)))))]]) ).
cnf(refute_0_497,plain,
( not(and(not(Y),or(not(not(Y)),Y))) != not(equiv(Y,not(Y)))
| implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) = not(equiv(Y,not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))),not(and(not(Y),or(not(not(Y)),Y)))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) = not(equiv(Y,not(Y))),
inference(resolve,[$cnf( $equal(not(and(not(Y),or(not(not(Y)),Y))),not(equiv(Y,not(Y)))) )],[refute_0_482,refute_0_497]) ).
cnf(refute_0_499,plain,
( implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))) != not(equiv(Y,not(Y)))
| ~ is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))))
| is_a_theorem(not(equiv(Y,not(Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y)))) ),[0],$fot(not(equiv(Y,not(Y))))]]) ).
cnf(refute_0_500,plain,
( ~ is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))))
| is_a_theorem(not(equiv(Y,not(Y)))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y))),not(equiv(Y,not(Y)))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
is_a_theorem(not(equiv(Y,not(Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(Y))),and(not(not(not(Y))),not(Y)))) )],[refute_0_463,refute_0_500]) ).
cnf(refute_0_502,plain,
is_a_theorem(not(equiv(X_7479,not(X_7479)))),
inference(subst,[],[refute_0_501:[bind(Y,$fot(X_7479))]]) ).
cnf(refute_0_503,plain,
is_a_theorem(or(X_7479,not(implies(not(X_7479),X_7479)))),
inference(resolve,[$cnf( is_a_theorem(not(equiv(X_7479,not(X_7479)))) )],[refute_0_502,refute_0_396]) ).
cnf(refute_0_504,plain,
is_a_theorem(or(X_7480,not(implies(not(X_7480),X_7480)))),
inference(subst,[],[refute_0_503:[bind(X_7479,$fot(X_7480))]]) ).
cnf(refute_0_505,plain,
is_a_theorem(or(not(implies(not(X_7480),X_7480)),X_7480)),
inference(resolve,[$cnf( is_a_theorem(or(X_7480,not(implies(not(X_7480),X_7480)))) )],[refute_0_504,refute_0_11]) ).
cnf(refute_0_506,plain,
or(not(implies(not(X_7480),X_7480)),X_7480) = implies(implies(not(X_7480),X_7480),X_7480),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(not(X_7480),X_7480))),bind(Y,$fot(X_7480))]]) ).
cnf(refute_0_507,plain,
( or(not(implies(not(X_7480),X_7480)),X_7480) != implies(implies(not(X_7480),X_7480),X_7480)
| ~ is_a_theorem(or(not(implies(not(X_7480),X_7480)),X_7480))
| is_a_theorem(implies(implies(not(X_7480),X_7480),X_7480)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(implies(not(X_7480),X_7480)),X_7480)) ),[0],$fot(implies(implies(not(X_7480),X_7480),X_7480))]]) ).
cnf(refute_0_508,plain,
( ~ is_a_theorem(or(not(implies(not(X_7480),X_7480)),X_7480))
| is_a_theorem(implies(implies(not(X_7480),X_7480),X_7480)) ),
inference(resolve,[$cnf( $equal(or(not(implies(not(X_7480),X_7480)),X_7480),implies(implies(not(X_7480),X_7480),X_7480)) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
is_a_theorem(implies(implies(not(X_7480),X_7480),X_7480)),
inference(resolve,[$cnf( is_a_theorem(or(not(implies(not(X_7480),X_7480)),X_7480)) )],[refute_0_505,refute_0_508]) ).
cnf(refute_0_510,plain,
is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)),
inference(subst,[],[refute_0_509:[bind(X_7480,$fot(skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_511,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_510,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL498+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 14:13:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 22.78/22.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.78/22.99
% 22.78/22.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.89/23.07
%------------------------------------------------------------------------------