TSTP Solution File: LCL495+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL495+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:52:41 EDT 2022
% Result : Theorem 251.96s 252.17s
% Output : CNFRefutation 252.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 238
% Number of leaves : 515
% Syntax : Number of formulae : 2414 (1238 unt; 0 def)
% Number of atoms : 4100 (2742 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 3351 (1665 ~;1648 |; 15 &)
% ( 16 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 17 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 4831 ( 156 sgn 79 !; 17 ?)
% 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(equivalence_3,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ) ).
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_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(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(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
fof(hilbert_op_equiv,axiom,
op_equiv ).
fof(hilbert_equivalence_3,conjecture,
equivalence_3 ).
fof(subgoal_0,plain,
equivalence_3,
inference(strip,[],[hilbert_equivalence_3]) ).
fof(negate_0_0,plain,
~ equivalence_3,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ equivalence_3
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(canonicalize,[],[equivalence_3]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14),implies(implies(skolemFOFtoCNF_Y_14,skolemFOFtoCNF_X_14),equiv(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14))))
| equivalence_3 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14),implies(implies(skolemFOFtoCNF_Y_14,skolemFOFtoCNF_X_14),equiv(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14))))
| equivalence_3 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ equivalence_3,
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,
( ~ r2
<=> ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[r2]) ).
fof(normalize_0_13,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_12]) ).
fof(normalize_0_14,plain,
! [P,Q] :
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
r2,
inference(canonicalize,[],[principia_r2]) ).
fof(normalize_0_16,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_17,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_16]) ).
fof(normalize_0_18,plain,
! [P,Q,R] :
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
r4,
inference(canonicalize,[],[principia_r4]) ).
fof(normalize_0_20,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_23,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_26,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
op_equiv,
inference(canonicalize,[],[hilbert_op_equiv]) ).
fof(normalize_0_29,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_30,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_32,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_33,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_35,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_36,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_35]) ).
fof(normalize_0_37,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_39,plain,
( ~ r1
<=> ? [P] : ~ is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[r1]) ).
fof(normalize_0_40,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_39]) ).
fof(normalize_0_41,plain,
! [P] :
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(conjunct,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
r1,
inference(canonicalize,[],[principia_r1]) ).
fof(normalize_0_43,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_44,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_43]) ).
fof(normalize_0_45,plain,
! [P,Q,R] :
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(conjunct,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
r5,
inference(canonicalize,[],[principia_r5]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14),implies(implies(skolemFOFtoCNF_Y_14,skolemFOFtoCNF_X_14),equiv(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14))))
| equivalence_3 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ equivalence_3,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14),implies(implies(skolemFOFtoCNF_Y_14,skolemFOFtoCNF_X_14),equiv(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14)))),
inference(resolve,[$cnf( equivalence_3 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r3,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$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_4418,implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420)))))
| is_a_theorem(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_4418)),bind(Q,$fot(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420)))))]]) ).
cnf(refute_0_12,plain,
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
r2,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(Q,or(P,Q))),
inference(resolve,[$cnf( r2 )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(X_370,or(P,X_370))),
inference(subst,[],[refute_0_14:[bind(Q,$fot(X_370))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(X_370)
| ~ is_a_theorem(implies(X_370,or(P,X_370)))
| is_a_theorem(or(P,X_370)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_370)),bind(Y,$fot(or(P,X_370)))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(X_370)
| is_a_theorem(or(P,X_370)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_370,or(P,X_370))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(or(X_2230,X_2229),or(equiv(X_2229,not(X_2230)),and(X_2229,X_2230))))
| is_a_theorem(or(P,implies(or(X_2230,X_2229),or(equiv(X_2229,not(X_2230)),and(X_2229,X_2230))))) ),
inference(subst,[],[refute_0_17:[bind(X_370,$fot(implies(or(X_2230,X_2229),or(equiv(X_2229,not(X_2230)),and(X_2229,X_2230)))))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(or(X_1815,X_1814),or(X_1814,X_1815))),
inference(subst,[],[refute_0_5:[bind(P,$fot(X_1815)),bind(Q,$fot(X_1814))]]) ).
cnf(refute_0_20,plain,
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_21,plain,
r4,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))),
inference(resolve,[$cnf( r4 )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,or(not(X),X_69)))),
inference(subst,[],[refute_0_22:[bind(P,$fot(not(X))),bind(Q,$fot(X_68)),bind(R,$fot(X_69))]]) ).
cnf(refute_0_24,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_25,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_26,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
implies(X,X_69) = or(not(X),X_69),
inference(subst,[],[refute_0_26:[bind(Y,$fot(X_69))]]) ).
cnf(refute_0_28,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_29,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_30,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( implies(X,X_69) != or(not(X),X_69)
| or(not(X),X_69) = implies(X,X_69) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,X_69))),bind(Y0,$fot(or(not(X),X_69)))]]) ).
cnf(refute_0_32,plain,
or(not(X),X_69) = implies(X,X_69),
inference(resolve,[$cnf( $equal(implies(X,X_69),or(not(X),X_69)) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
( or(not(X),X_69) != implies(X,X_69)
| ~ is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,or(not(X),X_69))))
| is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,or(not(X),X_69)))) ),[0,1,1],$fot(implies(X,X_69))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,or(not(X),X_69))))
| is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_69),implies(X,X_69)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,or(not(X),X_69)))) )],[refute_0_23,refute_0_34]) ).
cnf(refute_0_36,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_37,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_26,refute_0_36]) ).
cnf(refute_0_38,plain,
or(not(X),or(X_68,X_69)) = implies(X,or(X_68,X_69)),
inference(subst,[],[refute_0_37:[bind(Y,$fot(or(X_68,X_69)))]]) ).
cnf(refute_0_39,plain,
implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))) = implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))))]]) ).
cnf(refute_0_40,plain,
( implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))) != implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69)))
| or(not(X),or(X_68,X_69)) != implies(X,or(X_68,X_69))
| implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))) = implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))),implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69)))) ),[1,0],$fot(implies(X,or(X_68,X_69)))]]) ).
cnf(refute_0_41,plain,
( or(not(X),or(X_68,X_69)) != implies(X,or(X_68,X_69))
| implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))) = implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))),implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))) = implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_68,X_69)),implies(X,or(X_68,X_69))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))) != implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69)))
| ~ is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))))
| is_a_theorem(implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69)))) ),[0],$fot(implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69))))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))))
| is_a_theorem(implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69))),implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69)))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_68,X_69)),or(X_68,implies(X,X_69)))) )],[refute_0_35,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(X,or(X_68,X_69)))
| ~ is_a_theorem(implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69))))
| is_a_theorem(or(X_68,implies(X,X_69))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X,or(X_68,X_69)))),bind(Y,$fot(or(X_68,implies(X,X_69))))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(X,or(X_68,X_69)))
| is_a_theorem(or(X_68,implies(X,X_69))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,or(X_68,X_69)),or(X_68,implies(X,X_69)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(or(X_1815,X_1814),or(X_1814,X_1815)))
| is_a_theorem(or(X_1814,implies(or(X_1815,X_1814),X_1815))) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(or(X_1815,X_1814))),bind(X_68,$fot(X_1814)),bind(X_69,$fot(X_1815))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(or(X_1814,implies(or(X_1815,X_1814),X_1815))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_1815,X_1814),or(X_1814,X_1815))) )],[refute_0_19,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(or(not(or(X_9,X)),implies(or(and(X,X_9),not(or(X_9,X))),and(X,X_9)))),
inference(subst,[],[refute_0_49:[bind(X_1814,$fot(not(or(X_9,X)))),bind(X_1815,$fot(and(X,X_9)))]]) ).
cnf(refute_0_51,plain,
implies(implies(X,not(Y)),X_18) = or(not(implies(X,not(Y))),X_18),
inference(subst,[],[refute_0_26:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_52,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_53,plain,
op_and,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_54,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_53,refute_0_52]) ).
cnf(refute_0_55,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_37:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_56,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_57,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_58,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_61,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_54,refute_0_61]) ).
cnf(refute_0_63,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_64,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( implies(implies(X,not(Y)),X_18) != or(not(implies(X,not(Y))),X_18)
| not(implies(X,not(Y))) != and(X,Y)
| implies(implies(X,not(Y)),X_18) = or(and(X,Y),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(Y)),X_18),or(not(implies(X,not(Y))),X_18)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_66,plain,
( implies(implies(X,not(Y)),X_18) != or(not(implies(X,not(Y))),X_18)
| implies(implies(X,not(Y)),X_18) = or(and(X,Y),X_18) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(implies(X,not(Y)),X_18) = or(and(X,Y),X_18),
inference(resolve,[$cnf( $equal(implies(implies(X,not(Y)),X_18),or(not(implies(X,not(Y))),X_18)) )],[refute_0_51,refute_0_66]) ).
cnf(refute_0_68,plain,
implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) = or(and(not(and(X,X_9)),or(X_9,X)),X_78),
inference(subst,[],[refute_0_67:[bind(X,$fot(not(and(X,X_9)))),bind(Y,$fot(or(X_9,X))),bind(X_18,$fot(X_78))]]) ).
cnf(refute_0_69,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_70,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_71,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_70,refute_0_69]) ).
cnf(refute_0_72,plain,
equiv(X,not(X_9)) = and(implies(X,not(X_9)),implies(not(X_9),X)),
inference(subst,[],[refute_0_71:[bind(Y,$fot(not(X_9)))]]) ).
cnf(refute_0_73,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_74,plain,
op_or,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_75,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_74,refute_0_73]) ).
cnf(refute_0_76,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_77,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_78,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_77,refute_0_76]) ).
cnf(refute_0_79,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_80,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_80:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_82,plain,
( not(and(not(X),not(Y))) != implies(not(X),Y)
| or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) ),[1],$fot(implies(not(X),Y))]]) ).
cnf(refute_0_83,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_75,refute_0_83]) ).
cnf(refute_0_85,plain,
or(X_9,X) = implies(not(X_9),X),
inference(subst,[],[refute_0_84:[bind(X,$fot(X_9)),bind(Y,$fot(X))]]) ).
cnf(refute_0_86,plain,
( or(X_9,X) != implies(not(X_9),X)
| implies(not(X_9),X) = or(X_9,X) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X_9,X))),bind(Y0,$fot(implies(not(X_9),X)))]]) ).
cnf(refute_0_87,plain,
implies(not(X_9),X) = or(X_9,X),
inference(resolve,[$cnf( $equal(or(X_9,X),implies(not(X_9),X)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( equiv(X,not(X_9)) != and(implies(X,not(X_9)),implies(not(X_9),X))
| implies(not(X_9),X) != or(X_9,X)
| equiv(X,not(X_9)) = and(implies(X,not(X_9)),or(X_9,X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,not(X_9)),and(implies(X,not(X_9)),implies(not(X_9),X))) ),[1,1],$fot(or(X_9,X))]]) ).
cnf(refute_0_89,plain,
( equiv(X,not(X_9)) != and(implies(X,not(X_9)),implies(not(X_9),X))
| equiv(X,not(X_9)) = and(implies(X,not(X_9)),or(X_9,X)) ),
inference(resolve,[$cnf( $equal(implies(not(X_9),X),or(X_9,X)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
equiv(X,not(X_9)) = and(implies(X,not(X_9)),or(X_9,X)),
inference(resolve,[$cnf( $equal(equiv(X,not(X_9)),and(implies(X,not(X_9)),implies(not(X_9),X))) )],[refute_0_72,refute_0_89]) ).
cnf(refute_0_91,plain,
and(not(X_9),Y) = not(implies(not(X_9),not(Y))),
inference(subst,[],[refute_0_62:[bind(X,$fot(not(X_9)))]]) ).
cnf(refute_0_92,plain,
or(X_9,not(Y)) = implies(not(X_9),not(Y)),
inference(subst,[],[refute_0_84:[bind(X,$fot(X_9)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_93,plain,
( or(X_9,not(Y)) != implies(not(X_9),not(Y))
| implies(not(X_9),not(Y)) = or(X_9,not(Y)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X_9,not(Y)))),bind(Y0,$fot(implies(not(X_9),not(Y))))]]) ).
cnf(refute_0_94,plain,
implies(not(X_9),not(Y)) = or(X_9,not(Y)),
inference(resolve,[$cnf( $equal(or(X_9,not(Y)),implies(not(X_9),not(Y))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( and(not(X_9),Y) != not(implies(not(X_9),not(Y)))
| implies(not(X_9),not(Y)) != or(X_9,not(Y))
| and(not(X_9),Y) = not(or(X_9,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X_9),Y),not(implies(not(X_9),not(Y)))) ),[1,0],$fot(or(X_9,not(Y)))]]) ).
cnf(refute_0_96,plain,
( and(not(X_9),Y) != not(implies(not(X_9),not(Y)))
| and(not(X_9),Y) = not(or(X_9,not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_9),not(Y)),or(X_9,not(Y))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
and(not(X_9),Y) = not(or(X_9,not(Y))),
inference(resolve,[$cnf( $equal(and(not(X_9),Y),not(implies(not(X_9),not(Y)))) )],[refute_0_91,refute_0_96]) ).
cnf(refute_0_98,plain,
and(not(not(X_17)),Y) = not(or(not(X_17),not(Y))),
inference(subst,[],[refute_0_97:[bind(X_9,$fot(not(X_17)))]]) ).
cnf(refute_0_99,plain,
implies(X_17,not(Y)) = or(not(X_17),not(Y)),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_17)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_100,plain,
( implies(X_17,not(Y)) != or(not(X_17),not(Y))
| or(not(X_17),not(Y)) = implies(X_17,not(Y)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X_17,not(Y)))),bind(Y0,$fot(or(not(X_17),not(Y))))]]) ).
cnf(refute_0_101,plain,
or(not(X_17),not(Y)) = implies(X_17,not(Y)),
inference(resolve,[$cnf( $equal(implies(X_17,not(Y)),or(not(X_17),not(Y))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( and(not(not(X_17)),Y) != not(or(not(X_17),not(Y)))
| or(not(X_17),not(Y)) != implies(X_17,not(Y))
| and(not(not(X_17)),Y) = not(implies(X_17,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_17)),Y),not(or(not(X_17),not(Y)))) ),[1,0],$fot(implies(X_17,not(Y)))]]) ).
cnf(refute_0_103,plain,
( and(not(not(X_17)),Y) != not(or(not(X_17),not(Y)))
| and(not(not(X_17)),Y) = not(implies(X_17,not(Y))) ),
inference(resolve,[$cnf( $equal(or(not(X_17),not(Y)),implies(X_17,not(Y))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
and(not(not(X_17)),Y) = not(implies(X_17,not(Y))),
inference(resolve,[$cnf( $equal(and(not(not(X_17)),Y),not(or(not(X_17),not(Y)))) )],[refute_0_98,refute_0_103]) ).
cnf(refute_0_105,plain,
not(implies(X_17,not(Y))) = and(X_17,Y),
inference(subst,[],[refute_0_64:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_106,plain,
( and(not(not(X_17)),Y) != not(implies(X_17,not(Y)))
| not(implies(X_17,not(Y))) != and(X_17,Y)
| and(not(not(X_17)),Y) = and(X_17,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(not(X_17)),Y),and(X_17,Y)) ),[0],$fot(not(implies(X_17,not(Y))))]]) ).
cnf(refute_0_107,plain,
( and(not(not(X_17)),Y) != not(implies(X_17,not(Y)))
| and(not(not(X_17)),Y) = and(X_17,Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_17,not(Y))),and(X_17,Y)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
and(not(not(X_17)),Y) = and(X_17,Y),
inference(resolve,[$cnf( $equal(and(not(not(X_17)),Y),not(implies(X_17,not(Y)))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
and(not(not(implies(X,not(Y)))),X_20) = and(implies(X,not(Y)),X_20),
inference(subst,[],[refute_0_108:[bind(Y,$fot(X_20)),bind(X_17,$fot(implies(X,not(Y))))]]) ).
cnf(refute_0_110,plain,
( and(not(not(implies(X,not(Y)))),X_20) != and(implies(X,not(Y)),X_20)
| not(implies(X,not(Y))) != and(X,Y)
| and(not(and(X,Y)),X_20) = and(implies(X,not(Y)),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_20),and(implies(X,not(Y)),X_20)) ),[0,0,0],$fot(and(X,Y))]]) ).
cnf(refute_0_111,plain,
( and(not(not(implies(X,not(Y)))),X_20) != and(implies(X,not(Y)),X_20)
| and(not(and(X,Y)),X_20) = and(implies(X,not(Y)),X_20) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_64,refute_0_110]) ).
cnf(refute_0_112,plain,
and(not(and(X,Y)),X_20) = and(implies(X,not(Y)),X_20),
inference(resolve,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_20),and(implies(X,not(Y)),X_20)) )],[refute_0_109,refute_0_111]) ).
cnf(refute_0_113,plain,
( and(not(and(X,Y)),X_20) != and(implies(X,not(Y)),X_20)
| and(implies(X,not(Y)),X_20) = and(not(and(X,Y)),X_20) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(and(not(and(X,Y)),X_20))),bind(Y0,$fot(and(implies(X,not(Y)),X_20)))]]) ).
cnf(refute_0_114,plain,
and(implies(X,not(Y)),X_20) = and(not(and(X,Y)),X_20),
inference(resolve,[$cnf( $equal(and(not(and(X,Y)),X_20),and(implies(X,not(Y)),X_20)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
and(implies(X,not(X_9)),or(X_9,X)) = and(not(and(X,X_9)),or(X_9,X)),
inference(subst,[],[refute_0_114:[bind(Y,$fot(X_9)),bind(X_20,$fot(or(X_9,X)))]]) ).
cnf(refute_0_116,plain,
( and(implies(X,not(X_9)),or(X_9,X)) != and(not(and(X,X_9)),or(X_9,X))
| equiv(X,not(X_9)) != and(implies(X,not(X_9)),or(X_9,X))
| equiv(X,not(X_9)) = and(not(and(X,X_9)),or(X_9,X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,not(X_9)),and(implies(X,not(X_9)),or(X_9,X))) ),[1],$fot(and(not(and(X,X_9)),or(X_9,X)))]]) ).
cnf(refute_0_117,plain,
( equiv(X,not(X_9)) != and(implies(X,not(X_9)),or(X_9,X))
| equiv(X,not(X_9)) = and(not(and(X,X_9)),or(X_9,X)) ),
inference(resolve,[$cnf( $equal(and(implies(X,not(X_9)),or(X_9,X)),and(not(and(X,X_9)),or(X_9,X))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
equiv(X,not(X_9)) = and(not(and(X,X_9)),or(X_9,X)),
inference(resolve,[$cnf( $equal(equiv(X,not(X_9)),and(implies(X,not(X_9)),or(X_9,X))) )],[refute_0_90,refute_0_117]) ).
cnf(refute_0_119,plain,
( equiv(X,not(X_9)) != and(not(and(X,X_9)),or(X_9,X))
| and(not(and(X,X_9)),or(X_9,X)) = equiv(X,not(X_9)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X,not(X_9)))),bind(Y0,$fot(and(not(and(X,X_9)),or(X_9,X))))]]) ).
cnf(refute_0_120,plain,
and(not(and(X,X_9)),or(X_9,X)) = equiv(X,not(X_9)),
inference(resolve,[$cnf( $equal(equiv(X,not(X_9)),and(not(and(X,X_9)),or(X_9,X))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( and(not(and(X,X_9)),or(X_9,X)) != equiv(X,not(X_9))
| implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) != or(and(not(and(X,X_9)),or(X_9,X)),X_78)
| implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) = or(equiv(X,not(X_9)),X_78) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78),or(and(not(and(X,X_9)),or(X_9,X)),X_78)) ),[1,0],$fot(equiv(X,not(X_9)))]]) ).
cnf(refute_0_122,plain,
( implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) != or(and(not(and(X,X_9)),or(X_9,X)),X_78)
| implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) = or(equiv(X,not(X_9)),X_78) ),
inference(resolve,[$cnf( $equal(and(not(and(X,X_9)),or(X_9,X)),equiv(X,not(X_9))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) = or(equiv(X,not(X_9)),X_78),
inference(resolve,[$cnf( $equal(implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78),or(and(not(and(X,X_9)),or(X_9,X)),X_78)) )],[refute_0_68,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(or(X_9,not(Y)),X_18) = or(not(or(X_9,not(Y))),X_18),
inference(subst,[],[refute_0_26:[bind(X,$fot(or(X_9,not(Y)))),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_125,plain,
( and(not(X_9),Y) != not(or(X_9,not(Y)))
| not(or(X_9,not(Y))) = and(not(X_9),Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(and(not(X_9),Y))),bind(Y0,$fot(not(or(X_9,not(Y)))))]]) ).
cnf(refute_0_126,plain,
not(or(X_9,not(Y))) = and(not(X_9),Y),
inference(resolve,[$cnf( $equal(and(not(X_9),Y),not(or(X_9,not(Y)))) )],[refute_0_97,refute_0_125]) ).
cnf(refute_0_127,plain,
( implies(or(X_9,not(Y)),X_18) != or(not(or(X_9,not(Y))),X_18)
| not(or(X_9,not(Y))) != and(not(X_9),Y)
| implies(or(X_9,not(Y)),X_18) = or(and(not(X_9),Y),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_9,not(Y)),X_18),or(not(or(X_9,not(Y))),X_18)) ),[1,0],$fot(and(not(X_9),Y))]]) ).
cnf(refute_0_128,plain,
( implies(or(X_9,not(Y)),X_18) != or(not(or(X_9,not(Y))),X_18)
| implies(or(X_9,not(Y)),X_18) = or(and(not(X_9),Y),X_18) ),
inference(resolve,[$cnf( $equal(not(or(X_9,not(Y))),and(not(X_9),Y)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
implies(or(X_9,not(Y)),X_18) = or(and(not(X_9),Y),X_18),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(Y)),X_18),or(not(or(X_9,not(Y))),X_18)) )],[refute_0_124,refute_0_128]) ).
cnf(refute_0_130,plain,
( implies(or(X_9,not(Y)),X_18) != or(and(not(X_9),Y),X_18)
| or(and(not(X_9),Y),X_18) = implies(or(X_9,not(Y)),X_18) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(or(X_9,not(Y)),X_18))),bind(Y0,$fot(or(and(not(X_9),Y),X_18)))]]) ).
cnf(refute_0_131,plain,
or(and(not(X_9),Y),X_18) = implies(or(X_9,not(Y)),X_18),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(Y)),X_18),or(and(not(X_9),Y),X_18)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
or(and(not(and(X,X_9)),or(X_9,X)),X_78) = implies(or(and(X,X_9),not(or(X_9,X))),X_78),
inference(subst,[],[refute_0_131:[bind(Y,$fot(or(X_9,X))),bind(X_18,$fot(X_78)),bind(X_9,$fot(and(X,X_9)))]]) ).
cnf(refute_0_133,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_134,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_30,refute_0_133]) ).
cnf(refute_0_135,plain,
( implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) != or(and(not(and(X,X_9)),or(X_9,X)),X_78)
| or(and(not(and(X,X_9)),or(X_9,X)),X_78) != implies(or(and(X,X_9),not(or(X_9,X))),X_78)
| implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) = implies(or(and(X,X_9),not(or(X_9,X))),X_78) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78))),bind(Y0,$fot(or(and(not(and(X,X_9)),or(X_9,X)),X_78))),bind(Z,$fot(implies(or(and(X,X_9),not(or(X_9,X))),X_78)))]]) ).
cnf(refute_0_136,plain,
( or(and(not(and(X,X_9)),or(X_9,X)),X_78) != implies(or(and(X,X_9),not(or(X_9,X))),X_78)
| implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) = implies(or(and(X,X_9),not(or(X_9,X))),X_78) ),
inference(resolve,[$cnf( $equal(implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78),or(and(not(and(X,X_9)),or(X_9,X)),X_78)) )],[refute_0_68,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) = implies(or(and(X,X_9),not(or(X_9,X))),X_78),
inference(resolve,[$cnf( $equal(or(and(not(and(X,X_9)),or(X_9,X)),X_78),implies(or(and(X,X_9),not(or(X_9,X))),X_78)) )],[refute_0_132,refute_0_136]) ).
cnf(refute_0_138,plain,
( implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) != implies(or(and(X,X_9),not(or(X_9,X))),X_78)
| implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) != or(equiv(X,not(X_9)),X_78)
| implies(or(and(X,X_9),not(or(X_9,X))),X_78) = or(equiv(X,not(X_9)),X_78) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78),or(equiv(X,not(X_9)),X_78)) ),[0],$fot(implies(or(and(X,X_9),not(or(X_9,X))),X_78))]]) ).
cnf(refute_0_139,plain,
( implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78) != or(equiv(X,not(X_9)),X_78)
| implies(or(and(X,X_9),not(or(X_9,X))),X_78) = or(equiv(X,not(X_9)),X_78) ),
inference(resolve,[$cnf( $equal(implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78),implies(or(and(X,X_9),not(or(X_9,X))),X_78)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(or(and(X,X_9),not(or(X_9,X))),X_78) = or(equiv(X,not(X_9)),X_78),
inference(resolve,[$cnf( $equal(implies(implies(not(and(X,X_9)),not(or(X_9,X))),X_78),or(equiv(X,not(X_9)),X_78)) )],[refute_0_123,refute_0_139]) ).
cnf(refute_0_141,plain,
implies(or(and(X,X_9),not(or(X_9,X))),and(X,X_9)) = or(equiv(X,not(X_9)),and(X,X_9)),
inference(subst,[],[refute_0_140:[bind(X_78,$fot(and(X,X_9)))]]) ).
cnf(refute_0_142,plain,
( implies(or(and(X,X_9),not(or(X_9,X))),and(X,X_9)) != or(equiv(X,not(X_9)),and(X,X_9))
| ~ is_a_theorem(or(not(or(X_9,X)),implies(or(and(X,X_9),not(or(X_9,X))),and(X,X_9))))
| is_a_theorem(or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(or(X_9,X)),implies(or(and(X,X_9),not(or(X_9,X))),and(X,X_9)))) ),[0,1],$fot(or(equiv(X,not(X_9)),and(X,X_9)))]]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(or(not(or(X_9,X)),implies(or(and(X,X_9),not(or(X_9,X))),and(X,X_9))))
| is_a_theorem(or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9)))) ),
inference(resolve,[$cnf( $equal(implies(or(and(X,X_9),not(or(X_9,X))),and(X,X_9)),or(equiv(X,not(X_9)),and(X,X_9))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
is_a_theorem(or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9)))),
inference(resolve,[$cnf( is_a_theorem(or(not(or(X_9,X)),implies(or(and(X,X_9),not(or(X_9,X))),and(X,X_9)))) )],[refute_0_50,refute_0_143]) ).
cnf(refute_0_145,plain,
or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9))) = implies(or(X_9,X),or(equiv(X,not(X_9)),and(X,X_9))),
inference(subst,[],[refute_0_37:[bind(X,$fot(or(X_9,X))),bind(Y,$fot(or(equiv(X,not(X_9)),and(X,X_9))))]]) ).
cnf(refute_0_146,plain,
( or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9))) != implies(or(X_9,X),or(equiv(X,not(X_9)),and(X,X_9)))
| ~ is_a_theorem(or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9))))
| is_a_theorem(implies(or(X_9,X),or(equiv(X,not(X_9)),and(X,X_9)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9)))) ),[0],$fot(implies(or(X_9,X),or(equiv(X,not(X_9)),and(X,X_9))))]]) ).
cnf(refute_0_147,plain,
( ~ is_a_theorem(or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9))))
| is_a_theorem(implies(or(X_9,X),or(equiv(X,not(X_9)),and(X,X_9)))) ),
inference(resolve,[$cnf( $equal(or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9))),implies(or(X_9,X),or(equiv(X,not(X_9)),and(X,X_9)))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(or(X_9,X),or(equiv(X,not(X_9)),and(X,X_9)))),
inference(resolve,[$cnf( is_a_theorem(or(not(or(X_9,X)),or(equiv(X,not(X_9)),and(X,X_9)))) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(or(X_2230,X_2229),or(equiv(X_2229,not(X_2230)),and(X_2229,X_2230)))),
inference(subst,[],[refute_0_148:[bind(X,$fot(X_2229)),bind(X_9,$fot(X_2230))]]) ).
cnf(refute_0_150,plain,
is_a_theorem(or(P,implies(or(X_2230,X_2229),or(equiv(X_2229,not(X_2230)),and(X_2229,X_2230))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_2230,X_2229),or(equiv(X_2229,not(X_2230)),and(X_2229,X_2230)))) )],[refute_0_149,refute_0_18]) ).
cnf(refute_0_151,plain,
is_a_theorem(or(X_4418,implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))))),
inference(subst,[],[refute_0_150:[bind(P,$fot(X_4418)),bind(X_2229,$fot(X_4419)),bind(X_2230,$fot(X_4420))]]) ).
cnf(refute_0_152,plain,
is_a_theorem(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418)),
inference(resolve,[$cnf( is_a_theorem(or(X_4418,implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))))) )],[refute_0_151,refute_0_11]) ).
cnf(refute_0_153,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_154,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_155,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_154,refute_0_153]) ).
cnf(refute_0_156,plain,
( ~ is_a_theorem(equiv(or(X_58934,X_58933),or(X_58933,X_58934)))
| or(X_58934,X_58933) = or(X_58933,X_58934) ),
inference(subst,[],[refute_0_155:[bind(X,$fot(or(X_58934,X_58933))),bind(Y,$fot(or(X_58933,X_58934)))]]) ).
cnf(refute_0_157,plain,
( ~ is_a_theorem(implies(implies(or(X_58932,X_58931),or(X_58931,X_58932)),equiv(or(X_58932,X_58931),or(X_58931,X_58932))))
| ~ is_a_theorem(implies(or(X_58932,X_58931),or(X_58931,X_58932)))
| is_a_theorem(equiv(or(X_58932,X_58931),or(X_58931,X_58932))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(or(X_58932,X_58931),or(X_58931,X_58932)))),bind(Y,$fot(equiv(or(X_58932,X_58931),or(X_58931,X_58932))))]]) ).
cnf(refute_0_158,plain,
( ~ is_a_theorem(or(equiv(or(X_58930,X_58929),or(X_58929,X_58930)),not(implies(or(X_58930,X_58929),or(X_58929,X_58930)))))
| is_a_theorem(or(not(implies(or(X_58930,X_58929),or(X_58929,X_58930))),equiv(or(X_58930,X_58929),or(X_58929,X_58930)))) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(equiv(or(X_58930,X_58929),or(X_58929,X_58930)))),bind(Q,$fot(not(implies(or(X_58930,X_58929),or(X_58929,X_58930)))))]]) ).
cnf(refute_0_159,plain,
( ~ is_a_theorem(X_9167)
| ~ is_a_theorem(implies(X_9167,or(and(X_9167,X_9166),not(X_9166))))
| is_a_theorem(or(and(X_9167,X_9166),not(X_9166))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_9167)),bind(Y,$fot(or(and(X_9167,X_9166),not(X_9166))))]]) ).
cnf(refute_0_160,plain,
( ~ is_a_theorem(implies(or(X_2341,or(X_2342,X_2342)),or(X_2341,X_2342)))
| ~ is_a_theorem(or(X_2341,or(X_2342,X_2342)))
| is_a_theorem(or(X_2341,X_2342)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_2341,or(X_2342,X_2342)))),bind(Y,$fot(or(X_2341,X_2342)))]]) ).
cnf(refute_0_161,plain,
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_162,plain,
r1,
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_163,plain,
is_a_theorem(implies(or(P,P),P)),
inference(resolve,[$cnf( r1 )],[refute_0_162,refute_0_161]) ).
cnf(refute_0_164,plain,
is_a_theorem(implies(or(X_2336,X_2336),X_2336)),
inference(subst,[],[refute_0_163:[bind(P,$fot(X_2336))]]) ).
cnf(refute_0_165,plain,
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_166,plain,
r5,
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_167,plain,
is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))),
inference(resolve,[$cnf( r5 )],[refute_0_166,refute_0_165]) ).
cnf(refute_0_168,plain,
( ~ is_a_theorem(implies(Q,R))
| ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| is_a_theorem(implies(or(P,Q),or(P,R))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(Q,R))),bind(Y,$fot(implies(or(P,Q),or(P,R))))]]) ).
cnf(refute_0_169,plain,
( ~ is_a_theorem(implies(Q,R))
| is_a_theorem(implies(or(P,Q),or(P,R))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
( ~ is_a_theorem(implies(or(X_2336,X_2336),X_2336))
| is_a_theorem(implies(or(X_2334,or(X_2336,X_2336)),or(X_2334,X_2336))) ),
inference(subst,[],[refute_0_169:[bind(P,$fot(X_2334)),bind(Q,$fot(or(X_2336,X_2336))),bind(R,$fot(X_2336))]]) ).
cnf(refute_0_171,plain,
is_a_theorem(implies(or(X_2334,or(X_2336,X_2336)),or(X_2334,X_2336))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_2336,X_2336),X_2336)) )],[refute_0_164,refute_0_170]) ).
cnf(refute_0_172,plain,
is_a_theorem(implies(or(X_2341,or(X_2342,X_2342)),or(X_2341,X_2342))),
inference(subst,[],[refute_0_171:[bind(X_2334,$fot(X_2341)),bind(X_2336,$fot(X_2342))]]) ).
cnf(refute_0_173,plain,
( ~ is_a_theorem(or(X_2341,or(X_2342,X_2342)))
| is_a_theorem(or(X_2341,X_2342)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_2341,or(X_2342,X_2342)),or(X_2341,X_2342))) )],[refute_0_172,refute_0_160]) ).
cnf(refute_0_174,plain,
( ~ is_a_theorem(or(not(X),or(X_2673,X_2673)))
| is_a_theorem(or(not(X),X_2673)) ),
inference(subst,[],[refute_0_173:[bind(X_2341,$fot(not(X))),bind(X_2342,$fot(X_2673))]]) ).
cnf(refute_0_175,plain,
implies(X,or(X_2673,X_2673)) = or(not(X),or(X_2673,X_2673)),
inference(subst,[],[refute_0_26:[bind(Y,$fot(or(X_2673,X_2673)))]]) ).
cnf(refute_0_176,plain,
( implies(X,or(X_2673,X_2673)) != or(not(X),or(X_2673,X_2673))
| or(not(X),or(X_2673,X_2673)) = implies(X,or(X_2673,X_2673)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,or(X_2673,X_2673)))),bind(Y0,$fot(or(not(X),or(X_2673,X_2673))))]]) ).
cnf(refute_0_177,plain,
or(not(X),or(X_2673,X_2673)) = implies(X,or(X_2673,X_2673)),
inference(resolve,[$cnf( $equal(implies(X,or(X_2673,X_2673)),or(not(X),or(X_2673,X_2673))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
( or(not(X),or(X_2673,X_2673)) != implies(X,or(X_2673,X_2673))
| ~ is_a_theorem(implies(X,or(X_2673,X_2673)))
| is_a_theorem(or(not(X),or(X_2673,X_2673))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(or(not(X),or(X_2673,X_2673))) ),[0],$fot(implies(X,or(X_2673,X_2673)))]]) ).
cnf(refute_0_179,plain,
( ~ is_a_theorem(implies(X,or(X_2673,X_2673)))
| is_a_theorem(or(not(X),or(X_2673,X_2673))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_2673,X_2673)),implies(X,or(X_2673,X_2673))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
( ~ is_a_theorem(implies(X,or(X_2673,X_2673)))
| is_a_theorem(or(not(X),X_2673)) ),
inference(resolve,[$cnf( is_a_theorem(or(not(X),or(X_2673,X_2673))) )],[refute_0_179,refute_0_174]) ).
cnf(refute_0_181,plain,
or(not(X),X_2673) = implies(X,X_2673),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X_2673))]]) ).
cnf(refute_0_182,plain,
( or(not(X),X_2673) != implies(X,X_2673)
| ~ is_a_theorem(or(not(X),X_2673))
| is_a_theorem(implies(X,X_2673)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),X_2673)) ),[0],$fot(implies(X,X_2673))]]) ).
cnf(refute_0_183,plain,
( ~ is_a_theorem(or(not(X),X_2673))
| is_a_theorem(implies(X,X_2673)) ),
inference(resolve,[$cnf( $equal(or(not(X),X_2673),implies(X,X_2673)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
( ~ is_a_theorem(implies(X,or(X_2673,X_2673)))
| is_a_theorem(implies(X,X_2673)) ),
inference(resolve,[$cnf( is_a_theorem(or(not(X),X_2673)) )],[refute_0_180,refute_0_183]) ).
cnf(refute_0_185,plain,
( ~ is_a_theorem(implies(or(or(X_4957,X_4957),X_4957),or(X_4957,X_4957)))
| is_a_theorem(implies(or(or(X_4957,X_4957),X_4957),X_4957)) ),
inference(subst,[],[refute_0_184:[bind(X,$fot(or(or(X_4957,X_4957),X_4957))),bind(X_2673,$fot(X_4957))]]) ).
cnf(refute_0_186,plain,
is_a_theorem(implies(X_2335,or(P,X_2335))),
inference(subst,[],[refute_0_14:[bind(Q,$fot(X_2335))]]) ).
cnf(refute_0_187,plain,
( ~ is_a_theorem(implies(X_2335,or(P,X_2335)))
| is_a_theorem(implies(or(X_2334,X_2335),or(X_2334,or(P,X_2335)))) ),
inference(subst,[],[refute_0_169:[bind(P,$fot(X_2334)),bind(Q,$fot(X_2335)),bind(R,$fot(or(P,X_2335)))]]) ).
cnf(refute_0_188,plain,
is_a_theorem(implies(or(X_2334,X_2335),or(X_2334,or(P,X_2335)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_2335,or(P,X_2335))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
is_a_theorem(implies(or(or(P,X_2335),X_2335),or(or(P,X_2335),or(P,X_2335)))),
inference(subst,[],[refute_0_188:[bind(X_2334,$fot(or(P,X_2335)))]]) ).
cnf(refute_0_190,plain,
( ~ is_a_theorem(implies(or(or(P,X_2335),X_2335),or(or(P,X_2335),or(P,X_2335))))
| is_a_theorem(implies(or(or(P,X_2335),X_2335),or(P,X_2335))) ),
inference(subst,[],[refute_0_184:[bind(X,$fot(or(or(P,X_2335),X_2335))),bind(X_2673,$fot(or(P,X_2335)))]]) ).
cnf(refute_0_191,plain,
is_a_theorem(implies(or(or(P,X_2335),X_2335),or(P,X_2335))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(P,X_2335),X_2335),or(or(P,X_2335),or(P,X_2335)))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
is_a_theorem(implies(or(or(X_4957,X_4957),X_4957),or(X_4957,X_4957))),
inference(subst,[],[refute_0_191:[bind(P,$fot(X_4957)),bind(X_2335,$fot(X_4957))]]) ).
cnf(refute_0_193,plain,
is_a_theorem(implies(or(or(X_4957,X_4957),X_4957),X_4957)),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_4957,X_4957),X_4957),or(X_4957,X_4957))) )],[refute_0_192,refute_0_185]) ).
cnf(refute_0_194,plain,
is_a_theorem(implies(or(or(implies(X_5027,X_5029),implies(X_5027,X_5029)),implies(X_5027,X_5029)),implies(X_5027,X_5029))),
inference(subst,[],[refute_0_193:[bind(X_4957,$fot(implies(X_5027,X_5029)))]]) ).
cnf(refute_0_195,plain,
is_a_theorem(implies(implies(X_205,or(not(X),X_207)),or(not(X),implies(X_205,X_207)))),
inference(subst,[],[refute_0_45:[bind(X,$fot(X_205)),bind(X_68,$fot(not(X))),bind(X_69,$fot(X_207))]]) ).
cnf(refute_0_196,plain,
implies(X,implies(X_205,X_207)) = or(not(X),implies(X_205,X_207)),
inference(subst,[],[refute_0_26:[bind(Y,$fot(implies(X_205,X_207)))]]) ).
cnf(refute_0_197,plain,
( implies(X,implies(X_205,X_207)) != or(not(X),implies(X_205,X_207))
| or(not(X),implies(X_205,X_207)) = implies(X,implies(X_205,X_207)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,implies(X_205,X_207)))),bind(Y0,$fot(or(not(X),implies(X_205,X_207))))]]) ).
cnf(refute_0_198,plain,
or(not(X),implies(X_205,X_207)) = implies(X,implies(X_205,X_207)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_205,X_207)),or(not(X),implies(X_205,X_207))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
( or(not(X),implies(X_205,X_207)) != implies(X,implies(X_205,X_207))
| ~ is_a_theorem(implies(implies(X_205,or(not(X),X_207)),or(not(X),implies(X_205,X_207))))
| is_a_theorem(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_205,or(not(X),X_207)),or(not(X),implies(X_205,X_207)))) ),[0,1],$fot(implies(X,implies(X_205,X_207)))]]) ).
cnf(refute_0_200,plain,
( ~ is_a_theorem(implies(implies(X_205,or(not(X),X_207)),or(not(X),implies(X_205,X_207))))
| is_a_theorem(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_205,X_207)),implies(X,implies(X_205,X_207))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
is_a_theorem(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_205,or(not(X),X_207)),or(not(X),implies(X_205,X_207)))) )],[refute_0_195,refute_0_200]) ).
cnf(refute_0_202,plain,
or(not(X),X_207) = implies(X,X_207),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X_207))]]) ).
cnf(refute_0_203,plain,
implies(X_205,or(not(X),X_207)) = implies(X_205,or(not(X),X_207)),
introduced(tautology,[refl,[$fot(implies(X_205,or(not(X),X_207)))]]) ).
cnf(refute_0_204,plain,
( implies(X_205,or(not(X),X_207)) != implies(X_205,or(not(X),X_207))
| or(not(X),X_207) != implies(X,X_207)
| implies(X_205,or(not(X),X_207)) = implies(X_205,implies(X,X_207)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_205,or(not(X),X_207)),implies(X_205,or(not(X),X_207))) ),[1,1],$fot(implies(X,X_207))]]) ).
cnf(refute_0_205,plain,
( or(not(X),X_207) != implies(X,X_207)
| implies(X_205,or(not(X),X_207)) = implies(X_205,implies(X,X_207)) ),
inference(resolve,[$cnf( $equal(implies(X_205,or(not(X),X_207)),implies(X_205,or(not(X),X_207))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
implies(X_205,or(not(X),X_207)) = implies(X_205,implies(X,X_207)),
inference(resolve,[$cnf( $equal(or(not(X),X_207),implies(X,X_207)) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))) = implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))),
introduced(tautology,[refl,[$fot(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))))]]) ).
cnf(refute_0_208,plain,
( implies(X_205,or(not(X),X_207)) != implies(X_205,implies(X,X_207))
| implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))) != implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207)))
| implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))) = implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))),implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207)))) ),[1,0],$fot(implies(X_205,implies(X,X_207)))]]) ).
cnf(refute_0_209,plain,
( implies(X_205,or(not(X),X_207)) != implies(X_205,implies(X,X_207))
| implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))) = implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))),implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207)))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))) = implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207))),
inference(resolve,[$cnf( $equal(implies(X_205,or(not(X),X_207)),implies(X_205,implies(X,X_207))) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
( implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))) != implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207)))
| ~ is_a_theorem(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))))
| is_a_theorem(implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207)))) ),[0],$fot(implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207))))]]) ).
cnf(refute_0_212,plain,
( ~ is_a_theorem(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))))
| is_a_theorem(implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207))),implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207)))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
is_a_theorem(implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_205,or(not(X),X_207)),implies(X,implies(X_205,X_207)))) )],[refute_0_201,refute_0_212]) ).
cnf(refute_0_214,plain,
( ~ is_a_theorem(implies(X_205,implies(X,X_207)))
| ~ is_a_theorem(implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207))))
| is_a_theorem(implies(X,implies(X_205,X_207))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_205,implies(X,X_207)))),bind(Y,$fot(implies(X,implies(X_205,X_207))))]]) ).
cnf(refute_0_215,plain,
( ~ is_a_theorem(implies(X_205,implies(X,X_207)))
| is_a_theorem(implies(X,implies(X_205,X_207))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_205,implies(X,X_207)),implies(X,implies(X_205,X_207)))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
( ~ is_a_theorem(implies(or(or(implies(X_5027,X_5029),implies(X_5027,X_5029)),implies(X_5027,X_5029)),implies(X_5027,X_5029)))
| is_a_theorem(implies(X_5027,implies(or(or(implies(X_5027,X_5029),implies(X_5027,X_5029)),implies(X_5027,X_5029)),X_5029))) ),
inference(subst,[],[refute_0_215:[bind(X,$fot(X_5027)),bind(X_205,$fot(or(or(implies(X_5027,X_5029),implies(X_5027,X_5029)),implies(X_5027,X_5029)))),bind(X_207,$fot(X_5029))]]) ).
cnf(refute_0_217,plain,
is_a_theorem(implies(X_5027,implies(or(or(implies(X_5027,X_5029),implies(X_5027,X_5029)),implies(X_5027,X_5029)),X_5029))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(implies(X_5027,X_5029),implies(X_5027,X_5029)),implies(X_5027,X_5029)),implies(X_5027,X_5029))) )],[refute_0_194,refute_0_216]) ).
cnf(refute_0_218,plain,
is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),implies(X_5087,not(X_1833))),not(X_1833)))),
inference(subst,[],[refute_0_217:[bind(X_5027,$fot(X_5087)),bind(X_5029,$fot(not(X_1833)))]]) ).
cnf(refute_0_219,plain,
implies(X,not(X_1833)) = not(and(X,not(not(X_1833)))),
inference(subst,[],[refute_0_78:[bind(Y,$fot(not(X_1833)))]]) ).
cnf(refute_0_220,plain,
( ~ is_a_theorem(equiv(X_102,not(not(X))))
| X_102 = not(not(X)) ),
inference(subst,[],[refute_0_155:[bind(X,$fot(X_102)),bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_221,plain,
equiv(X_32,not(not(X))) = and(not(and(X_32,not(X))),or(not(X),X_32)),
inference(subst,[],[refute_0_118:[bind(X,$fot(X_32)),bind(X_9,$fot(not(X)))]]) ).
cnf(refute_0_222,plain,
implies(X,X_32) = or(not(X),X_32),
inference(subst,[],[refute_0_26:[bind(Y,$fot(X_32))]]) ).
cnf(refute_0_223,plain,
( implies(X,X_32) != or(not(X),X_32)
| or(not(X),X_32) = implies(X,X_32) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,X_32))),bind(Y0,$fot(or(not(X),X_32)))]]) ).
cnf(refute_0_224,plain,
or(not(X),X_32) = implies(X,X_32),
inference(resolve,[$cnf( $equal(implies(X,X_32),or(not(X),X_32)) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
( equiv(X_32,not(not(X))) != and(not(and(X_32,not(X))),or(not(X),X_32))
| or(not(X),X_32) != implies(X,X_32)
| equiv(X_32,not(not(X))) = and(not(and(X_32,not(X))),implies(X,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_32,not(not(X))),and(not(and(X_32,not(X))),or(not(X),X_32))) ),[1,1],$fot(implies(X,X_32))]]) ).
cnf(refute_0_226,plain,
( equiv(X_32,not(not(X))) != and(not(and(X_32,not(X))),or(not(X),X_32))
| equiv(X_32,not(not(X))) = and(not(and(X_32,not(X))),implies(X,X_32)) ),
inference(resolve,[$cnf( $equal(or(not(X),X_32),implies(X,X_32)) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
equiv(X_32,not(not(X))) = and(not(and(X_32,not(X))),implies(X,X_32)),
inference(resolve,[$cnf( $equal(equiv(X_32,not(not(X))),and(not(and(X_32,not(X))),or(not(X),X_32))) )],[refute_0_221,refute_0_226]) ).
cnf(refute_0_228,plain,
( equiv(X,Y) != and(implies(X,Y),implies(Y,X))
| and(implies(X,Y),implies(Y,X)) = equiv(X,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_229,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_71,refute_0_228]) ).
cnf(refute_0_230,plain,
and(implies(X_32,X),implies(X,X_32)) = equiv(X_32,X),
inference(subst,[],[refute_0_229:[bind(X,$fot(X_32)),bind(Y,$fot(X))]]) ).
cnf(refute_0_231,plain,
not(and(X_32,not(X))) = implies(X_32,X),
inference(subst,[],[refute_0_80:[bind(X,$fot(X_32)),bind(Y,$fot(X))]]) ).
cnf(refute_0_232,plain,
and(not(and(X_32,not(X))),implies(X,X_32)) = and(not(and(X_32,not(X))),implies(X,X_32)),
introduced(tautology,[refl,[$fot(and(not(and(X_32,not(X))),implies(X,X_32)))]]) ).
cnf(refute_0_233,plain,
( and(not(and(X_32,not(X))),implies(X,X_32)) != and(not(and(X_32,not(X))),implies(X,X_32))
| not(and(X_32,not(X))) != implies(X_32,X)
| and(not(and(X_32,not(X))),implies(X,X_32)) = and(implies(X_32,X),implies(X,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_32,not(X))),implies(X,X_32)),and(not(and(X_32,not(X))),implies(X,X_32))) ),[1,0],$fot(implies(X_32,X))]]) ).
cnf(refute_0_234,plain,
( not(and(X_32,not(X))) != implies(X_32,X)
| and(not(and(X_32,not(X))),implies(X,X_32)) = and(implies(X_32,X),implies(X,X_32)) ),
inference(resolve,[$cnf( $equal(and(not(and(X_32,not(X))),implies(X,X_32)),and(not(and(X_32,not(X))),implies(X,X_32))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
and(not(and(X_32,not(X))),implies(X,X_32)) = and(implies(X_32,X),implies(X,X_32)),
inference(resolve,[$cnf( $equal(not(and(X_32,not(X))),implies(X_32,X)) )],[refute_0_231,refute_0_234]) ).
cnf(refute_0_236,plain,
( and(implies(X_32,X),implies(X,X_32)) != equiv(X_32,X)
| and(not(and(X_32,not(X))),implies(X,X_32)) != and(implies(X_32,X),implies(X,X_32))
| and(not(and(X_32,not(X))),implies(X,X_32)) = equiv(X_32,X) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(not(and(X_32,not(X))),implies(X,X_32)))),bind(Y0,$fot(and(implies(X_32,X),implies(X,X_32)))),bind(Z,$fot(equiv(X_32,X)))]]) ).
cnf(refute_0_237,plain,
( and(implies(X_32,X),implies(X,X_32)) != equiv(X_32,X)
| and(not(and(X_32,not(X))),implies(X,X_32)) = equiv(X_32,X) ),
inference(resolve,[$cnf( $equal(and(not(and(X_32,not(X))),implies(X,X_32)),and(implies(X_32,X),implies(X,X_32))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
and(not(and(X_32,not(X))),implies(X,X_32)) = equiv(X_32,X),
inference(resolve,[$cnf( $equal(and(implies(X_32,X),implies(X,X_32)),equiv(X_32,X)) )],[refute_0_230,refute_0_237]) ).
cnf(refute_0_239,plain,
( and(not(and(X_32,not(X))),implies(X,X_32)) != equiv(X_32,X)
| equiv(X_32,not(not(X))) != and(not(and(X_32,not(X))),implies(X,X_32))
| equiv(X_32,not(not(X))) = equiv(X_32,X) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_32,not(not(X))),and(not(and(X_32,not(X))),implies(X,X_32))) ),[1],$fot(equiv(X_32,X))]]) ).
cnf(refute_0_240,plain,
( equiv(X_32,not(not(X))) != and(not(and(X_32,not(X))),implies(X,X_32))
| equiv(X_32,not(not(X))) = equiv(X_32,X) ),
inference(resolve,[$cnf( $equal(and(not(and(X_32,not(X))),implies(X,X_32)),equiv(X_32,X)) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
equiv(X_32,not(not(X))) = equiv(X_32,X),
inference(resolve,[$cnf( $equal(equiv(X_32,not(not(X))),and(not(and(X_32,not(X))),implies(X,X_32))) )],[refute_0_227,refute_0_240]) ).
cnf(refute_0_242,plain,
equiv(X_102,not(not(X))) = equiv(X_102,X),
inference(subst,[],[refute_0_241:[bind(X_32,$fot(X_102))]]) ).
cnf(refute_0_243,plain,
( equiv(X_102,not(not(X))) != equiv(X_102,X)
| ~ is_a_theorem(equiv(X_102,X))
| is_a_theorem(equiv(X_102,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(equiv(X_102,not(not(X)))) ),[0],$fot(equiv(X_102,X))]]) ).
cnf(refute_0_244,plain,
( ~ is_a_theorem(equiv(X_102,X))
| is_a_theorem(equiv(X_102,not(not(X)))) ),
inference(resolve,[$cnf( $equal(equiv(X_102,not(not(X))),equiv(X_102,X)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
( ~ is_a_theorem(equiv(X_102,X))
| X_102 = not(not(X)) ),
inference(resolve,[$cnf( is_a_theorem(equiv(X_102,not(not(X)))) )],[refute_0_244,refute_0_220]) ).
cnf(refute_0_246,plain,
( ~ is_a_theorem(equiv(X_1832,X_1832))
| X_1832 = not(not(X_1832)) ),
inference(subst,[],[refute_0_245:[bind(X,$fot(X_1832)),bind(X_102,$fot(X_1832))]]) ).
cnf(refute_0_247,plain,
( ~ is_a_theorem(X_470)
| ~ is_a_theorem(implies(X_470,and(X_470,X_470)))
| is_a_theorem(and(X_470,X_470)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_470)),bind(Y,$fot(and(X_470,X_470)))]]) ).
cnf(refute_0_248,plain,
is_a_theorem(implies(or(not(X_17),not(X_17)),not(X_17))),
inference(subst,[],[refute_0_163:[bind(P,$fot(not(X_17)))]]) ).
cnf(refute_0_249,plain,
implies(X_17,not(X_17)) = or(not(X_17),not(X_17)),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_17)),bind(Y,$fot(not(X_17)))]]) ).
cnf(refute_0_250,plain,
( implies(X_17,not(X_17)) != or(not(X_17),not(X_17))
| or(not(X_17),not(X_17)) = implies(X_17,not(X_17)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X_17,not(X_17)))),bind(Y0,$fot(or(not(X_17),not(X_17))))]]) ).
cnf(refute_0_251,plain,
or(not(X_17),not(X_17)) = implies(X_17,not(X_17)),
inference(resolve,[$cnf( $equal(implies(X_17,not(X_17)),or(not(X_17),not(X_17))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
( or(not(X_17),not(X_17)) != implies(X_17,not(X_17))
| ~ is_a_theorem(implies(or(not(X_17),not(X_17)),not(X_17)))
| is_a_theorem(implies(implies(X_17,not(X_17)),not(X_17))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_17),not(X_17)),not(X_17))) ),[0,0],$fot(implies(X_17,not(X_17)))]]) ).
cnf(refute_0_253,plain,
( ~ is_a_theorem(implies(or(not(X_17),not(X_17)),not(X_17)))
| is_a_theorem(implies(implies(X_17,not(X_17)),not(X_17))) ),
inference(resolve,[$cnf( $equal(or(not(X_17),not(X_17)),implies(X_17,not(X_17))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
is_a_theorem(implies(implies(X_17,not(X_17)),not(X_17))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_17),not(X_17)),not(X_17))) )],[refute_0_248,refute_0_253]) ).
cnf(refute_0_255,plain,
implies(implies(X_17,not(X_17)),not(X_17)) = or(and(X_17,X_17),not(X_17)),
inference(subst,[],[refute_0_67:[bind(X,$fot(X_17)),bind(Y,$fot(X_17)),bind(X_18,$fot(not(X_17)))]]) ).
cnf(refute_0_256,plain,
( implies(implies(X_17,not(X_17)),not(X_17)) != or(and(X_17,X_17),not(X_17))
| ~ is_a_theorem(implies(implies(X_17,not(X_17)),not(X_17)))
| is_a_theorem(or(and(X_17,X_17),not(X_17))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_17,not(X_17)),not(X_17))) ),[0],$fot(or(and(X_17,X_17),not(X_17)))]]) ).
cnf(refute_0_257,plain,
( ~ is_a_theorem(implies(implies(X_17,not(X_17)),not(X_17)))
| is_a_theorem(or(and(X_17,X_17),not(X_17))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,not(X_17)),not(X_17)),or(and(X_17,X_17),not(X_17))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
is_a_theorem(or(and(X_17,X_17),not(X_17))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_17,not(X_17)),not(X_17))) )],[refute_0_254,refute_0_257]) ).
cnf(refute_0_259,plain,
is_a_theorem(or(and(not(not(X_21)),not(not(X_21))),not(not(not(X_21))))),
inference(subst,[],[refute_0_258:[bind(X_17,$fot(not(not(X_21))))]]) ).
cnf(refute_0_260,plain,
and(not(not(X_21)),not(not(X_21))) = and(X_21,not(not(X_21))),
inference(subst,[],[refute_0_108:[bind(Y,$fot(not(not(X_21)))),bind(X_17,$fot(X_21))]]) ).
cnf(refute_0_261,plain,
( and(not(not(X_21)),not(not(X_21))) != and(X_21,not(not(X_21)))
| ~ is_a_theorem(or(and(not(not(X_21)),not(not(X_21))),not(not(not(X_21)))))
| is_a_theorem(or(and(X_21,not(not(X_21))),not(not(not(X_21))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(X_21)),not(not(X_21))),not(not(not(X_21))))) ),[0,0],$fot(and(X_21,not(not(X_21))))]]) ).
cnf(refute_0_262,plain,
( ~ is_a_theorem(or(and(not(not(X_21)),not(not(X_21))),not(not(not(X_21)))))
| is_a_theorem(or(and(X_21,not(not(X_21))),not(not(not(X_21))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X_21)),not(not(X_21))),and(X_21,not(not(X_21)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
is_a_theorem(or(and(X_21,not(not(X_21))),not(not(not(X_21))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(X_21)),not(not(X_21))),not(not(not(X_21))))) )],[refute_0_259,refute_0_262]) ).
cnf(refute_0_264,plain,
implies(implies(X_21,not(X_21)),not(not(not(X_21)))) = or(and(X_21,X_21),not(not(not(X_21)))),
inference(subst,[],[refute_0_67:[bind(X,$fot(X_21)),bind(Y,$fot(X_21)),bind(X_18,$fot(not(not(not(X_21)))))]]) ).
cnf(refute_0_265,plain,
or(and(X,not(Y)),X_10) = implies(not(and(X,not(Y))),X_10),
inference(subst,[],[refute_0_84:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_266,plain,
( not(and(X,not(Y))) != implies(X,Y)
| or(and(X,not(Y)),X_10) != implies(not(and(X,not(Y))),X_10)
| or(and(X,not(Y)),X_10) = implies(implies(X,Y),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),X_10),implies(not(and(X,not(Y))),X_10)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_267,plain,
( or(and(X,not(Y)),X_10) != implies(not(and(X,not(Y))),X_10)
| or(and(X,not(Y)),X_10) = implies(implies(X,Y),X_10) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_80,refute_0_266]) ).
cnf(refute_0_268,plain,
or(and(X,not(Y)),X_10) = implies(implies(X,Y),X_10),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),X_10),implies(not(and(X,not(Y))),X_10)) )],[refute_0_265,refute_0_267]) ).
cnf(refute_0_269,plain,
or(and(X_21,not(not(X_21))),not(not(not(X_21)))) = implies(implies(X_21,not(X_21)),not(not(not(X_21)))),
inference(subst,[],[refute_0_268:[bind(X,$fot(X_21)),bind(Y,$fot(not(X_21))),bind(X_10,$fot(not(not(not(X_21)))))]]) ).
cnf(refute_0_270,plain,
( implies(implies(X_21,not(X_21)),not(not(not(X_21)))) != or(and(X_21,X_21),not(not(not(X_21))))
| or(and(X_21,not(not(X_21))),not(not(not(X_21)))) != implies(implies(X_21,not(X_21)),not(not(not(X_21))))
| or(and(X_21,not(not(X_21))),not(not(not(X_21)))) = or(and(X_21,X_21),not(not(not(X_21)))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(and(X_21,not(not(X_21))),not(not(not(X_21)))))),bind(Y0,$fot(implies(implies(X_21,not(X_21)),not(not(not(X_21)))))),bind(Z,$fot(or(and(X_21,X_21),not(not(not(X_21))))))]]) ).
cnf(refute_0_271,plain,
( implies(implies(X_21,not(X_21)),not(not(not(X_21)))) != or(and(X_21,X_21),not(not(not(X_21))))
| or(and(X_21,not(not(X_21))),not(not(not(X_21)))) = or(and(X_21,X_21),not(not(not(X_21)))) ),
inference(resolve,[$cnf( $equal(or(and(X_21,not(not(X_21))),not(not(not(X_21)))),implies(implies(X_21,not(X_21)),not(not(not(X_21))))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
or(and(X_21,not(not(X_21))),not(not(not(X_21)))) = or(and(X_21,X_21),not(not(not(X_21)))),
inference(resolve,[$cnf( $equal(implies(implies(X_21,not(X_21)),not(not(not(X_21)))),or(and(X_21,X_21),not(not(not(X_21))))) )],[refute_0_264,refute_0_271]) ).
cnf(refute_0_273,plain,
( or(and(X_21,not(not(X_21))),not(not(not(X_21)))) != or(and(X_21,X_21),not(not(not(X_21))))
| ~ is_a_theorem(or(and(X_21,not(not(X_21))),not(not(not(X_21)))))
| is_a_theorem(or(and(X_21,X_21),not(not(not(X_21))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_21,not(not(X_21))),not(not(not(X_21))))) ),[0],$fot(or(and(X_21,X_21),not(not(not(X_21)))))]]) ).
cnf(refute_0_274,plain,
( ~ is_a_theorem(or(and(X_21,not(not(X_21))),not(not(not(X_21)))))
| is_a_theorem(or(and(X_21,X_21),not(not(not(X_21))))) ),
inference(resolve,[$cnf( $equal(or(and(X_21,not(not(X_21))),not(not(not(X_21)))),or(and(X_21,X_21),not(not(not(X_21))))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
is_a_theorem(or(and(X_21,X_21),not(not(not(X_21))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_21,not(not(X_21))),not(not(not(X_21))))) )],[refute_0_263,refute_0_274]) ).
cnf(refute_0_276,plain,
is_a_theorem(or(and(not(not(X_17)),not(not(X_17))),not(not(not(not(not(X_17))))))),
inference(subst,[],[refute_0_275:[bind(X_21,$fot(not(not(X_17))))]]) ).
cnf(refute_0_277,plain,
and(not(not(X_17)),not(not(X_17))) = and(X_17,not(not(X_17))),
inference(subst,[],[refute_0_108:[bind(Y,$fot(not(not(X_17))))]]) ).
cnf(refute_0_278,plain,
( and(not(not(X_17)),not(not(X_17))) != and(X_17,not(not(X_17)))
| ~ is_a_theorem(or(and(not(not(X_17)),not(not(X_17))),not(not(not(not(not(X_17)))))))
| is_a_theorem(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(X_17)),not(not(X_17))),not(not(not(not(not(X_17))))))) ),[0,0],$fot(and(X_17,not(not(X_17))))]]) ).
cnf(refute_0_279,plain,
( ~ is_a_theorem(or(and(not(not(X_17)),not(not(X_17))),not(not(not(not(not(X_17)))))))
| is_a_theorem(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17))))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X_17)),not(not(X_17))),and(X_17,not(not(X_17)))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
is_a_theorem(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(X_17)),not(not(X_17))),not(not(not(not(not(X_17))))))) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
implies(implies(X_17,not(X_17)),not(not(not(not(not(X_17)))))) = or(and(X_17,X_17),not(not(not(not(not(X_17)))))),
inference(subst,[],[refute_0_67:[bind(X,$fot(X_17)),bind(Y,$fot(X_17)),bind(X_18,$fot(not(not(not(not(not(X_17)))))))]]) ).
cnf(refute_0_282,plain,
or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))) = implies(implies(X_17,not(X_17)),not(not(not(not(not(X_17)))))),
inference(subst,[],[refute_0_268:[bind(X,$fot(X_17)),bind(Y,$fot(not(X_17))),bind(X_10,$fot(not(not(not(not(not(X_17)))))))]]) ).
cnf(refute_0_283,plain,
( implies(implies(X_17,not(X_17)),not(not(not(not(not(X_17)))))) != or(and(X_17,X_17),not(not(not(not(not(X_17))))))
| or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))) != implies(implies(X_17,not(X_17)),not(not(not(not(not(X_17))))))
| or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))) = or(and(X_17,X_17),not(not(not(not(not(X_17)))))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))))),bind(Y0,$fot(implies(implies(X_17,not(X_17)),not(not(not(not(not(X_17)))))))),bind(Z,$fot(or(and(X_17,X_17),not(not(not(not(not(X_17))))))))]]) ).
cnf(refute_0_284,plain,
( implies(implies(X_17,not(X_17)),not(not(not(not(not(X_17)))))) != or(and(X_17,X_17),not(not(not(not(not(X_17))))))
| or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))) = or(and(X_17,X_17),not(not(not(not(not(X_17)))))) ),
inference(resolve,[$cnf( $equal(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))),implies(implies(X_17,not(X_17)),not(not(not(not(not(X_17))))))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))) = or(and(X_17,X_17),not(not(not(not(not(X_17)))))),
inference(resolve,[$cnf( $equal(implies(implies(X_17,not(X_17)),not(not(not(not(not(X_17)))))),or(and(X_17,X_17),not(not(not(not(not(X_17))))))) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
( or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))) != or(and(X_17,X_17),not(not(not(not(not(X_17))))))
| ~ is_a_theorem(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))))
| is_a_theorem(or(and(X_17,X_17),not(not(not(not(not(X_17))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17))))))) ),[0],$fot(or(and(X_17,X_17),not(not(not(not(not(X_17)))))))]]) ).
cnf(refute_0_287,plain,
( ~ is_a_theorem(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))))
| is_a_theorem(or(and(X_17,X_17),not(not(not(not(not(X_17))))))) ),
inference(resolve,[$cnf( $equal(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17)))))),or(and(X_17,X_17),not(not(not(not(not(X_17))))))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
is_a_theorem(or(and(X_17,X_17),not(not(not(not(not(X_17))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_17,not(not(X_17))),not(not(not(not(not(X_17))))))) )],[refute_0_280,refute_0_287]) ).
cnf(refute_0_289,plain,
is_a_theorem(or(and(not(X_171),not(X_171)),not(not(not(not(not(not(X_171)))))))),
inference(subst,[],[refute_0_288:[bind(X_17,$fot(not(X_171)))]]) ).
cnf(refute_0_290,plain,
or(and(not(X_171),not(X_171)),not(not(not(not(not(not(X_171))))))) = implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))),
inference(subst,[],[refute_0_268:[bind(X,$fot(not(X_171))),bind(Y,$fot(X_171)),bind(X_10,$fot(not(not(not(not(not(not(X_171))))))))]]) ).
cnf(refute_0_291,plain,
( or(and(not(X_171),not(X_171)),not(not(not(not(not(not(X_171))))))) != implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))
| ~ is_a_theorem(or(and(not(X_171),not(X_171)),not(not(not(not(not(not(X_171))))))))
| is_a_theorem(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_171),not(X_171)),not(not(not(not(not(not(X_171)))))))) ),[0],$fot(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))))]]) ).
cnf(refute_0_292,plain,
( ~ is_a_theorem(or(and(not(X_171),not(X_171)),not(not(not(not(not(not(X_171))))))))
| is_a_theorem(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_171),not(X_171)),not(not(not(not(not(not(X_171))))))),implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
is_a_theorem(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_171),not(X_171)),not(not(not(not(not(not(X_171)))))))) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_295,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_84,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(not(X_171),X_171) = or(X_171,X_171),
inference(subst,[],[refute_0_295:[bind(X,$fot(X_171)),bind(Y,$fot(X_171))]]) ).
cnf(refute_0_297,plain,
implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))) = implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))),
introduced(tautology,[refl,[$fot(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))))]]) ).
cnf(refute_0_298,plain,
( implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))) != implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))
| implies(not(X_171),X_171) != or(X_171,X_171)
| implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))) = implies(or(X_171,X_171),not(not(not(not(not(not(X_171))))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))),implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))) ),[1,0],$fot(or(X_171,X_171))]]) ).
cnf(refute_0_299,plain,
( implies(not(X_171),X_171) != or(X_171,X_171)
| implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))) = implies(or(X_171,X_171),not(not(not(not(not(not(X_171))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))),implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))) = implies(or(X_171,X_171),not(not(not(not(not(not(X_171))))))),
inference(resolve,[$cnf( $equal(implies(not(X_171),X_171),or(X_171,X_171)) )],[refute_0_296,refute_0_299]) ).
cnf(refute_0_301,plain,
( implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))) != implies(or(X_171,X_171),not(not(not(not(not(not(X_171)))))))
| ~ is_a_theorem(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))))
| is_a_theorem(implies(or(X_171,X_171),not(not(not(not(not(not(X_171)))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))) ),[0],$fot(implies(or(X_171,X_171),not(not(not(not(not(not(X_171))))))))]]) ).
cnf(refute_0_302,plain,
( ~ is_a_theorem(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))))
| is_a_theorem(implies(or(X_171,X_171),not(not(not(not(not(not(X_171)))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171))))))),implies(or(X_171,X_171),not(not(not(not(not(not(X_171)))))))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
is_a_theorem(implies(or(X_171,X_171),not(not(not(not(not(not(X_171)))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_171),X_171),not(not(not(not(not(not(X_171)))))))) )],[refute_0_293,refute_0_302]) ).
cnf(refute_0_304,plain,
is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(X))))))))),
inference(subst,[],[refute_0_303:[bind(X_171,$fot(not(X)))]]) ).
cnf(refute_0_305,plain,
implies(X,not(X)) = or(not(X),not(X)),
inference(subst,[],[refute_0_26:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_306,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) = implies(X,not(X)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,not(X)))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_307,plain,
or(not(X),not(X)) = implies(X,not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(X))))))))) ),[0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_309,plain,
( ~ is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(X))))))))) )],[refute_0_304,refute_0_309]) ).
cnf(refute_0_311,plain,
implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))) = or(and(X,X),not(not(not(not(not(not(not(X)))))))),
inference(subst,[],[refute_0_67:[bind(Y,$fot(X)),bind(X_18,$fot(not(not(not(not(not(not(not(X)))))))))]]) ).
cnf(refute_0_312,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))) != or(and(X,X),not(not(not(not(not(not(not(X))))))))
| ~ is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(not(not(X)))))))))]]) ).
cnf(refute_0_313,plain,
( ~ is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))),or(and(X,X),not(not(not(not(not(not(not(X))))))))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
is_a_theorem(or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9)))))))))),
inference(subst,[],[refute_0_314:[bind(X,$fot(not(X_9)))]]) ).
cnf(refute_0_316,plain,
implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))) = or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9))))))))),
inference(subst,[],[refute_0_129:[bind(Y,$fot(not(X_9))),bind(X_18,$fot(not(not(not(not(not(not(not(not(X_9))))))))))]]) ).
cnf(refute_0_317,plain,
( implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))) != or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9)))))))))
| or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9))))))))) = implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))))),bind(Y0,$fot(or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9)))))))))))]]) ).
cnf(refute_0_318,plain,
or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9))))))))) = implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))),or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9)))))))))) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
( or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9))))))))) != implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9)))))))))
| ~ is_a_theorem(or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9))))))))))
| is_a_theorem(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9)))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9)))))))))) ),[0],$fot(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))))]]) ).
cnf(refute_0_320,plain,
( ~ is_a_theorem(or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9))))))))))
| is_a_theorem(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9)))))))))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9))))))))),implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9)))))))))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
is_a_theorem(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9)))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_9),not(X_9)),not(not(not(not(not(not(not(not(X_9)))))))))) )],[refute_0_315,refute_0_320]) ).
cnf(refute_0_322,plain,
implies(or(X_9,not(not(X_171))),X_18) = or(and(not(X_9),not(X_171)),X_18),
inference(subst,[],[refute_0_129:[bind(Y,$fot(not(X_171)))]]) ).
cnf(refute_0_323,plain,
or(and(not(X_9),not(X_171)),X_18) = implies(implies(not(X_9),X_171),X_18),
inference(subst,[],[refute_0_268:[bind(X,$fot(not(X_9))),bind(Y,$fot(X_171)),bind(X_10,$fot(X_18))]]) ).
cnf(refute_0_324,plain,
( implies(or(X_9,not(not(X_171))),X_18) != or(and(not(X_9),not(X_171)),X_18)
| or(and(not(X_9),not(X_171)),X_18) != implies(implies(not(X_9),X_171),X_18)
| implies(or(X_9,not(not(X_171))),X_18) = implies(implies(not(X_9),X_171),X_18) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(or(X_9,not(not(X_171))),X_18),implies(implies(not(X_9),X_171),X_18)) ),[0],$fot(or(and(not(X_9),not(X_171)),X_18))]]) ).
cnf(refute_0_325,plain,
( implies(or(X_9,not(not(X_171))),X_18) != or(and(not(X_9),not(X_171)),X_18)
| implies(or(X_9,not(not(X_171))),X_18) = implies(implies(not(X_9),X_171),X_18) ),
inference(resolve,[$cnf( $equal(or(and(not(X_9),not(X_171)),X_18),implies(implies(not(X_9),X_171),X_18)) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
implies(or(X_9,not(not(X_171))),X_18) = implies(implies(not(X_9),X_171),X_18),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(not(X_171))),X_18),or(and(not(X_9),not(X_171)),X_18)) )],[refute_0_322,refute_0_325]) ).
cnf(refute_0_327,plain,
implies(not(X_9),X_171) = or(X_9,X_171),
inference(subst,[],[refute_0_295:[bind(X,$fot(X_9)),bind(Y,$fot(X_171))]]) ).
cnf(refute_0_328,plain,
implies(implies(not(X_9),X_171),X_18) = implies(implies(not(X_9),X_171),X_18),
introduced(tautology,[refl,[$fot(implies(implies(not(X_9),X_171),X_18))]]) ).
cnf(refute_0_329,plain,
( implies(implies(not(X_9),X_171),X_18) != implies(implies(not(X_9),X_171),X_18)
| implies(not(X_9),X_171) != or(X_9,X_171)
| implies(implies(not(X_9),X_171),X_18) = implies(or(X_9,X_171),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_9),X_171),X_18),implies(implies(not(X_9),X_171),X_18)) ),[1,0],$fot(or(X_9,X_171))]]) ).
cnf(refute_0_330,plain,
( implies(not(X_9),X_171) != or(X_9,X_171)
| implies(implies(not(X_9),X_171),X_18) = implies(or(X_9,X_171),X_18) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_9),X_171),X_18),implies(implies(not(X_9),X_171),X_18)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
implies(implies(not(X_9),X_171),X_18) = implies(or(X_9,X_171),X_18),
inference(resolve,[$cnf( $equal(implies(not(X_9),X_171),or(X_9,X_171)) )],[refute_0_327,refute_0_330]) ).
cnf(refute_0_332,plain,
( implies(implies(not(X_9),X_171),X_18) != implies(or(X_9,X_171),X_18)
| implies(or(X_9,not(not(X_171))),X_18) != implies(implies(not(X_9),X_171),X_18)
| implies(or(X_9,not(not(X_171))),X_18) = implies(or(X_9,X_171),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_9,not(not(X_171))),X_18),implies(implies(not(X_9),X_171),X_18)) ),[1],$fot(implies(or(X_9,X_171),X_18))]]) ).
cnf(refute_0_333,plain,
( implies(or(X_9,not(not(X_171))),X_18) != implies(implies(not(X_9),X_171),X_18)
| implies(or(X_9,not(not(X_171))),X_18) = implies(or(X_9,X_171),X_18) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_9),X_171),X_18),implies(or(X_9,X_171),X_18)) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
implies(or(X_9,not(not(X_171))),X_18) = implies(or(X_9,X_171),X_18),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(not(X_171))),X_18),implies(implies(not(X_9),X_171),X_18)) )],[refute_0_326,refute_0_333]) ).
cnf(refute_0_335,plain,
implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))) = implies(or(X_9,X_9),not(not(not(not(not(not(not(not(X_9))))))))),
inference(subst,[],[refute_0_334:[bind(X_171,$fot(X_9)),bind(X_18,$fot(not(not(not(not(not(not(not(not(X_9))))))))))]]) ).
cnf(refute_0_336,plain,
( implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))) != implies(or(X_9,X_9),not(not(not(not(not(not(not(not(X_9)))))))))
| ~ is_a_theorem(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))))
| is_a_theorem(implies(or(X_9,X_9),not(not(not(not(not(not(not(not(X_9)))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9)))))))))) ),[0],$fot(implies(or(X_9,X_9),not(not(not(not(not(not(not(not(X_9))))))))))]]) ).
cnf(refute_0_337,plain,
( ~ is_a_theorem(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))))
| is_a_theorem(implies(or(X_9,X_9),not(not(not(not(not(not(not(not(X_9)))))))))) ),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9))))))))),implies(or(X_9,X_9),not(not(not(not(not(not(not(not(X_9)))))))))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
is_a_theorem(implies(or(X_9,X_9),not(not(not(not(not(not(not(not(X_9)))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_9,not(not(X_9))),not(not(not(not(not(not(not(not(X_9)))))))))) )],[refute_0_321,refute_0_337]) ).
cnf(refute_0_339,plain,
is_a_theorem(implies(or(not(not(X_331)),not(not(X_331))),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))),
inference(subst,[],[refute_0_338:[bind(X_9,$fot(not(not(X_331))))]]) ).
cnf(refute_0_340,plain,
implies(or(not(not(X_331)),not(not(X_331))),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) = implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))),
inference(subst,[],[refute_0_334:[bind(X_171,$fot(X_331)),bind(X_18,$fot(not(not(not(not(not(not(not(not(not(not(X_331)))))))))))),bind(X_9,$fot(not(not(X_331))))]]) ).
cnf(refute_0_341,plain,
( implies(or(not(not(X_331)),not(not(X_331))),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) != implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))
| ~ is_a_theorem(implies(or(not(not(X_331)),not(not(X_331))),not(not(not(not(not(not(not(not(not(not(X_331))))))))))))
| is_a_theorem(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(not(X_331)),not(not(X_331))),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) ),[0],$fot(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))))]]) ).
cnf(refute_0_342,plain,
( ~ is_a_theorem(implies(or(not(not(X_331)),not(not(X_331))),not(not(not(not(not(not(not(not(not(not(X_331))))))))))))
| is_a_theorem(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(X_331)),not(not(X_331))),not(not(not(not(not(not(not(not(not(not(X_331))))))))))),implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
is_a_theorem(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(not(X_331)),not(not(X_331))),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) )],[refute_0_339,refute_0_342]) ).
cnf(refute_0_344,plain,
implies(not(X_331),X_331) = or(X_331,X_331),
inference(subst,[],[refute_0_295:[bind(X,$fot(X_331)),bind(Y,$fot(X_331))]]) ).
cnf(refute_0_345,plain,
or(not(not(X_331)),X_331) = implies(not(X_331),X_331),
inference(subst,[],[refute_0_37:[bind(X,$fot(not(X_331))),bind(Y,$fot(X_331))]]) ).
cnf(refute_0_346,plain,
( implies(not(X_331),X_331) != or(X_331,X_331)
| or(not(not(X_331)),X_331) != implies(not(X_331),X_331)
| or(not(not(X_331)),X_331) = or(X_331,X_331) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(not(X_331)),X_331))),bind(Y0,$fot(implies(not(X_331),X_331))),bind(Z,$fot(or(X_331,X_331)))]]) ).
cnf(refute_0_347,plain,
( implies(not(X_331),X_331) != or(X_331,X_331)
| or(not(not(X_331)),X_331) = or(X_331,X_331) ),
inference(resolve,[$cnf( $equal(or(not(not(X_331)),X_331),implies(not(X_331),X_331)) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
or(not(not(X_331)),X_331) = or(X_331,X_331),
inference(resolve,[$cnf( $equal(implies(not(X_331),X_331),or(X_331,X_331)) )],[refute_0_344,refute_0_347]) ).
cnf(refute_0_349,plain,
implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) = implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))),
introduced(tautology,[refl,[$fot(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))))]]) ).
cnf(refute_0_350,plain,
( implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) != implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))
| or(not(not(X_331)),X_331) != or(X_331,X_331)
| implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) = implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))),implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) ),[1,0],$fot(or(X_331,X_331))]]) ).
cnf(refute_0_351,plain,
( or(not(not(X_331)),X_331) != or(X_331,X_331)
| implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) = implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))),implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) = implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))),
inference(resolve,[$cnf( $equal(or(not(not(X_331)),X_331),or(X_331,X_331)) )],[refute_0_348,refute_0_351]) ).
cnf(refute_0_353,plain,
( implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))) != implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))
| ~ is_a_theorem(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))))
| is_a_theorem(implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) ),[0],$fot(implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))))]]) ).
cnf(refute_0_354,plain,
( ~ is_a_theorem(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))))
| is_a_theorem(implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))),implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
is_a_theorem(implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(not(X_331)),X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) )],[refute_0_343,refute_0_354]) ).
cnf(refute_0_356,plain,
is_a_theorem(implies(or(not(X_17),Q),or(Q,not(X_17)))),
inference(subst,[],[refute_0_5:[bind(P,$fot(not(X_17)))]]) ).
cnf(refute_0_357,plain,
implies(X_17,Q) = or(not(X_17),Q),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_17)),bind(Y,$fot(Q))]]) ).
cnf(refute_0_358,plain,
( implies(X_17,Q) != or(not(X_17),Q)
| or(not(X_17),Q) = implies(X_17,Q) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X_17,Q))),bind(Y0,$fot(or(not(X_17),Q)))]]) ).
cnf(refute_0_359,plain,
or(not(X_17),Q) = implies(X_17,Q),
inference(resolve,[$cnf( $equal(implies(X_17,Q),or(not(X_17),Q)) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
( or(not(X_17),Q) != implies(X_17,Q)
| ~ is_a_theorem(implies(or(not(X_17),Q),or(Q,not(X_17))))
| is_a_theorem(implies(implies(X_17,Q),or(Q,not(X_17)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_17),Q),or(Q,not(X_17)))) ),[0,0],$fot(implies(X_17,Q))]]) ).
cnf(refute_0_361,plain,
( ~ is_a_theorem(implies(or(not(X_17),Q),or(Q,not(X_17))))
| is_a_theorem(implies(implies(X_17,Q),or(Q,not(X_17)))) ),
inference(resolve,[$cnf( $equal(or(not(X_17),Q),implies(X_17,Q)) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
is_a_theorem(implies(implies(X_17,Q),or(Q,not(X_17)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_17),Q),or(Q,not(X_17)))) )],[refute_0_356,refute_0_361]) ).
cnf(refute_0_363,plain,
( ~ is_a_theorem(implies(X_17,Q))
| ~ is_a_theorem(implies(implies(X_17,Q),or(Q,not(X_17))))
| is_a_theorem(or(Q,not(X_17))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_17,Q))),bind(Y,$fot(or(Q,not(X_17))))]]) ).
cnf(refute_0_364,plain,
( ~ is_a_theorem(implies(X_17,Q))
| is_a_theorem(or(Q,not(X_17))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_17,Q),or(Q,not(X_17)))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
( ~ is_a_theorem(implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331))))))))))))
| is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331)))) ),
inference(subst,[],[refute_0_364:[bind(Q,$fot(not(not(not(not(not(not(not(not(not(not(X_331)))))))))))),bind(X_17,$fot(or(X_331,X_331)))]]) ).
cnf(refute_0_366,plain,
is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_331,X_331),not(not(not(not(not(not(not(not(not(not(X_331)))))))))))) )],[refute_0_355,refute_0_365]) ).
cnf(refute_0_367,plain,
implies(not(X_331),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(subst,[],[refute_0_295:[bind(X,$fot(X_331)),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_368,plain,
or(not(not(X_331)),not(or(X_331,X_331))) = implies(not(X_331),not(or(X_331,X_331))),
inference(subst,[],[refute_0_37:[bind(X,$fot(not(X_331))),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_369,plain,
( implies(not(X_331),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(X_331)),not(or(X_331,X_331))) != implies(not(X_331),not(or(X_331,X_331)))
| or(not(not(X_331)),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(not(X_331)),not(or(X_331,X_331))))),bind(Y0,$fot(implies(not(X_331),not(or(X_331,X_331))))),bind(Z,$fot(or(X_331,not(or(X_331,X_331)))))]]) ).
cnf(refute_0_370,plain,
( implies(not(X_331),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(X_331)),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(resolve,[$cnf( $equal(or(not(not(X_331)),not(or(X_331,X_331))),implies(not(X_331),not(or(X_331,X_331)))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
or(not(not(X_331)),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(resolve,[$cnf( $equal(implies(not(X_331),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_367,refute_0_370]) ).
cnf(refute_0_372,plain,
implies(not(not(not(X_331))),not(or(X_331,X_331))) = or(not(not(X_331)),not(or(X_331,X_331))),
inference(subst,[],[refute_0_295:[bind(X,$fot(not(not(X_331)))),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_373,plain,
( implies(not(not(not(X_331))),not(or(X_331,X_331))) != or(not(not(X_331)),not(or(X_331,X_331)))
| or(not(not(X_331)),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| implies(not(not(not(X_331))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(not(not(not(X_331))),not(or(X_331,X_331))))),bind(Y0,$fot(or(not(not(X_331)),not(or(X_331,X_331))))),bind(Z,$fot(or(X_331,not(or(X_331,X_331)))))]]) ).
cnf(refute_0_374,plain,
( or(not(not(X_331)),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| implies(not(not(not(X_331))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_331))),not(or(X_331,X_331))),or(not(not(X_331)),not(or(X_331,X_331)))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
implies(not(not(not(X_331))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(resolve,[$cnf( $equal(or(not(not(X_331)),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_371,refute_0_374]) ).
cnf(refute_0_376,plain,
or(not(not(not(not(X_331)))),not(or(X_331,X_331))) = implies(not(not(not(X_331))),not(or(X_331,X_331))),
inference(subst,[],[refute_0_37:[bind(X,$fot(not(not(not(X_331))))),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_377,plain,
( implies(not(not(not(X_331))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(not(not(X_331)))),not(or(X_331,X_331))) != implies(not(not(not(X_331))),not(or(X_331,X_331)))
| or(not(not(not(not(X_331)))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(not(not(not(X_331)))),not(or(X_331,X_331))))),bind(Y0,$fot(implies(not(not(not(X_331))),not(or(X_331,X_331))))),bind(Z,$fot(or(X_331,not(or(X_331,X_331)))))]]) ).
cnf(refute_0_378,plain,
( implies(not(not(not(X_331))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(not(not(X_331)))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(X_331)))),not(or(X_331,X_331))),implies(not(not(not(X_331))),not(or(X_331,X_331)))) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
or(not(not(not(not(X_331)))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_331))),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_375,refute_0_378]) ).
cnf(refute_0_380,plain,
implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))) = or(not(not(not(not(X_331)))),not(or(X_331,X_331))),
inference(subst,[],[refute_0_295:[bind(X,$fot(not(not(not(not(X_331)))))),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_381,plain,
( implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))) != or(not(not(not(not(X_331)))),not(or(X_331,X_331)))
| or(not(not(not(not(X_331)))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))))),bind(Y0,$fot(or(not(not(not(not(X_331)))),not(or(X_331,X_331))))),bind(Z,$fot(or(X_331,not(or(X_331,X_331)))))]]) ).
cnf(refute_0_382,plain,
( or(not(not(not(not(X_331)))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))),or(not(not(not(not(X_331)))),not(or(X_331,X_331)))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(X_331)))),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_379,refute_0_382]) ).
cnf(refute_0_384,plain,
or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))) = implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))),
inference(subst,[],[refute_0_37:[bind(X,$fot(not(not(not(not(not(X_331))))))),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_385,plain,
( implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))) != implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331)))
| or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))))),bind(Y0,$fot(implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))))),bind(Z,$fot(or(X_331,not(or(X_331,X_331)))))]]) ).
cnf(refute_0_386,plain,
( implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))),implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331)))) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(X_331))))),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_383,refute_0_386]) ).
cnf(refute_0_388,plain,
implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))) = or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))),
inference(subst,[],[refute_0_295:[bind(X,$fot(not(not(not(not(not(not(X_331)))))))),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_389,plain,
( implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))) != or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331)))
| or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))))),bind(Y0,$fot(or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))))),bind(Z,$fot(or(X_331,not(or(X_331,X_331)))))]]) ).
cnf(refute_0_390,plain,
( or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))),or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331)))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(X_331)))))),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_387,refute_0_390]) ).
cnf(refute_0_392,plain,
or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))) = implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))),
inference(subst,[],[refute_0_37:[bind(X,$fot(not(not(not(not(not(not(not(X_331))))))))),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_393,plain,
( implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))) != implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331)))
| or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))))),bind(Y0,$fot(implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))))),bind(Z,$fot(or(X_331,not(or(X_331,X_331)))))]]) ).
cnf(refute_0_394,plain,
( implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))),implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331)))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(X_331))))))),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))) = or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))),
inference(subst,[],[refute_0_295:[bind(X,$fot(not(not(not(not(not(not(not(not(X_331)))))))))),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_397,plain,
( implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))) != or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331)))
| or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))))),bind(Y0,$fot(or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))))),bind(Z,$fot(or(X_331,not(or(X_331,X_331)))))]]) ).
cnf(refute_0_398,plain,
( or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))),or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331)))) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(X_331)))))))),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_395,refute_0_398]) ).
cnf(refute_0_400,plain,
or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))) = implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))),
inference(subst,[],[refute_0_37:[bind(X,$fot(not(not(not(not(not(not(not(not(not(X_331))))))))))),bind(Y,$fot(not(or(X_331,X_331))))]]) ).
cnf(refute_0_401,plain,
( implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))) != implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331)))
| or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))))),bind(Y0,$fot(implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))))),bind(Z,$fot(or(X_331,not(or(X_331,X_331)))))]]) ).
cnf(refute_0_402,plain,
( implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))),implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331)))) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))) = or(X_331,not(or(X_331,X_331))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(not(not(X_331))))))))),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_399,refute_0_402]) ).
cnf(refute_0_404,plain,
( or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))) != or(X_331,not(or(X_331,X_331)))
| ~ is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))))
| is_a_theorem(or(X_331,not(or(X_331,X_331)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331)))) ),[0],$fot(or(X_331,not(or(X_331,X_331))))]]) ).
cnf(refute_0_405,plain,
( ~ is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))))
| is_a_theorem(or(X_331,not(or(X_331,X_331)))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331))),or(X_331,not(or(X_331,X_331)))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
is_a_theorem(or(X_331,not(or(X_331,X_331)))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_331)))))))))),not(or(X_331,X_331)))) )],[refute_0_366,refute_0_405]) ).
cnf(refute_0_407,plain,
is_a_theorem(or(not(X),not(or(not(X),not(X))))),
inference(subst,[],[refute_0_406:[bind(X_331,$fot(not(X)))]]) ).
cnf(refute_0_408,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(or(not(X),not(or(not(X),not(X)))))
| is_a_theorem(or(not(X),not(implies(X,not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),not(or(not(X),not(X))))) ),[0,1,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_409,plain,
( ~ is_a_theorem(or(not(X),not(or(not(X),not(X)))))
| is_a_theorem(or(not(X),not(implies(X,not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_307,refute_0_408]) ).
cnf(refute_0_410,plain,
is_a_theorem(or(not(X),not(implies(X,not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(or(not(X),not(X))))) )],[refute_0_407,refute_0_409]) ).
cnf(refute_0_411,plain,
not(implies(X,not(X))) = and(X,X),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X))]]) ).
cnf(refute_0_412,plain,
implies(X,not(implies(X,not(X)))) = implies(X,not(implies(X,not(X)))),
introduced(tautology,[refl,[$fot(implies(X,not(implies(X,not(X)))))]]) ).
cnf(refute_0_413,plain,
( implies(X,not(implies(X,not(X)))) != implies(X,not(implies(X,not(X))))
| not(implies(X,not(X))) != and(X,X)
| implies(X,not(implies(X,not(X)))) = implies(X,and(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(implies(X,not(X)))),implies(X,not(implies(X,not(X))))) ),[1,1],$fot(and(X,X))]]) ).
cnf(refute_0_414,plain,
( not(implies(X,not(X))) != and(X,X)
| implies(X,not(implies(X,not(X)))) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(X)))),implies(X,not(implies(X,not(X))))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
implies(X,not(implies(X,not(X)))) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X))),and(X,X)) )],[refute_0_411,refute_0_414]) ).
cnf(refute_0_416,plain,
or(not(X),not(implies(X,not(X)))) = implies(X,not(implies(X,not(X)))),
inference(subst,[],[refute_0_37:[bind(Y,$fot(not(implies(X,not(X)))))]]) ).
cnf(refute_0_417,plain,
( implies(X,not(implies(X,not(X)))) != implies(X,and(X,X))
| or(not(X),not(implies(X,not(X)))) != implies(X,not(implies(X,not(X))))
| or(not(X),not(implies(X,not(X)))) = implies(X,and(X,X)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(X),not(implies(X,not(X)))))),bind(Y0,$fot(implies(X,not(implies(X,not(X)))))),bind(Z,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_418,plain,
( implies(X,not(implies(X,not(X)))) != implies(X,and(X,X))
| or(not(X),not(implies(X,not(X)))) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(implies(X,not(X)))),implies(X,not(implies(X,not(X))))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
or(not(X),not(implies(X,not(X)))) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(X)))),implies(X,and(X,X))) )],[refute_0_415,refute_0_418]) ).
cnf(refute_0_420,plain,
( or(not(X),not(implies(X,not(X)))) != implies(X,and(X,X))
| ~ is_a_theorem(or(not(X),not(implies(X,not(X)))))
| is_a_theorem(implies(X,and(X,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),not(implies(X,not(X))))) ),[0],$fot(implies(X,and(X,X)))]]) ).
cnf(refute_0_421,plain,
( ~ is_a_theorem(or(not(X),not(implies(X,not(X)))))
| is_a_theorem(implies(X,and(X,X))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(implies(X,not(X)))),implies(X,and(X,X))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
is_a_theorem(implies(X,and(X,X))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(implies(X,not(X))))) )],[refute_0_410,refute_0_421]) ).
cnf(refute_0_423,plain,
is_a_theorem(implies(X_470,and(X_470,X_470))),
inference(subst,[],[refute_0_422:[bind(X,$fot(X_470))]]) ).
cnf(refute_0_424,plain,
( ~ is_a_theorem(X_470)
| is_a_theorem(and(X_470,X_470)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_470,and(X_470,X_470))) )],[refute_0_423,refute_0_247]) ).
cnf(refute_0_425,plain,
( ~ is_a_theorem(implies(X_1831,X_1831))
| is_a_theorem(and(implies(X_1831,X_1831),implies(X_1831,X_1831))) ),
inference(subst,[],[refute_0_424:[bind(X_470,$fot(implies(X_1831,X_1831)))]]) ).
cnf(refute_0_426,plain,
is_a_theorem(implies(or(X_371,X_371),X_371)),
inference(subst,[],[refute_0_163:[bind(P,$fot(X_371))]]) ).
cnf(refute_0_427,plain,
( ~ is_a_theorem(implies(or(X_371,X_371),X_371))
| ~ is_a_theorem(or(X_371,X_371))
| is_a_theorem(X_371) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_371,X_371))),bind(Y,$fot(X_371))]]) ).
cnf(refute_0_428,plain,
( ~ is_a_theorem(or(X_371,X_371))
| is_a_theorem(X_371) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_371,X_371),X_371)) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
( ~ is_a_theorem(or(implies(X_1830,X_1830),implies(X_1830,X_1830)))
| is_a_theorem(implies(X_1830,X_1830)) ),
inference(subst,[],[refute_0_428:[bind(X_371,$fot(implies(X_1830,X_1830)))]]) ).
cnf(refute_0_430,plain,
is_a_theorem(implies(X_1815,or(X_1814,X_1815))),
inference(subst,[],[refute_0_14:[bind(P,$fot(X_1814)),bind(Q,$fot(X_1815))]]) ).
cnf(refute_0_431,plain,
( ~ is_a_theorem(implies(X_1815,or(X_1814,X_1815)))
| is_a_theorem(or(X_1814,implies(X_1815,X_1815))) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(X_1815)),bind(X_68,$fot(X_1814)),bind(X_69,$fot(X_1815))]]) ).
cnf(refute_0_432,plain,
is_a_theorem(or(X_1814,implies(X_1815,X_1815))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1815,or(X_1814,X_1815))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
is_a_theorem(or(implies(X_1830,X_1830),implies(X_1830,X_1830))),
inference(subst,[],[refute_0_432:[bind(X_1814,$fot(implies(X_1830,X_1830))),bind(X_1815,$fot(X_1830))]]) ).
cnf(refute_0_434,plain,
is_a_theorem(implies(X_1830,X_1830)),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_1830,X_1830),implies(X_1830,X_1830))) )],[refute_0_433,refute_0_429]) ).
cnf(refute_0_435,plain,
is_a_theorem(implies(X_1831,X_1831)),
inference(subst,[],[refute_0_434:[bind(X_1830,$fot(X_1831))]]) ).
cnf(refute_0_436,plain,
is_a_theorem(and(implies(X_1831,X_1831),implies(X_1831,X_1831))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1831,X_1831)) )],[refute_0_435,refute_0_425]) ).
cnf(refute_0_437,plain,
and(implies(X_1831,X_1831),implies(X_1831,X_1831)) = equiv(X_1831,X_1831),
inference(subst,[],[refute_0_229:[bind(X,$fot(X_1831)),bind(Y,$fot(X_1831))]]) ).
cnf(refute_0_438,plain,
( and(implies(X_1831,X_1831),implies(X_1831,X_1831)) != equiv(X_1831,X_1831)
| ~ is_a_theorem(and(implies(X_1831,X_1831),implies(X_1831,X_1831)))
| is_a_theorem(equiv(X_1831,X_1831)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(and(implies(X_1831,X_1831),implies(X_1831,X_1831))) ),[0],$fot(equiv(X_1831,X_1831))]]) ).
cnf(refute_0_439,plain,
( ~ is_a_theorem(and(implies(X_1831,X_1831),implies(X_1831,X_1831)))
| is_a_theorem(equiv(X_1831,X_1831)) ),
inference(resolve,[$cnf( $equal(and(implies(X_1831,X_1831),implies(X_1831,X_1831)),equiv(X_1831,X_1831)) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
is_a_theorem(equiv(X_1831,X_1831)),
inference(resolve,[$cnf( is_a_theorem(and(implies(X_1831,X_1831),implies(X_1831,X_1831))) )],[refute_0_436,refute_0_439]) ).
cnf(refute_0_441,plain,
is_a_theorem(equiv(X_1832,X_1832)),
inference(subst,[],[refute_0_440:[bind(X_1831,$fot(X_1832))]]) ).
cnf(refute_0_442,plain,
X_1832 = not(not(X_1832)),
inference(resolve,[$cnf( is_a_theorem(equiv(X_1832,X_1832)) )],[refute_0_441,refute_0_246]) ).
cnf(refute_0_443,plain,
X_1833 = not(not(X_1833)),
inference(subst,[],[refute_0_442:[bind(X_1832,$fot(X_1833))]]) ).
cnf(refute_0_444,plain,
( X_1833 != not(not(X_1833))
| not(not(X_1833)) = X_1833 ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(X_1833)),bind(Y0,$fot(not(not(X_1833))))]]) ).
cnf(refute_0_445,plain,
not(not(X_1833)) = X_1833,
inference(resolve,[$cnf( $equal(X_1833,not(not(X_1833))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
( implies(X,not(X_1833)) != not(and(X,not(not(X_1833))))
| not(not(X_1833)) != X_1833
| implies(X,not(X_1833)) = not(and(X,X_1833)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(X_1833)),not(and(X,not(not(X_1833))))) ),[1,0,1],$fot(X_1833)]]) ).
cnf(refute_0_447,plain,
( implies(X,not(X_1833)) != not(and(X,not(not(X_1833))))
| implies(X,not(X_1833)) = not(and(X,X_1833)) ),
inference(resolve,[$cnf( $equal(not(not(X_1833)),X_1833) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
implies(X,not(X_1833)) = not(and(X,X_1833)),
inference(resolve,[$cnf( $equal(implies(X,not(X_1833)),not(and(X,not(not(X_1833))))) )],[refute_0_219,refute_0_447]) ).
cnf(refute_0_449,plain,
implies(X_5087,not(X_1833)) = not(and(X_5087,X_1833)),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_5087))]]) ).
cnf(refute_0_450,plain,
( implies(X_5087,not(X_1833)) != not(and(X_5087,X_1833))
| ~ is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),implies(X_5087,not(X_1833))),not(X_1833))))
| is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),implies(X_5087,not(X_1833))),not(X_1833)))) ),[0,1,0,1],$fot(not(and(X_5087,X_1833)))]]) ).
cnf(refute_0_451,plain,
( ~ is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),implies(X_5087,not(X_1833))),not(X_1833))))
| is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)))) ),
inference(resolve,[$cnf( $equal(implies(X_5087,not(X_1833)),not(and(X_5087,X_1833))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),implies(X_5087,not(X_1833))),not(X_1833)))) )],[refute_0_218,refute_0_451]) ).
cnf(refute_0_453,plain,
or(X_9,not(Y)) = not(not(or(X_9,not(Y)))),
inference(subst,[],[refute_0_442:[bind(X_1832,$fot(or(X_9,not(Y))))]]) ).
cnf(refute_0_454,plain,
( not(or(X_9,not(Y))) != and(not(X_9),Y)
| or(X_9,not(Y)) != not(not(or(X_9,not(Y))))
| or(X_9,not(Y)) = not(and(not(X_9),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_9,not(Y)),not(not(or(X_9,not(Y))))) ),[1,0],$fot(and(not(X_9),Y))]]) ).
cnf(refute_0_455,plain,
( or(X_9,not(Y)) != not(not(or(X_9,not(Y))))
| or(X_9,not(Y)) = not(and(not(X_9),Y)) ),
inference(resolve,[$cnf( $equal(not(or(X_9,not(Y))),and(not(X_9),Y)) )],[refute_0_126,refute_0_454]) ).
cnf(refute_0_456,plain,
or(X_9,not(Y)) = not(and(not(X_9),Y)),
inference(resolve,[$cnf( $equal(or(X_9,not(Y)),not(not(or(X_9,not(Y))))) )],[refute_0_453,refute_0_455]) ).
cnf(refute_0_457,plain,
( or(X_9,not(Y)) != not(and(not(X_9),Y))
| not(and(not(X_9),Y)) = or(X_9,not(Y)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X_9,not(Y)))),bind(Y0,$fot(not(and(not(X_9),Y))))]]) ).
cnf(refute_0_458,plain,
not(and(not(X_9),Y)) = or(X_9,not(Y)),
inference(resolve,[$cnf( $equal(or(X_9,not(Y)),not(and(not(X_9),Y))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)) = or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)),
inference(subst,[],[refute_0_458:[bind(Y,$fot(X_1833)),bind(X_9,$fot(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))))]]) ).
cnf(refute_0_460,plain,
implies(and(and(X_5087,X_1833),and(X_5087,X_1833)),not(and(X_5087,X_1833))) = not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),
inference(subst,[],[refute_0_448:[bind(X,$fot(and(and(X_5087,X_1833),and(X_5087,X_1833)))),bind(X_1833,$fot(and(X_5087,X_1833)))]]) ).
cnf(refute_0_461,plain,
or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))) = implies(and(and(X_5087,X_1833),and(X_5087,X_1833)),not(and(X_5087,X_1833))),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(and(X_5087,X_1833),and(X_5087,X_1833)))),bind(Y,$fot(not(and(X_5087,X_1833))))]]) ).
cnf(refute_0_462,plain,
( implies(and(and(X_5087,X_1833),and(X_5087,X_1833)),not(and(X_5087,X_1833))) != not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))
| or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))) != implies(and(and(X_5087,X_1833),and(X_5087,X_1833)),not(and(X_5087,X_1833)))
| or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))) = not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))))),bind(Y0,$fot(implies(and(and(X_5087,X_1833),and(X_5087,X_1833)),not(and(X_5087,X_1833))))),bind(Z,$fot(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))))]]) ).
cnf(refute_0_463,plain,
( implies(and(and(X_5087,X_1833),and(X_5087,X_1833)),not(and(X_5087,X_1833))) != not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))
| or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))) = not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))) ),
inference(resolve,[$cnf( $equal(or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))),implies(and(and(X_5087,X_1833),and(X_5087,X_1833)),not(and(X_5087,X_1833)))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))) = not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),
inference(resolve,[$cnf( $equal(implies(and(and(X_5087,X_1833),and(X_5087,X_1833)),not(and(X_5087,X_1833))),not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))) )],[refute_0_460,refute_0_463]) ).
cnf(refute_0_465,plain,
implies(and(X_5087,X_1833),not(and(X_5087,X_1833))) = not(and(and(X_5087,X_1833),and(X_5087,X_1833))),
inference(subst,[],[refute_0_448:[bind(X,$fot(and(X_5087,X_1833))),bind(X_1833,$fot(and(X_5087,X_1833)))]]) ).
cnf(refute_0_466,plain,
or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) = implies(and(X_5087,X_1833),not(and(X_5087,X_1833))),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(X_5087,X_1833))),bind(Y,$fot(not(and(X_5087,X_1833))))]]) ).
cnf(refute_0_467,plain,
( implies(and(X_5087,X_1833),not(and(X_5087,X_1833))) != not(and(and(X_5087,X_1833),and(X_5087,X_1833)))
| or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) != implies(and(X_5087,X_1833),not(and(X_5087,X_1833)))
| or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) = not(and(and(X_5087,X_1833),and(X_5087,X_1833))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))))),bind(Y0,$fot(implies(and(X_5087,X_1833),not(and(X_5087,X_1833))))),bind(Z,$fot(not(and(and(X_5087,X_1833),and(X_5087,X_1833)))))]]) ).
cnf(refute_0_468,plain,
( implies(and(X_5087,X_1833),not(and(X_5087,X_1833))) != not(and(and(X_5087,X_1833),and(X_5087,X_1833)))
| or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) = not(and(and(X_5087,X_1833),and(X_5087,X_1833))) ),
inference(resolve,[$cnf( $equal(or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))),implies(and(X_5087,X_1833),not(and(X_5087,X_1833)))) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) = not(and(and(X_5087,X_1833),and(X_5087,X_1833))),
inference(resolve,[$cnf( $equal(implies(and(X_5087,X_1833),not(and(X_5087,X_1833))),not(and(and(X_5087,X_1833),and(X_5087,X_1833)))) )],[refute_0_465,refute_0_468]) ).
cnf(refute_0_470,plain,
or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))),
introduced(tautology,[refl,[$fot(or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))))]]) ).
cnf(refute_0_471,plain,
( implies(X_5087,not(X_1833)) != not(and(X_5087,X_1833))
| or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))) != or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833)))
| or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))),or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833)))) ),[1,1],$fot(not(and(X_5087,X_1833)))]]) ).
cnf(refute_0_472,plain,
( implies(X_5087,not(X_1833)) != not(and(X_5087,X_1833))
| or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) ),
inference(resolve,[$cnf( $equal(or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))),or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833)))) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))),
inference(resolve,[$cnf( $equal(implies(X_5087,not(X_1833)),not(and(X_5087,X_1833))) )],[refute_0_449,refute_0_472]) ).
cnf(refute_0_474,plain,
or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),
introduced(tautology,[refl,[$fot(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))))]]) ).
cnf(refute_0_475,plain,
( implies(X_5087,not(X_1833)) != not(and(X_5087,X_1833))
| or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) != or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833)))
| or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833)))) ),[1,0],$fot(not(and(X_5087,X_1833)))]]) ).
cnf(refute_0_476,plain,
( implies(X_5087,not(X_1833)) != not(and(X_5087,X_1833))
| or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))) ),
inference(resolve,[$cnf( $equal(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833)))) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))),
inference(resolve,[$cnf( $equal(implies(X_5087,not(X_1833)),not(and(X_5087,X_1833))) )],[refute_0_449,refute_0_476]) ).
cnf(refute_0_478,plain,
( or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) != or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833)))
| or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))) != or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833)))
| or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))))),bind(Y0,$fot(or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))))),bind(Z,$fot(or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833)))))]]) ).
cnf(refute_0_479,plain,
( or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))) != or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833)))
| or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) ),
inference(resolve,[$cnf( $equal(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833)))) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))),
inference(resolve,[$cnf( $equal(or(not(and(X_5087,X_1833)),implies(X_5087,not(X_1833))),or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833)))) )],[refute_0_473,refute_0_479]) ).
cnf(refute_0_481,plain,
( or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) != or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833)))
| or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) != not(and(and(X_5087,X_1833),and(X_5087,X_1833)))
| or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = not(and(and(X_5087,X_1833),and(X_5087,X_1833))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))))),bind(Y0,$fot(or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))))),bind(Z,$fot(not(and(and(X_5087,X_1833),and(X_5087,X_1833)))))]]) ).
cnf(refute_0_482,plain,
( or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))) != not(and(and(X_5087,X_1833),and(X_5087,X_1833)))
| or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = not(and(and(X_5087,X_1833),and(X_5087,X_1833))) ),
inference(resolve,[$cnf( $equal(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833)))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) = not(and(and(X_5087,X_1833),and(X_5087,X_1833))),
inference(resolve,[$cnf( $equal(or(not(and(X_5087,X_1833)),not(and(X_5087,X_1833))),not(and(and(X_5087,X_1833),and(X_5087,X_1833)))) )],[refute_0_469,refute_0_482]) ).
cnf(refute_0_484,plain,
or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) = or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),
introduced(tautology,[refl,[$fot(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))))]]) ).
cnf(refute_0_485,plain,
( or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) != not(and(and(X_5087,X_1833),and(X_5087,X_1833)))
| or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) != or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833)))
| or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) = or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833)))) ),[1,0],$fot(not(and(and(X_5087,X_1833),and(X_5087,X_1833))))]]) ).
cnf(refute_0_486,plain,
( or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))) != not(and(and(X_5087,X_1833),and(X_5087,X_1833)))
| or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) = or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))) ),
inference(resolve,[$cnf( $equal(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833)))) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) = or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))),
inference(resolve,[$cnf( $equal(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(and(X_5087,X_1833),and(X_5087,X_1833)))) )],[refute_0_483,refute_0_486]) ).
cnf(refute_0_488,plain,
( or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))) != not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))
| or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) != or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833)))
| or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) = not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))))),bind(Y0,$fot(or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))))),bind(Z,$fot(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))))]]) ).
cnf(refute_0_489,plain,
( or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))) != not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))
| or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) = not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))) ),
inference(resolve,[$cnf( $equal(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833)))) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) = not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),
inference(resolve,[$cnf( $equal(or(not(and(and(X_5087,X_1833),and(X_5087,X_1833))),not(and(X_5087,X_1833))),not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))) )],[refute_0_464,refute_0_489]) ).
cnf(refute_0_491,plain,
and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833) = and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833),
introduced(tautology,[refl,[$fot(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833))]]) ).
cnf(refute_0_492,plain,
( and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833) != and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)
| or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) != not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))
| and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833) = and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833),and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) ),[1,0],$fot(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))))]]) ).
cnf(refute_0_493,plain,
( or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))) != not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))
| and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833) = and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833) ),
inference(resolve,[$cnf( $equal(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833),and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833) = and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833),
inference(resolve,[$cnf( $equal(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))) )],[refute_0_490,refute_0_493]) ).
cnf(refute_0_495,plain,
not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) = not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)),
introduced(tautology,[refl,[$fot(not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)))]]) ).
cnf(refute_0_496,plain,
( and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833) != and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)
| not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) != not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833))
| not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) = not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)),not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833))) ),[1,0],$fot(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833))]]) ).
cnf(refute_0_497,plain,
( and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833) != and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)
| not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) = not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)) ),
inference(resolve,[$cnf( $equal(not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)),not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) = not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)),
inference(resolve,[$cnf( $equal(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833),and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)) )],[refute_0_494,refute_0_497]) ).
cnf(refute_0_499,plain,
( not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)) != or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))
| not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) != not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833))
| not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) = or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)))),bind(Y0,$fot(not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)))),bind(Z,$fot(or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))))]]) ).
cnf(refute_0_500,plain,
( not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)) != or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))
| not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) = or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) ),
inference(resolve,[$cnf( $equal(not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)),not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) = or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)),
inference(resolve,[$cnf( $equal(not(and(not(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))),X_1833)),or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) )],[refute_0_459,refute_0_500]) ).
cnf(refute_0_502,plain,
implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)) = not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)),
inference(subst,[],[refute_0_448:[bind(X,$fot(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833)))))]]) ).
cnf(refute_0_503,plain,
( implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)) != not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833))
| not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) != or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))
| implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)) = or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)))),bind(Y0,$fot(not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)))),bind(Z,$fot(or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))))]]) ).
cnf(refute_0_504,plain,
( not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)) != or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))
| implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)) = or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) ),
inference(resolve,[$cnf( $equal(implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)),not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)) = or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)),
inference(resolve,[$cnf( $equal(not(and(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),X_1833)),or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) )],[refute_0_501,refute_0_504]) ).
cnf(refute_0_506,plain,
implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))) = implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))),
introduced(tautology,[refl,[$fot(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))))]]) ).
cnf(refute_0_507,plain,
( implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))) != implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)))
| implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)) != or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))
| implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))) = implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))),implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)))) ),[1,1],$fot(or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))]]) ).
cnf(refute_0_508,plain,
( implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)) != or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))
| implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))) = implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) ),
inference(resolve,[$cnf( $equal(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))),implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)))) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))) = implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))),
inference(resolve,[$cnf( $equal(implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)),or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) )],[refute_0_505,refute_0_508]) ).
cnf(refute_0_510,plain,
( implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))) != implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))
| ~ is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))))
| is_a_theorem(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)))) ),[0],$fot(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))))]]) ).
cnf(refute_0_511,plain,
( ~ is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))))
| is_a_theorem(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))) ),
inference(resolve,[$cnf( $equal(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833))),implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
is_a_theorem(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_5087,implies(or(or(implies(X_5087,not(X_1833)),implies(X_5087,not(X_1833))),not(and(X_5087,X_1833))),not(X_1833)))) )],[refute_0_452,refute_0_511]) ).
cnf(refute_0_513,plain,
and(not(not(Y)),Y) = not(or(not(Y),not(Y))),
inference(subst,[],[refute_0_97:[bind(X_9,$fot(not(Y)))]]) ).
cnf(refute_0_514,plain,
( ~ is_a_theorem(equiv(X_8900,or(X_8900,X_8900)))
| X_8900 = or(X_8900,X_8900) ),
inference(subst,[],[refute_0_155:[bind(X,$fot(X_8900)),bind(Y,$fot(or(X_8900,X_8900)))]]) ).
cnf(refute_0_515,plain,
( ~ is_a_theorem(implies(X_8899,or(X_8899,X_8899)))
| ~ is_a_theorem(implies(implies(X_8899,or(X_8899,X_8899)),equiv(X_8899,or(X_8899,X_8899))))
| is_a_theorem(equiv(X_8899,or(X_8899,X_8899))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_8899,or(X_8899,X_8899)))),bind(Y,$fot(equiv(X_8899,or(X_8899,X_8899))))]]) ).
cnf(refute_0_516,plain,
( ~ is_a_theorem(implies(X_8895,or(and(X_8895,implies(or(X_8894,X_8894),X_8894)),and(X_8895,implies(or(X_8894,X_8894),X_8894)))))
| is_a_theorem(implies(X_8895,and(X_8895,implies(or(X_8894,X_8894),X_8894)))) ),
inference(subst,[],[refute_0_184:[bind(X,$fot(X_8895)),bind(X_2673,$fot(and(X_8895,implies(or(X_8894,X_8894),X_8894))))]]) ).
cnf(refute_0_517,plain,
( ~ is_a_theorem(implies(or(P,P),P))
| is_a_theorem(or(X_372,implies(or(P,P),P))) ),
inference(subst,[],[refute_0_17:[bind(P,$fot(X_372)),bind(X_370,$fot(implies(or(P,P),P)))]]) ).
cnf(refute_0_518,plain,
is_a_theorem(or(X_372,implies(or(P,P),P))),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,P),P)) )],[refute_0_163,refute_0_517]) ).
cnf(refute_0_519,plain,
is_a_theorem(or(X_854,implies(or(P,P),P))),
inference(subst,[],[refute_0_518:[bind(X_372,$fot(X_854))]]) ).
cnf(refute_0_520,plain,
( ~ is_a_theorem(or(X_854,implies(or(P,P),P)))
| is_a_theorem(or(implies(or(P,P),P),X_854)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_854)),bind(Q,$fot(implies(or(P,P),P)))]]) ).
cnf(refute_0_521,plain,
is_a_theorem(or(implies(or(P,P),P),X_854)),
inference(resolve,[$cnf( is_a_theorem(or(X_854,implies(or(P,P),P))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_857)),
inference(subst,[],[refute_0_521:[bind(P,$fot(not(X))),bind(X_854,$fot(X_857))]]) ).
cnf(refute_0_523,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_857))
| is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_857)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_857)) ),[0,0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_524,plain,
( ~ is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_857))
| is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_857)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_307,refute_0_523]) ).
cnf(refute_0_525,plain,
is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_857)),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(not(X),not(X)),not(X)),X_857)) )],[refute_0_522,refute_0_524]) ).
cnf(refute_0_526,plain,
and(implies(X,not(X)),X) = and(not(and(X,X)),X),
inference(subst,[],[refute_0_114:[bind(Y,$fot(X)),bind(X_20,$fot(X))]]) ).
cnf(refute_0_527,plain,
implies(and(implies(X,not(X)),X),X_857) = implies(and(implies(X,not(X)),X),X_857),
introduced(tautology,[refl,[$fot(implies(and(implies(X,not(X)),X),X_857))]]) ).
cnf(refute_0_528,plain,
( and(implies(X,not(X)),X) != and(not(and(X,X)),X)
| implies(and(implies(X,not(X)),X),X_857) != implies(and(implies(X,not(X)),X),X_857)
| implies(and(implies(X,not(X)),X),X_857) = implies(and(not(and(X,X)),X),X_857) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(implies(X,not(X)),X),X_857),implies(and(implies(X,not(X)),X),X_857)) ),[1,0],$fot(and(not(and(X,X)),X))]]) ).
cnf(refute_0_529,plain,
( and(implies(X,not(X)),X) != and(not(and(X,X)),X)
| implies(and(implies(X,not(X)),X),X_857) = implies(and(not(and(X,X)),X),X_857) ),
inference(resolve,[$cnf( $equal(implies(and(implies(X,not(X)),X),X_857),implies(and(implies(X,not(X)),X),X_857)) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
implies(and(implies(X,not(X)),X),X_857) = implies(and(not(and(X,X)),X),X_857),
inference(resolve,[$cnf( $equal(and(implies(X,not(X)),X),and(not(and(X,X)),X)) )],[refute_0_526,refute_0_529]) ).
cnf(refute_0_531,plain,
or(implies(X,not(Y)),X_10) = implies(not(implies(X,not(Y))),X_10),
inference(subst,[],[refute_0_84:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_532,plain,
( not(implies(X,not(Y))) != and(X,Y)
| or(implies(X,not(Y)),X_10) != implies(not(implies(X,not(Y))),X_10)
| or(implies(X,not(Y)),X_10) = implies(and(X,Y),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X,not(Y)),X_10),implies(not(implies(X,not(Y))),X_10)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_533,plain,
( or(implies(X,not(Y)),X_10) != implies(not(implies(X,not(Y))),X_10)
| or(implies(X,not(Y)),X_10) = implies(and(X,Y),X_10) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_64,refute_0_532]) ).
cnf(refute_0_534,plain,
or(implies(X,not(Y)),X_10) = implies(and(X,Y),X_10),
inference(resolve,[$cnf( $equal(or(implies(X,not(Y)),X_10),implies(not(implies(X,not(Y))),X_10)) )],[refute_0_531,refute_0_533]) ).
cnf(refute_0_535,plain,
or(implies(implies(X,not(X)),not(X)),X_857) = implies(and(implies(X,not(X)),X),X_857),
inference(subst,[],[refute_0_534:[bind(X,$fot(implies(X,not(X)))),bind(Y,$fot(X)),bind(X_10,$fot(X_857))]]) ).
cnf(refute_0_536,plain,
( implies(and(implies(X,not(X)),X),X_857) != implies(and(not(and(X,X)),X),X_857)
| or(implies(implies(X,not(X)),not(X)),X_857) != implies(and(implies(X,not(X)),X),X_857)
| or(implies(implies(X,not(X)),not(X)),X_857) = implies(and(not(and(X,X)),X),X_857) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(implies(implies(X,not(X)),not(X)),X_857))),bind(Y0,$fot(implies(and(implies(X,not(X)),X),X_857))),bind(Z,$fot(implies(and(not(and(X,X)),X),X_857)))]]) ).
cnf(refute_0_537,plain,
( implies(and(implies(X,not(X)),X),X_857) != implies(and(not(and(X,X)),X),X_857)
| or(implies(implies(X,not(X)),not(X)),X_857) = implies(and(not(and(X,X)),X),X_857) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,not(X)),not(X)),X_857),implies(and(implies(X,not(X)),X),X_857)) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
or(implies(implies(X,not(X)),not(X)),X_857) = implies(and(not(and(X,X)),X),X_857),
inference(resolve,[$cnf( $equal(implies(and(implies(X,not(X)),X),X_857),implies(and(not(and(X,X)),X),X_857)) )],[refute_0_530,refute_0_537]) ).
cnf(refute_0_539,plain,
( or(implies(implies(X,not(X)),not(X)),X_857) != implies(and(not(and(X,X)),X),X_857)
| ~ is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_857))
| is_a_theorem(implies(and(not(and(X,X)),X),X_857)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_857)) ),[0],$fot(implies(and(not(and(X,X)),X),X_857))]]) ).
cnf(refute_0_540,plain,
( ~ is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_857))
| is_a_theorem(implies(and(not(and(X,X)),X),X_857)) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,not(X)),not(X)),X_857),implies(and(not(and(X,X)),X),X_857)) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
is_a_theorem(implies(and(not(and(X,X)),X),X_857)),
inference(resolve,[$cnf( is_a_theorem(or(implies(implies(X,not(X)),not(X)),X_857)) )],[refute_0_525,refute_0_540]) ).
cnf(refute_0_542,plain,
is_a_theorem(implies(and(not(and(X,X)),X),X_2336)),
inference(subst,[],[refute_0_541:[bind(X_857,$fot(X_2336))]]) ).
cnf(refute_0_543,plain,
( ~ is_a_theorem(implies(and(not(and(X,X)),X),X_2336))
| is_a_theorem(implies(or(X_2334,and(not(and(X,X)),X)),or(X_2334,X_2336))) ),
inference(subst,[],[refute_0_169:[bind(P,$fot(X_2334)),bind(Q,$fot(and(not(and(X,X)),X))),bind(R,$fot(X_2336))]]) ).
cnf(refute_0_544,plain,
is_a_theorem(implies(or(X_2334,and(not(and(X,X)),X)),or(X_2334,X_2336))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(and(X,X)),X),X_2336)) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),or(not(X),X_3264))),
inference(subst,[],[refute_0_544:[bind(X,$fot(X_3262)),bind(X_2334,$fot(not(X))),bind(X_2336,$fot(X_3264))]]) ).
cnf(refute_0_546,plain,
implies(X,X_3264) = or(not(X),X_3264),
inference(subst,[],[refute_0_26:[bind(Y,$fot(X_3264))]]) ).
cnf(refute_0_547,plain,
( implies(X,X_3264) != or(not(X),X_3264)
| or(not(X),X_3264) = implies(X,X_3264) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,X_3264))),bind(Y0,$fot(or(not(X),X_3264)))]]) ).
cnf(refute_0_548,plain,
or(not(X),X_3264) = implies(X,X_3264),
inference(resolve,[$cnf( $equal(implies(X,X_3264),or(not(X),X_3264)) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
( or(not(X),X_3264) != implies(X,X_3264)
| ~ is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),or(not(X),X_3264)))
| is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),or(not(X),X_3264))) ),[0,1],$fot(implies(X,X_3264))]]) ).
cnf(refute_0_550,plain,
( ~ is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),or(not(X),X_3264)))
| is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_3264),implies(X,X_3264)) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),or(not(X),X_3264))) )],[refute_0_545,refute_0_550]) ).
cnf(refute_0_552,plain,
or(not(X),and(not(and(X_3262,X_3262)),X_3262)) = implies(X,and(not(and(X_3262,X_3262)),X_3262)),
inference(subst,[],[refute_0_37:[bind(Y,$fot(and(not(and(X_3262,X_3262)),X_3262)))]]) ).
cnf(refute_0_553,plain,
implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)) = implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)),
introduced(tautology,[refl,[$fot(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)))]]) ).
cnf(refute_0_554,plain,
( implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)) != implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))
| or(not(X),and(not(and(X_3262,X_3262)),X_3262)) != implies(X,and(not(and(X_3262,X_3262)),X_3262))
| implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)) = implies(implies(X,and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)),implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))) ),[1,0],$fot(implies(X,and(not(and(X_3262,X_3262)),X_3262)))]]) ).
cnf(refute_0_555,plain,
( or(not(X),and(not(and(X_3262,X_3262)),X_3262)) != implies(X,and(not(and(X_3262,X_3262)),X_3262))
| implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)) = implies(implies(X,and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)),implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)) = implies(implies(X,and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)),
inference(resolve,[$cnf( $equal(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,and(not(and(X_3262,X_3262)),X_3262))) )],[refute_0_552,refute_0_555]) ).
cnf(refute_0_557,plain,
( implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)) != implies(implies(X,and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))
| ~ is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)))
| is_a_theorem(implies(implies(X,and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))) ),[0],$fot(implies(implies(X,and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)))]]) ).
cnf(refute_0_558,plain,
( ~ is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)))
| is_a_theorem(implies(implies(X,and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264)),implies(implies(X,and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
is_a_theorem(implies(implies(X,and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),and(not(and(X_3262,X_3262)),X_3262)),implies(X,X_3264))) )],[refute_0_551,refute_0_558]) ).
cnf(refute_0_560,plain,
is_a_theorem(implies(implies(X_5027,and(not(and(X_3262,X_3262)),X_3262)),implies(X_5027,X_5029))),
inference(subst,[],[refute_0_559:[bind(X,$fot(X_5027)),bind(X_3264,$fot(X_5029))]]) ).
cnf(refute_0_561,plain,
( ~ is_a_theorem(implies(implies(X_5027,and(not(and(X_3262,X_3262)),X_3262)),implies(X_5027,X_5029)))
| is_a_theorem(implies(X_5027,implies(implies(X_5027,and(not(and(X_3262,X_3262)),X_3262)),X_5029))) ),
inference(subst,[],[refute_0_215:[bind(X,$fot(X_5027)),bind(X_205,$fot(implies(X_5027,and(not(and(X_3262,X_3262)),X_3262)))),bind(X_207,$fot(X_5029))]]) ).
cnf(refute_0_562,plain,
is_a_theorem(implies(X_5027,implies(implies(X_5027,and(not(and(X_3262,X_3262)),X_3262)),X_5029))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_5027,and(not(and(X_3262,X_3262)),X_3262)),implies(X_5027,X_5029))) )],[refute_0_560,refute_0_561]) ).
cnf(refute_0_563,plain,
is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(and(not(X_1833),not(X_1833))),not(X_1833))),X_8893))),
inference(subst,[],[refute_0_562:[bind(X_3262,$fot(not(X_1833))),bind(X_5027,$fot(X_8892)),bind(X_5029,$fot(X_8893))]]) ).
cnf(refute_0_564,plain,
and(X,not(X_1833)) = not(implies(X,not(not(X_1833)))),
inference(subst,[],[refute_0_62:[bind(Y,$fot(not(X_1833)))]]) ).
cnf(refute_0_565,plain,
( and(X,not(X_1833)) != not(implies(X,not(not(X_1833))))
| not(not(X_1833)) != X_1833
| and(X,not(X_1833)) = not(implies(X,X_1833)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,not(X_1833)),not(implies(X,not(not(X_1833))))) ),[1,0,1],$fot(X_1833)]]) ).
cnf(refute_0_566,plain,
( and(X,not(X_1833)) != not(implies(X,not(not(X_1833))))
| and(X,not(X_1833)) = not(implies(X,X_1833)) ),
inference(resolve,[$cnf( $equal(not(not(X_1833)),X_1833) )],[refute_0_445,refute_0_565]) ).
cnf(refute_0_567,plain,
and(X,not(X_1833)) = not(implies(X,X_1833)),
inference(resolve,[$cnf( $equal(and(X,not(X_1833)),not(implies(X,not(not(X_1833))))) )],[refute_0_564,refute_0_566]) ).
cnf(refute_0_568,plain,
and(not(X_1833),not(X_1833)) = not(implies(not(X_1833),X_1833)),
inference(subst,[],[refute_0_567:[bind(X,$fot(not(X_1833)))]]) ).
cnf(refute_0_569,plain,
( and(not(X_1833),not(X_1833)) != not(implies(not(X_1833),X_1833))
| ~ is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(and(not(X_1833),not(X_1833))),not(X_1833))),X_8893)))
| is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(and(not(X_1833),not(X_1833))),not(X_1833))),X_8893))) ),[0,1,0,1,0,0],$fot(not(implies(not(X_1833),X_1833)))]]) ).
cnf(refute_0_570,plain,
( ~ is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(and(not(X_1833),not(X_1833))),not(X_1833))),X_8893)))
| is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))) ),
inference(resolve,[$cnf( $equal(and(not(X_1833),not(X_1833)),not(implies(not(X_1833),X_1833))) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))),
inference(resolve,[$cnf( is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(and(not(X_1833),not(X_1833))),not(X_1833))),X_8893))) )],[refute_0_563,refute_0_570]) ).
cnf(refute_0_572,plain,
implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893) = or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893),
inference(subst,[],[refute_0_295:[bind(X,$fot(and(X_8892,implies(or(X_1833,X_1833),X_1833)))),bind(Y,$fot(X_8893))]]) ).
cnf(refute_0_573,plain,
implies(X_8892,not(implies(or(X_1833,X_1833),X_1833))) = not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_8892)),bind(X_1833,$fot(implies(or(X_1833,X_1833),X_1833)))]]) ).
cnf(refute_0_574,plain,
implies(not(X_1833),X_1833) = or(X_1833,X_1833),
inference(subst,[],[refute_0_295:[bind(X,$fot(X_1833)),bind(Y,$fot(X_1833))]]) ).
cnf(refute_0_575,plain,
implies(implies(not(X_1833),X_1833),X_1833) = implies(implies(not(X_1833),X_1833),X_1833),
introduced(tautology,[refl,[$fot(implies(implies(not(X_1833),X_1833),X_1833))]]) ).
cnf(refute_0_576,plain,
( implies(implies(not(X_1833),X_1833),X_1833) != implies(implies(not(X_1833),X_1833),X_1833)
| implies(not(X_1833),X_1833) != or(X_1833,X_1833)
| implies(implies(not(X_1833),X_1833),X_1833) = implies(or(X_1833,X_1833),X_1833) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_1833),X_1833),X_1833),implies(implies(not(X_1833),X_1833),X_1833)) ),[1,0],$fot(or(X_1833,X_1833))]]) ).
cnf(refute_0_577,plain,
( implies(not(X_1833),X_1833) != or(X_1833,X_1833)
| implies(implies(not(X_1833),X_1833),X_1833) = implies(or(X_1833,X_1833),X_1833) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_1833),X_1833),X_1833),implies(implies(not(X_1833),X_1833),X_1833)) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
implies(implies(not(X_1833),X_1833),X_1833) = implies(or(X_1833,X_1833),X_1833),
inference(resolve,[$cnf( $equal(implies(not(X_1833),X_1833),or(X_1833,X_1833)) )],[refute_0_574,refute_0_577]) ).
cnf(refute_0_579,plain,
or(not(implies(not(X_1833),X_1833)),X_1833) = implies(implies(not(X_1833),X_1833),X_1833),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(not(X_1833),X_1833))),bind(Y,$fot(X_1833))]]) ).
cnf(refute_0_580,plain,
implies(not(not(implies(not(X_1833),X_1833))),X_1833) = or(not(implies(not(X_1833),X_1833)),X_1833),
inference(subst,[],[refute_0_295:[bind(X,$fot(not(implies(not(X_1833),X_1833)))),bind(Y,$fot(X_1833))]]) ).
cnf(refute_0_581,plain,
( implies(not(not(implies(not(X_1833),X_1833))),X_1833) != or(not(implies(not(X_1833),X_1833)),X_1833)
| or(not(implies(not(X_1833),X_1833)),X_1833) != implies(implies(not(X_1833),X_1833),X_1833)
| implies(not(not(implies(not(X_1833),X_1833))),X_1833) = implies(implies(not(X_1833),X_1833),X_1833) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(not(not(implies(not(X_1833),X_1833))),X_1833))),bind(Y0,$fot(or(not(implies(not(X_1833),X_1833)),X_1833))),bind(Z,$fot(implies(implies(not(X_1833),X_1833),X_1833)))]]) ).
cnf(refute_0_582,plain,
( or(not(implies(not(X_1833),X_1833)),X_1833) != implies(implies(not(X_1833),X_1833),X_1833)
| implies(not(not(implies(not(X_1833),X_1833))),X_1833) = implies(implies(not(X_1833),X_1833),X_1833) ),
inference(resolve,[$cnf( $equal(implies(not(not(implies(not(X_1833),X_1833))),X_1833),or(not(implies(not(X_1833),X_1833)),X_1833)) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
implies(not(not(implies(not(X_1833),X_1833))),X_1833) = implies(implies(not(X_1833),X_1833),X_1833),
inference(resolve,[$cnf( $equal(or(not(implies(not(X_1833),X_1833)),X_1833),implies(implies(not(X_1833),X_1833),X_1833)) )],[refute_0_579,refute_0_582]) ).
cnf(refute_0_584,plain,
( implies(implies(not(X_1833),X_1833),X_1833) != implies(or(X_1833,X_1833),X_1833)
| implies(not(not(implies(not(X_1833),X_1833))),X_1833) != implies(implies(not(X_1833),X_1833),X_1833)
| implies(not(not(implies(not(X_1833),X_1833))),X_1833) = implies(or(X_1833,X_1833),X_1833) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(not(not(implies(not(X_1833),X_1833))),X_1833))),bind(Y0,$fot(implies(implies(not(X_1833),X_1833),X_1833))),bind(Z,$fot(implies(or(X_1833,X_1833),X_1833)))]]) ).
cnf(refute_0_585,plain,
( implies(implies(not(X_1833),X_1833),X_1833) != implies(or(X_1833,X_1833),X_1833)
| implies(not(not(implies(not(X_1833),X_1833))),X_1833) = implies(or(X_1833,X_1833),X_1833) ),
inference(resolve,[$cnf( $equal(implies(not(not(implies(not(X_1833),X_1833))),X_1833),implies(implies(not(X_1833),X_1833),X_1833)) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
implies(not(not(implies(not(X_1833),X_1833))),X_1833) = implies(or(X_1833,X_1833),X_1833),
inference(resolve,[$cnf( $equal(implies(implies(not(X_1833),X_1833),X_1833),implies(or(X_1833,X_1833),X_1833)) )],[refute_0_578,refute_0_585]) ).
cnf(refute_0_587,plain,
not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)) = not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)),
introduced(tautology,[refl,[$fot(not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)))]]) ).
cnf(refute_0_588,plain,
( implies(not(not(implies(not(X_1833),X_1833))),X_1833) != implies(or(X_1833,X_1833),X_1833)
| not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)) != not(implies(not(not(implies(not(X_1833),X_1833))),X_1833))
| not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)) = not(implies(or(X_1833,X_1833),X_1833)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)),not(implies(not(not(implies(not(X_1833),X_1833))),X_1833))) ),[1,0],$fot(implies(or(X_1833,X_1833),X_1833))]]) ).
cnf(refute_0_589,plain,
( implies(not(not(implies(not(X_1833),X_1833))),X_1833) != implies(or(X_1833,X_1833),X_1833)
| not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)) = not(implies(or(X_1833,X_1833),X_1833)) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)),not(implies(not(not(implies(not(X_1833),X_1833))),X_1833))) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)) = not(implies(or(X_1833,X_1833),X_1833)),
inference(resolve,[$cnf( $equal(implies(not(not(implies(not(X_1833),X_1833))),X_1833),implies(or(X_1833,X_1833),X_1833)) )],[refute_0_586,refute_0_589]) ).
cnf(refute_0_591,plain,
and(not(not(implies(not(X_1833),X_1833))),not(X_1833)) = not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)),
inference(subst,[],[refute_0_567:[bind(X,$fot(not(not(implies(not(X_1833),X_1833)))))]]) ).
cnf(refute_0_592,plain,
( and(not(not(implies(not(X_1833),X_1833))),not(X_1833)) != not(implies(not(not(implies(not(X_1833),X_1833))),X_1833))
| not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)) != not(implies(or(X_1833,X_1833),X_1833))
| and(not(not(implies(not(X_1833),X_1833))),not(X_1833)) = not(implies(or(X_1833,X_1833),X_1833)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(not(not(implies(not(X_1833),X_1833))),not(X_1833)))),bind(Y0,$fot(not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)))),bind(Z,$fot(not(implies(or(X_1833,X_1833),X_1833))))]]) ).
cnf(refute_0_593,plain,
( not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)) != not(implies(or(X_1833,X_1833),X_1833))
| and(not(not(implies(not(X_1833),X_1833))),not(X_1833)) = not(implies(or(X_1833,X_1833),X_1833)) ),
inference(resolve,[$cnf( $equal(and(not(not(implies(not(X_1833),X_1833))),not(X_1833)),not(implies(not(not(implies(not(X_1833),X_1833))),X_1833))) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
and(not(not(implies(not(X_1833),X_1833))),not(X_1833)) = not(implies(or(X_1833,X_1833),X_1833)),
inference(resolve,[$cnf( $equal(not(implies(not(not(implies(not(X_1833),X_1833))),X_1833)),not(implies(or(X_1833,X_1833),X_1833))) )],[refute_0_590,refute_0_593]) ).
cnf(refute_0_595,plain,
implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) = implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),
introduced(tautology,[refl,[$fot(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))))]]) ).
cnf(refute_0_596,plain,
( and(not(not(implies(not(X_1833),X_1833))),not(X_1833)) != not(implies(or(X_1833,X_1833),X_1833))
| implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) != implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833)))
| implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) = implies(X_8892,not(implies(or(X_1833,X_1833),X_1833))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833)))) ),[1,1],$fot(not(implies(or(X_1833,X_1833),X_1833)))]]) ).
cnf(refute_0_597,plain,
( and(not(not(implies(not(X_1833),X_1833))),not(X_1833)) != not(implies(or(X_1833,X_1833),X_1833))
| implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) = implies(X_8892,not(implies(or(X_1833,X_1833),X_1833))) ),
inference(resolve,[$cnf( $equal(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833)))) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) = implies(X_8892,not(implies(or(X_1833,X_1833),X_1833))),
inference(resolve,[$cnf( $equal(and(not(not(implies(not(X_1833),X_1833))),not(X_1833)),not(implies(or(X_1833,X_1833),X_1833))) )],[refute_0_594,refute_0_597]) ).
cnf(refute_0_599,plain,
( implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) != implies(X_8892,not(implies(or(X_1833,X_1833),X_1833)))
| implies(X_8892,not(implies(or(X_1833,X_1833),X_1833))) != not(and(X_8892,implies(or(X_1833,X_1833),X_1833)))
| implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) = not(and(X_8892,implies(or(X_1833,X_1833),X_1833))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))))),bind(Y0,$fot(implies(X_8892,not(implies(or(X_1833,X_1833),X_1833))))),bind(Z,$fot(not(and(X_8892,implies(or(X_1833,X_1833),X_1833)))))]]) ).
cnf(refute_0_600,plain,
( implies(X_8892,not(implies(or(X_1833,X_1833),X_1833))) != not(and(X_8892,implies(or(X_1833,X_1833),X_1833)))
| implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) = not(and(X_8892,implies(or(X_1833,X_1833),X_1833))) ),
inference(resolve,[$cnf( $equal(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),implies(X_8892,not(implies(or(X_1833,X_1833),X_1833)))) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) = not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),
inference(resolve,[$cnf( $equal(implies(X_8892,not(implies(or(X_1833,X_1833),X_1833))),not(and(X_8892,implies(or(X_1833,X_1833),X_1833)))) )],[refute_0_573,refute_0_600]) ).
cnf(refute_0_602,plain,
implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) = implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893),
introduced(tautology,[refl,[$fot(implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))]]) ).
cnf(refute_0_603,plain,
( implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) != not(and(X_8892,implies(or(X_1833,X_1833),X_1833)))
| implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) != implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)
| implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) = implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893),implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)) ),[1,0],$fot(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))))]]) ).
cnf(refute_0_604,plain,
( implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))) != not(and(X_8892,implies(or(X_1833,X_1833),X_1833)))
| implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) = implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893) ),
inference(resolve,[$cnf( $equal(implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893),implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) = implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893),
inference(resolve,[$cnf( $equal(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),not(and(X_8892,implies(or(X_1833,X_1833),X_1833)))) )],[refute_0_601,refute_0_604]) ).
cnf(refute_0_606,plain,
( implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) != implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893)
| implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893) != or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)
| implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) = or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))),bind(Y0,$fot(implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893))),bind(Z,$fot(or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)))]]) ).
cnf(refute_0_607,plain,
( implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893) != or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)
| implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) = or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893) ),
inference(resolve,[$cnf( $equal(implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893),implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893)) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) = or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893),
inference(resolve,[$cnf( $equal(implies(not(and(X_8892,implies(or(X_1833,X_1833),X_1833))),X_8893),or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)) )],[refute_0_572,refute_0_607]) ).
cnf(refute_0_609,plain,
implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)) = implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)),
introduced(tautology,[refl,[$fot(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)))]]) ).
cnf(refute_0_610,plain,
( implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)) != implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))
| implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) != or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)
| implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)) = implies(X_8892,or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)),implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))) ),[1,1],$fot(or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893))]]) ).
cnf(refute_0_611,plain,
( implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893) != or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)
| implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)) = implies(X_8892,or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)) ),
inference(resolve,[$cnf( $equal(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)),implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)) = implies(X_8892,or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)),
inference(resolve,[$cnf( $equal(implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893),or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)) )],[refute_0_608,refute_0_611]) ).
cnf(refute_0_613,plain,
( implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)) != implies(X_8892,or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893))
| ~ is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)))
| is_a_theorem(implies(X_8892,or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))) ),[0],$fot(implies(X_8892,or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893)))]]) ).
cnf(refute_0_614,plain,
( ~ is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)))
| is_a_theorem(implies(X_8892,or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893))) ),
inference(resolve,[$cnf( $equal(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893)),implies(X_8892,or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893))) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
is_a_theorem(implies(X_8892,or(and(X_8892,implies(or(X_1833,X_1833),X_1833)),X_8893))),
inference(resolve,[$cnf( is_a_theorem(implies(X_8892,implies(implies(X_8892,and(not(not(implies(not(X_1833),X_1833))),not(X_1833))),X_8893))) )],[refute_0_571,refute_0_614]) ).
cnf(refute_0_616,plain,
is_a_theorem(implies(X_8895,or(and(X_8895,implies(or(X_8894,X_8894),X_8894)),and(X_8895,implies(or(X_8894,X_8894),X_8894))))),
inference(subst,[],[refute_0_615:[bind(X_1833,$fot(X_8894)),bind(X_8892,$fot(X_8895)),bind(X_8893,$fot(and(X_8895,implies(or(X_8894,X_8894),X_8894))))]]) ).
cnf(refute_0_617,plain,
is_a_theorem(implies(X_8895,and(X_8895,implies(or(X_8894,X_8894),X_8894)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_8895,or(and(X_8895,implies(or(X_8894,X_8894),X_8894)),and(X_8895,implies(or(X_8894,X_8894),X_8894))))) )],[refute_0_616,refute_0_516]) ).
cnf(refute_0_618,plain,
is_a_theorem(implies(implies(X_8897,or(X_8897,X_8897)),and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897)))),
inference(subst,[],[refute_0_617:[bind(X_8894,$fot(X_8897)),bind(X_8895,$fot(implies(X_8897,or(X_8897,X_8897))))]]) ).
cnf(refute_0_619,plain,
equiv(X_8897,or(X_8897,X_8897)) = and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897)),
inference(subst,[],[refute_0_71:[bind(X,$fot(X_8897)),bind(Y,$fot(or(X_8897,X_8897)))]]) ).
cnf(refute_0_620,plain,
( equiv(X_8897,or(X_8897,X_8897)) != and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897))
| and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897)) = equiv(X_8897,or(X_8897,X_8897)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X_8897,or(X_8897,X_8897)))),bind(Y0,$fot(and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897))))]]) ).
cnf(refute_0_621,plain,
and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897)) = equiv(X_8897,or(X_8897,X_8897)),
inference(resolve,[$cnf( $equal(equiv(X_8897,or(X_8897,X_8897)),and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897))) )],[refute_0_619,refute_0_620]) ).
cnf(refute_0_622,plain,
( and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897)) != equiv(X_8897,or(X_8897,X_8897))
| ~ is_a_theorem(implies(implies(X_8897,or(X_8897,X_8897)),and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897))))
| is_a_theorem(implies(implies(X_8897,or(X_8897,X_8897)),equiv(X_8897,or(X_8897,X_8897)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_8897,or(X_8897,X_8897)),and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897)))) ),[0,1],$fot(equiv(X_8897,or(X_8897,X_8897)))]]) ).
cnf(refute_0_623,plain,
( ~ is_a_theorem(implies(implies(X_8897,or(X_8897,X_8897)),and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897))))
| is_a_theorem(implies(implies(X_8897,or(X_8897,X_8897)),equiv(X_8897,or(X_8897,X_8897)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897)),equiv(X_8897,or(X_8897,X_8897))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
is_a_theorem(implies(implies(X_8897,or(X_8897,X_8897)),equiv(X_8897,or(X_8897,X_8897)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_8897,or(X_8897,X_8897)),and(implies(X_8897,or(X_8897,X_8897)),implies(or(X_8897,X_8897),X_8897)))) )],[refute_0_618,refute_0_623]) ).
cnf(refute_0_625,plain,
is_a_theorem(implies(implies(X_8899,or(X_8899,X_8899)),equiv(X_8899,or(X_8899,X_8899)))),
inference(subst,[],[refute_0_624:[bind(X_8897,$fot(X_8899))]]) ).
cnf(refute_0_626,plain,
( ~ is_a_theorem(implies(X_8899,or(X_8899,X_8899)))
| is_a_theorem(equiv(X_8899,or(X_8899,X_8899))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_8899,or(X_8899,X_8899)),equiv(X_8899,or(X_8899,X_8899)))) )],[refute_0_625,refute_0_515]) ).
cnf(refute_0_627,plain,
is_a_theorem(implies(X_8899,or(X_8899,X_8899))),
inference(subst,[],[refute_0_14:[bind(P,$fot(X_8899)),bind(Q,$fot(X_8899))]]) ).
cnf(refute_0_628,plain,
is_a_theorem(equiv(X_8899,or(X_8899,X_8899))),
inference(resolve,[$cnf( is_a_theorem(implies(X_8899,or(X_8899,X_8899))) )],[refute_0_627,refute_0_626]) ).
cnf(refute_0_629,plain,
is_a_theorem(equiv(X_8900,or(X_8900,X_8900))),
inference(subst,[],[refute_0_628:[bind(X_8899,$fot(X_8900))]]) ).
cnf(refute_0_630,plain,
X_8900 = or(X_8900,X_8900),
inference(resolve,[$cnf( is_a_theorem(equiv(X_8900,or(X_8900,X_8900))) )],[refute_0_629,refute_0_514]) ).
cnf(refute_0_631,plain,
not(Y) = or(not(Y),not(Y)),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(not(Y)))]]) ).
cnf(refute_0_632,plain,
( not(Y) != or(not(Y),not(Y))
| or(not(Y),not(Y)) = not(Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(not(Y))),bind(Y0,$fot(or(not(Y),not(Y))))]]) ).
cnf(refute_0_633,plain,
or(not(Y),not(Y)) = not(Y),
inference(resolve,[$cnf( $equal(not(Y),or(not(Y),not(Y))) )],[refute_0_631,refute_0_632]) ).
cnf(refute_0_634,plain,
( and(not(not(Y)),Y) != not(or(not(Y),not(Y)))
| or(not(Y),not(Y)) != not(Y)
| and(not(not(Y)),Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(Y)),Y),not(or(not(Y),not(Y)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_635,plain,
( and(not(not(Y)),Y) != not(or(not(Y),not(Y)))
| and(not(not(Y)),Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(or(not(Y),not(Y)),not(Y)) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
and(not(not(Y)),Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(and(not(not(Y)),Y),not(or(not(Y),not(Y)))) )],[refute_0_513,refute_0_635]) ).
cnf(refute_0_637,plain,
( X_1832 != not(not(X_1832))
| not(not(X_1832)) = X_1832 ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(X_1832)),bind(Y0,$fot(not(not(X_1832))))]]) ).
cnf(refute_0_638,plain,
not(not(X_1832)) = X_1832,
inference(resolve,[$cnf( $equal(X_1832,not(not(X_1832))) )],[refute_0_442,refute_0_637]) ).
cnf(refute_0_639,plain,
not(not(Y)) = Y,
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(Y))]]) ).
cnf(refute_0_640,plain,
and(not(not(Y)),Y) = and(not(not(Y)),Y),
introduced(tautology,[refl,[$fot(and(not(not(Y)),Y))]]) ).
cnf(refute_0_641,plain,
( and(not(not(Y)),Y) != and(not(not(Y)),Y)
| not(not(Y)) != Y
| and(not(not(Y)),Y) = and(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(Y)),Y),and(not(not(Y)),Y)) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_642,plain,
( not(not(Y)) != Y
| and(not(not(Y)),Y) = and(Y,Y) ),
inference(resolve,[$cnf( $equal(and(not(not(Y)),Y),and(not(not(Y)),Y)) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
and(not(not(Y)),Y) = and(Y,Y),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_639,refute_0_642]) ).
cnf(refute_0_644,plain,
( and(not(not(Y)),Y) != and(Y,Y)
| and(not(not(Y)),Y) != not(not(Y))
| and(Y,Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(Y)),Y),not(not(Y))) ),[0],$fot(and(Y,Y))]]) ).
cnf(refute_0_645,plain,
( and(not(not(Y)),Y) != not(not(Y))
| and(Y,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(and(not(not(Y)),Y),and(Y,Y)) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
( and(Y,Y) != not(not(Y))
| not(not(Y)) != Y
| and(Y,Y) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(Y,Y),Y) ),[0],$fot(not(not(Y)))]]) ).
cnf(refute_0_647,plain,
( and(Y,Y) != not(not(Y))
| and(Y,Y) = Y ),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_639,refute_0_646]) ).
cnf(refute_0_648,plain,
( and(not(not(Y)),Y) != not(not(Y))
| and(Y,Y) = Y ),
inference(resolve,[$cnf( $equal(and(Y,Y),not(not(Y))) )],[refute_0_645,refute_0_647]) ).
cnf(refute_0_649,plain,
and(Y,Y) = Y,
inference(resolve,[$cnf( $equal(and(not(not(Y)),Y),not(not(Y))) )],[refute_0_636,refute_0_648]) ).
cnf(refute_0_650,plain,
and(and(X_5087,X_1833),and(X_5087,X_1833)) = and(X_5087,X_1833),
inference(subst,[],[refute_0_649:[bind(Y,$fot(and(X_5087,X_1833)))]]) ).
cnf(refute_0_651,plain,
and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) = and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),
introduced(tautology,[refl,[$fot(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))]]) ).
cnf(refute_0_652,plain,
( and(and(X_5087,X_1833),and(X_5087,X_1833)) != and(X_5087,X_1833)
| and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) != and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))
| and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) = and(and(X_5087,X_1833),and(X_5087,X_1833)) ),
introduced(tautology,[equality,[$cnf( $equal(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))) ),[1,0],$fot(and(X_5087,X_1833))]]) ).
cnf(refute_0_653,plain,
( and(and(X_5087,X_1833),and(X_5087,X_1833)) != and(X_5087,X_1833)
| and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) = and(and(X_5087,X_1833),and(X_5087,X_1833)) ),
inference(resolve,[$cnf( $equal(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833))) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) = and(and(X_5087,X_1833),and(X_5087,X_1833)),
inference(resolve,[$cnf( $equal(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) )],[refute_0_650,refute_0_653]) ).
cnf(refute_0_655,plain,
( and(and(X_5087,X_1833),and(X_5087,X_1833)) != and(X_5087,X_1833)
| and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) != and(and(X_5087,X_1833),and(X_5087,X_1833))
| and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) = and(X_5087,X_1833) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)))),bind(Y0,$fot(and(and(X_5087,X_1833),and(X_5087,X_1833)))),bind(Z,$fot(and(X_5087,X_1833)))]]) ).
cnf(refute_0_656,plain,
( and(and(X_5087,X_1833),and(X_5087,X_1833)) != and(X_5087,X_1833)
| and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) = and(X_5087,X_1833) ),
inference(resolve,[$cnf( $equal(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),and(and(X_5087,X_1833),and(X_5087,X_1833))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) = and(X_5087,X_1833),
inference(resolve,[$cnf( $equal(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) )],[refute_0_650,refute_0_656]) ).
cnf(refute_0_658,plain,
or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) = or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)),
introduced(tautology,[refl,[$fot(or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))]]) ).
cnf(refute_0_659,plain,
( and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) != and(X_5087,X_1833)
| or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) != or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))
| or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) = or(and(X_5087,X_1833),not(X_1833)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)),or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) ),[1,0],$fot(and(X_5087,X_1833))]]) ).
cnf(refute_0_660,plain,
( and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)) != and(X_5087,X_1833)
| or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) = or(and(X_5087,X_1833),not(X_1833)) ),
inference(resolve,[$cnf( $equal(or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)),or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) = or(and(X_5087,X_1833),not(X_1833)),
inference(resolve,[$cnf( $equal(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),and(X_5087,X_1833)) )],[refute_0_657,refute_0_660]) ).
cnf(refute_0_662,plain,
implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) = implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))),
introduced(tautology,[refl,[$fot(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))))]]) ).
cnf(refute_0_663,plain,
( implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) != implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))
| or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) != or(and(X_5087,X_1833),not(X_1833))
| implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) = implies(X_5087,or(and(X_5087,X_1833),not(X_1833))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))),implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))) ),[1,1],$fot(or(and(X_5087,X_1833),not(X_1833)))]]) ).
cnf(refute_0_664,plain,
( or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)) != or(and(X_5087,X_1833),not(X_1833))
| implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) = implies(X_5087,or(and(X_5087,X_1833),not(X_1833))) ),
inference(resolve,[$cnf( $equal(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))),implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) = implies(X_5087,or(and(X_5087,X_1833),not(X_1833))),
inference(resolve,[$cnf( $equal(or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)),or(and(X_5087,X_1833),not(X_1833))) )],[refute_0_661,refute_0_664]) ).
cnf(refute_0_666,plain,
( implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))) != implies(X_5087,or(and(X_5087,X_1833),not(X_1833)))
| ~ is_a_theorem(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))))
| is_a_theorem(implies(X_5087,or(and(X_5087,X_1833),not(X_1833)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))) ),[0],$fot(implies(X_5087,or(and(X_5087,X_1833),not(X_1833))))]]) ).
cnf(refute_0_667,plain,
( ~ is_a_theorem(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))))
| is_a_theorem(implies(X_5087,or(and(X_5087,X_1833),not(X_1833)))) ),
inference(resolve,[$cnf( $equal(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833))),implies(X_5087,or(and(X_5087,X_1833),not(X_1833)))) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
is_a_theorem(implies(X_5087,or(and(X_5087,X_1833),not(X_1833)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_5087,or(and(and(and(X_5087,X_1833),and(X_5087,X_1833)),and(X_5087,X_1833)),not(X_1833)))) )],[refute_0_512,refute_0_667]) ).
cnf(refute_0_669,plain,
is_a_theorem(implies(X_9167,or(and(X_9167,X_9166),not(X_9166)))),
inference(subst,[],[refute_0_668:[bind(X_1833,$fot(X_9166)),bind(X_5087,$fot(X_9167))]]) ).
cnf(refute_0_670,plain,
( ~ is_a_theorem(X_9167)
| is_a_theorem(or(and(X_9167,X_9166),not(X_9166))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_9167,or(and(X_9167,X_9166),not(X_9166)))) )],[refute_0_669,refute_0_159]) ).
cnf(refute_0_671,plain,
( ~ is_a_theorem(implies(or(X_26385,X_26387),or(or(X_26386,X_26387),X_26385)))
| is_a_theorem(or(and(implies(or(X_26385,X_26387),or(or(X_26386,X_26387),X_26385)),X_9166),not(X_9166))) ),
inference(subst,[],[refute_0_670:[bind(X_9167,$fot(implies(or(X_26385,X_26387),or(or(X_26386,X_26387),X_26385))))]]) ).
cnf(refute_0_672,plain,
( ~ is_a_theorem(implies(and(implies(X_5218,X_5220),X_5218),implies(X_5219,X_5220)))
| is_a_theorem(or(implies(X_5219,X_5220),not(and(implies(X_5218,X_5220),X_5218)))) ),
inference(subst,[],[refute_0_364:[bind(Q,$fot(implies(X_5219,X_5220))),bind(X_17,$fot(and(implies(X_5218,X_5220),X_5218)))]]) ).
cnf(refute_0_673,plain,
is_a_theorem(implies(Q,or(not(X_17),Q))),
inference(subst,[],[refute_0_14:[bind(P,$fot(not(X_17)))]]) ).
cnf(refute_0_674,plain,
( or(not(X_17),Q) != implies(X_17,Q)
| ~ is_a_theorem(implies(Q,or(not(X_17),Q)))
| is_a_theorem(implies(Q,implies(X_17,Q))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(Q,or(not(X_17),Q))) ),[0,1],$fot(implies(X_17,Q))]]) ).
cnf(refute_0_675,plain,
( ~ is_a_theorem(implies(Q,or(not(X_17),Q)))
| is_a_theorem(implies(Q,implies(X_17,Q))) ),
inference(resolve,[$cnf( $equal(or(not(X_17),Q),implies(X_17,Q)) )],[refute_0_359,refute_0_674]) ).
cnf(refute_0_676,plain,
is_a_theorem(implies(Q,implies(X_17,Q))),
inference(resolve,[$cnf( is_a_theorem(implies(Q,or(not(X_17),Q))) )],[refute_0_673,refute_0_675]) ).
cnf(refute_0_677,plain,
is_a_theorem(implies(X_370,implies(X_17,X_370))),
inference(subst,[],[refute_0_676:[bind(Q,$fot(X_370))]]) ).
cnf(refute_0_678,plain,
( ~ is_a_theorem(X_370)
| ~ is_a_theorem(implies(X_370,implies(X_17,X_370)))
| is_a_theorem(implies(X_17,X_370)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_370)),bind(Y,$fot(implies(X_17,X_370)))]]) ).
cnf(refute_0_679,plain,
( ~ is_a_theorem(X_370)
| is_a_theorem(implies(X_17,X_370)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_370,implies(X_17,X_370))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
( ~ is_a_theorem(or(implies(or(X_1963,X_1964),X_1963),X_1964))
| is_a_theorem(implies(X_17,or(implies(or(X_1963,X_1964),X_1963),X_1964))) ),
inference(subst,[],[refute_0_679:[bind(X_370,$fot(or(implies(or(X_1963,X_1964),X_1963),X_1964)))]]) ).
cnf(refute_0_681,plain,
( ~ is_a_theorem(or(X_1851,not(and(implies(X_1850,X_1851),X_1850))))
| is_a_theorem(or(not(and(implies(X_1850,X_1851),X_1850)),X_1851)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_1851)),bind(Q,$fot(not(and(implies(X_1850,X_1851),X_1850))))]]) ).
cnf(refute_0_682,plain,
is_a_theorem(implies(implies(X_17,X_1814),or(X_1814,not(X_17)))),
inference(subst,[],[refute_0_362:[bind(Q,$fot(X_1814))]]) ).
cnf(refute_0_683,plain,
( ~ is_a_theorem(implies(implies(X_17,X_1814),or(X_1814,not(X_17))))
| is_a_theorem(or(X_1814,implies(implies(X_17,X_1814),not(X_17)))) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(implies(X_17,X_1814))),bind(X_68,$fot(X_1814)),bind(X_69,$fot(not(X_17)))]]) ).
cnf(refute_0_684,plain,
is_a_theorem(or(X_1814,implies(implies(X_17,X_1814),not(X_17)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_17,X_1814),or(X_1814,not(X_17)))) )],[refute_0_682,refute_0_683]) ).
cnf(refute_0_685,plain,
implies(implies(X_17,X_1814),not(X_17)) = not(and(implies(X_17,X_1814),X_17)),
inference(subst,[],[refute_0_448:[bind(X,$fot(implies(X_17,X_1814))),bind(X_1833,$fot(X_17))]]) ).
cnf(refute_0_686,plain,
or(X_1814,implies(implies(X_17,X_1814),not(X_17))) = or(X_1814,implies(implies(X_17,X_1814),not(X_17))),
introduced(tautology,[refl,[$fot(or(X_1814,implies(implies(X_17,X_1814),not(X_17))))]]) ).
cnf(refute_0_687,plain,
( implies(implies(X_17,X_1814),not(X_17)) != not(and(implies(X_17,X_1814),X_17))
| or(X_1814,implies(implies(X_17,X_1814),not(X_17))) != or(X_1814,implies(implies(X_17,X_1814),not(X_17)))
| or(X_1814,implies(implies(X_17,X_1814),not(X_17))) = or(X_1814,not(and(implies(X_17,X_1814),X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_1814,implies(implies(X_17,X_1814),not(X_17))),or(X_1814,implies(implies(X_17,X_1814),not(X_17)))) ),[1,1],$fot(not(and(implies(X_17,X_1814),X_17)))]]) ).
cnf(refute_0_688,plain,
( implies(implies(X_17,X_1814),not(X_17)) != not(and(implies(X_17,X_1814),X_17))
| or(X_1814,implies(implies(X_17,X_1814),not(X_17))) = or(X_1814,not(and(implies(X_17,X_1814),X_17))) ),
inference(resolve,[$cnf( $equal(or(X_1814,implies(implies(X_17,X_1814),not(X_17))),or(X_1814,implies(implies(X_17,X_1814),not(X_17)))) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
or(X_1814,implies(implies(X_17,X_1814),not(X_17))) = or(X_1814,not(and(implies(X_17,X_1814),X_17))),
inference(resolve,[$cnf( $equal(implies(implies(X_17,X_1814),not(X_17)),not(and(implies(X_17,X_1814),X_17))) )],[refute_0_685,refute_0_688]) ).
cnf(refute_0_690,plain,
( or(X_1814,implies(implies(X_17,X_1814),not(X_17))) != or(X_1814,not(and(implies(X_17,X_1814),X_17)))
| ~ is_a_theorem(or(X_1814,implies(implies(X_17,X_1814),not(X_17))))
| is_a_theorem(or(X_1814,not(and(implies(X_17,X_1814),X_17)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_1814,implies(implies(X_17,X_1814),not(X_17)))) ),[0],$fot(or(X_1814,not(and(implies(X_17,X_1814),X_17))))]]) ).
cnf(refute_0_691,plain,
( ~ is_a_theorem(or(X_1814,implies(implies(X_17,X_1814),not(X_17))))
| is_a_theorem(or(X_1814,not(and(implies(X_17,X_1814),X_17)))) ),
inference(resolve,[$cnf( $equal(or(X_1814,implies(implies(X_17,X_1814),not(X_17))),or(X_1814,not(and(implies(X_17,X_1814),X_17)))) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
is_a_theorem(or(X_1814,not(and(implies(X_17,X_1814),X_17)))),
inference(resolve,[$cnf( is_a_theorem(or(X_1814,implies(implies(X_17,X_1814),not(X_17)))) )],[refute_0_684,refute_0_691]) ).
cnf(refute_0_693,plain,
is_a_theorem(or(X_1851,not(and(implies(X_1850,X_1851),X_1850)))),
inference(subst,[],[refute_0_692:[bind(X_17,$fot(X_1850)),bind(X_1814,$fot(X_1851))]]) ).
cnf(refute_0_694,plain,
is_a_theorem(or(not(and(implies(X_1850,X_1851),X_1850)),X_1851)),
inference(resolve,[$cnf( is_a_theorem(or(X_1851,not(and(implies(X_1850,X_1851),X_1850)))) )],[refute_0_693,refute_0_681]) ).
cnf(refute_0_695,plain,
or(not(and(implies(X_1850,X_1851),X_1850)),X_1851) = implies(and(implies(X_1850,X_1851),X_1850),X_1851),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(implies(X_1850,X_1851),X_1850))),bind(Y,$fot(X_1851))]]) ).
cnf(refute_0_696,plain,
( or(not(and(implies(X_1850,X_1851),X_1850)),X_1851) != implies(and(implies(X_1850,X_1851),X_1850),X_1851)
| ~ is_a_theorem(or(not(and(implies(X_1850,X_1851),X_1850)),X_1851))
| is_a_theorem(implies(and(implies(X_1850,X_1851),X_1850),X_1851)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(and(implies(X_1850,X_1851),X_1850)),X_1851)) ),[0],$fot(implies(and(implies(X_1850,X_1851),X_1850),X_1851))]]) ).
cnf(refute_0_697,plain,
( ~ is_a_theorem(or(not(and(implies(X_1850,X_1851),X_1850)),X_1851))
| is_a_theorem(implies(and(implies(X_1850,X_1851),X_1850),X_1851)) ),
inference(resolve,[$cnf( $equal(or(not(and(implies(X_1850,X_1851),X_1850)),X_1851),implies(and(implies(X_1850,X_1851),X_1850),X_1851)) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
is_a_theorem(implies(and(implies(X_1850,X_1851),X_1850),X_1851)),
inference(resolve,[$cnf( is_a_theorem(or(not(and(implies(X_1850,X_1851),X_1850)),X_1851)) )],[refute_0_694,refute_0_697]) ).
cnf(refute_0_699,plain,
is_a_theorem(implies(and(implies(not(X),X_1962),not(X)),X_1962)),
inference(subst,[],[refute_0_698:[bind(X_1850,$fot(not(X))),bind(X_1851,$fot(X_1962))]]) ).
cnf(refute_0_700,plain,
or(X,X_1962) = implies(not(X),X_1962),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_1962))]]) ).
cnf(refute_0_701,plain,
( or(X,X_1962) != implies(not(X),X_1962)
| implies(not(X),X_1962) = or(X,X_1962) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,X_1962))),bind(Y0,$fot(implies(not(X),X_1962)))]]) ).
cnf(refute_0_702,plain,
implies(not(X),X_1962) = or(X,X_1962),
inference(resolve,[$cnf( $equal(or(X,X_1962),implies(not(X),X_1962)) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
( implies(not(X),X_1962) != or(X,X_1962)
| ~ is_a_theorem(implies(and(implies(not(X),X_1962),not(X)),X_1962))
| is_a_theorem(implies(and(or(X,X_1962),not(X)),X_1962)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(implies(not(X),X_1962),not(X)),X_1962)) ),[0,0,0],$fot(or(X,X_1962))]]) ).
cnf(refute_0_704,plain,
( ~ is_a_theorem(implies(and(implies(not(X),X_1962),not(X)),X_1962))
| is_a_theorem(implies(and(or(X,X_1962),not(X)),X_1962)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_1962),or(X,X_1962)) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
is_a_theorem(implies(and(or(X,X_1962),not(X)),X_1962)),
inference(resolve,[$cnf( is_a_theorem(implies(and(implies(not(X),X_1962),not(X)),X_1962)) )],[refute_0_699,refute_0_704]) ).
cnf(refute_0_706,plain,
implies(not(implies(or(X,X_1962),X)),X_1962) = or(implies(or(X,X_1962),X),X_1962),
inference(subst,[],[refute_0_295:[bind(X,$fot(implies(or(X,X_1962),X))),bind(Y,$fot(X_1962))]]) ).
cnf(refute_0_707,plain,
and(or(X,X_1962),not(X)) = not(implies(or(X,X_1962),X)),
inference(subst,[],[refute_0_567:[bind(X,$fot(or(X,X_1962))),bind(X_1833,$fot(X))]]) ).
cnf(refute_0_708,plain,
implies(and(or(X,X_1962),not(X)),X_1962) = implies(and(or(X,X_1962),not(X)),X_1962),
introduced(tautology,[refl,[$fot(implies(and(or(X,X_1962),not(X)),X_1962))]]) ).
cnf(refute_0_709,plain,
( and(or(X,X_1962),not(X)) != not(implies(or(X,X_1962),X))
| implies(and(or(X,X_1962),not(X)),X_1962) != implies(and(or(X,X_1962),not(X)),X_1962)
| implies(and(or(X,X_1962),not(X)),X_1962) = implies(not(implies(or(X,X_1962),X)),X_1962) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(or(X,X_1962),not(X)),X_1962),implies(and(or(X,X_1962),not(X)),X_1962)) ),[1,0],$fot(not(implies(or(X,X_1962),X)))]]) ).
cnf(refute_0_710,plain,
( and(or(X,X_1962),not(X)) != not(implies(or(X,X_1962),X))
| implies(and(or(X,X_1962),not(X)),X_1962) = implies(not(implies(or(X,X_1962),X)),X_1962) ),
inference(resolve,[$cnf( $equal(implies(and(or(X,X_1962),not(X)),X_1962),implies(and(or(X,X_1962),not(X)),X_1962)) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
implies(and(or(X,X_1962),not(X)),X_1962) = implies(not(implies(or(X,X_1962),X)),X_1962),
inference(resolve,[$cnf( $equal(and(or(X,X_1962),not(X)),not(implies(or(X,X_1962),X))) )],[refute_0_707,refute_0_710]) ).
cnf(refute_0_712,plain,
( implies(and(or(X,X_1962),not(X)),X_1962) != implies(not(implies(or(X,X_1962),X)),X_1962)
| implies(not(implies(or(X,X_1962),X)),X_1962) != or(implies(or(X,X_1962),X),X_1962)
| implies(and(or(X,X_1962),not(X)),X_1962) = or(implies(or(X,X_1962),X),X_1962) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(and(or(X,X_1962),not(X)),X_1962))),bind(Y0,$fot(implies(not(implies(or(X,X_1962),X)),X_1962))),bind(Z,$fot(or(implies(or(X,X_1962),X),X_1962)))]]) ).
cnf(refute_0_713,plain,
( implies(not(implies(or(X,X_1962),X)),X_1962) != or(implies(or(X,X_1962),X),X_1962)
| implies(and(or(X,X_1962),not(X)),X_1962) = or(implies(or(X,X_1962),X),X_1962) ),
inference(resolve,[$cnf( $equal(implies(and(or(X,X_1962),not(X)),X_1962),implies(not(implies(or(X,X_1962),X)),X_1962)) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
implies(and(or(X,X_1962),not(X)),X_1962) = or(implies(or(X,X_1962),X),X_1962),
inference(resolve,[$cnf( $equal(implies(not(implies(or(X,X_1962),X)),X_1962),or(implies(or(X,X_1962),X),X_1962)) )],[refute_0_706,refute_0_713]) ).
cnf(refute_0_715,plain,
( implies(and(or(X,X_1962),not(X)),X_1962) != or(implies(or(X,X_1962),X),X_1962)
| ~ is_a_theorem(implies(and(or(X,X_1962),not(X)),X_1962))
| is_a_theorem(or(implies(or(X,X_1962),X),X_1962)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(or(X,X_1962),not(X)),X_1962)) ),[0],$fot(or(implies(or(X,X_1962),X),X_1962))]]) ).
cnf(refute_0_716,plain,
( ~ is_a_theorem(implies(and(or(X,X_1962),not(X)),X_1962))
| is_a_theorem(or(implies(or(X,X_1962),X),X_1962)) ),
inference(resolve,[$cnf( $equal(implies(and(or(X,X_1962),not(X)),X_1962),or(implies(or(X,X_1962),X),X_1962)) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
is_a_theorem(or(implies(or(X,X_1962),X),X_1962)),
inference(resolve,[$cnf( is_a_theorem(implies(and(or(X,X_1962),not(X)),X_1962)) )],[refute_0_705,refute_0_716]) ).
cnf(refute_0_718,plain,
is_a_theorem(or(implies(or(X_1963,X_1964),X_1963),X_1964)),
inference(subst,[],[refute_0_717:[bind(X,$fot(X_1963)),bind(X_1962,$fot(X_1964))]]) ).
cnf(refute_0_719,plain,
is_a_theorem(implies(X_17,or(implies(or(X_1963,X_1964),X_1963),X_1964))),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(X_1963,X_1964),X_1963),X_1964)) )],[refute_0_718,refute_0_680]) ).
cnf(refute_0_720,plain,
is_a_theorem(implies(X_4011,or(implies(or(not(X),X_4013),not(X)),X_4013))),
inference(subst,[],[refute_0_719:[bind(X_17,$fot(X_4011)),bind(X_1963,$fot(not(X))),bind(X_1964,$fot(X_4013))]]) ).
cnf(refute_0_721,plain,
implies(X,X_4013) = or(not(X),X_4013),
inference(subst,[],[refute_0_26:[bind(Y,$fot(X_4013))]]) ).
cnf(refute_0_722,plain,
( implies(X,X_4013) != or(not(X),X_4013)
| or(not(X),X_4013) = implies(X,X_4013) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,X_4013))),bind(Y0,$fot(or(not(X),X_4013)))]]) ).
cnf(refute_0_723,plain,
or(not(X),X_4013) = implies(X,X_4013),
inference(resolve,[$cnf( $equal(implies(X,X_4013),or(not(X),X_4013)) )],[refute_0_721,refute_0_722]) ).
cnf(refute_0_724,plain,
( or(not(X),X_4013) != implies(X,X_4013)
| ~ is_a_theorem(implies(X_4011,or(implies(or(not(X),X_4013),not(X)),X_4013)))
| is_a_theorem(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_4011,or(implies(or(not(X),X_4013),not(X)),X_4013))) ),[0,1,0,0],$fot(implies(X,X_4013))]]) ).
cnf(refute_0_725,plain,
( ~ is_a_theorem(implies(X_4011,or(implies(or(not(X),X_4013),not(X)),X_4013)))
| is_a_theorem(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_4013),implies(X,X_4013)) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
is_a_theorem(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013))),
inference(resolve,[$cnf( is_a_theorem(implies(X_4011,or(implies(or(not(X),X_4013),not(X)),X_4013))) )],[refute_0_720,refute_0_725]) ).
cnf(refute_0_727,plain,
or(not(and(implies(X,X_4013),X)),X_4013) = implies(and(implies(X,X_4013),X),X_4013),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(implies(X,X_4013),X))),bind(Y,$fot(X_4013))]]) ).
cnf(refute_0_728,plain,
implies(implies(X,X_4013),not(X)) = not(and(implies(X,X_4013),X)),
inference(subst,[],[refute_0_448:[bind(X,$fot(implies(X,X_4013))),bind(X_1833,$fot(X))]]) ).
cnf(refute_0_729,plain,
or(implies(implies(X,X_4013),not(X)),X_4013) = or(implies(implies(X,X_4013),not(X)),X_4013),
introduced(tautology,[refl,[$fot(or(implies(implies(X,X_4013),not(X)),X_4013))]]) ).
cnf(refute_0_730,plain,
( implies(implies(X,X_4013),not(X)) != not(and(implies(X,X_4013),X))
| or(implies(implies(X,X_4013),not(X)),X_4013) != or(implies(implies(X,X_4013),not(X)),X_4013)
| or(implies(implies(X,X_4013),not(X)),X_4013) = or(not(and(implies(X,X_4013),X)),X_4013) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(implies(X,X_4013),not(X)),X_4013),or(implies(implies(X,X_4013),not(X)),X_4013)) ),[1,0],$fot(not(and(implies(X,X_4013),X)))]]) ).
cnf(refute_0_731,plain,
( implies(implies(X,X_4013),not(X)) != not(and(implies(X,X_4013),X))
| or(implies(implies(X,X_4013),not(X)),X_4013) = or(not(and(implies(X,X_4013),X)),X_4013) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,X_4013),not(X)),X_4013),or(implies(implies(X,X_4013),not(X)),X_4013)) )],[refute_0_729,refute_0_730]) ).
cnf(refute_0_732,plain,
or(implies(implies(X,X_4013),not(X)),X_4013) = or(not(and(implies(X,X_4013),X)),X_4013),
inference(resolve,[$cnf( $equal(implies(implies(X,X_4013),not(X)),not(and(implies(X,X_4013),X))) )],[refute_0_728,refute_0_731]) ).
cnf(refute_0_733,plain,
( or(implies(implies(X,X_4013),not(X)),X_4013) != or(not(and(implies(X,X_4013),X)),X_4013)
| or(not(and(implies(X,X_4013),X)),X_4013) != implies(and(implies(X,X_4013),X),X_4013)
| or(implies(implies(X,X_4013),not(X)),X_4013) = implies(and(implies(X,X_4013),X),X_4013) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(implies(implies(X,X_4013),not(X)),X_4013))),bind(Y0,$fot(or(not(and(implies(X,X_4013),X)),X_4013))),bind(Z,$fot(implies(and(implies(X,X_4013),X),X_4013)))]]) ).
cnf(refute_0_734,plain,
( or(not(and(implies(X,X_4013),X)),X_4013) != implies(and(implies(X,X_4013),X),X_4013)
| or(implies(implies(X,X_4013),not(X)),X_4013) = implies(and(implies(X,X_4013),X),X_4013) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,X_4013),not(X)),X_4013),or(not(and(implies(X,X_4013),X)),X_4013)) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
or(implies(implies(X,X_4013),not(X)),X_4013) = implies(and(implies(X,X_4013),X),X_4013),
inference(resolve,[$cnf( $equal(or(not(and(implies(X,X_4013),X)),X_4013),implies(and(implies(X,X_4013),X),X_4013)) )],[refute_0_727,refute_0_734]) ).
cnf(refute_0_736,plain,
implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)) = implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)),
introduced(tautology,[refl,[$fot(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)))]]) ).
cnf(refute_0_737,plain,
( implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)) != implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013))
| or(implies(implies(X,X_4013),not(X)),X_4013) != implies(and(implies(X,X_4013),X),X_4013)
| implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)) = implies(X_4011,implies(and(implies(X,X_4013),X),X_4013)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)),implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013))) ),[1,1],$fot(implies(and(implies(X,X_4013),X),X_4013))]]) ).
cnf(refute_0_738,plain,
( or(implies(implies(X,X_4013),not(X)),X_4013) != implies(and(implies(X,X_4013),X),X_4013)
| implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)) = implies(X_4011,implies(and(implies(X,X_4013),X),X_4013)) ),
inference(resolve,[$cnf( $equal(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)),implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013))) )],[refute_0_736,refute_0_737]) ).
cnf(refute_0_739,plain,
implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)) = implies(X_4011,implies(and(implies(X,X_4013),X),X_4013)),
inference(resolve,[$cnf( $equal(or(implies(implies(X,X_4013),not(X)),X_4013),implies(and(implies(X,X_4013),X),X_4013)) )],[refute_0_735,refute_0_738]) ).
cnf(refute_0_740,plain,
( implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)) != implies(X_4011,implies(and(implies(X,X_4013),X),X_4013))
| ~ is_a_theorem(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)))
| is_a_theorem(implies(X_4011,implies(and(implies(X,X_4013),X),X_4013))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013))) ),[0],$fot(implies(X_4011,implies(and(implies(X,X_4013),X),X_4013)))]]) ).
cnf(refute_0_741,plain,
( ~ is_a_theorem(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)))
| is_a_theorem(implies(X_4011,implies(and(implies(X,X_4013),X),X_4013))) ),
inference(resolve,[$cnf( $equal(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013)),implies(X_4011,implies(and(implies(X,X_4013),X),X_4013))) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
is_a_theorem(implies(X_4011,implies(and(implies(X,X_4013),X),X_4013))),
inference(resolve,[$cnf( is_a_theorem(implies(X_4011,or(implies(implies(X,X_4013),not(X)),X_4013))) )],[refute_0_726,refute_0_741]) ).
cnf(refute_0_743,plain,
is_a_theorem(implies(X_5028,implies(and(implies(X,X_5029),X),X_5029))),
inference(subst,[],[refute_0_742:[bind(X_4011,$fot(X_5028)),bind(X_4013,$fot(X_5029))]]) ).
cnf(refute_0_744,plain,
( ~ is_a_theorem(implies(X_5028,implies(and(implies(X,X_5029),X),X_5029)))
| is_a_theorem(implies(and(implies(X,X_5029),X),implies(X_5028,X_5029))) ),
inference(subst,[],[refute_0_215:[bind(X,$fot(and(implies(X,X_5029),X))),bind(X_205,$fot(X_5028)),bind(X_207,$fot(X_5029))]]) ).
cnf(refute_0_745,plain,
is_a_theorem(implies(and(implies(X,X_5029),X),implies(X_5028,X_5029))),
inference(resolve,[$cnf( is_a_theorem(implies(X_5028,implies(and(implies(X,X_5029),X),X_5029))) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
is_a_theorem(implies(and(implies(X_5218,X_5220),X_5218),implies(X_5219,X_5220))),
inference(subst,[],[refute_0_745:[bind(X,$fot(X_5218)),bind(X_5028,$fot(X_5219)),bind(X_5029,$fot(X_5220))]]) ).
cnf(refute_0_747,plain,
is_a_theorem(or(implies(X_5219,X_5220),not(and(implies(X_5218,X_5220),X_5218)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(implies(X_5218,X_5220),X_5218),implies(X_5219,X_5220))) )],[refute_0_746,refute_0_672]) ).
cnf(refute_0_748,plain,
is_a_theorem(or(implies(not(X),X_6023),not(and(implies(X_6021,X_6023),X_6021)))),
inference(subst,[],[refute_0_747:[bind(X_5218,$fot(X_6021)),bind(X_5219,$fot(not(X))),bind(X_5220,$fot(X_6023))]]) ).
cnf(refute_0_749,plain,
or(X,X_6023) = implies(not(X),X_6023),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_6023))]]) ).
cnf(refute_0_750,plain,
( or(X,X_6023) != implies(not(X),X_6023)
| implies(not(X),X_6023) = or(X,X_6023) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,X_6023))),bind(Y0,$fot(implies(not(X),X_6023)))]]) ).
cnf(refute_0_751,plain,
implies(not(X),X_6023) = or(X,X_6023),
inference(resolve,[$cnf( $equal(or(X,X_6023),implies(not(X),X_6023)) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
( implies(not(X),X_6023) != or(X,X_6023)
| ~ is_a_theorem(or(implies(not(X),X_6023),not(and(implies(X_6021,X_6023),X_6021))))
| is_a_theorem(or(or(X,X_6023),not(and(implies(X_6021,X_6023),X_6021)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(not(X),X_6023),not(and(implies(X_6021,X_6023),X_6021)))) ),[0,0],$fot(or(X,X_6023))]]) ).
cnf(refute_0_753,plain,
( ~ is_a_theorem(or(implies(not(X),X_6023),not(and(implies(X_6021,X_6023),X_6021))))
| is_a_theorem(or(or(X,X_6023),not(and(implies(X_6021,X_6023),X_6021)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_6023),or(X,X_6023)) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
is_a_theorem(or(or(X,X_6023),not(and(implies(X_6021,X_6023),X_6021)))),
inference(resolve,[$cnf( is_a_theorem(or(implies(not(X),X_6023),not(and(implies(X_6021,X_6023),X_6021)))) )],[refute_0_748,refute_0_753]) ).
cnf(refute_0_755,plain,
is_a_theorem(or(or(X_6024,X_6026),not(and(implies(not(X),X_6026),not(X))))),
inference(subst,[],[refute_0_754:[bind(X,$fot(X_6024)),bind(X_6021,$fot(not(X))),bind(X_6023,$fot(X_6026))]]) ).
cnf(refute_0_756,plain,
or(X,X_6026) = implies(not(X),X_6026),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_6026))]]) ).
cnf(refute_0_757,plain,
( or(X,X_6026) != implies(not(X),X_6026)
| implies(not(X),X_6026) = or(X,X_6026) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,X_6026))),bind(Y0,$fot(implies(not(X),X_6026)))]]) ).
cnf(refute_0_758,plain,
implies(not(X),X_6026) = or(X,X_6026),
inference(resolve,[$cnf( $equal(or(X,X_6026),implies(not(X),X_6026)) )],[refute_0_756,refute_0_757]) ).
cnf(refute_0_759,plain,
( implies(not(X),X_6026) != or(X,X_6026)
| ~ is_a_theorem(or(or(X_6024,X_6026),not(and(implies(not(X),X_6026),not(X)))))
| is_a_theorem(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(X_6024,X_6026),not(and(implies(not(X),X_6026),not(X))))) ),[0,1,0,0],$fot(or(X,X_6026))]]) ).
cnf(refute_0_760,plain,
( ~ is_a_theorem(or(or(X_6024,X_6026),not(and(implies(not(X),X_6026),not(X)))))
| is_a_theorem(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_6026),or(X,X_6026)) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
is_a_theorem(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_6024,X_6026),not(and(implies(not(X),X_6026),not(X))))) )],[refute_0_755,refute_0_760]) ).
cnf(refute_0_762,plain,
not(not(implies(or(X,X_6026),X))) = implies(or(X,X_6026),X),
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(implies(or(X,X_6026),X)))]]) ).
cnf(refute_0_763,plain,
and(or(X,X_6026),not(X)) = not(implies(or(X,X_6026),X)),
inference(subst,[],[refute_0_567:[bind(X,$fot(or(X,X_6026))),bind(X_1833,$fot(X))]]) ).
cnf(refute_0_764,plain,
not(and(or(X,X_6026),not(X))) = not(and(or(X,X_6026),not(X))),
introduced(tautology,[refl,[$fot(not(and(or(X,X_6026),not(X))))]]) ).
cnf(refute_0_765,plain,
( and(or(X,X_6026),not(X)) != not(implies(or(X,X_6026),X))
| not(and(or(X,X_6026),not(X))) != not(and(or(X,X_6026),not(X)))
| not(and(or(X,X_6026),not(X))) = not(not(implies(or(X,X_6026),X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(X,X_6026),not(X))),not(and(or(X,X_6026),not(X)))) ),[1,0],$fot(not(implies(or(X,X_6026),X)))]]) ).
cnf(refute_0_766,plain,
( and(or(X,X_6026),not(X)) != not(implies(or(X,X_6026),X))
| not(and(or(X,X_6026),not(X))) = not(not(implies(or(X,X_6026),X))) ),
inference(resolve,[$cnf( $equal(not(and(or(X,X_6026),not(X))),not(and(or(X,X_6026),not(X)))) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
not(and(or(X,X_6026),not(X))) = not(not(implies(or(X,X_6026),X))),
inference(resolve,[$cnf( $equal(and(or(X,X_6026),not(X)),not(implies(or(X,X_6026),X))) )],[refute_0_763,refute_0_766]) ).
cnf(refute_0_768,plain,
( not(and(or(X,X_6026),not(X))) != not(not(implies(or(X,X_6026),X)))
| not(not(implies(or(X,X_6026),X))) != implies(or(X,X_6026),X)
| not(and(or(X,X_6026),not(X))) = implies(or(X,X_6026),X) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(and(or(X,X_6026),not(X))))),bind(Y0,$fot(not(not(implies(or(X,X_6026),X))))),bind(Z,$fot(implies(or(X,X_6026),X)))]]) ).
cnf(refute_0_769,plain,
( not(not(implies(or(X,X_6026),X))) != implies(or(X,X_6026),X)
| not(and(or(X,X_6026),not(X))) = implies(or(X,X_6026),X) ),
inference(resolve,[$cnf( $equal(not(and(or(X,X_6026),not(X))),not(not(implies(or(X,X_6026),X)))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
not(and(or(X,X_6026),not(X))) = implies(or(X,X_6026),X),
inference(resolve,[$cnf( $equal(not(not(implies(or(X,X_6026),X))),implies(or(X,X_6026),X)) )],[refute_0_762,refute_0_769]) ).
cnf(refute_0_771,plain,
or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))) = or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))),
introduced(tautology,[refl,[$fot(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))))]]) ).
cnf(refute_0_772,plain,
( not(and(or(X,X_6026),not(X))) != implies(or(X,X_6026),X)
| or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))) != or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X))))
| or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))) = or(or(X_6024,X_6026),implies(or(X,X_6026),X)) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))),or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X))))) ),[1,1],$fot(implies(or(X,X_6026),X))]]) ).
cnf(refute_0_773,plain,
( not(and(or(X,X_6026),not(X))) != implies(or(X,X_6026),X)
| or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))) = or(or(X_6024,X_6026),implies(or(X,X_6026),X)) ),
inference(resolve,[$cnf( $equal(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))),or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X))))) )],[refute_0_771,refute_0_772]) ).
cnf(refute_0_774,plain,
or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))) = or(or(X_6024,X_6026),implies(or(X,X_6026),X)),
inference(resolve,[$cnf( $equal(not(and(or(X,X_6026),not(X))),implies(or(X,X_6026),X)) )],[refute_0_770,refute_0_773]) ).
cnf(refute_0_775,plain,
( or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))) != or(or(X_6024,X_6026),implies(or(X,X_6026),X))
| ~ is_a_theorem(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))))
| is_a_theorem(or(or(X_6024,X_6026),implies(or(X,X_6026),X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X))))) ),[0],$fot(or(or(X_6024,X_6026),implies(or(X,X_6026),X)))]]) ).
cnf(refute_0_776,plain,
( ~ is_a_theorem(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))))
| is_a_theorem(or(or(X_6024,X_6026),implies(or(X,X_6026),X))) ),
inference(resolve,[$cnf( $equal(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X)))),or(or(X_6024,X_6026),implies(or(X,X_6026),X))) )],[refute_0_774,refute_0_775]) ).
cnf(refute_0_777,plain,
is_a_theorem(or(or(X_6024,X_6026),implies(or(X,X_6026),X))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_6024,X_6026),not(and(or(X,X_6026),not(X))))) )],[refute_0_761,refute_0_776]) ).
cnf(refute_0_778,plain,
is_a_theorem(or(or(X_6024,X_6026),implies(or(X_26285,X_6026),X_26285))),
inference(subst,[],[refute_0_777:[bind(X,$fot(X_26285))]]) ).
cnf(refute_0_779,plain,
is_a_theorem(implies(or(X_67,or(not(X),X_69)),or(not(X),or(X_67,X_69)))),
inference(subst,[],[refute_0_22:[bind(P,$fot(X_67)),bind(Q,$fot(not(X))),bind(R,$fot(X_69))]]) ).
cnf(refute_0_780,plain,
implies(X,or(X_67,X_69)) = or(not(X),or(X_67,X_69)),
inference(subst,[],[refute_0_26:[bind(Y,$fot(or(X_67,X_69)))]]) ).
cnf(refute_0_781,plain,
( implies(X,or(X_67,X_69)) != or(not(X),or(X_67,X_69))
| or(not(X),or(X_67,X_69)) = implies(X,or(X_67,X_69)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,or(X_67,X_69)))),bind(Y0,$fot(or(not(X),or(X_67,X_69))))]]) ).
cnf(refute_0_782,plain,
or(not(X),or(X_67,X_69)) = implies(X,or(X_67,X_69)),
inference(resolve,[$cnf( $equal(implies(X,or(X_67,X_69)),or(not(X),or(X_67,X_69))) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
( or(not(X),or(X_67,X_69)) != implies(X,or(X_67,X_69))
| ~ is_a_theorem(implies(or(X_67,or(not(X),X_69)),or(not(X),or(X_67,X_69))))
| is_a_theorem(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_67,or(not(X),X_69)),or(not(X),or(X_67,X_69)))) ),[0,1],$fot(implies(X,or(X_67,X_69)))]]) ).
cnf(refute_0_784,plain,
( ~ is_a_theorem(implies(or(X_67,or(not(X),X_69)),or(not(X),or(X_67,X_69))))
| is_a_theorem(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_67,X_69)),implies(X,or(X_67,X_69))) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
is_a_theorem(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_67,or(not(X),X_69)),or(not(X),or(X_67,X_69)))) )],[refute_0_779,refute_0_784]) ).
cnf(refute_0_786,plain,
or(X_67,or(not(X),X_69)) = or(X_67,or(not(X),X_69)),
introduced(tautology,[refl,[$fot(or(X_67,or(not(X),X_69)))]]) ).
cnf(refute_0_787,plain,
( or(X_67,or(not(X),X_69)) != or(X_67,or(not(X),X_69))
| or(not(X),X_69) != implies(X,X_69)
| or(X_67,or(not(X),X_69)) = or(X_67,implies(X,X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_67,or(not(X),X_69)),or(X_67,or(not(X),X_69))) ),[1,1],$fot(implies(X,X_69))]]) ).
cnf(refute_0_788,plain,
( or(not(X),X_69) != implies(X,X_69)
| or(X_67,or(not(X),X_69)) = or(X_67,implies(X,X_69)) ),
inference(resolve,[$cnf( $equal(or(X_67,or(not(X),X_69)),or(X_67,or(not(X),X_69))) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
or(X_67,or(not(X),X_69)) = or(X_67,implies(X,X_69)),
inference(resolve,[$cnf( $equal(or(not(X),X_69),implies(X,X_69)) )],[refute_0_32,refute_0_788]) ).
cnf(refute_0_790,plain,
implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))) = implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))),
introduced(tautology,[refl,[$fot(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))))]]) ).
cnf(refute_0_791,plain,
( implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))) != implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69)))
| or(X_67,or(not(X),X_69)) != or(X_67,implies(X,X_69))
| implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))) = implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))),implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69)))) ),[1,0],$fot(or(X_67,implies(X,X_69)))]]) ).
cnf(refute_0_792,plain,
( or(X_67,or(not(X),X_69)) != or(X_67,implies(X,X_69))
| implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))) = implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69))) ),
inference(resolve,[$cnf( $equal(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))),implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69)))) )],[refute_0_790,refute_0_791]) ).
cnf(refute_0_793,plain,
implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))) = implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69))),
inference(resolve,[$cnf( $equal(or(X_67,or(not(X),X_69)),or(X_67,implies(X,X_69))) )],[refute_0_789,refute_0_792]) ).
cnf(refute_0_794,plain,
( implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))) != implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69)))
| ~ is_a_theorem(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))))
| is_a_theorem(implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69)))) ),[0],$fot(implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69))))]]) ).
cnf(refute_0_795,plain,
( ~ is_a_theorem(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))))
| is_a_theorem(implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69))),implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69)))) )],[refute_0_793,refute_0_794]) ).
cnf(refute_0_796,plain,
is_a_theorem(implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_67,or(not(X),X_69)),implies(X,or(X_67,X_69)))) )],[refute_0_785,refute_0_795]) ).
cnf(refute_0_797,plain,
( ~ is_a_theorem(implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69))))
| ~ is_a_theorem(or(X_67,implies(X,X_69)))
| is_a_theorem(implies(X,or(X_67,X_69))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_67,implies(X,X_69)))),bind(Y,$fot(implies(X,or(X_67,X_69))))]]) ).
cnf(refute_0_798,plain,
( ~ is_a_theorem(or(X_67,implies(X,X_69)))
| is_a_theorem(implies(X,or(X_67,X_69))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_67,implies(X,X_69)),implies(X,or(X_67,X_69)))) )],[refute_0_796,refute_0_797]) ).
cnf(refute_0_799,plain,
( ~ is_a_theorem(or(or(X_6024,X_6026),implies(or(X_26285,X_6026),X_26285)))
| is_a_theorem(implies(or(X_26285,X_6026),or(or(X_6024,X_6026),X_26285))) ),
inference(subst,[],[refute_0_798:[bind(X,$fot(or(X_26285,X_6026))),bind(X_67,$fot(or(X_6024,X_6026))),bind(X_69,$fot(X_26285))]]) ).
cnf(refute_0_800,plain,
is_a_theorem(implies(or(X_26285,X_6026),or(or(X_6024,X_6026),X_26285))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_6024,X_6026),implies(or(X_26285,X_6026),X_26285))) )],[refute_0_778,refute_0_799]) ).
cnf(refute_0_801,plain,
is_a_theorem(implies(or(X_26385,X_26387),or(or(X_26386,X_26387),X_26385))),
inference(subst,[],[refute_0_800:[bind(X_26285,$fot(X_26385)),bind(X_6024,$fot(X_26386)),bind(X_6026,$fot(X_26387))]]) ).
cnf(refute_0_802,plain,
is_a_theorem(or(and(implies(or(X_26385,X_26387),or(or(X_26386,X_26387),X_26385)),X_9166),not(X_9166))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_26385,X_26387),or(or(X_26386,X_26387),X_26385))) )],[refute_0_801,refute_0_671]) ).
cnf(refute_0_803,plain,
is_a_theorem(or(and(implies(or(X_29756,X_29758),or(or(X_29758,X_29758),X_29756)),X_29759),not(X_29759))),
inference(subst,[],[refute_0_802:[bind(X_26385,$fot(X_29756)),bind(X_26386,$fot(X_29758)),bind(X_26387,$fot(X_29758)),bind(X_9166,$fot(X_29759))]]) ).
cnf(refute_0_804,plain,
X_29758 = or(X_29758,X_29758),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(X_29758))]]) ).
cnf(refute_0_805,plain,
( X_29758 != or(X_29758,X_29758)
| or(X_29758,X_29758) = X_29758 ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(X_29758)),bind(Y0,$fot(or(X_29758,X_29758)))]]) ).
cnf(refute_0_806,plain,
or(X_29758,X_29758) = X_29758,
inference(resolve,[$cnf( $equal(X_29758,or(X_29758,X_29758)) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
( or(X_29758,X_29758) != X_29758
| ~ is_a_theorem(or(and(implies(or(X_29756,X_29758),or(or(X_29758,X_29758),X_29756)),X_29759),not(X_29759)))
| is_a_theorem(or(and(implies(or(X_29756,X_29758),or(X_29758,X_29756)),X_29759),not(X_29759))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(or(X_29756,X_29758),or(or(X_29758,X_29758),X_29756)),X_29759),not(X_29759))) ),[0,0,0,1,0],$fot(X_29758)]]) ).
cnf(refute_0_808,plain,
( ~ is_a_theorem(or(and(implies(or(X_29756,X_29758),or(or(X_29758,X_29758),X_29756)),X_29759),not(X_29759)))
| is_a_theorem(or(and(implies(or(X_29756,X_29758),or(X_29758,X_29756)),X_29759),not(X_29759))) ),
inference(resolve,[$cnf( $equal(or(X_29758,X_29758),X_29758) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
is_a_theorem(or(and(implies(or(X_29756,X_29758),or(X_29758,X_29756)),X_29759),not(X_29759))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(or(X_29756,X_29758),or(or(X_29758,X_29758),X_29756)),X_29759),not(X_29759))) )],[refute_0_803,refute_0_808]) ).
cnf(refute_0_810,plain,
is_a_theorem(implies(implies(not(X),X_72),implies(or(X_70,not(X)),or(X_70,X_72)))),
inference(subst,[],[refute_0_167:[bind(P,$fot(X_70)),bind(Q,$fot(not(X))),bind(R,$fot(X_72))]]) ).
cnf(refute_0_811,plain,
or(X,X_72) = implies(not(X),X_72),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_72))]]) ).
cnf(refute_0_812,plain,
( or(X,X_72) != implies(not(X),X_72)
| implies(not(X),X_72) = or(X,X_72) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,X_72))),bind(Y0,$fot(implies(not(X),X_72)))]]) ).
cnf(refute_0_813,plain,
implies(not(X),X_72) = or(X,X_72),
inference(resolve,[$cnf( $equal(or(X,X_72),implies(not(X),X_72)) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
( implies(not(X),X_72) != or(X,X_72)
| ~ is_a_theorem(implies(implies(not(X),X_72),implies(or(X_70,not(X)),or(X_70,X_72))))
| is_a_theorem(implies(or(X,X_72),implies(or(X_70,not(X)),or(X_70,X_72)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),X_72),implies(or(X_70,not(X)),or(X_70,X_72)))) ),[0,0],$fot(or(X,X_72))]]) ).
cnf(refute_0_815,plain,
( ~ is_a_theorem(implies(implies(not(X),X_72),implies(or(X_70,not(X)),or(X_70,X_72))))
| is_a_theorem(implies(or(X,X_72),implies(or(X_70,not(X)),or(X_70,X_72)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_72),or(X,X_72)) )],[refute_0_813,refute_0_814]) ).
cnf(refute_0_816,plain,
is_a_theorem(implies(or(X,X_72),implies(or(X_70,not(X)),or(X_70,X_72)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_72),implies(or(X_70,not(X)),or(X_70,X_72)))) )],[refute_0_810,refute_0_815]) ).
cnf(refute_0_817,plain,
( ~ is_a_theorem(implies(or(X,X_72),implies(or(X_70,not(X)),or(X_70,X_72))))
| ~ is_a_theorem(or(X,X_72))
| is_a_theorem(implies(or(X_70,not(X)),or(X_70,X_72))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X,X_72))),bind(Y,$fot(implies(or(X_70,not(X)),or(X_70,X_72))))]]) ).
cnf(refute_0_818,plain,
( ~ is_a_theorem(or(X,X_72))
| is_a_theorem(implies(or(X_70,not(X)),or(X_70,X_72))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X,X_72),implies(or(X_70,not(X)),or(X_70,X_72)))) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
( ~ is_a_theorem(or(and(implies(or(X_29756,X_29758),or(X_29758,X_29756)),X_29759),not(X_29759)))
| is_a_theorem(implies(or(X_54220,not(and(implies(or(X_29756,X_29758),or(X_29758,X_29756)),X_29759))),or(X_54220,not(X_29759)))) ),
inference(subst,[],[refute_0_818:[bind(X,$fot(and(implies(or(X_29756,X_29758),or(X_29758,X_29756)),X_29759))),bind(X_70,$fot(X_54220)),bind(X_72,$fot(not(X_29759)))]]) ).
cnf(refute_0_820,plain,
is_a_theorem(implies(or(X_54220,not(and(implies(or(X_29756,X_29758),or(X_29758,X_29756)),X_29759))),or(X_54220,not(X_29759)))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(or(X_29756,X_29758),or(X_29758,X_29756)),X_29759),not(X_29759))) )],[refute_0_809,refute_0_819]) ).
cnf(refute_0_821,plain,
is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_31901,X_31901))))),
inference(subst,[],[refute_0_820:[bind(X_29756,$fot(X_55999)),bind(X_29758,$fot(X_56000)),bind(X_29759,$fot(equiv(X_31901,X_31901))),bind(X_54220,$fot(X_56002))]]) ).
cnf(refute_0_822,plain,
implies(or(X_9,Y),and(Y,X_9)) = not(not(implies(or(X_9,Y),and(Y,X_9)))),
inference(subst,[],[refute_0_442:[bind(X_1832,$fot(implies(or(X_9,Y),and(Y,X_9))))]]) ).
cnf(refute_0_823,plain,
equiv(not(X_9),Y) = and(implies(not(X_9),Y),implies(Y,not(X_9))),
inference(subst,[],[refute_0_71:[bind(X,$fot(not(X_9)))]]) ).
cnf(refute_0_824,plain,
or(X_9,Y) = implies(not(X_9),Y),
inference(subst,[],[refute_0_84:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_825,plain,
( or(X_9,Y) != implies(not(X_9),Y)
| implies(not(X_9),Y) = or(X_9,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X_9,Y))),bind(Y0,$fot(implies(not(X_9),Y)))]]) ).
cnf(refute_0_826,plain,
implies(not(X_9),Y) = or(X_9,Y),
inference(resolve,[$cnf( $equal(or(X_9,Y),implies(not(X_9),Y)) )],[refute_0_824,refute_0_825]) ).
cnf(refute_0_827,plain,
( equiv(not(X_9),Y) != and(implies(not(X_9),Y),implies(Y,not(X_9)))
| implies(not(X_9),Y) != or(X_9,Y)
| equiv(not(X_9),Y) = and(or(X_9,Y),implies(Y,not(X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_9),Y),and(implies(not(X_9),Y),implies(Y,not(X_9)))) ),[1,0],$fot(or(X_9,Y))]]) ).
cnf(refute_0_828,plain,
( equiv(not(X_9),Y) != and(implies(not(X_9),Y),implies(Y,not(X_9)))
| equiv(not(X_9),Y) = and(or(X_9,Y),implies(Y,not(X_9))) ),
inference(resolve,[$cnf( $equal(implies(not(X_9),Y),or(X_9,Y)) )],[refute_0_826,refute_0_827]) ).
cnf(refute_0_829,plain,
equiv(not(X_9),Y) = and(or(X_9,Y),implies(Y,not(X_9))),
inference(resolve,[$cnf( $equal(equiv(not(X_9),Y),and(implies(not(X_9),Y),implies(Y,not(X_9)))) )],[refute_0_823,refute_0_828]) ).
cnf(refute_0_830,plain,
and(X,implies(X_1,not(X_2))) = not(implies(X,not(implies(X_1,not(X_2))))),
inference(subst,[],[refute_0_62:[bind(Y,$fot(implies(X_1,not(X_2))))]]) ).
cnf(refute_0_831,plain,
and(X_1,X_2) = not(implies(X_1,not(X_2))),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_1)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_832,plain,
( and(X_1,X_2) != not(implies(X_1,not(X_2)))
| not(implies(X_1,not(X_2))) = and(X_1,X_2) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(and(X_1,X_2))),bind(Y0,$fot(not(implies(X_1,not(X_2)))))]]) ).
cnf(refute_0_833,plain,
not(implies(X_1,not(X_2))) = and(X_1,X_2),
inference(resolve,[$cnf( $equal(and(X_1,X_2),not(implies(X_1,not(X_2)))) )],[refute_0_831,refute_0_832]) ).
cnf(refute_0_834,plain,
( and(X,implies(X_1,not(X_2))) != not(implies(X,not(implies(X_1,not(X_2)))))
| not(implies(X_1,not(X_2))) != and(X_1,X_2)
| and(X,implies(X_1,not(X_2))) = not(implies(X,and(X_1,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(X_1,not(X_2))),not(implies(X,not(implies(X_1,not(X_2)))))) ),[1,0,1],$fot(and(X_1,X_2))]]) ).
cnf(refute_0_835,plain,
( and(X,implies(X_1,not(X_2))) != not(implies(X,not(implies(X_1,not(X_2)))))
| and(X,implies(X_1,not(X_2))) = not(implies(X,and(X_1,X_2))) ),
inference(resolve,[$cnf( $equal(not(implies(X_1,not(X_2))),and(X_1,X_2)) )],[refute_0_833,refute_0_834]) ).
cnf(refute_0_836,plain,
and(X,implies(X_1,not(X_2))) = not(implies(X,and(X_1,X_2))),
inference(resolve,[$cnf( $equal(and(X,implies(X_1,not(X_2))),not(implies(X,not(implies(X_1,not(X_2)))))) )],[refute_0_830,refute_0_835]) ).
cnf(refute_0_837,plain,
and(or(X_9,Y),implies(Y,not(X_9))) = not(implies(or(X_9,Y),and(Y,X_9))),
inference(subst,[],[refute_0_836:[bind(X,$fot(or(X_9,Y))),bind(X_1,$fot(Y)),bind(X_2,$fot(X_9))]]) ).
cnf(refute_0_838,plain,
( and(or(X_9,Y),implies(Y,not(X_9))) != not(implies(or(X_9,Y),and(Y,X_9)))
| equiv(not(X_9),Y) != and(or(X_9,Y),implies(Y,not(X_9)))
| equiv(not(X_9),Y) = not(implies(or(X_9,Y),and(Y,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_9),Y),and(or(X_9,Y),implies(Y,not(X_9)))) ),[1],$fot(not(implies(or(X_9,Y),and(Y,X_9))))]]) ).
cnf(refute_0_839,plain,
( equiv(not(X_9),Y) != and(or(X_9,Y),implies(Y,not(X_9)))
| equiv(not(X_9),Y) = not(implies(or(X_9,Y),and(Y,X_9))) ),
inference(resolve,[$cnf( $equal(and(or(X_9,Y),implies(Y,not(X_9))),not(implies(or(X_9,Y),and(Y,X_9)))) )],[refute_0_837,refute_0_838]) ).
cnf(refute_0_840,plain,
equiv(not(X_9),Y) = not(implies(or(X_9,Y),and(Y,X_9))),
inference(resolve,[$cnf( $equal(equiv(not(X_9),Y),and(or(X_9,Y),implies(Y,not(X_9)))) )],[refute_0_829,refute_0_839]) ).
cnf(refute_0_841,plain,
( equiv(not(X_9),Y) != not(implies(or(X_9,Y),and(Y,X_9)))
| not(implies(or(X_9,Y),and(Y,X_9))) = equiv(not(X_9),Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(not(X_9),Y))),bind(Y0,$fot(not(implies(or(X_9,Y),and(Y,X_9)))))]]) ).
cnf(refute_0_842,plain,
not(implies(or(X_9,Y),and(Y,X_9))) = equiv(not(X_9),Y),
inference(resolve,[$cnf( $equal(equiv(not(X_9),Y),not(implies(or(X_9,Y),and(Y,X_9)))) )],[refute_0_840,refute_0_841]) ).
cnf(refute_0_843,plain,
( implies(or(X_9,Y),and(Y,X_9)) != not(not(implies(or(X_9,Y),and(Y,X_9))))
| not(implies(or(X_9,Y),and(Y,X_9))) != equiv(not(X_9),Y)
| implies(or(X_9,Y),and(Y,X_9)) = not(equiv(not(X_9),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_9,Y),and(Y,X_9)),not(not(implies(or(X_9,Y),and(Y,X_9))))) ),[1,0],$fot(equiv(not(X_9),Y))]]) ).
cnf(refute_0_844,plain,
( implies(or(X_9,Y),and(Y,X_9)) != not(not(implies(or(X_9,Y),and(Y,X_9))))
| implies(or(X_9,Y),and(Y,X_9)) = not(equiv(not(X_9),Y)) ),
inference(resolve,[$cnf( $equal(not(implies(or(X_9,Y),and(Y,X_9))),equiv(not(X_9),Y)) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
implies(or(X_9,Y),and(Y,X_9)) = not(equiv(not(X_9),Y)),
inference(resolve,[$cnf( $equal(implies(or(X_9,Y),and(Y,X_9)),not(not(implies(or(X_9,Y),and(Y,X_9))))) )],[refute_0_822,refute_0_844]) ).
cnf(refute_0_846,plain,
implies(or(X_9,not(X_9)),and(not(X_9),X_9)) = not(equiv(not(X_9),not(X_9))),
inference(subst,[],[refute_0_845:[bind(Y,$fot(not(X_9)))]]) ).
cnf(refute_0_847,plain,
( ~ is_a_theorem(equiv(equiv(X_31900,X_31900),equiv(X_31899,X_31899)))
| equiv(X_31900,X_31900) = equiv(X_31899,X_31899) ),
inference(subst,[],[refute_0_155:[bind(X,$fot(equiv(X_31900,X_31900))),bind(Y,$fot(equiv(X_31899,X_31899)))]]) ).
cnf(refute_0_848,plain,
( ~ is_a_theorem(implies(and(X_3011,and(not(and(X_3010,X_3010)),X_3010)),X_3012))
| is_a_theorem(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012))) ),
inference(subst,[],[refute_0_169:[bind(Q,$fot(and(X_3011,and(not(and(X_3010,X_3010)),X_3010)))),bind(R,$fot(X_3012))]]) ).
cnf(refute_0_849,plain,
( ~ is_a_theorem(or(X_2070,implies(X_2069,or(and(X_2068,X_2068),not(X_2068)))))
| is_a_theorem(or(implies(X_2069,or(and(X_2068,X_2068),not(X_2068))),X_2070)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_2070)),bind(Q,$fot(implies(X_2069,or(and(X_2068,X_2068),not(X_2068)))))]]) ).
cnf(refute_0_850,plain,
( ~ is_a_theorem(or(and(X_17,X_17),not(X_17)))
| is_a_theorem(or(X_372,or(and(X_17,X_17),not(X_17)))) ),
inference(subst,[],[refute_0_17:[bind(P,$fot(X_372)),bind(X_370,$fot(or(and(X_17,X_17),not(X_17))))]]) ).
cnf(refute_0_851,plain,
is_a_theorem(or(X_372,or(and(X_17,X_17),not(X_17)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_17,X_17),not(X_17))) )],[refute_0_258,refute_0_850]) ).
cnf(refute_0_852,plain,
( ~ is_a_theorem(or(X_372,or(and(X_17,X_17),not(X_17))))
| is_a_theorem(implies(X_412,or(X_372,or(and(X_17,X_17),not(X_17))))) ),
inference(subst,[],[refute_0_679:[bind(X_17,$fot(X_412)),bind(X_370,$fot(or(X_372,or(and(X_17,X_17),not(X_17)))))]]) ).
cnf(refute_0_853,plain,
is_a_theorem(implies(X_412,or(X_372,or(and(X_17,X_17),not(X_17))))),
inference(resolve,[$cnf( is_a_theorem(or(X_372,or(and(X_17,X_17),not(X_17)))) )],[refute_0_851,refute_0_852]) ).
cnf(refute_0_854,plain,
is_a_theorem(implies(X_1813,or(X_1814,or(and(X_17,X_17),not(X_17))))),
inference(subst,[],[refute_0_853:[bind(X_372,$fot(X_1814)),bind(X_412,$fot(X_1813))]]) ).
cnf(refute_0_855,plain,
( ~ is_a_theorem(implies(X_1813,or(X_1814,or(and(X_17,X_17),not(X_17)))))
| is_a_theorem(or(X_1814,implies(X_1813,or(and(X_17,X_17),not(X_17))))) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(X_1813)),bind(X_68,$fot(X_1814)),bind(X_69,$fot(or(and(X_17,X_17),not(X_17))))]]) ).
cnf(refute_0_856,plain,
is_a_theorem(or(X_1814,implies(X_1813,or(and(X_17,X_17),not(X_17))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1813,or(X_1814,or(and(X_17,X_17),not(X_17))))) )],[refute_0_854,refute_0_855]) ).
cnf(refute_0_857,plain,
is_a_theorem(or(X_2070,implies(X_2069,or(and(X_2068,X_2068),not(X_2068))))),
inference(subst,[],[refute_0_856:[bind(X_17,$fot(X_2068)),bind(X_1813,$fot(X_2069)),bind(X_1814,$fot(X_2070))]]) ).
cnf(refute_0_858,plain,
is_a_theorem(or(implies(X_2069,or(and(X_2068,X_2068),not(X_2068))),X_2070)),
inference(resolve,[$cnf( is_a_theorem(or(X_2070,implies(X_2069,or(and(X_2068,X_2068),not(X_2068))))) )],[refute_0_857,refute_0_849]) ).
cnf(refute_0_859,plain,
implies(and(X,not(Y)),X_18) = or(not(and(X,not(Y))),X_18),
inference(subst,[],[refute_0_26:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_860,plain,
( implies(and(X,not(Y)),X_18) != or(not(and(X,not(Y))),X_18)
| not(and(X,not(Y))) != implies(X,Y)
| implies(and(X,not(Y)),X_18) = or(implies(X,Y),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(X,not(Y)),X_18),or(not(and(X,not(Y))),X_18)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_861,plain,
( implies(and(X,not(Y)),X_18) != or(not(and(X,not(Y))),X_18)
| implies(and(X,not(Y)),X_18) = or(implies(X,Y),X_18) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_80,refute_0_860]) ).
cnf(refute_0_862,plain,
implies(and(X,not(Y)),X_18) = or(implies(X,Y),X_18),
inference(resolve,[$cnf( $equal(implies(and(X,not(Y)),X_18),or(not(and(X,not(Y))),X_18)) )],[refute_0_859,refute_0_861]) ).
cnf(refute_0_863,plain,
implies(and(X_73,not(or(X_9,not(Y)))),X_75) = or(implies(X_73,or(X_9,not(Y))),X_75),
inference(subst,[],[refute_0_862:[bind(X,$fot(X_73)),bind(Y,$fot(or(X_9,not(Y)))),bind(X_18,$fot(X_75))]]) ).
cnf(refute_0_864,plain,
( implies(and(X_73,not(or(X_9,not(Y)))),X_75) != or(implies(X_73,or(X_9,not(Y))),X_75)
| not(or(X_9,not(Y))) != and(not(X_9),Y)
| implies(and(X_73,and(not(X_9),Y)),X_75) = or(implies(X_73,or(X_9,not(Y))),X_75) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(X_73,not(or(X_9,not(Y)))),X_75),or(implies(X_73,or(X_9,not(Y))),X_75)) ),[0,0,1],$fot(and(not(X_9),Y))]]) ).
cnf(refute_0_865,plain,
( implies(and(X_73,not(or(X_9,not(Y)))),X_75) != or(implies(X_73,or(X_9,not(Y))),X_75)
| implies(and(X_73,and(not(X_9),Y)),X_75) = or(implies(X_73,or(X_9,not(Y))),X_75) ),
inference(resolve,[$cnf( $equal(not(or(X_9,not(Y))),and(not(X_9),Y)) )],[refute_0_126,refute_0_864]) ).
cnf(refute_0_866,plain,
implies(and(X_73,and(not(X_9),Y)),X_75) = or(implies(X_73,or(X_9,not(Y))),X_75),
inference(resolve,[$cnf( $equal(implies(and(X_73,not(or(X_9,not(Y)))),X_75),or(implies(X_73,or(X_9,not(Y))),X_75)) )],[refute_0_863,refute_0_865]) ).
cnf(refute_0_867,plain,
( implies(and(X_73,and(not(X_9),Y)),X_75) != or(implies(X_73,or(X_9,not(Y))),X_75)
| or(implies(X_73,or(X_9,not(Y))),X_75) = implies(and(X_73,and(not(X_9),Y)),X_75) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(and(X_73,and(not(X_9),Y)),X_75))),bind(Y0,$fot(or(implies(X_73,or(X_9,not(Y))),X_75)))]]) ).
cnf(refute_0_868,plain,
or(implies(X_73,or(X_9,not(Y))),X_75) = implies(and(X_73,and(not(X_9),Y)),X_75),
inference(resolve,[$cnf( $equal(implies(and(X_73,and(not(X_9),Y)),X_75),or(implies(X_73,or(X_9,not(Y))),X_75)) )],[refute_0_866,refute_0_867]) ).
cnf(refute_0_869,plain,
or(implies(X_2069,or(and(X_2068,X_2068),not(X_2068))),X_2070) = implies(and(X_2069,and(not(and(X_2068,X_2068)),X_2068)),X_2070),
inference(subst,[],[refute_0_868:[bind(Y,$fot(X_2068)),bind(X_73,$fot(X_2069)),bind(X_75,$fot(X_2070)),bind(X_9,$fot(and(X_2068,X_2068)))]]) ).
cnf(refute_0_870,plain,
( or(implies(X_2069,or(and(X_2068,X_2068),not(X_2068))),X_2070) != implies(and(X_2069,and(not(and(X_2068,X_2068)),X_2068)),X_2070)
| ~ is_a_theorem(or(implies(X_2069,or(and(X_2068,X_2068),not(X_2068))),X_2070))
| is_a_theorem(implies(and(X_2069,and(not(and(X_2068,X_2068)),X_2068)),X_2070)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_2069,or(and(X_2068,X_2068),not(X_2068))),X_2070)) ),[0],$fot(implies(and(X_2069,and(not(and(X_2068,X_2068)),X_2068)),X_2070))]]) ).
cnf(refute_0_871,plain,
( ~ is_a_theorem(or(implies(X_2069,or(and(X_2068,X_2068),not(X_2068))),X_2070))
| is_a_theorem(implies(and(X_2069,and(not(and(X_2068,X_2068)),X_2068)),X_2070)) ),
inference(resolve,[$cnf( $equal(or(implies(X_2069,or(and(X_2068,X_2068),not(X_2068))),X_2070),implies(and(X_2069,and(not(and(X_2068,X_2068)),X_2068)),X_2070)) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
is_a_theorem(implies(and(X_2069,and(not(and(X_2068,X_2068)),X_2068)),X_2070)),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_2069,or(and(X_2068,X_2068),not(X_2068))),X_2070)) )],[refute_0_858,refute_0_871]) ).
cnf(refute_0_873,plain,
is_a_theorem(implies(and(X_3011,and(not(and(X_3010,X_3010)),X_3010)),X_3012)),
inference(subst,[],[refute_0_872:[bind(X_2068,$fot(X_3010)),bind(X_2069,$fot(X_3011)),bind(X_2070,$fot(X_3012))]]) ).
cnf(refute_0_874,plain,
is_a_theorem(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_3011,and(not(and(X_3010,X_3010)),X_3010)),X_3012)) )],[refute_0_873,refute_0_848]) ).
cnf(refute_0_875,plain,
and(X_3010,X_3010) = X_3010,
inference(subst,[],[refute_0_649:[bind(Y,$fot(X_3010))]]) ).
cnf(refute_0_876,plain,
not(and(X_3010,X_3010)) = not(and(X_3010,X_3010)),
introduced(tautology,[refl,[$fot(not(and(X_3010,X_3010)))]]) ).
cnf(refute_0_877,plain,
( and(X_3010,X_3010) != X_3010
| not(and(X_3010,X_3010)) != not(and(X_3010,X_3010))
| not(and(X_3010,X_3010)) = not(X_3010) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X_3010,X_3010)),not(and(X_3010,X_3010))) ),[1,0],$fot(X_3010)]]) ).
cnf(refute_0_878,plain,
( and(X_3010,X_3010) != X_3010
| not(and(X_3010,X_3010)) = not(X_3010) ),
inference(resolve,[$cnf( $equal(not(and(X_3010,X_3010)),not(and(X_3010,X_3010))) )],[refute_0_876,refute_0_877]) ).
cnf(refute_0_879,plain,
not(and(X_3010,X_3010)) = not(X_3010),
inference(resolve,[$cnf( $equal(and(X_3010,X_3010),X_3010) )],[refute_0_875,refute_0_878]) ).
cnf(refute_0_880,plain,
and(not(and(X_3010,X_3010)),X_3010) = and(not(and(X_3010,X_3010)),X_3010),
introduced(tautology,[refl,[$fot(and(not(and(X_3010,X_3010)),X_3010))]]) ).
cnf(refute_0_881,plain,
( and(not(and(X_3010,X_3010)),X_3010) != and(not(and(X_3010,X_3010)),X_3010)
| not(and(X_3010,X_3010)) != not(X_3010)
| and(not(and(X_3010,X_3010)),X_3010) = and(not(X_3010),X_3010) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_3010,X_3010)),X_3010),and(not(and(X_3010,X_3010)),X_3010)) ),[1,0],$fot(not(X_3010))]]) ).
cnf(refute_0_882,plain,
( not(and(X_3010,X_3010)) != not(X_3010)
| and(not(and(X_3010,X_3010)),X_3010) = and(not(X_3010),X_3010) ),
inference(resolve,[$cnf( $equal(and(not(and(X_3010,X_3010)),X_3010),and(not(and(X_3010,X_3010)),X_3010)) )],[refute_0_880,refute_0_881]) ).
cnf(refute_0_883,plain,
and(not(and(X_3010,X_3010)),X_3010) = and(not(X_3010),X_3010),
inference(resolve,[$cnf( $equal(not(and(X_3010,X_3010)),not(X_3010)) )],[refute_0_879,refute_0_882]) ).
cnf(refute_0_884,plain,
and(X_3011,and(not(and(X_3010,X_3010)),X_3010)) = and(X_3011,and(not(and(X_3010,X_3010)),X_3010)),
introduced(tautology,[refl,[$fot(and(X_3011,and(not(and(X_3010,X_3010)),X_3010)))]]) ).
cnf(refute_0_885,plain,
( and(X_3011,and(not(and(X_3010,X_3010)),X_3010)) != and(X_3011,and(not(and(X_3010,X_3010)),X_3010))
| and(not(and(X_3010,X_3010)),X_3010) != and(not(X_3010),X_3010)
| and(X_3011,and(not(and(X_3010,X_3010)),X_3010)) = and(X_3011,and(not(X_3010),X_3010)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_3011,and(not(and(X_3010,X_3010)),X_3010)),and(X_3011,and(not(and(X_3010,X_3010)),X_3010))) ),[1,1],$fot(and(not(X_3010),X_3010))]]) ).
cnf(refute_0_886,plain,
( and(not(and(X_3010,X_3010)),X_3010) != and(not(X_3010),X_3010)
| and(X_3011,and(not(and(X_3010,X_3010)),X_3010)) = and(X_3011,and(not(X_3010),X_3010)) ),
inference(resolve,[$cnf( $equal(and(X_3011,and(not(and(X_3010,X_3010)),X_3010)),and(X_3011,and(not(and(X_3010,X_3010)),X_3010))) )],[refute_0_884,refute_0_885]) ).
cnf(refute_0_887,plain,
and(X_3011,and(not(and(X_3010,X_3010)),X_3010)) = and(X_3011,and(not(X_3010),X_3010)),
inference(resolve,[$cnf( $equal(and(not(and(X_3010,X_3010)),X_3010),and(not(X_3010),X_3010)) )],[refute_0_883,refute_0_886]) ).
cnf(refute_0_888,plain,
or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))) = or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),
introduced(tautology,[refl,[$fot(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))))]]) ).
cnf(refute_0_889,plain,
( and(X_3011,and(not(and(X_3010,X_3010)),X_3010)) != and(X_3011,and(not(X_3010),X_3010))
| or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))) != or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010)))
| or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))) = or(P,and(X_3011,and(not(X_3010),X_3010))) ),
introduced(tautology,[equality,[$cnf( $equal(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010)))) ),[1,1],$fot(and(X_3011,and(not(X_3010),X_3010)))]]) ).
cnf(refute_0_890,plain,
( and(X_3011,and(not(and(X_3010,X_3010)),X_3010)) != and(X_3011,and(not(X_3010),X_3010))
| or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))) = or(P,and(X_3011,and(not(X_3010),X_3010))) ),
inference(resolve,[$cnf( $equal(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010)))) )],[refute_0_888,refute_0_889]) ).
cnf(refute_0_891,plain,
or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))) = or(P,and(X_3011,and(not(X_3010),X_3010))),
inference(resolve,[$cnf( $equal(and(X_3011,and(not(and(X_3010,X_3010)),X_3010)),and(X_3011,and(not(X_3010),X_3010))) )],[refute_0_887,refute_0_890]) ).
cnf(refute_0_892,plain,
implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)) = implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)),
introduced(tautology,[refl,[$fot(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)))]]) ).
cnf(refute_0_893,plain,
( implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)) != implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012))
| or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))) != or(P,and(X_3011,and(not(X_3010),X_3010)))
| implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)) = implies(or(P,and(X_3011,and(not(X_3010),X_3010))),or(P,X_3012)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)),implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012))) ),[1,0],$fot(or(P,and(X_3011,and(not(X_3010),X_3010))))]]) ).
cnf(refute_0_894,plain,
( or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))) != or(P,and(X_3011,and(not(X_3010),X_3010)))
| implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)) = implies(or(P,and(X_3011,and(not(X_3010),X_3010))),or(P,X_3012)) ),
inference(resolve,[$cnf( $equal(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)),implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012))) )],[refute_0_892,refute_0_893]) ).
cnf(refute_0_895,plain,
implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)) = implies(or(P,and(X_3011,and(not(X_3010),X_3010))),or(P,X_3012)),
inference(resolve,[$cnf( $equal(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,and(X_3011,and(not(X_3010),X_3010)))) )],[refute_0_891,refute_0_894]) ).
cnf(refute_0_896,plain,
( implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)) != implies(or(P,and(X_3011,and(not(X_3010),X_3010))),or(P,X_3012))
| ~ is_a_theorem(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)))
| is_a_theorem(implies(or(P,and(X_3011,and(not(X_3010),X_3010))),or(P,X_3012))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012))) ),[0],$fot(implies(or(P,and(X_3011,and(not(X_3010),X_3010))),or(P,X_3012)))]]) ).
cnf(refute_0_897,plain,
( ~ is_a_theorem(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)))
| is_a_theorem(implies(or(P,and(X_3011,and(not(X_3010),X_3010))),or(P,X_3012))) ),
inference(resolve,[$cnf( $equal(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012)),implies(or(P,and(X_3011,and(not(X_3010),X_3010))),or(P,X_3012))) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
is_a_theorem(implies(or(P,and(X_3011,and(not(X_3010),X_3010))),or(P,X_3012))),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,and(X_3011,and(not(and(X_3010,X_3010)),X_3010))),or(P,X_3012))) )],[refute_0_874,refute_0_897]) ).
cnf(refute_0_899,plain,
is_a_theorem(implies(or(X_11982,and(X_11981,and(not(X_11980),X_11980))),or(X_11982,X_11982))),
inference(subst,[],[refute_0_898:[bind(P,$fot(X_11982)),bind(X_3010,$fot(X_11980)),bind(X_3011,$fot(X_11981)),bind(X_3012,$fot(X_11982))]]) ).
cnf(refute_0_900,plain,
X_11982 = or(X_11982,X_11982),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(X_11982))]]) ).
cnf(refute_0_901,plain,
( X_11982 != or(X_11982,X_11982)
| or(X_11982,X_11982) = X_11982 ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(X_11982)),bind(Y0,$fot(or(X_11982,X_11982)))]]) ).
cnf(refute_0_902,plain,
or(X_11982,X_11982) = X_11982,
inference(resolve,[$cnf( $equal(X_11982,or(X_11982,X_11982)) )],[refute_0_900,refute_0_901]) ).
cnf(refute_0_903,plain,
( or(X_11982,X_11982) != X_11982
| ~ is_a_theorem(implies(or(X_11982,and(X_11981,and(not(X_11980),X_11980))),or(X_11982,X_11982)))
| is_a_theorem(implies(or(X_11982,and(X_11981,and(not(X_11980),X_11980))),X_11982)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_11982,and(X_11981,and(not(X_11980),X_11980))),or(X_11982,X_11982))) ),[0,1],$fot(X_11982)]]) ).
cnf(refute_0_904,plain,
( ~ is_a_theorem(implies(or(X_11982,and(X_11981,and(not(X_11980),X_11980))),or(X_11982,X_11982)))
| is_a_theorem(implies(or(X_11982,and(X_11981,and(not(X_11980),X_11980))),X_11982)) ),
inference(resolve,[$cnf( $equal(or(X_11982,X_11982),X_11982) )],[refute_0_902,refute_0_903]) ).
cnf(refute_0_905,plain,
is_a_theorem(implies(or(X_11982,and(X_11981,and(not(X_11980),X_11980))),X_11982)),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_11982,and(X_11981,and(not(X_11980),X_11980))),or(X_11982,X_11982))) )],[refute_0_899,refute_0_904]) ).
cnf(refute_0_906,plain,
is_a_theorem(implies(or(not(X),and(X_11984,and(not(X_11983),X_11983))),not(X))),
inference(subst,[],[refute_0_905:[bind(X_11980,$fot(X_11983)),bind(X_11981,$fot(X_11984)),bind(X_11982,$fot(not(X)))]]) ).
cnf(refute_0_907,plain,
implies(X,and(X_11984,and(not(X_11983),X_11983))) = or(not(X),and(X_11984,and(not(X_11983),X_11983))),
inference(subst,[],[refute_0_26:[bind(Y,$fot(and(X_11984,and(not(X_11983),X_11983))))]]) ).
cnf(refute_0_908,plain,
( implies(X,and(X_11984,and(not(X_11983),X_11983))) != or(not(X),and(X_11984,and(not(X_11983),X_11983)))
| or(not(X),and(X_11984,and(not(X_11983),X_11983))) = implies(X,and(X_11984,and(not(X_11983),X_11983))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,and(X_11984,and(not(X_11983),X_11983))))),bind(Y0,$fot(or(not(X),and(X_11984,and(not(X_11983),X_11983)))))]]) ).
cnf(refute_0_909,plain,
or(not(X),and(X_11984,and(not(X_11983),X_11983))) = implies(X,and(X_11984,and(not(X_11983),X_11983))),
inference(resolve,[$cnf( $equal(implies(X,and(X_11984,and(not(X_11983),X_11983))),or(not(X),and(X_11984,and(not(X_11983),X_11983)))) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
( or(not(X),and(X_11984,and(not(X_11983),X_11983))) != implies(X,and(X_11984,and(not(X_11983),X_11983)))
| ~ is_a_theorem(implies(or(not(X),and(X_11984,and(not(X_11983),X_11983))),not(X)))
| is_a_theorem(implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),and(X_11984,and(not(X_11983),X_11983))),not(X))) ),[0,0],$fot(implies(X,and(X_11984,and(not(X_11983),X_11983))))]]) ).
cnf(refute_0_911,plain,
( ~ is_a_theorem(implies(or(not(X),and(X_11984,and(not(X_11983),X_11983))),not(X)))
| is_a_theorem(implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X))) ),
inference(resolve,[$cnf( $equal(or(not(X),and(X_11984,and(not(X_11983),X_11983))),implies(X,and(X_11984,and(not(X_11983),X_11983)))) )],[refute_0_909,refute_0_910]) ).
cnf(refute_0_912,plain,
is_a_theorem(implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),and(X_11984,and(not(X_11983),X_11983))),not(X))) )],[refute_0_906,refute_0_911]) ).
cnf(refute_0_913,plain,
implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X)) = not(and(implies(X,and(X_11984,and(not(X_11983),X_11983))),X)),
inference(subst,[],[refute_0_448:[bind(X,$fot(implies(X,and(X_11984,and(not(X_11983),X_11983))))),bind(X_1833,$fot(X))]]) ).
cnf(refute_0_914,plain,
( implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X)) != not(and(implies(X,and(X_11984,and(not(X_11983),X_11983))),X))
| ~ is_a_theorem(implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X)))
| is_a_theorem(not(and(implies(X,and(X_11984,and(not(X_11983),X_11983))),X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X))) ),[0],$fot(not(and(implies(X,and(X_11984,and(not(X_11983),X_11983))),X)))]]) ).
cnf(refute_0_915,plain,
( ~ is_a_theorem(implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X)))
| is_a_theorem(not(and(implies(X,and(X_11984,and(not(X_11983),X_11983))),X))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X)),not(and(implies(X,and(X_11984,and(not(X_11983),X_11983))),X))) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
is_a_theorem(not(and(implies(X,and(X_11984,and(not(X_11983),X_11983))),X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,and(X_11984,and(not(X_11983),X_11983))),not(X))) )],[refute_0_912,refute_0_915]) ).
cnf(refute_0_917,plain,
is_a_theorem(not(and(implies(X_15236,and(X_11984,and(not(X_11983),X_11983))),X_15236))),
inference(subst,[],[refute_0_916:[bind(X,$fot(X_15236))]]) ).
cnf(refute_0_918,plain,
is_a_theorem(implies(or(P,not(X_17)),or(not(X_17),P))),
inference(subst,[],[refute_0_5:[bind(Q,$fot(not(X_17)))]]) ).
cnf(refute_0_919,plain,
implies(X_17,P) = or(not(X_17),P),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_17)),bind(Y,$fot(P))]]) ).
cnf(refute_0_920,plain,
( implies(X_17,P) != or(not(X_17),P)
| or(not(X_17),P) = implies(X_17,P) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X_17,P))),bind(Y0,$fot(or(not(X_17),P)))]]) ).
cnf(refute_0_921,plain,
or(not(X_17),P) = implies(X_17,P),
inference(resolve,[$cnf( $equal(implies(X_17,P),or(not(X_17),P)) )],[refute_0_919,refute_0_920]) ).
cnf(refute_0_922,plain,
( or(not(X_17),P) != implies(X_17,P)
| ~ is_a_theorem(implies(or(P,not(X_17)),or(not(X_17),P)))
| is_a_theorem(implies(or(P,not(X_17)),implies(X_17,P))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(P,not(X_17)),or(not(X_17),P))) ),[0,1],$fot(implies(X_17,P))]]) ).
cnf(refute_0_923,plain,
( ~ is_a_theorem(implies(or(P,not(X_17)),or(not(X_17),P)))
| is_a_theorem(implies(or(P,not(X_17)),implies(X_17,P))) ),
inference(resolve,[$cnf( $equal(or(not(X_17),P),implies(X_17,P)) )],[refute_0_921,refute_0_922]) ).
cnf(refute_0_924,plain,
is_a_theorem(implies(or(P,not(X_17)),implies(X_17,P))),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,not(X_17)),or(not(X_17),P))) )],[refute_0_918,refute_0_923]) ).
cnf(refute_0_925,plain,
( ~ is_a_theorem(implies(or(P,not(X_17)),implies(X_17,P)))
| ~ is_a_theorem(or(P,not(X_17)))
| is_a_theorem(implies(X_17,P)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(P,not(X_17)))),bind(Y,$fot(implies(X_17,P)))]]) ).
cnf(refute_0_926,plain,
( ~ is_a_theorem(or(P,not(X_17)))
| is_a_theorem(implies(X_17,P)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,not(X_17)),implies(X_17,P))) )],[refute_0_924,refute_0_925]) ).
cnf(refute_0_927,plain,
( ~ is_a_theorem(or(not(X),not(X_1303)))
| is_a_theorem(implies(X_1303,not(X))) ),
inference(subst,[],[refute_0_926:[bind(P,$fot(not(X))),bind(X_17,$fot(X_1303))]]) ).
cnf(refute_0_928,plain,
implies(X,not(X_1303)) = or(not(X),not(X_1303)),
inference(subst,[],[refute_0_26:[bind(Y,$fot(not(X_1303)))]]) ).
cnf(refute_0_929,plain,
( implies(X,not(X_1303)) != or(not(X),not(X_1303))
| or(not(X),not(X_1303)) = implies(X,not(X_1303)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,not(X_1303)))),bind(Y0,$fot(or(not(X),not(X_1303))))]]) ).
cnf(refute_0_930,plain,
or(not(X),not(X_1303)) = implies(X,not(X_1303)),
inference(resolve,[$cnf( $equal(implies(X,not(X_1303)),or(not(X),not(X_1303))) )],[refute_0_928,refute_0_929]) ).
cnf(refute_0_931,plain,
( or(not(X),not(X_1303)) != implies(X,not(X_1303))
| ~ is_a_theorem(implies(X,not(X_1303)))
| is_a_theorem(or(not(X),not(X_1303))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(or(not(X),not(X_1303))) ),[0],$fot(implies(X,not(X_1303)))]]) ).
cnf(refute_0_932,plain,
( ~ is_a_theorem(implies(X,not(X_1303)))
| is_a_theorem(or(not(X),not(X_1303))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_1303)),implies(X,not(X_1303))) )],[refute_0_930,refute_0_931]) ).
cnf(refute_0_933,plain,
( ~ is_a_theorem(implies(X,not(X_1303)))
| is_a_theorem(implies(X_1303,not(X))) ),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(X_1303))) )],[refute_0_932,refute_0_927]) ).
cnf(refute_0_934,plain,
implies(X,not(X_1303)) = not(and(X,X_1303)),
inference(subst,[],[refute_0_448:[bind(X_1833,$fot(X_1303))]]) ).
cnf(refute_0_935,plain,
( implies(X,not(X_1303)) != not(and(X,X_1303))
| ~ is_a_theorem(not(and(X,X_1303)))
| is_a_theorem(implies(X,not(X_1303))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(X,not(X_1303))) ),[0],$fot(not(and(X,X_1303)))]]) ).
cnf(refute_0_936,plain,
( ~ is_a_theorem(not(and(X,X_1303)))
| is_a_theorem(implies(X,not(X_1303))) ),
inference(resolve,[$cnf( $equal(implies(X,not(X_1303)),not(and(X,X_1303))) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
( ~ is_a_theorem(not(and(X,X_1303)))
| is_a_theorem(implies(X_1303,not(X))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X,not(X_1303))) )],[refute_0_936,refute_0_933]) ).
cnf(refute_0_938,plain,
implies(X_1303,not(X)) = not(and(X_1303,X)),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_1303)),bind(X_1833,$fot(X))]]) ).
cnf(refute_0_939,plain,
( implies(X_1303,not(X)) != not(and(X_1303,X))
| ~ is_a_theorem(implies(X_1303,not(X)))
| is_a_theorem(not(and(X_1303,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_1303,not(X))) ),[0],$fot(not(and(X_1303,X)))]]) ).
cnf(refute_0_940,plain,
( ~ is_a_theorem(implies(X_1303,not(X)))
| is_a_theorem(not(and(X_1303,X))) ),
inference(resolve,[$cnf( $equal(implies(X_1303,not(X)),not(and(X_1303,X))) )],[refute_0_938,refute_0_939]) ).
cnf(refute_0_941,plain,
( ~ is_a_theorem(not(and(X,X_1303)))
| is_a_theorem(not(and(X_1303,X))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1303,not(X))) )],[refute_0_937,refute_0_940]) ).
cnf(refute_0_942,plain,
( ~ is_a_theorem(not(and(implies(X_15236,and(X_11984,and(not(X_11983),X_11983))),X_15236)))
| is_a_theorem(not(and(X_15236,implies(X_15236,and(X_11984,and(not(X_11983),X_11983)))))) ),
inference(subst,[],[refute_0_941:[bind(X,$fot(implies(X_15236,and(X_11984,and(not(X_11983),X_11983))))),bind(X_1303,$fot(X_15236))]]) ).
cnf(refute_0_943,plain,
is_a_theorem(not(and(X_15236,implies(X_15236,and(X_11984,and(not(X_11983),X_11983)))))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(X_15236,and(X_11984,and(not(X_11983),X_11983))),X_15236))) )],[refute_0_917,refute_0_942]) ).
cnf(refute_0_944,plain,
implies(X,and(X_7,not(X_8))) = not(and(X,not(and(X_7,not(X_8))))),
inference(subst,[],[refute_0_78:[bind(Y,$fot(and(X_7,not(X_8))))]]) ).
cnf(refute_0_945,plain,
implies(X_7,X_8) = not(and(X_7,not(X_8))),
inference(subst,[],[refute_0_78:[bind(X,$fot(X_7)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_946,plain,
( implies(X_7,X_8) != not(and(X_7,not(X_8)))
| not(and(X_7,not(X_8))) = implies(X_7,X_8) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X_7,X_8))),bind(Y0,$fot(not(and(X_7,not(X_8)))))]]) ).
cnf(refute_0_947,plain,
not(and(X_7,not(X_8))) = implies(X_7,X_8),
inference(resolve,[$cnf( $equal(implies(X_7,X_8),not(and(X_7,not(X_8)))) )],[refute_0_945,refute_0_946]) ).
cnf(refute_0_948,plain,
( implies(X,and(X_7,not(X_8))) != not(and(X,not(and(X_7,not(X_8)))))
| not(and(X_7,not(X_8))) != implies(X_7,X_8)
| implies(X,and(X_7,not(X_8))) = not(and(X,implies(X_7,X_8))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_7,not(X_8))),not(and(X,not(and(X_7,not(X_8)))))) ),[1,0,1],$fot(implies(X_7,X_8))]]) ).
cnf(refute_0_949,plain,
( implies(X,and(X_7,not(X_8))) != not(and(X,not(and(X_7,not(X_8)))))
| implies(X,and(X_7,not(X_8))) = not(and(X,implies(X_7,X_8))) ),
inference(resolve,[$cnf( $equal(not(and(X_7,not(X_8))),implies(X_7,X_8)) )],[refute_0_947,refute_0_948]) ).
cnf(refute_0_950,plain,
implies(X,and(X_7,not(X_8))) = not(and(X,implies(X_7,X_8))),
inference(resolve,[$cnf( $equal(implies(X,and(X_7,not(X_8))),not(and(X,not(and(X_7,not(X_8)))))) )],[refute_0_944,refute_0_949]) ).
cnf(refute_0_951,plain,
implies(X,and(X_7,not(and(X_149,and(not(X_151),X_150))))) = not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150))))),
inference(subst,[],[refute_0_950:[bind(X_8,$fot(and(X_149,and(not(X_151),X_150))))]]) ).
cnf(refute_0_952,plain,
implies(X,or(X_12,not(X_11))) = not(and(X,not(or(X_12,not(X_11))))),
inference(subst,[],[refute_0_78:[bind(Y,$fot(or(X_12,not(X_11))))]]) ).
cnf(refute_0_953,plain,
and(not(X_12),X_11) = not(or(X_12,not(X_11))),
inference(subst,[],[refute_0_97:[bind(Y,$fot(X_11)),bind(X_9,$fot(X_12))]]) ).
cnf(refute_0_954,plain,
( and(not(X_12),X_11) != not(or(X_12,not(X_11)))
| not(or(X_12,not(X_11))) = and(not(X_12),X_11) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(and(not(X_12),X_11))),bind(Y0,$fot(not(or(X_12,not(X_11)))))]]) ).
cnf(refute_0_955,plain,
not(or(X_12,not(X_11))) = and(not(X_12),X_11),
inference(resolve,[$cnf( $equal(and(not(X_12),X_11),not(or(X_12,not(X_11)))) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
( implies(X,or(X_12,not(X_11))) != not(and(X,not(or(X_12,not(X_11)))))
| not(or(X_12,not(X_11))) != and(not(X_12),X_11)
| implies(X,or(X_12,not(X_11))) = not(and(X,and(not(X_12),X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,or(X_12,not(X_11))),not(and(X,not(or(X_12,not(X_11)))))) ),[1,0,1],$fot(and(not(X_12),X_11))]]) ).
cnf(refute_0_957,plain,
( implies(X,or(X_12,not(X_11))) != not(and(X,not(or(X_12,not(X_11)))))
| implies(X,or(X_12,not(X_11))) = not(and(X,and(not(X_12),X_11))) ),
inference(resolve,[$cnf( $equal(not(or(X_12,not(X_11))),and(not(X_12),X_11)) )],[refute_0_955,refute_0_956]) ).
cnf(refute_0_958,plain,
implies(X,or(X_12,not(X_11))) = not(and(X,and(not(X_12),X_11))),
inference(resolve,[$cnf( $equal(implies(X,or(X_12,not(X_11))),not(and(X,not(or(X_12,not(X_11)))))) )],[refute_0_952,refute_0_957]) ).
cnf(refute_0_959,plain,
implies(X_149,or(X_151,not(X_150))) = not(and(X_149,and(not(X_151),X_150))),
inference(subst,[],[refute_0_958:[bind(X,$fot(X_149)),bind(X_11,$fot(X_150)),bind(X_12,$fot(X_151))]]) ).
cnf(refute_0_960,plain,
( implies(X_149,or(X_151,not(X_150))) != not(and(X_149,and(not(X_151),X_150)))
| not(and(X_149,and(not(X_151),X_150))) = implies(X_149,or(X_151,not(X_150))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X_149,or(X_151,not(X_150))))),bind(Y0,$fot(not(and(X_149,and(not(X_151),X_150)))))]]) ).
cnf(refute_0_961,plain,
not(and(X_149,and(not(X_151),X_150))) = implies(X_149,or(X_151,not(X_150))),
inference(resolve,[$cnf( $equal(implies(X_149,or(X_151,not(X_150))),not(and(X_149,and(not(X_151),X_150)))) )],[refute_0_959,refute_0_960]) ).
cnf(refute_0_962,plain,
( implies(X,and(X_7,not(and(X_149,and(not(X_151),X_150))))) != not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150)))))
| not(and(X_149,and(not(X_151),X_150))) != implies(X_149,or(X_151,not(X_150)))
| implies(X,and(X_7,implies(X_149,or(X_151,not(X_150))))) = not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_7,not(and(X_149,and(not(X_151),X_150))))),not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150)))))) ),[0,1,1],$fot(implies(X_149,or(X_151,not(X_150))))]]) ).
cnf(refute_0_963,plain,
( implies(X,and(X_7,not(and(X_149,and(not(X_151),X_150))))) != not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150)))))
| implies(X,and(X_7,implies(X_149,or(X_151,not(X_150))))) = not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150))))) ),
inference(resolve,[$cnf( $equal(not(and(X_149,and(not(X_151),X_150))),implies(X_149,or(X_151,not(X_150)))) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
implies(X,and(X_7,implies(X_149,or(X_151,not(X_150))))) = not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150))))),
inference(resolve,[$cnf( $equal(implies(X,and(X_7,not(and(X_149,and(not(X_151),X_150))))),not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150)))))) )],[refute_0_951,refute_0_963]) ).
cnf(refute_0_965,plain,
( implies(X,and(X_7,implies(X_149,or(X_151,not(X_150))))) != not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150)))))
| not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150))))) = implies(X,and(X_7,implies(X_149,or(X_151,not(X_150))))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,and(X_7,implies(X_149,or(X_151,not(X_150))))))),bind(Y0,$fot(not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150)))))))]]) ).
cnf(refute_0_966,plain,
not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150))))) = implies(X,and(X_7,implies(X_149,or(X_151,not(X_150))))),
inference(resolve,[$cnf( $equal(implies(X,and(X_7,implies(X_149,or(X_151,not(X_150))))),not(and(X,implies(X_7,and(X_149,and(not(X_151),X_150)))))) )],[refute_0_964,refute_0_965]) ).
cnf(refute_0_967,plain,
not(and(X_15236,implies(X_15236,and(X_11984,and(not(X_11983),X_11983))))) = implies(X_15236,and(X_15236,implies(X_11984,or(X_11983,not(X_11983))))),
inference(subst,[],[refute_0_966:[bind(X,$fot(X_15236)),bind(X_149,$fot(X_11984)),bind(X_150,$fot(X_11983)),bind(X_151,$fot(X_11983)),bind(X_7,$fot(X_15236))]]) ).
cnf(refute_0_968,plain,
( not(and(X_15236,implies(X_15236,and(X_11984,and(not(X_11983),X_11983))))) != implies(X_15236,and(X_15236,implies(X_11984,or(X_11983,not(X_11983)))))
| ~ is_a_theorem(not(and(X_15236,implies(X_15236,and(X_11984,and(not(X_11983),X_11983))))))
| is_a_theorem(implies(X_15236,and(X_15236,implies(X_11984,or(X_11983,not(X_11983)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(X_15236,implies(X_15236,and(X_11984,and(not(X_11983),X_11983)))))) ),[0],$fot(implies(X_15236,and(X_15236,implies(X_11984,or(X_11983,not(X_11983))))))]]) ).
cnf(refute_0_969,plain,
( ~ is_a_theorem(not(and(X_15236,implies(X_15236,and(X_11984,and(not(X_11983),X_11983))))))
| is_a_theorem(implies(X_15236,and(X_15236,implies(X_11984,or(X_11983,not(X_11983)))))) ),
inference(resolve,[$cnf( $equal(not(and(X_15236,implies(X_15236,and(X_11984,and(not(X_11983),X_11983))))),implies(X_15236,and(X_15236,implies(X_11984,or(X_11983,not(X_11983)))))) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
is_a_theorem(implies(X_15236,and(X_15236,implies(X_11984,or(X_11983,not(X_11983)))))),
inference(resolve,[$cnf( is_a_theorem(not(and(X_15236,implies(X_15236,and(X_11984,and(not(X_11983),X_11983)))))) )],[refute_0_943,refute_0_969]) ).
cnf(refute_0_971,plain,
is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),not(not(X_1832))))))),
inference(subst,[],[refute_0_970:[bind(X_11983,$fot(not(X_1832))),bind(X_11984,$fot(X_15429)),bind(X_15236,$fot(X_15430))]]) ).
cnf(refute_0_972,plain,
( not(not(X_1832)) != X_1832
| ~ is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),not(not(X_1832)))))))
| is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),not(not(X_1832))))))) ),[0,1,1,1,1],$fot(X_1832)]]) ).
cnf(refute_0_973,plain,
( ~ is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),not(not(X_1832)))))))
| is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832))))) ),
inference(resolve,[$cnf( $equal(not(not(X_1832)),X_1832) )],[refute_0_638,refute_0_972]) ).
cnf(refute_0_974,plain,
is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),not(not(X_1832))))))) )],[refute_0_971,refute_0_973]) ).
cnf(refute_0_975,plain,
equiv(implies(X,Y),not(implies(Y,X))) = and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y))),
inference(subst,[],[refute_0_118:[bind(X,$fot(implies(X,Y))),bind(X_9,$fot(implies(Y,X)))]]) ).
cnf(refute_0_976,plain,
( and(implies(X,Y),implies(Y,X)) != equiv(X,Y)
| equiv(implies(X,Y),not(implies(Y,X))) != and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y)))
| equiv(implies(X,Y),not(implies(Y,X))) = and(not(equiv(X,Y)),or(implies(Y,X),implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(implies(X,Y),not(implies(Y,X))),and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y)))) ),[1,0,0],$fot(equiv(X,Y))]]) ).
cnf(refute_0_977,plain,
( equiv(implies(X,Y),not(implies(Y,X))) != and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y)))
| equiv(implies(X,Y),not(implies(Y,X))) = and(not(equiv(X,Y)),or(implies(Y,X),implies(X,Y))) ),
inference(resolve,[$cnf( $equal(and(implies(X,Y),implies(Y,X)),equiv(X,Y)) )],[refute_0_229,refute_0_976]) ).
cnf(refute_0_978,plain,
equiv(implies(X,Y),not(implies(Y,X))) = and(not(equiv(X,Y)),or(implies(Y,X),implies(X,Y))),
inference(resolve,[$cnf( $equal(equiv(implies(X,Y),not(implies(Y,X))),and(not(and(implies(X,Y),implies(Y,X))),or(implies(Y,X),implies(X,Y)))) )],[refute_0_975,refute_0_977]) ).
cnf(refute_0_979,plain,
equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),implies(not(X),X_224))),
inference(subst,[],[refute_0_978:[bind(X,$fot(not(X))),bind(Y,$fot(X_224))]]) ).
cnf(refute_0_980,plain,
or(X,X_224) = implies(not(X),X_224),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_224))]]) ).
cnf(refute_0_981,plain,
( or(X,X_224) != implies(not(X),X_224)
| implies(not(X),X_224) = or(X,X_224) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,X_224))),bind(Y0,$fot(implies(not(X),X_224)))]]) ).
cnf(refute_0_982,plain,
implies(not(X),X_224) = or(X,X_224),
inference(resolve,[$cnf( $equal(or(X,X_224),implies(not(X),X_224)) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
( equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) != and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),implies(not(X),X_224)))
| implies(not(X),X_224) != or(X,X_224)
| equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))),and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),implies(not(X),X_224)))) ),[1,1,1],$fot(or(X,X_224))]]) ).
cnf(refute_0_984,plain,
( equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) != and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),implies(not(X),X_224)))
| equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_224),or(X,X_224)) )],[refute_0_982,refute_0_983]) ).
cnf(refute_0_985,plain,
equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))),
inference(resolve,[$cnf( $equal(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))),and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),implies(not(X),X_224)))) )],[refute_0_979,refute_0_984]) ).
cnf(refute_0_986,plain,
not(implies(X_224,not(X))) = and(X_224,X),
inference(subst,[],[refute_0_64:[bind(X,$fot(X_224)),bind(Y,$fot(X))]]) ).
cnf(refute_0_987,plain,
equiv(or(X,X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),not(implies(X_224,not(X)))),
introduced(tautology,[refl,[$fot(equiv(or(X,X_224),not(implies(X_224,not(X)))))]]) ).
cnf(refute_0_988,plain,
( equiv(or(X,X_224),not(implies(X_224,not(X)))) != equiv(or(X,X_224),not(implies(X_224,not(X))))
| not(implies(X_224,not(X))) != and(X_224,X)
| equiv(or(X,X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),and(X_224,X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(or(X,X_224),not(implies(X_224,not(X)))),equiv(or(X,X_224),not(implies(X_224,not(X))))) ),[1,1],$fot(and(X_224,X))]]) ).
cnf(refute_0_989,plain,
( not(implies(X_224,not(X))) != and(X_224,X)
| equiv(or(X,X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),and(X_224,X)) ),
inference(resolve,[$cnf( $equal(equiv(or(X,X_224),not(implies(X_224,not(X)))),equiv(or(X,X_224),not(implies(X_224,not(X))))) )],[refute_0_987,refute_0_988]) ).
cnf(refute_0_990,plain,
equiv(or(X,X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),and(X_224,X)),
inference(resolve,[$cnf( $equal(not(implies(X_224,not(X))),and(X_224,X)) )],[refute_0_986,refute_0_989]) ).
cnf(refute_0_991,plain,
equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = equiv(implies(not(X),X_224),not(implies(X_224,not(X)))),
introduced(tautology,[refl,[$fot(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))))]]) ).
cnf(refute_0_992,plain,
( equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) != equiv(implies(not(X),X_224),not(implies(X_224,not(X))))
| implies(not(X),X_224) != or(X,X_224)
| equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),not(implies(X_224,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))),equiv(implies(not(X),X_224),not(implies(X_224,not(X))))) ),[1,0],$fot(or(X,X_224))]]) ).
cnf(refute_0_993,plain,
( implies(not(X),X_224) != or(X,X_224)
| equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),not(implies(X_224,not(X)))) ),
inference(resolve,[$cnf( $equal(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))),equiv(implies(not(X),X_224),not(implies(X_224,not(X))))) )],[refute_0_991,refute_0_992]) ).
cnf(refute_0_994,plain,
equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),not(implies(X_224,not(X)))),
inference(resolve,[$cnf( $equal(implies(not(X),X_224),or(X,X_224)) )],[refute_0_982,refute_0_993]) ).
cnf(refute_0_995,plain,
( equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) != equiv(or(X,X_224),not(implies(X_224,not(X))))
| equiv(or(X,X_224),not(implies(X_224,not(X)))) != equiv(or(X,X_224),and(X_224,X))
| equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),and(X_224,X)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))))),bind(Y0,$fot(equiv(or(X,X_224),not(implies(X_224,not(X)))))),bind(Z,$fot(equiv(or(X,X_224),and(X_224,X))))]]) ).
cnf(refute_0_996,plain,
( equiv(or(X,X_224),not(implies(X_224,not(X)))) != equiv(or(X,X_224),and(X_224,X))
| equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),and(X_224,X)) ),
inference(resolve,[$cnf( $equal(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))),equiv(or(X,X_224),not(implies(X_224,not(X))))) )],[refute_0_994,refute_0_995]) ).
cnf(refute_0_997,plain,
equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) = equiv(or(X,X_224),and(X_224,X)),
inference(resolve,[$cnf( $equal(equiv(or(X,X_224),not(implies(X_224,not(X)))),equiv(or(X,X_224),and(X_224,X))) )],[refute_0_990,refute_0_996]) ).
cnf(refute_0_998,plain,
( equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) != and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))
| equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) != equiv(or(X,X_224),and(X_224,X))
| equiv(or(X,X_224),and(X_224,X)) = and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))),and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))) ),[0],$fot(equiv(or(X,X_224),and(X_224,X)))]]) ).
cnf(refute_0_999,plain,
( equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) != and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))
| equiv(or(X,X_224),and(X_224,X)) = and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) ),
inference(resolve,[$cnf( $equal(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))),equiv(or(X,X_224),and(X_224,X))) )],[refute_0_997,refute_0_998]) ).
cnf(refute_0_1000,plain,
or(implies(X_224,not(X)),or(X,X_224)) = implies(and(X_224,X),or(X,X_224)),
inference(subst,[],[refute_0_534:[bind(X,$fot(X_224)),bind(Y,$fot(X)),bind(X_10,$fot(or(X,X_224)))]]) ).
cnf(refute_0_1001,plain,
and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) = and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))),
introduced(tautology,[refl,[$fot(and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))))]]) ).
cnf(refute_0_1002,plain,
( and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) != and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))
| or(implies(X_224,not(X)),or(X,X_224)) != implies(and(X_224,X),or(X,X_224))
| and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) = and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))),and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))) ),[1,1],$fot(implies(and(X_224,X),or(X,X_224)))]]) ).
cnf(refute_0_1003,plain,
( or(implies(X_224,not(X)),or(X,X_224)) != implies(and(X_224,X),or(X,X_224))
| and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) = and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224))) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))),and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) = and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224))),
inference(resolve,[$cnf( $equal(or(implies(X_224,not(X)),or(X,X_224)),implies(and(X_224,X),or(X,X_224))) )],[refute_0_1000,refute_0_1003]) ).
cnf(refute_0_1005,plain,
( and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))) != and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224)))
| equiv(or(X,X_224),and(X_224,X)) != and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))
| equiv(or(X,X_224),and(X_224,X)) = and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(or(X,X_224),and(X_224,X)),and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))) ),[1],$fot(and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224))))]]) ).
cnf(refute_0_1006,plain,
( equiv(or(X,X_224),and(X_224,X)) != and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))
| equiv(or(X,X_224),and(X_224,X)) = and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224))) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224))),and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224)))) )],[refute_0_1004,refute_0_1005]) ).
cnf(refute_0_1007,plain,
( equiv(implies(not(X),X_224),not(implies(X_224,not(X)))) != and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))
| equiv(or(X,X_224),and(X_224,X)) = and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224))) ),
inference(resolve,[$cnf( $equal(equiv(or(X,X_224),and(X_224,X)),and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))) )],[refute_0_999,refute_0_1006]) ).
cnf(refute_0_1008,plain,
equiv(or(X,X_224),and(X_224,X)) = and(not(equiv(not(X),X_224)),implies(and(X_224,X),or(X,X_224))),
inference(resolve,[$cnf( $equal(equiv(implies(not(X),X_224),not(implies(X_224,not(X)))),and(not(equiv(not(X),X_224)),or(implies(X_224,not(X)),or(X,X_224)))) )],[refute_0_985,refute_0_1007]) ).
cnf(refute_0_1009,plain,
equiv(or(X_224,X_224),and(X_224,X_224)) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),or(X_224,X_224))),
inference(subst,[],[refute_0_1008:[bind(X,$fot(X_224))]]) ).
cnf(refute_0_1010,plain,
X_224 = or(X_224,X_224),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(X_224))]]) ).
cnf(refute_0_1011,plain,
( X_224 != or(X_224,X_224)
| or(X_224,X_224) = X_224 ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(X_224)),bind(Y0,$fot(or(X_224,X_224)))]]) ).
cnf(refute_0_1012,plain,
or(X_224,X_224) = X_224,
inference(resolve,[$cnf( $equal(X_224,or(X_224,X_224)) )],[refute_0_1010,refute_0_1011]) ).
cnf(refute_0_1013,plain,
( equiv(or(X_224,X_224),and(X_224,X_224)) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),or(X_224,X_224)))
| or(X_224,X_224) != X_224
| equiv(or(X_224,X_224),and(X_224,X_224)) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(or(X_224,X_224),and(X_224,X_224)),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),or(X_224,X_224)))) ),[1,1,1],$fot(X_224)]]) ).
cnf(refute_0_1014,plain,
( equiv(or(X_224,X_224),and(X_224,X_224)) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),or(X_224,X_224)))
| equiv(or(X_224,X_224),and(X_224,X_224)) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) ),
inference(resolve,[$cnf( $equal(or(X_224,X_224),X_224) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
equiv(or(X_224,X_224),and(X_224,X_224)) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)),
inference(resolve,[$cnf( $equal(equiv(or(X_224,X_224),and(X_224,X_224)),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),or(X_224,X_224)))) )],[refute_0_1009,refute_0_1014]) ).
cnf(refute_0_1016,plain,
equiv(or(X_224,X_224),and(X_224,X_224)) = equiv(or(X_224,X_224),and(X_224,X_224)),
introduced(tautology,[refl,[$fot(equiv(or(X_224,X_224),and(X_224,X_224)))]]) ).
cnf(refute_0_1017,plain,
( equiv(or(X_224,X_224),and(X_224,X_224)) != equiv(or(X_224,X_224),and(X_224,X_224))
| or(X_224,X_224) != X_224
| equiv(or(X_224,X_224),and(X_224,X_224)) = equiv(X_224,and(X_224,X_224)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(or(X_224,X_224),and(X_224,X_224)),equiv(or(X_224,X_224),and(X_224,X_224))) ),[1,0],$fot(X_224)]]) ).
cnf(refute_0_1018,plain,
( or(X_224,X_224) != X_224
| equiv(or(X_224,X_224),and(X_224,X_224)) = equiv(X_224,and(X_224,X_224)) ),
inference(resolve,[$cnf( $equal(equiv(or(X_224,X_224),and(X_224,X_224)),equiv(or(X_224,X_224),and(X_224,X_224))) )],[refute_0_1016,refute_0_1017]) ).
cnf(refute_0_1019,plain,
equiv(or(X_224,X_224),and(X_224,X_224)) = equiv(X_224,and(X_224,X_224)),
inference(resolve,[$cnf( $equal(or(X_224,X_224),X_224) )],[refute_0_1012,refute_0_1018]) ).
cnf(refute_0_1020,plain,
( equiv(or(X_224,X_224),and(X_224,X_224)) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))
| equiv(or(X_224,X_224),and(X_224,X_224)) != equiv(X_224,and(X_224,X_224))
| equiv(X_224,and(X_224,X_224)) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(or(X_224,X_224),and(X_224,X_224)),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))) ),[0],$fot(equiv(X_224,and(X_224,X_224)))]]) ).
cnf(refute_0_1021,plain,
( equiv(or(X_224,X_224),and(X_224,X_224)) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))
| equiv(X_224,and(X_224,X_224)) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) ),
inference(resolve,[$cnf( $equal(equiv(or(X_224,X_224),and(X_224,X_224)),equiv(X_224,and(X_224,X_224))) )],[refute_0_1019,refute_0_1020]) ).
cnf(refute_0_1022,plain,
equiv(X_224,and(X_224,X_224)) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)),
inference(resolve,[$cnf( $equal(equiv(or(X_224,X_224),and(X_224,X_224)),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))) )],[refute_0_1015,refute_0_1021]) ).
cnf(refute_0_1023,plain,
and(X_224,X_224) = X_224,
inference(subst,[],[refute_0_649:[bind(Y,$fot(X_224))]]) ).
cnf(refute_0_1024,plain,
equiv(X_224,and(X_224,X_224)) = equiv(X_224,and(X_224,X_224)),
introduced(tautology,[refl,[$fot(equiv(X_224,and(X_224,X_224)))]]) ).
cnf(refute_0_1025,plain,
( and(X_224,X_224) != X_224
| equiv(X_224,and(X_224,X_224)) != equiv(X_224,and(X_224,X_224))
| equiv(X_224,and(X_224,X_224)) = equiv(X_224,X_224) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_224,and(X_224,X_224)),equiv(X_224,and(X_224,X_224))) ),[1,1],$fot(X_224)]]) ).
cnf(refute_0_1026,plain,
( and(X_224,X_224) != X_224
| equiv(X_224,and(X_224,X_224)) = equiv(X_224,X_224) ),
inference(resolve,[$cnf( $equal(equiv(X_224,and(X_224,X_224)),equiv(X_224,and(X_224,X_224))) )],[refute_0_1024,refute_0_1025]) ).
cnf(refute_0_1027,plain,
equiv(X_224,and(X_224,X_224)) = equiv(X_224,X_224),
inference(resolve,[$cnf( $equal(and(X_224,X_224),X_224) )],[refute_0_1023,refute_0_1026]) ).
cnf(refute_0_1028,plain,
( equiv(X_224,and(X_224,X_224)) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))
| equiv(X_224,and(X_224,X_224)) != equiv(X_224,X_224)
| equiv(X_224,X_224) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_224,and(X_224,X_224)),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))) ),[0],$fot(equiv(X_224,X_224))]]) ).
cnf(refute_0_1029,plain,
( equiv(X_224,and(X_224,X_224)) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))
| equiv(X_224,X_224) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) ),
inference(resolve,[$cnf( $equal(equiv(X_224,and(X_224,X_224)),equiv(X_224,X_224)) )],[refute_0_1027,refute_0_1028]) ).
cnf(refute_0_1030,plain,
and(implies(X_224,X_224),implies(X_224,X_224)) = implies(X_224,X_224),
inference(subst,[],[refute_0_649:[bind(Y,$fot(implies(X_224,X_224)))]]) ).
cnf(refute_0_1031,plain,
or(or(X_12,not(X_11)),Y) = implies(not(or(X_12,not(X_11))),Y),
inference(subst,[],[refute_0_84:[bind(X,$fot(or(X_12,not(X_11))))]]) ).
cnf(refute_0_1032,plain,
( not(or(X_12,not(X_11))) != and(not(X_12),X_11)
| or(or(X_12,not(X_11)),Y) != implies(not(or(X_12,not(X_11))),Y)
| or(or(X_12,not(X_11)),Y) = implies(and(not(X_12),X_11),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X_12,not(X_11)),Y),implies(not(or(X_12,not(X_11))),Y)) ),[1,0],$fot(and(not(X_12),X_11))]]) ).
cnf(refute_0_1033,plain,
( or(or(X_12,not(X_11)),Y) != implies(not(or(X_12,not(X_11))),Y)
| or(or(X_12,not(X_11)),Y) = implies(and(not(X_12),X_11),Y) ),
inference(resolve,[$cnf( $equal(not(or(X_12,not(X_11))),and(not(X_12),X_11)) )],[refute_0_955,refute_0_1032]) ).
cnf(refute_0_1034,plain,
or(or(X_12,not(X_11)),Y) = implies(and(not(X_12),X_11),Y),
inference(resolve,[$cnf( $equal(or(or(X_12,not(X_11)),Y),implies(not(or(X_12,not(X_11))),Y)) )],[refute_0_1031,refute_0_1033]) ).
cnf(refute_0_1035,plain,
or(or(not(X_11),not(X_11)),Y) = implies(and(not(not(X_11)),X_11),Y),
inference(subst,[],[refute_0_1034:[bind(X_12,$fot(not(X_11)))]]) ).
cnf(refute_0_1036,plain,
not(X_11) = or(not(X_11),not(X_11)),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(not(X_11)))]]) ).
cnf(refute_0_1037,plain,
( not(X_11) != or(not(X_11),not(X_11))
| or(not(X_11),not(X_11)) = not(X_11) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(not(X_11))),bind(Y0,$fot(or(not(X_11),not(X_11))))]]) ).
cnf(refute_0_1038,plain,
or(not(X_11),not(X_11)) = not(X_11),
inference(resolve,[$cnf( $equal(not(X_11),or(not(X_11),not(X_11))) )],[refute_0_1036,refute_0_1037]) ).
cnf(refute_0_1039,plain,
( or(not(X_11),not(X_11)) != not(X_11)
| or(or(not(X_11),not(X_11)),Y) != implies(and(not(not(X_11)),X_11),Y)
| or(not(X_11),Y) = implies(and(not(not(X_11)),X_11),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(not(X_11),not(X_11)),Y),implies(and(not(not(X_11)),X_11),Y)) ),[0,0],$fot(not(X_11))]]) ).
cnf(refute_0_1040,plain,
( or(or(not(X_11),not(X_11)),Y) != implies(and(not(not(X_11)),X_11),Y)
| or(not(X_11),Y) = implies(and(not(not(X_11)),X_11),Y) ),
inference(resolve,[$cnf( $equal(or(not(X_11),not(X_11)),not(X_11)) )],[refute_0_1038,refute_0_1039]) ).
cnf(refute_0_1041,plain,
or(not(X_11),Y) = implies(and(not(not(X_11)),X_11),Y),
inference(resolve,[$cnf( $equal(or(or(not(X_11),not(X_11)),Y),implies(and(not(not(X_11)),X_11),Y)) )],[refute_0_1035,refute_0_1040]) ).
cnf(refute_0_1042,plain,
or(not(X_11),Y) = implies(X_11,Y),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_1043,plain,
( or(not(X_11),Y) != implies(X_11,Y)
| or(not(X_11),Y) != implies(and(not(not(X_11)),X_11),Y)
| implies(X_11,Y) = implies(and(not(not(X_11)),X_11),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X_11),Y),implies(and(not(not(X_11)),X_11),Y)) ),[0],$fot(implies(X_11,Y))]]) ).
cnf(refute_0_1044,plain,
( or(not(X_11),Y) != implies(and(not(not(X_11)),X_11),Y)
| implies(X_11,Y) = implies(and(not(not(X_11)),X_11),Y) ),
inference(resolve,[$cnf( $equal(or(not(X_11),Y),implies(X_11,Y)) )],[refute_0_1042,refute_0_1043]) ).
cnf(refute_0_1045,plain,
not(not(X_11)) = X_11,
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(X_11))]]) ).
cnf(refute_0_1046,plain,
and(not(not(X_11)),X_11) = and(not(not(X_11)),X_11),
introduced(tautology,[refl,[$fot(and(not(not(X_11)),X_11))]]) ).
cnf(refute_0_1047,plain,
( and(not(not(X_11)),X_11) != and(not(not(X_11)),X_11)
| not(not(X_11)) != X_11
| and(not(not(X_11)),X_11) = and(X_11,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_11)),X_11),and(not(not(X_11)),X_11)) ),[1,0],$fot(X_11)]]) ).
cnf(refute_0_1048,plain,
( not(not(X_11)) != X_11
| and(not(not(X_11)),X_11) = and(X_11,X_11) ),
inference(resolve,[$cnf( $equal(and(not(not(X_11)),X_11),and(not(not(X_11)),X_11)) )],[refute_0_1046,refute_0_1047]) ).
cnf(refute_0_1049,plain,
and(not(not(X_11)),X_11) = and(X_11,X_11),
inference(resolve,[$cnf( $equal(not(not(X_11)),X_11) )],[refute_0_1045,refute_0_1048]) ).
cnf(refute_0_1050,plain,
implies(and(not(not(X_11)),X_11),Y) = implies(and(not(not(X_11)),X_11),Y),
introduced(tautology,[refl,[$fot(implies(and(not(not(X_11)),X_11),Y))]]) ).
cnf(refute_0_1051,plain,
( and(not(not(X_11)),X_11) != and(X_11,X_11)
| implies(and(not(not(X_11)),X_11),Y) != implies(and(not(not(X_11)),X_11),Y)
| implies(and(not(not(X_11)),X_11),Y) = implies(and(X_11,X_11),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(not(X_11)),X_11),Y),implies(and(not(not(X_11)),X_11),Y)) ),[1,0],$fot(and(X_11,X_11))]]) ).
cnf(refute_0_1052,plain,
( and(not(not(X_11)),X_11) != and(X_11,X_11)
| implies(and(not(not(X_11)),X_11),Y) = implies(and(X_11,X_11),Y) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_11)),X_11),Y),implies(and(not(not(X_11)),X_11),Y)) )],[refute_0_1050,refute_0_1051]) ).
cnf(refute_0_1053,plain,
implies(and(not(not(X_11)),X_11),Y) = implies(and(X_11,X_11),Y),
inference(resolve,[$cnf( $equal(and(not(not(X_11)),X_11),and(X_11,X_11)) )],[refute_0_1049,refute_0_1052]) ).
cnf(refute_0_1054,plain,
( implies(X_11,Y) != implies(and(not(not(X_11)),X_11),Y)
| implies(and(not(not(X_11)),X_11),Y) != implies(and(X_11,X_11),Y)
| implies(X_11,Y) = implies(and(X_11,X_11),Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_11,Y),implies(and(X_11,X_11),Y)) ),[0],$fot(implies(and(not(not(X_11)),X_11),Y))]]) ).
cnf(refute_0_1055,plain,
( implies(X_11,Y) != implies(and(not(not(X_11)),X_11),Y)
| implies(X_11,Y) = implies(and(X_11,X_11),Y) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_11)),X_11),Y),implies(and(X_11,X_11),Y)) )],[refute_0_1053,refute_0_1054]) ).
cnf(refute_0_1056,plain,
( or(not(X_11),Y) != implies(and(not(not(X_11)),X_11),Y)
| implies(X_11,Y) = implies(and(X_11,X_11),Y) ),
inference(resolve,[$cnf( $equal(implies(X_11,Y),implies(and(not(not(X_11)),X_11),Y)) )],[refute_0_1044,refute_0_1055]) ).
cnf(refute_0_1057,plain,
implies(X_11,Y) = implies(and(X_11,X_11),Y),
inference(resolve,[$cnf( $equal(or(not(X_11),Y),implies(and(not(not(X_11)),X_11),Y)) )],[refute_0_1041,refute_0_1056]) ).
cnf(refute_0_1058,plain,
( implies(X_11,Y) != implies(and(X_11,X_11),Y)
| implies(and(X_11,X_11),Y) = implies(X_11,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X_11,Y))),bind(Y0,$fot(implies(and(X_11,X_11),Y)))]]) ).
cnf(refute_0_1059,plain,
implies(and(X_11,X_11),Y) = implies(X_11,Y),
inference(resolve,[$cnf( $equal(implies(X_11,Y),implies(and(X_11,X_11),Y)) )],[refute_0_1057,refute_0_1058]) ).
cnf(refute_0_1060,plain,
implies(and(X_224,X_224),X_224) = implies(X_224,X_224),
inference(subst,[],[refute_0_1059:[bind(Y,$fot(X_224)),bind(X_11,$fot(X_224))]]) ).
cnf(refute_0_1061,plain,
and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)),
introduced(tautology,[refl,[$fot(and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)))]]) ).
cnf(refute_0_1062,plain,
( and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)) != and(implies(X_224,X_224),implies(and(X_224,X_224),X_224))
| implies(and(X_224,X_224),X_224) != implies(X_224,X_224)
| and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(X_224,X_224)) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)),and(implies(X_224,X_224),implies(and(X_224,X_224),X_224))) ),[1,1],$fot(implies(X_224,X_224))]]) ).
cnf(refute_0_1063,plain,
( implies(and(X_224,X_224),X_224) != implies(X_224,X_224)
| and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(X_224,X_224)) ),
inference(resolve,[$cnf( $equal(and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)),and(implies(X_224,X_224),implies(and(X_224,X_224),X_224))) )],[refute_0_1061,refute_0_1062]) ).
cnf(refute_0_1064,plain,
and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(X_224,X_224)),
inference(resolve,[$cnf( $equal(implies(and(X_224,X_224),X_224),implies(X_224,X_224)) )],[refute_0_1060,refute_0_1063]) ).
cnf(refute_0_1065,plain,
implies(or(Y,Y),and(Y,Y)) = not(equiv(not(Y),Y)),
inference(subst,[],[refute_0_845:[bind(X_9,$fot(Y))]]) ).
cnf(refute_0_1066,plain,
Y = or(Y,Y),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(Y))]]) ).
cnf(refute_0_1067,plain,
( Y != or(Y,Y)
| or(Y,Y) = Y ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(Y)),bind(Y0,$fot(or(Y,Y)))]]) ).
cnf(refute_0_1068,plain,
or(Y,Y) = Y,
inference(resolve,[$cnf( $equal(Y,or(Y,Y)) )],[refute_0_1066,refute_0_1067]) ).
cnf(refute_0_1069,plain,
( implies(or(Y,Y),and(Y,Y)) != not(equiv(not(Y),Y))
| or(Y,Y) != Y
| implies(Y,and(Y,Y)) = not(equiv(not(Y),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(Y,Y),and(Y,Y)),not(equiv(not(Y),Y))) ),[0,0],$fot(Y)]]) ).
cnf(refute_0_1070,plain,
( implies(or(Y,Y),and(Y,Y)) != not(equiv(not(Y),Y))
| implies(Y,and(Y,Y)) = not(equiv(not(Y),Y)) ),
inference(resolve,[$cnf( $equal(or(Y,Y),Y) )],[refute_0_1068,refute_0_1069]) ).
cnf(refute_0_1071,plain,
implies(Y,and(Y,Y)) = not(equiv(not(Y),Y)),
inference(resolve,[$cnf( $equal(implies(or(Y,Y),and(Y,Y)),not(equiv(not(Y),Y))) )],[refute_0_1065,refute_0_1070]) ).
cnf(refute_0_1072,plain,
implies(Y,and(Y,Y)) = implies(Y,and(Y,Y)),
introduced(tautology,[refl,[$fot(implies(Y,and(Y,Y)))]]) ).
cnf(refute_0_1073,plain,
( and(Y,Y) != Y
| implies(Y,and(Y,Y)) != implies(Y,and(Y,Y))
| implies(Y,and(Y,Y)) = implies(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,and(Y,Y)),implies(Y,and(Y,Y))) ),[1,1],$fot(Y)]]) ).
cnf(refute_0_1074,plain,
( and(Y,Y) != Y
| implies(Y,and(Y,Y)) = implies(Y,Y) ),
inference(resolve,[$cnf( $equal(implies(Y,and(Y,Y)),implies(Y,and(Y,Y))) )],[refute_0_1072,refute_0_1073]) ).
cnf(refute_0_1075,plain,
implies(Y,and(Y,Y)) = implies(Y,Y),
inference(resolve,[$cnf( $equal(and(Y,Y),Y) )],[refute_0_649,refute_0_1074]) ).
cnf(refute_0_1076,plain,
( implies(Y,and(Y,Y)) != implies(Y,Y)
| implies(Y,and(Y,Y)) != not(equiv(not(Y),Y))
| implies(Y,Y) = not(equiv(not(Y),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,and(Y,Y)),not(equiv(not(Y),Y))) ),[0],$fot(implies(Y,Y))]]) ).
cnf(refute_0_1077,plain,
( implies(Y,and(Y,Y)) != not(equiv(not(Y),Y))
| implies(Y,Y) = not(equiv(not(Y),Y)) ),
inference(resolve,[$cnf( $equal(implies(Y,and(Y,Y)),implies(Y,Y)) )],[refute_0_1075,refute_0_1076]) ).
cnf(refute_0_1078,plain,
implies(Y,Y) = not(equiv(not(Y),Y)),
inference(resolve,[$cnf( $equal(implies(Y,and(Y,Y)),not(equiv(not(Y),Y))) )],[refute_0_1071,refute_0_1077]) ).
cnf(refute_0_1079,plain,
( implies(Y,Y) != not(equiv(not(Y),Y))
| not(equiv(not(Y),Y)) = implies(Y,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(Y,Y))),bind(Y0,$fot(not(equiv(not(Y),Y))))]]) ).
cnf(refute_0_1080,plain,
not(equiv(not(Y),Y)) = implies(Y,Y),
inference(resolve,[$cnf( $equal(implies(Y,Y),not(equiv(not(Y),Y))) )],[refute_0_1078,refute_0_1079]) ).
cnf(refute_0_1081,plain,
not(equiv(not(X_224),X_224)) = implies(X_224,X_224),
inference(subst,[],[refute_0_1080:[bind(Y,$fot(X_224))]]) ).
cnf(refute_0_1082,plain,
and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)),
introduced(tautology,[refl,[$fot(and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)))]]) ).
cnf(refute_0_1083,plain,
( and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))
| not(equiv(not(X_224),X_224)) != implies(X_224,X_224)
| and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))) ),[1,0],$fot(implies(X_224,X_224))]]) ).
cnf(refute_0_1084,plain,
( not(equiv(not(X_224),X_224)) != implies(X_224,X_224)
| and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))) )],[refute_0_1082,refute_0_1083]) ).
cnf(refute_0_1085,plain,
and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)),
inference(resolve,[$cnf( $equal(not(equiv(not(X_224),X_224)),implies(X_224,X_224)) )],[refute_0_1081,refute_0_1084]) ).
cnf(refute_0_1086,plain,
( and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)) != and(implies(X_224,X_224),implies(X_224,X_224))
| and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) != and(implies(X_224,X_224),implies(and(X_224,X_224),X_224))
| and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(X_224,X_224)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)))),bind(Y0,$fot(and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)))),bind(Z,$fot(and(implies(X_224,X_224),implies(X_224,X_224))))]]) ).
cnf(refute_0_1087,plain,
( and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)) != and(implies(X_224,X_224),implies(X_224,X_224))
| and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(X_224,X_224)) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)),and(implies(X_224,X_224),implies(and(X_224,X_224),X_224))) )],[refute_0_1085,refute_0_1086]) ).
cnf(refute_0_1088,plain,
and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = and(implies(X_224,X_224),implies(X_224,X_224)),
inference(resolve,[$cnf( $equal(and(implies(X_224,X_224),implies(and(X_224,X_224),X_224)),and(implies(X_224,X_224),implies(X_224,X_224))) )],[refute_0_1064,refute_0_1087]) ).
cnf(refute_0_1089,plain,
( and(implies(X_224,X_224),implies(X_224,X_224)) != implies(X_224,X_224)
| and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) != and(implies(X_224,X_224),implies(X_224,X_224))
| and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = implies(X_224,X_224) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)))),bind(Y0,$fot(and(implies(X_224,X_224),implies(X_224,X_224)))),bind(Z,$fot(implies(X_224,X_224)))]]) ).
cnf(refute_0_1090,plain,
( and(implies(X_224,X_224),implies(X_224,X_224)) != implies(X_224,X_224)
| and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = implies(X_224,X_224) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)),and(implies(X_224,X_224),implies(X_224,X_224))) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) = implies(X_224,X_224),
inference(resolve,[$cnf( $equal(and(implies(X_224,X_224),implies(X_224,X_224)),implies(X_224,X_224)) )],[refute_0_1030,refute_0_1090]) ).
cnf(refute_0_1092,plain,
( and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)) != implies(X_224,X_224)
| equiv(X_224,X_224) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))
| equiv(X_224,X_224) = implies(X_224,X_224) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_224,X_224),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))) ),[1],$fot(implies(X_224,X_224))]]) ).
cnf(refute_0_1093,plain,
( equiv(X_224,X_224) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))
| equiv(X_224,X_224) = implies(X_224,X_224) ),
inference(resolve,[$cnf( $equal(and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224)),implies(X_224,X_224)) )],[refute_0_1091,refute_0_1092]) ).
cnf(refute_0_1094,plain,
( equiv(X_224,and(X_224,X_224)) != and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))
| equiv(X_224,X_224) = implies(X_224,X_224) ),
inference(resolve,[$cnf( $equal(equiv(X_224,X_224),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))) )],[refute_0_1029,refute_0_1093]) ).
cnf(refute_0_1095,plain,
equiv(X_224,X_224) = implies(X_224,X_224),
inference(resolve,[$cnf( $equal(equiv(X_224,and(X_224,X_224)),and(not(equiv(not(X_224),X_224)),implies(and(X_224,X_224),X_224))) )],[refute_0_1022,refute_0_1094]) ).
cnf(refute_0_1096,plain,
( equiv(X_224,X_224) != implies(X_224,X_224)
| implies(X_224,X_224) = equiv(X_224,X_224) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X_224,X_224))),bind(Y0,$fot(implies(X_224,X_224)))]]) ).
cnf(refute_0_1097,plain,
implies(X_224,X_224) = equiv(X_224,X_224),
inference(resolve,[$cnf( $equal(equiv(X_224,X_224),implies(X_224,X_224)) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
implies(X_1832,X_1832) = equiv(X_1832,X_1832),
inference(subst,[],[refute_0_1097:[bind(X_224,$fot(X_1832))]]) ).
cnf(refute_0_1099,plain,
or(not(X_1832),X_1832) = implies(X_1832,X_1832),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_1832)),bind(Y,$fot(X_1832))]]) ).
cnf(refute_0_1100,plain,
( implies(X_1832,X_1832) != equiv(X_1832,X_1832)
| or(not(X_1832),X_1832) != implies(X_1832,X_1832)
| or(not(X_1832),X_1832) = equiv(X_1832,X_1832) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(X_1832),X_1832))),bind(Y0,$fot(implies(X_1832,X_1832))),bind(Z,$fot(equiv(X_1832,X_1832)))]]) ).
cnf(refute_0_1101,plain,
( implies(X_1832,X_1832) != equiv(X_1832,X_1832)
| or(not(X_1832),X_1832) = equiv(X_1832,X_1832) ),
inference(resolve,[$cnf( $equal(or(not(X_1832),X_1832),implies(X_1832,X_1832)) )],[refute_0_1099,refute_0_1100]) ).
cnf(refute_0_1102,plain,
or(not(X_1832),X_1832) = equiv(X_1832,X_1832),
inference(resolve,[$cnf( $equal(implies(X_1832,X_1832),equiv(X_1832,X_1832)) )],[refute_0_1098,refute_0_1101]) ).
cnf(refute_0_1103,plain,
implies(X_15429,or(not(X_1832),X_1832)) = implies(X_15429,or(not(X_1832),X_1832)),
introduced(tautology,[refl,[$fot(implies(X_15429,or(not(X_1832),X_1832)))]]) ).
cnf(refute_0_1104,plain,
( implies(X_15429,or(not(X_1832),X_1832)) != implies(X_15429,or(not(X_1832),X_1832))
| or(not(X_1832),X_1832) != equiv(X_1832,X_1832)
| implies(X_15429,or(not(X_1832),X_1832)) = implies(X_15429,equiv(X_1832,X_1832)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_15429,or(not(X_1832),X_1832)),implies(X_15429,or(not(X_1832),X_1832))) ),[1,1],$fot(equiv(X_1832,X_1832))]]) ).
cnf(refute_0_1105,plain,
( or(not(X_1832),X_1832) != equiv(X_1832,X_1832)
| implies(X_15429,or(not(X_1832),X_1832)) = implies(X_15429,equiv(X_1832,X_1832)) ),
inference(resolve,[$cnf( $equal(implies(X_15429,or(not(X_1832),X_1832)),implies(X_15429,or(not(X_1832),X_1832))) )],[refute_0_1103,refute_0_1104]) ).
cnf(refute_0_1106,plain,
implies(X_15429,or(not(X_1832),X_1832)) = implies(X_15429,equiv(X_1832,X_1832)),
inference(resolve,[$cnf( $equal(or(not(X_1832),X_1832),equiv(X_1832,X_1832)) )],[refute_0_1102,refute_0_1105]) ).
cnf(refute_0_1107,plain,
and(X_15430,implies(X_15429,or(not(X_1832),X_1832))) = and(X_15430,implies(X_15429,or(not(X_1832),X_1832))),
introduced(tautology,[refl,[$fot(and(X_15430,implies(X_15429,or(not(X_1832),X_1832))))]]) ).
cnf(refute_0_1108,plain,
( and(X_15430,implies(X_15429,or(not(X_1832),X_1832))) != and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))
| implies(X_15429,or(not(X_1832),X_1832)) != implies(X_15429,equiv(X_1832,X_1832))
| and(X_15430,implies(X_15429,or(not(X_1832),X_1832))) = and(X_15430,implies(X_15429,equiv(X_1832,X_1832))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_15430,implies(X_15429,or(not(X_1832),X_1832))),and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))) ),[1,1],$fot(implies(X_15429,equiv(X_1832,X_1832)))]]) ).
cnf(refute_0_1109,plain,
( implies(X_15429,or(not(X_1832),X_1832)) != implies(X_15429,equiv(X_1832,X_1832))
| and(X_15430,implies(X_15429,or(not(X_1832),X_1832))) = and(X_15430,implies(X_15429,equiv(X_1832,X_1832))) ),
inference(resolve,[$cnf( $equal(and(X_15430,implies(X_15429,or(not(X_1832),X_1832))),and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))) )],[refute_0_1107,refute_0_1108]) ).
cnf(refute_0_1110,plain,
and(X_15430,implies(X_15429,or(not(X_1832),X_1832))) = and(X_15430,implies(X_15429,equiv(X_1832,X_1832))),
inference(resolve,[$cnf( $equal(implies(X_15429,or(not(X_1832),X_1832)),implies(X_15429,equiv(X_1832,X_1832))) )],[refute_0_1106,refute_0_1109]) ).
cnf(refute_0_1111,plain,
implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))) = implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))),
introduced(tautology,[refl,[$fot(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))))]]) ).
cnf(refute_0_1112,plain,
( and(X_15430,implies(X_15429,or(not(X_1832),X_1832))) != and(X_15430,implies(X_15429,equiv(X_1832,X_1832)))
| implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))) != implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832))))
| implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))) = implies(X_15430,and(X_15430,implies(X_15429,equiv(X_1832,X_1832)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))),implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832))))) ),[1,1],$fot(and(X_15430,implies(X_15429,equiv(X_1832,X_1832))))]]) ).
cnf(refute_0_1113,plain,
( and(X_15430,implies(X_15429,or(not(X_1832),X_1832))) != and(X_15430,implies(X_15429,equiv(X_1832,X_1832)))
| implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))) = implies(X_15430,and(X_15430,implies(X_15429,equiv(X_1832,X_1832)))) ),
inference(resolve,[$cnf( $equal(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))),implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832))))) )],[refute_0_1111,refute_0_1112]) ).
cnf(refute_0_1114,plain,
implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))) = implies(X_15430,and(X_15430,implies(X_15429,equiv(X_1832,X_1832)))),
inference(resolve,[$cnf( $equal(and(X_15430,implies(X_15429,or(not(X_1832),X_1832))),and(X_15430,implies(X_15429,equiv(X_1832,X_1832)))) )],[refute_0_1110,refute_0_1113]) ).
cnf(refute_0_1115,plain,
( implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))) != implies(X_15430,and(X_15430,implies(X_15429,equiv(X_1832,X_1832))))
| ~ is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))))
| is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,equiv(X_1832,X_1832))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832))))) ),[0],$fot(implies(X_15430,and(X_15430,implies(X_15429,equiv(X_1832,X_1832)))))]]) ).
cnf(refute_0_1116,plain,
( ~ is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))))
| is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,equiv(X_1832,X_1832))))) ),
inference(resolve,[$cnf( $equal(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832)))),implies(X_15430,and(X_15430,implies(X_15429,equiv(X_1832,X_1832))))) )],[refute_0_1114,refute_0_1115]) ).
cnf(refute_0_1117,plain,
is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,equiv(X_1832,X_1832))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_15430,and(X_15430,implies(X_15429,or(not(X_1832),X_1832))))) )],[refute_0_974,refute_0_1116]) ).
cnf(refute_0_1118,plain,
is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433))))),
inference(subst,[],[refute_0_1117:[bind(X_15429,$fot(X_15431)),bind(X_15430,$fot(implies(equiv(X_15433,X_15433),X_15431))),bind(X_1832,$fot(X_15433))]]) ).
cnf(refute_0_1119,plain,
equiv(equiv(X_15433,X_15433),X_15431) = and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433))),
inference(subst,[],[refute_0_71:[bind(X,$fot(equiv(X_15433,X_15433))),bind(Y,$fot(X_15431))]]) ).
cnf(refute_0_1120,plain,
( equiv(equiv(X_15433,X_15433),X_15431) != and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433)))
| and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433))) = equiv(equiv(X_15433,X_15433),X_15431) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(equiv(X_15433,X_15433),X_15431))),bind(Y0,$fot(and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433)))))]]) ).
cnf(refute_0_1121,plain,
and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433))) = equiv(equiv(X_15433,X_15433),X_15431),
inference(resolve,[$cnf( $equal(equiv(equiv(X_15433,X_15433),X_15431),and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433)))) )],[refute_0_1119,refute_0_1120]) ).
cnf(refute_0_1122,plain,
( and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433))) != equiv(equiv(X_15433,X_15433),X_15431)
| ~ is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433)))))
| is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433))))) ),[0,1],$fot(equiv(equiv(X_15433,X_15433),X_15431))]]) ).
cnf(refute_0_1123,plain,
( ~ is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433)))))
| is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431))) ),
inference(resolve,[$cnf( $equal(and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433))),equiv(equiv(X_15433,X_15433),X_15431)) )],[refute_0_1121,refute_0_1122]) ).
cnf(refute_0_1124,plain,
is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),and(implies(equiv(X_15433,X_15433),X_15431),implies(X_15431,equiv(X_15433,X_15433))))) )],[refute_0_1118,refute_0_1123]) ).
cnf(refute_0_1125,plain,
( ~ is_a_theorem(equiv(implies(equiv(X_31830,X_31830),X_31831),X_31831))
| implies(equiv(X_31830,X_31830),X_31831) = X_31831 ),
inference(subst,[],[refute_0_155:[bind(X,$fot(implies(equiv(X_31830,X_31830),X_31831))),bind(Y,$fot(X_31831))]]) ).
cnf(refute_0_1126,plain,
( ~ is_a_theorem(implies(X_31829,implies(equiv(X_31828,X_31828),X_31829)))
| ~ is_a_theorem(implies(implies(X_31829,implies(equiv(X_31828,X_31828),X_31829)),equiv(implies(equiv(X_31828,X_31828),X_31829),X_31829)))
| is_a_theorem(equiv(implies(equiv(X_31828,X_31828),X_31829),X_31829)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_31829,implies(equiv(X_31828,X_31828),X_31829)))),bind(Y,$fot(equiv(implies(equiv(X_31828,X_31828),X_31829),X_31829)))]]) ).
cnf(refute_0_1127,plain,
( ~ is_a_theorem(or(and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653),not(X_30653)))
| is_a_theorem(or(not(X_30653),and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))),bind(Q,$fot(not(X_30653)))]]) ).
cnf(refute_0_1128,plain,
( ~ is_a_theorem(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)))
| is_a_theorem(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))) ),
inference(subst,[],[refute_0_670:[bind(X_9167,$fot(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621))))]]) ).
cnf(refute_0_1129,plain,
( ~ is_a_theorem(implies(or(X_8362,implies(X_8363,X_8363)),or(X_8362,implies(implies(equiv(X_8363,X_8363),X_8364),X_8364))))
| ~ is_a_theorem(or(X_8362,implies(X_8363,X_8363)))
| is_a_theorem(or(X_8362,implies(implies(equiv(X_8363,X_8363),X_8364),X_8364))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_8362,implies(X_8363,X_8363)))),bind(Y,$fot(or(X_8362,implies(implies(equiv(X_8363,X_8363),X_8364),X_8364))))]]) ).
cnf(refute_0_1130,plain,
( ~ is_a_theorem(or(implies(or(or(not(X_17),not(X_17)),X_4874),X_4874),not(X_17)))
| is_a_theorem(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874))) ),
inference(subst,[],[refute_0_926:[bind(P,$fot(implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)))]]) ).
cnf(refute_0_1131,plain,
( ~ is_a_theorem(or(X_1899,implies(or(X_1899,X_1900),X_1900)))
| is_a_theorem(or(implies(or(X_1899,X_1900),X_1900),X_1899)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_1899)),bind(Q,$fot(implies(or(X_1899,X_1900),X_1900)))]]) ).
cnf(refute_0_1132,plain,
( ~ is_a_theorem(implies(or(X_68,X_69),or(X_68,X_69)))
| is_a_theorem(or(X_68,implies(or(X_68,X_69),X_69))) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(or(X_68,X_69)))]]) ).
cnf(refute_0_1133,plain,
is_a_theorem(implies(or(X_68,X_69),or(X_68,X_69))),
inference(subst,[],[refute_0_434:[bind(X_1830,$fot(or(X_68,X_69)))]]) ).
cnf(refute_0_1134,plain,
is_a_theorem(or(X_68,implies(or(X_68,X_69),X_69))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_68,X_69),or(X_68,X_69))) )],[refute_0_1133,refute_0_1132]) ).
cnf(refute_0_1135,plain,
is_a_theorem(or(X_1899,implies(or(X_1899,X_1900),X_1900))),
inference(subst,[],[refute_0_1134:[bind(X_68,$fot(X_1899)),bind(X_69,$fot(X_1900))]]) ).
cnf(refute_0_1136,plain,
is_a_theorem(or(implies(or(X_1899,X_1900),X_1900),X_1899)),
inference(resolve,[$cnf( is_a_theorem(or(X_1899,implies(or(X_1899,X_1900),X_1900))) )],[refute_0_1135,refute_0_1131]) ).
cnf(refute_0_1137,plain,
is_a_theorem(or(implies(or(or(X_2673,X_2673),X_1900),X_1900),or(X_2673,X_2673))),
inference(subst,[],[refute_0_1136:[bind(X_1899,$fot(or(X_2673,X_2673)))]]) ).
cnf(refute_0_1138,plain,
( ~ is_a_theorem(or(implies(or(or(X_2673,X_2673),X_1900),X_1900),or(X_2673,X_2673)))
| is_a_theorem(or(implies(or(or(X_2673,X_2673),X_1900),X_1900),X_2673)) ),
inference(subst,[],[refute_0_173:[bind(X_2341,$fot(implies(or(or(X_2673,X_2673),X_1900),X_1900))),bind(X_2342,$fot(X_2673))]]) ).
cnf(refute_0_1139,plain,
is_a_theorem(or(implies(or(or(X_2673,X_2673),X_1900),X_1900),X_2673)),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(or(X_2673,X_2673),X_1900),X_1900),or(X_2673,X_2673))) )],[refute_0_1137,refute_0_1138]) ).
cnf(refute_0_1140,plain,
is_a_theorem(or(implies(or(or(not(X_17),not(X_17)),X_4874),X_4874),not(X_17))),
inference(subst,[],[refute_0_1139:[bind(X_1900,$fot(X_4874)),bind(X_2673,$fot(not(X_17)))]]) ).
cnf(refute_0_1141,plain,
is_a_theorem(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874))),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(or(not(X_17),not(X_17)),X_4874),X_4874),not(X_17))) )],[refute_0_1140,refute_0_1130]) ).
cnf(refute_0_1142,plain,
not(not(X_17)) = X_17,
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(X_17))]]) ).
cnf(refute_0_1143,plain,
and(not(not(X_17)),X_17) = and(not(not(X_17)),X_17),
introduced(tautology,[refl,[$fot(and(not(not(X_17)),X_17))]]) ).
cnf(refute_0_1144,plain,
( and(not(not(X_17)),X_17) != and(not(not(X_17)),X_17)
| not(not(X_17)) != X_17
| and(not(not(X_17)),X_17) = and(X_17,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_17)),X_17),and(not(not(X_17)),X_17)) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_1145,plain,
( not(not(X_17)) != X_17
| and(not(not(X_17)),X_17) = and(X_17,X_17) ),
inference(resolve,[$cnf( $equal(and(not(not(X_17)),X_17),and(not(not(X_17)),X_17)) )],[refute_0_1143,refute_0_1144]) ).
cnf(refute_0_1146,plain,
and(not(not(X_17)),X_17) = and(X_17,X_17),
inference(resolve,[$cnf( $equal(not(not(X_17)),X_17) )],[refute_0_1142,refute_0_1145]) ).
cnf(refute_0_1147,plain,
implies(and(not(not(X_17)),X_17),X_4874) = implies(and(not(not(X_17)),X_17),X_4874),
introduced(tautology,[refl,[$fot(implies(and(not(not(X_17)),X_17),X_4874))]]) ).
cnf(refute_0_1148,plain,
( and(not(not(X_17)),X_17) != and(X_17,X_17)
| implies(and(not(not(X_17)),X_17),X_4874) != implies(and(not(not(X_17)),X_17),X_4874)
| implies(and(not(not(X_17)),X_17),X_4874) = implies(and(X_17,X_17),X_4874) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(not(X_17)),X_17),X_4874),implies(and(not(not(X_17)),X_17),X_4874)) ),[1,0],$fot(and(X_17,X_17))]]) ).
cnf(refute_0_1149,plain,
( and(not(not(X_17)),X_17) != and(X_17,X_17)
| implies(and(not(not(X_17)),X_17),X_4874) = implies(and(X_17,X_17),X_4874) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_17)),X_17),X_4874),implies(and(not(not(X_17)),X_17),X_4874)) )],[refute_0_1147,refute_0_1148]) ).
cnf(refute_0_1150,plain,
implies(and(not(not(X_17)),X_17),X_4874) = implies(and(X_17,X_17),X_4874),
inference(resolve,[$cnf( $equal(and(not(not(X_17)),X_17),and(X_17,X_17)) )],[refute_0_1146,refute_0_1149]) ).
cnf(refute_0_1151,plain,
or(or(not(X_17),not(X_17)),X_4874) = implies(and(not(not(X_17)),X_17),X_4874),
inference(subst,[],[refute_0_1034:[bind(Y,$fot(X_4874)),bind(X_11,$fot(X_17)),bind(X_12,$fot(not(X_17)))]]) ).
cnf(refute_0_1152,plain,
( implies(and(not(not(X_17)),X_17),X_4874) != implies(and(X_17,X_17),X_4874)
| or(or(not(X_17),not(X_17)),X_4874) != implies(and(not(not(X_17)),X_17),X_4874)
| or(or(not(X_17),not(X_17)),X_4874) = implies(and(X_17,X_17),X_4874) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(or(not(X_17),not(X_17)),X_4874))),bind(Y0,$fot(implies(and(not(not(X_17)),X_17),X_4874))),bind(Z,$fot(implies(and(X_17,X_17),X_4874)))]]) ).
cnf(refute_0_1153,plain,
( implies(and(not(not(X_17)),X_17),X_4874) != implies(and(X_17,X_17),X_4874)
| or(or(not(X_17),not(X_17)),X_4874) = implies(and(X_17,X_17),X_4874) ),
inference(resolve,[$cnf( $equal(or(or(not(X_17),not(X_17)),X_4874),implies(and(not(not(X_17)),X_17),X_4874)) )],[refute_0_1151,refute_0_1152]) ).
cnf(refute_0_1154,plain,
or(or(not(X_17),not(X_17)),X_4874) = implies(and(X_17,X_17),X_4874),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_17)),X_17),X_4874),implies(and(X_17,X_17),X_4874)) )],[refute_0_1150,refute_0_1153]) ).
cnf(refute_0_1155,plain,
implies(or(or(not(X_17),not(X_17)),X_4874),X_4874) = implies(or(or(not(X_17),not(X_17)),X_4874),X_4874),
introduced(tautology,[refl,[$fot(implies(or(or(not(X_17),not(X_17)),X_4874),X_4874))]]) ).
cnf(refute_0_1156,plain,
( implies(or(or(not(X_17),not(X_17)),X_4874),X_4874) != implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)
| or(or(not(X_17),not(X_17)),X_4874) != implies(and(X_17,X_17),X_4874)
| implies(or(or(not(X_17),not(X_17)),X_4874),X_4874) = implies(implies(and(X_17,X_17),X_4874),X_4874) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(or(not(X_17),not(X_17)),X_4874),X_4874),implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)) ),[1,0],$fot(implies(and(X_17,X_17),X_4874))]]) ).
cnf(refute_0_1157,plain,
( or(or(not(X_17),not(X_17)),X_4874) != implies(and(X_17,X_17),X_4874)
| implies(or(or(not(X_17),not(X_17)),X_4874),X_4874) = implies(implies(and(X_17,X_17),X_4874),X_4874) ),
inference(resolve,[$cnf( $equal(implies(or(or(not(X_17),not(X_17)),X_4874),X_4874),implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)) )],[refute_0_1155,refute_0_1156]) ).
cnf(refute_0_1158,plain,
implies(or(or(not(X_17),not(X_17)),X_4874),X_4874) = implies(implies(and(X_17,X_17),X_4874),X_4874),
inference(resolve,[$cnf( $equal(or(or(not(X_17),not(X_17)),X_4874),implies(and(X_17,X_17),X_4874)) )],[refute_0_1154,refute_0_1157]) ).
cnf(refute_0_1159,plain,
implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)) = implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)),
introduced(tautology,[refl,[$fot(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)))]]) ).
cnf(refute_0_1160,plain,
( implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)) != implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874))
| implies(or(or(not(X_17),not(X_17)),X_4874),X_4874) != implies(implies(and(X_17,X_17),X_4874),X_4874)
| implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)) = implies(X_17,implies(implies(and(X_17,X_17),X_4874),X_4874)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)),implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874))) ),[1,1],$fot(implies(implies(and(X_17,X_17),X_4874),X_4874))]]) ).
cnf(refute_0_1161,plain,
( implies(or(or(not(X_17),not(X_17)),X_4874),X_4874) != implies(implies(and(X_17,X_17),X_4874),X_4874)
| implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)) = implies(X_17,implies(implies(and(X_17,X_17),X_4874),X_4874)) ),
inference(resolve,[$cnf( $equal(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)),implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874))) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)) = implies(X_17,implies(implies(and(X_17,X_17),X_4874),X_4874)),
inference(resolve,[$cnf( $equal(implies(or(or(not(X_17),not(X_17)),X_4874),X_4874),implies(implies(and(X_17,X_17),X_4874),X_4874)) )],[refute_0_1158,refute_0_1161]) ).
cnf(refute_0_1163,plain,
( implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)) != implies(X_17,implies(implies(and(X_17,X_17),X_4874),X_4874))
| ~ is_a_theorem(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)))
| is_a_theorem(implies(X_17,implies(implies(and(X_17,X_17),X_4874),X_4874))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874))) ),[0],$fot(implies(X_17,implies(implies(and(X_17,X_17),X_4874),X_4874)))]]) ).
cnf(refute_0_1164,plain,
( ~ is_a_theorem(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)))
| is_a_theorem(implies(X_17,implies(implies(and(X_17,X_17),X_4874),X_4874))) ),
inference(resolve,[$cnf( $equal(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874)),implies(X_17,implies(implies(and(X_17,X_17),X_4874),X_4874))) )],[refute_0_1162,refute_0_1163]) ).
cnf(refute_0_1165,plain,
is_a_theorem(implies(X_17,implies(implies(and(X_17,X_17),X_4874),X_4874))),
inference(resolve,[$cnf( is_a_theorem(implies(X_17,implies(or(or(not(X_17),not(X_17)),X_4874),X_4874))) )],[refute_0_1141,refute_0_1164]) ).
cnf(refute_0_1166,plain,
is_a_theorem(implies(implies(X,X),implies(implies(and(implies(X,X),implies(X,X)),X_4877),X_4877))),
inference(subst,[],[refute_0_1165:[bind(X_17,$fot(implies(X,X))),bind(X_4874,$fot(X_4877))]]) ).
cnf(refute_0_1167,plain,
equiv(X,X) = and(implies(X,X),implies(X,X)),
inference(subst,[],[refute_0_71:[bind(Y,$fot(X))]]) ).
cnf(refute_0_1168,plain,
( equiv(X,X) != and(implies(X,X),implies(X,X))
| and(implies(X,X),implies(X,X)) = equiv(X,X) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X,X))),bind(Y0,$fot(and(implies(X,X),implies(X,X))))]]) ).
cnf(refute_0_1169,plain,
and(implies(X,X),implies(X,X)) = equiv(X,X),
inference(resolve,[$cnf( $equal(equiv(X,X),and(implies(X,X),implies(X,X))) )],[refute_0_1167,refute_0_1168]) ).
cnf(refute_0_1170,plain,
( and(implies(X,X),implies(X,X)) != equiv(X,X)
| ~ is_a_theorem(implies(implies(X,X),implies(implies(and(implies(X,X),implies(X,X)),X_4877),X_4877)))
| is_a_theorem(implies(implies(X,X),implies(implies(equiv(X,X),X_4877),X_4877))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,X),implies(implies(and(implies(X,X),implies(X,X)),X_4877),X_4877))) ),[0,1,0,0],$fot(equiv(X,X))]]) ).
cnf(refute_0_1171,plain,
( ~ is_a_theorem(implies(implies(X,X),implies(implies(and(implies(X,X),implies(X,X)),X_4877),X_4877)))
| is_a_theorem(implies(implies(X,X),implies(implies(equiv(X,X),X_4877),X_4877))) ),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),equiv(X,X)) )],[refute_0_1169,refute_0_1170]) ).
cnf(refute_0_1172,plain,
is_a_theorem(implies(implies(X,X),implies(implies(equiv(X,X),X_4877),X_4877))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,X),implies(implies(and(implies(X,X),implies(X,X)),X_4877),X_4877))) )],[refute_0_1166,refute_0_1171]) ).
cnf(refute_0_1173,plain,
is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),or(not(X),X_72)))),
inference(subst,[],[refute_0_167:[bind(P,$fot(not(X))),bind(Q,$fot(X_71)),bind(R,$fot(X_72))]]) ).
cnf(refute_0_1174,plain,
implies(X,X_72) = or(not(X),X_72),
inference(subst,[],[refute_0_26:[bind(Y,$fot(X_72))]]) ).
cnf(refute_0_1175,plain,
( implies(X,X_72) != or(not(X),X_72)
| or(not(X),X_72) = implies(X,X_72) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,X_72))),bind(Y0,$fot(or(not(X),X_72)))]]) ).
cnf(refute_0_1176,plain,
or(not(X),X_72) = implies(X,X_72),
inference(resolve,[$cnf( $equal(implies(X,X_72),or(not(X),X_72)) )],[refute_0_1174,refute_0_1175]) ).
cnf(refute_0_1177,plain,
( or(not(X),X_72) != implies(X,X_72)
| ~ is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),or(not(X),X_72))))
| is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),or(not(X),X_72)))) ),[0,1,1],$fot(implies(X,X_72))]]) ).
cnf(refute_0_1178,plain,
( ~ is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),or(not(X),X_72))))
| is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_72),implies(X,X_72)) )],[refute_0_1176,refute_0_1177]) ).
cnf(refute_0_1179,plain,
is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),or(not(X),X_72)))) )],[refute_0_1173,refute_0_1178]) ).
cnf(refute_0_1180,plain,
or(not(X),X_71) = implies(X,X_71),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X_71))]]) ).
cnf(refute_0_1181,plain,
implies(or(not(X),X_71),implies(X,X_72)) = implies(or(not(X),X_71),implies(X,X_72)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_71),implies(X,X_72)))]]) ).
cnf(refute_0_1182,plain,
( implies(or(not(X),X_71),implies(X,X_72)) != implies(or(not(X),X_71),implies(X,X_72))
| or(not(X),X_71) != implies(X,X_71)
| implies(or(not(X),X_71),implies(X,X_72)) = implies(implies(X,X_71),implies(X,X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_71),implies(X,X_72)),implies(or(not(X),X_71),implies(X,X_72))) ),[1,0],$fot(implies(X,X_71))]]) ).
cnf(refute_0_1183,plain,
( or(not(X),X_71) != implies(X,X_71)
| implies(or(not(X),X_71),implies(X,X_72)) = implies(implies(X,X_71),implies(X,X_72)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_71),implies(X,X_72)),implies(or(not(X),X_71),implies(X,X_72))) )],[refute_0_1181,refute_0_1182]) ).
cnf(refute_0_1184,plain,
implies(or(not(X),X_71),implies(X,X_72)) = implies(implies(X,X_71),implies(X,X_72)),
inference(resolve,[$cnf( $equal(or(not(X),X_71),implies(X,X_71)) )],[refute_0_1180,refute_0_1183]) ).
cnf(refute_0_1185,plain,
implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))) = implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))),
introduced(tautology,[refl,[$fot(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))))]]) ).
cnf(refute_0_1186,plain,
( implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))) != implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72)))
| implies(or(not(X),X_71),implies(X,X_72)) != implies(implies(X,X_71),implies(X,X_72))
| implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))) = implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))),implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72)))) ),[1,1],$fot(implies(implies(X,X_71),implies(X,X_72)))]]) ).
cnf(refute_0_1187,plain,
( implies(or(not(X),X_71),implies(X,X_72)) != implies(implies(X,X_71),implies(X,X_72))
| implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))) = implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))),implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72)))) )],[refute_0_1185,refute_0_1186]) ).
cnf(refute_0_1188,plain,
implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))) = implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_71),implies(X,X_72)),implies(implies(X,X_71),implies(X,X_72))) )],[refute_0_1184,refute_0_1187]) ).
cnf(refute_0_1189,plain,
( implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))) != implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72)))
| ~ is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))))
| is_a_theorem(implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72)))) ),[0],$fot(implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72))))]]) ).
cnf(refute_0_1190,plain,
( ~ is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))))
| is_a_theorem(implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72))),implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72)))) )],[refute_0_1188,refute_0_1189]) ).
cnf(refute_0_1191,plain,
is_a_theorem(implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_71,X_72),implies(or(not(X),X_71),implies(X,X_72)))) )],[refute_0_1179,refute_0_1190]) ).
cnf(refute_0_1192,plain,
( ~ is_a_theorem(implies(X_71,X_72))
| ~ is_a_theorem(implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72))))
| is_a_theorem(implies(implies(X,X_71),implies(X,X_72))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_71,X_72))),bind(Y,$fot(implies(implies(X,X_71),implies(X,X_72))))]]) ).
cnf(refute_0_1193,plain,
( ~ is_a_theorem(implies(X_71,X_72))
| is_a_theorem(implies(implies(X,X_71),implies(X,X_72))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_71,X_72),implies(implies(X,X_71),implies(X,X_72)))) )],[refute_0_1191,refute_0_1192]) ).
cnf(refute_0_1194,plain,
( ~ is_a_theorem(implies(implies(X,X),implies(implies(equiv(X,X),X_4877),X_4877)))
| is_a_theorem(implies(implies(X_6809,implies(X,X)),implies(X_6809,implies(implies(equiv(X,X),X_4877),X_4877)))) ),
inference(subst,[],[refute_0_1193:[bind(X,$fot(X_6809)),bind(X_71,$fot(implies(X,X))),bind(X_72,$fot(implies(implies(equiv(X,X),X_4877),X_4877)))]]) ).
cnf(refute_0_1195,plain,
is_a_theorem(implies(implies(X_6809,implies(X,X)),implies(X_6809,implies(implies(equiv(X,X),X_4877),X_4877)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,X),implies(implies(equiv(X,X),X_4877),X_4877))) )],[refute_0_1172,refute_0_1194]) ).
cnf(refute_0_1196,plain,
is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))),
inference(subst,[],[refute_0_1195:[bind(X,$fot(X_8359)),bind(X_4877,$fot(X_8360)),bind(X_6809,$fot(not(X)))]]) ).
cnf(refute_0_1197,plain,
or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)) = implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)),
inference(subst,[],[refute_0_84:[bind(Y,$fot(implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))]]) ).
cnf(refute_0_1198,plain,
( or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)) != implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))
| implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)) = or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))),bind(Y0,$fot(implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))))]]) ).
cnf(refute_0_1199,plain,
implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)) = or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)),
inference(resolve,[$cnf( $equal(or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)),implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) )],[refute_0_1197,refute_0_1198]) ).
cnf(refute_0_1200,plain,
( implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)) != or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))
| ~ is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))))
| is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) ),[0,1],$fot(or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))]]) ).
cnf(refute_0_1201,plain,
( ~ is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))))
| is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) )],[refute_0_1199,refute_0_1200]) ).
cnf(refute_0_1202,plain,
is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),implies(not(X),implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) )],[refute_0_1196,refute_0_1201]) ).
cnf(refute_0_1203,plain,
implies(not(X),implies(X_8359,X_8359)) = or(X,implies(X_8359,X_8359)),
inference(subst,[],[refute_0_295:[bind(Y,$fot(implies(X_8359,X_8359)))]]) ).
cnf(refute_0_1204,plain,
implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) = implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))),
introduced(tautology,[refl,[$fot(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))))]]) ).
cnf(refute_0_1205,plain,
( implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) != implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))
| implies(not(X),implies(X_8359,X_8359)) != or(X,implies(X_8359,X_8359))
| implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) = implies(or(X,implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))),implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) ),[1,0],$fot(or(X,implies(X_8359,X_8359)))]]) ).
cnf(refute_0_1206,plain,
( implies(not(X),implies(X_8359,X_8359)) != or(X,implies(X_8359,X_8359))
| implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) = implies(or(X,implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))),implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) )],[refute_0_1204,refute_0_1205]) ).
cnf(refute_0_1207,plain,
implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) = implies(or(X,implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))),
inference(resolve,[$cnf( $equal(implies(not(X),implies(X_8359,X_8359)),or(X,implies(X_8359,X_8359))) )],[refute_0_1203,refute_0_1206]) ).
cnf(refute_0_1208,plain,
( implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))) != implies(or(X,implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))
| ~ is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))))
| is_a_theorem(implies(or(X,implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) ),[0],$fot(implies(or(X,implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))))]]) ).
cnf(refute_0_1209,plain,
( ~ is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))))
| is_a_theorem(implies(or(X,implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360))),implies(or(X,implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) )],[refute_0_1207,refute_0_1208]) ).
cnf(refute_0_1210,plain,
is_a_theorem(implies(or(X,implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),implies(X_8359,X_8359)),or(X,implies(implies(equiv(X_8359,X_8359),X_8360),X_8360)))) )],[refute_0_1202,refute_0_1209]) ).
cnf(refute_0_1211,plain,
is_a_theorem(implies(or(X_8362,implies(X_8363,X_8363)),or(X_8362,implies(implies(equiv(X_8363,X_8363),X_8364),X_8364)))),
inference(subst,[],[refute_0_1210:[bind(X,$fot(X_8362)),bind(X_8359,$fot(X_8363)),bind(X_8360,$fot(X_8364))]]) ).
cnf(refute_0_1212,plain,
( ~ is_a_theorem(or(X_8362,implies(X_8363,X_8363)))
| is_a_theorem(or(X_8362,implies(implies(equiv(X_8363,X_8363),X_8364),X_8364))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_8362,implies(X_8363,X_8363)),or(X_8362,implies(implies(equiv(X_8363,X_8363),X_8364),X_8364)))) )],[refute_0_1211,refute_0_1129]) ).
cnf(refute_0_1213,plain,
is_a_theorem(or(X_8362,implies(X_8363,X_8363))),
inference(subst,[],[refute_0_432:[bind(X_1814,$fot(X_8362)),bind(X_1815,$fot(X_8363))]]) ).
cnf(refute_0_1214,plain,
is_a_theorem(or(X_8362,implies(implies(equiv(X_8363,X_8363),X_8364),X_8364))),
inference(resolve,[$cnf( is_a_theorem(or(X_8362,implies(X_8363,X_8363))) )],[refute_0_1213,refute_0_1212]) ).
cnf(refute_0_1215,plain,
is_a_theorem(or(X_9205,implies(implies(equiv(not(X_154),not(X_154)),X_9207),X_9207))),
inference(subst,[],[refute_0_1214:[bind(X_8362,$fot(X_9205)),bind(X_8363,$fot(not(X_154))),bind(X_8364,$fot(X_9207))]]) ).
cnf(refute_0_1216,plain,
equiv(not(X_9),not(X_154)) = not(implies(or(X_9,not(X_154)),and(not(X_154),X_9))),
inference(subst,[],[refute_0_840:[bind(Y,$fot(not(X_154)))]]) ).
cnf(refute_0_1217,plain,
and(X,or(X_12,not(X_11))) = not(implies(X,not(or(X_12,not(X_11))))),
inference(subst,[],[refute_0_62:[bind(Y,$fot(or(X_12,not(X_11))))]]) ).
cnf(refute_0_1218,plain,
( and(X,or(X_12,not(X_11))) != not(implies(X,not(or(X_12,not(X_11)))))
| not(or(X_12,not(X_11))) != and(not(X_12),X_11)
| and(X,or(X_12,not(X_11))) = not(implies(X,and(not(X_12),X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,or(X_12,not(X_11))),not(implies(X,not(or(X_12,not(X_11)))))) ),[1,0,1],$fot(and(not(X_12),X_11))]]) ).
cnf(refute_0_1219,plain,
( and(X,or(X_12,not(X_11))) != not(implies(X,not(or(X_12,not(X_11)))))
| and(X,or(X_12,not(X_11))) = not(implies(X,and(not(X_12),X_11))) ),
inference(resolve,[$cnf( $equal(not(or(X_12,not(X_11))),and(not(X_12),X_11)) )],[refute_0_955,refute_0_1218]) ).
cnf(refute_0_1220,plain,
and(X,or(X_12,not(X_11))) = not(implies(X,and(not(X_12),X_11))),
inference(resolve,[$cnf( $equal(and(X,or(X_12,not(X_11))),not(implies(X,not(or(X_12,not(X_11)))))) )],[refute_0_1217,refute_0_1219]) ).
cnf(refute_0_1221,plain,
and(or(X_9,not(X_154)),or(X_154,not(X_9))) = not(implies(or(X_9,not(X_154)),and(not(X_154),X_9))),
inference(subst,[],[refute_0_1220:[bind(X,$fot(or(X_9,not(X_154)))),bind(X_11,$fot(X_9)),bind(X_12,$fot(X_154))]]) ).
cnf(refute_0_1222,plain,
( and(or(X_9,not(X_154)),or(X_154,not(X_9))) != not(implies(or(X_9,not(X_154)),and(not(X_154),X_9)))
| not(implies(or(X_9,not(X_154)),and(not(X_154),X_9))) = and(or(X_9,not(X_154)),or(X_154,not(X_9))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(and(or(X_9,not(X_154)),or(X_154,not(X_9))))),bind(Y0,$fot(not(implies(or(X_9,not(X_154)),and(not(X_154),X_9)))))]]) ).
cnf(refute_0_1223,plain,
not(implies(or(X_9,not(X_154)),and(not(X_154),X_9))) = and(or(X_9,not(X_154)),or(X_154,not(X_9))),
inference(resolve,[$cnf( $equal(and(or(X_9,not(X_154)),or(X_154,not(X_9))),not(implies(or(X_9,not(X_154)),and(not(X_154),X_9)))) )],[refute_0_1221,refute_0_1222]) ).
cnf(refute_0_1224,plain,
( equiv(not(X_9),not(X_154)) != not(implies(or(X_9,not(X_154)),and(not(X_154),X_9)))
| not(implies(or(X_9,not(X_154)),and(not(X_154),X_9))) != and(or(X_9,not(X_154)),or(X_154,not(X_9)))
| equiv(not(X_9),not(X_154)) = and(or(X_9,not(X_154)),or(X_154,not(X_9))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(equiv(not(X_9),not(X_154)),and(or(X_9,not(X_154)),or(X_154,not(X_9)))) ),[0],$fot(not(implies(or(X_9,not(X_154)),and(not(X_154),X_9))))]]) ).
cnf(refute_0_1225,plain,
( equiv(not(X_9),not(X_154)) != not(implies(or(X_9,not(X_154)),and(not(X_154),X_9)))
| equiv(not(X_9),not(X_154)) = and(or(X_9,not(X_154)),or(X_154,not(X_9))) ),
inference(resolve,[$cnf( $equal(not(implies(or(X_9,not(X_154)),and(not(X_154),X_9))),and(or(X_9,not(X_154)),or(X_154,not(X_9)))) )],[refute_0_1223,refute_0_1224]) ).
cnf(refute_0_1226,plain,
equiv(not(X_9),not(X_154)) = and(or(X_9,not(X_154)),or(X_154,not(X_9))),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(X_154)),not(implies(or(X_9,not(X_154)),and(not(X_154),X_9)))) )],[refute_0_1216,refute_0_1225]) ).
cnf(refute_0_1227,plain,
equiv(not(X_154),not(X_154)) = and(or(X_154,not(X_154)),or(X_154,not(X_154))),
inference(subst,[],[refute_0_1226:[bind(X_9,$fot(X_154))]]) ).
cnf(refute_0_1228,plain,
and(or(X_154,not(X_154)),or(X_154,not(X_154))) = or(X_154,not(X_154)),
inference(subst,[],[refute_0_649:[bind(Y,$fot(or(X_154,not(X_154))))]]) ).
cnf(refute_0_1229,plain,
( and(or(X_154,not(X_154)),or(X_154,not(X_154))) != or(X_154,not(X_154))
| equiv(not(X_154),not(X_154)) != and(or(X_154,not(X_154)),or(X_154,not(X_154)))
| equiv(not(X_154),not(X_154)) = or(X_154,not(X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_154),not(X_154)),and(or(X_154,not(X_154)),or(X_154,not(X_154)))) ),[1],$fot(or(X_154,not(X_154)))]]) ).
cnf(refute_0_1230,plain,
( equiv(not(X_154),not(X_154)) != and(or(X_154,not(X_154)),or(X_154,not(X_154)))
| equiv(not(X_154),not(X_154)) = or(X_154,not(X_154)) ),
inference(resolve,[$cnf( $equal(and(or(X_154,not(X_154)),or(X_154,not(X_154))),or(X_154,not(X_154))) )],[refute_0_1228,refute_0_1229]) ).
cnf(refute_0_1231,plain,
equiv(not(X_154),not(X_154)) = or(X_154,not(X_154)),
inference(resolve,[$cnf( $equal(equiv(not(X_154),not(X_154)),and(or(X_154,not(X_154)),or(X_154,not(X_154)))) )],[refute_0_1227,refute_0_1230]) ).
cnf(refute_0_1232,plain,
( equiv(not(X_154),not(X_154)) != or(X_154,not(X_154))
| ~ is_a_theorem(or(X_9205,implies(implies(equiv(not(X_154),not(X_154)),X_9207),X_9207)))
| is_a_theorem(or(X_9205,implies(implies(or(X_154,not(X_154)),X_9207),X_9207))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_9205,implies(implies(equiv(not(X_154),not(X_154)),X_9207),X_9207))) ),[0,1,0,0],$fot(or(X_154,not(X_154)))]]) ).
cnf(refute_0_1233,plain,
( ~ is_a_theorem(or(X_9205,implies(implies(equiv(not(X_154),not(X_154)),X_9207),X_9207)))
| is_a_theorem(or(X_9205,implies(implies(or(X_154,not(X_154)),X_9207),X_9207))) ),
inference(resolve,[$cnf( $equal(equiv(not(X_154),not(X_154)),or(X_154,not(X_154))) )],[refute_0_1231,refute_0_1232]) ).
cnf(refute_0_1234,plain,
is_a_theorem(or(X_9205,implies(implies(or(X_154,not(X_154)),X_9207),X_9207))),
inference(resolve,[$cnf( is_a_theorem(or(X_9205,implies(implies(equiv(not(X_154),not(X_154)),X_9207),X_9207))) )],[refute_0_1215,refute_0_1233]) ).
cnf(refute_0_1235,plain,
is_a_theorem(or(X_26284,implies(implies(or(X_154,not(X_154)),X_26285),X_26285))),
inference(subst,[],[refute_0_1234:[bind(X_9205,$fot(X_26284)),bind(X_9207,$fot(X_26285))]]) ).
cnf(refute_0_1236,plain,
( ~ is_a_theorem(or(X_26284,implies(implies(or(X_154,not(X_154)),X_26285),X_26285)))
| is_a_theorem(implies(implies(or(X_154,not(X_154)),X_26285),or(X_26284,X_26285))) ),
inference(subst,[],[refute_0_798:[bind(X,$fot(implies(or(X_154,not(X_154)),X_26285))),bind(X_67,$fot(X_26284)),bind(X_69,$fot(X_26285))]]) ).
cnf(refute_0_1237,plain,
is_a_theorem(implies(implies(or(X_154,not(X_154)),X_26285),or(X_26284,X_26285))),
inference(resolve,[$cnf( is_a_theorem(or(X_26284,implies(implies(or(X_154,not(X_154)),X_26285),X_26285))) )],[refute_0_1235,refute_0_1236]) ).
cnf(refute_0_1238,plain,
is_a_theorem(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621))),
inference(subst,[],[refute_0_1237:[bind(X_154,$fot(X_26619)),bind(X_26284,$fot(X_26620)),bind(X_26285,$fot(X_26621))]]) ).
cnf(refute_0_1239,plain,
is_a_theorem(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621))) )],[refute_0_1238,refute_0_1128]) ).
cnf(refute_0_1240,plain,
implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) = not(equiv(not(X_9),not(not(X_9)))),
inference(subst,[],[refute_0_845:[bind(Y,$fot(not(not(X_9))))]]) ).
cnf(refute_0_1241,plain,
equiv(X,not(X)) = and(not(and(X,X)),or(X,X)),
inference(subst,[],[refute_0_118:[bind(X_9,$fot(X))]]) ).
cnf(refute_0_1242,plain,
X = or(X,X),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(X))]]) ).
cnf(refute_0_1243,plain,
( X != or(X,X)
| or(X,X) = X ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(X)),bind(Y0,$fot(or(X,X)))]]) ).
cnf(refute_0_1244,plain,
or(X,X) = X,
inference(resolve,[$cnf( $equal(X,or(X,X)) )],[refute_0_1242,refute_0_1243]) ).
cnf(refute_0_1245,plain,
( equiv(X,not(X)) != and(not(and(X,X)),or(X,X))
| or(X,X) != X
| equiv(X,not(X)) = and(not(and(X,X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,not(X)),and(not(and(X,X)),or(X,X))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_1246,plain,
( equiv(X,not(X)) != and(not(and(X,X)),or(X,X))
| equiv(X,not(X)) = and(not(and(X,X)),X) ),
inference(resolve,[$cnf( $equal(or(X,X),X) )],[refute_0_1244,refute_0_1245]) ).
cnf(refute_0_1247,plain,
equiv(X,not(X)) = and(not(and(X,X)),X),
inference(resolve,[$cnf( $equal(equiv(X,not(X)),and(not(and(X,X)),or(X,X))) )],[refute_0_1241,refute_0_1246]) ).
cnf(refute_0_1248,plain,
not(X) = or(not(X),not(X)),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(not(X)))]]) ).
cnf(refute_0_1249,plain,
( not(X) != or(not(X),not(X))
| or(not(X),not(X)) = not(X) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(not(X))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_1250,plain,
or(not(X),not(X)) = not(X),
inference(resolve,[$cnf( $equal(not(X),or(not(X),not(X))) )],[refute_0_1248,refute_0_1249]) ).
cnf(refute_0_1251,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) != not(X)
| implies(X,not(X)) = not(X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(X)),not(X)) ),[0],$fot(or(not(X),not(X)))]]) ).
cnf(refute_0_1252,plain,
( implies(X,not(X)) != or(not(X),not(X))
| implies(X,not(X)) = not(X) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(X)) )],[refute_0_1250,refute_0_1251]) ).
cnf(refute_0_1253,plain,
implies(X,not(X)) = not(X),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_305,refute_0_1252]) ).
cnf(refute_0_1254,plain,
implies(X,not(X)) = not(and(X,X)),
inference(subst,[],[refute_0_448:[bind(X_1833,$fot(X))]]) ).
cnf(refute_0_1255,plain,
( implies(X,not(X)) != not(X)
| implies(X,not(X)) != not(and(X,X))
| not(and(X,X)) = not(X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(X)),not(X)) ),[0],$fot(not(and(X,X)))]]) ).
cnf(refute_0_1256,plain,
( implies(X,not(X)) != not(X)
| not(and(X,X)) = not(X) ),
inference(resolve,[$cnf( $equal(implies(X,not(X)),not(and(X,X))) )],[refute_0_1254,refute_0_1255]) ).
cnf(refute_0_1257,plain,
not(and(X,X)) = not(X),
inference(resolve,[$cnf( $equal(implies(X,not(X)),not(X)) )],[refute_0_1253,refute_0_1256]) ).
cnf(refute_0_1258,plain,
and(not(and(X,X)),X) = and(not(and(X,X)),X),
introduced(tautology,[refl,[$fot(and(not(and(X,X)),X))]]) ).
cnf(refute_0_1259,plain,
( and(not(and(X,X)),X) != and(not(and(X,X)),X)
| not(and(X,X)) != not(X)
| and(not(and(X,X)),X) = and(not(X),X) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X,X)),X),and(not(and(X,X)),X)) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_1260,plain,
( not(and(X,X)) != not(X)
| and(not(and(X,X)),X) = and(not(X),X) ),
inference(resolve,[$cnf( $equal(and(not(and(X,X)),X),and(not(and(X,X)),X)) )],[refute_0_1258,refute_0_1259]) ).
cnf(refute_0_1261,plain,
and(not(and(X,X)),X) = and(not(X),X),
inference(resolve,[$cnf( $equal(not(and(X,X)),not(X)) )],[refute_0_1257,refute_0_1260]) ).
cnf(refute_0_1262,plain,
( and(not(and(X,X)),X) != and(not(X),X)
| equiv(X,not(X)) != and(not(and(X,X)),X)
| equiv(X,not(X)) = and(not(X),X) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,not(X)),and(not(and(X,X)),X)) ),[1],$fot(and(not(X),X))]]) ).
cnf(refute_0_1263,plain,
( equiv(X,not(X)) != and(not(and(X,X)),X)
| equiv(X,not(X)) = and(not(X),X) ),
inference(resolve,[$cnf( $equal(and(not(and(X,X)),X),and(not(X),X)) )],[refute_0_1261,refute_0_1262]) ).
cnf(refute_0_1264,plain,
equiv(X,not(X)) = and(not(X),X),
inference(resolve,[$cnf( $equal(equiv(X,not(X)),and(not(and(X,X)),X)) )],[refute_0_1247,refute_0_1263]) ).
cnf(refute_0_1265,plain,
( ~ is_a_theorem(equiv(not(equiv(X_27252,X_27252)),and(not(X_27252),X_27252)))
| not(equiv(X_27252,X_27252)) = and(not(X_27252),X_27252) ),
inference(subst,[],[refute_0_155:[bind(X,$fot(not(equiv(X_27252,X_27252)))),bind(Y,$fot(and(not(X_27252),X_27252)))]]) ).
cnf(refute_0_1266,plain,
( ~ is_a_theorem(implies(or(X_27251,not(X_27251)),equiv(not(equiv(X_27251,X_27251)),and(not(X_27251),X_27251))))
| ~ is_a_theorem(or(X_27251,not(X_27251)))
| is_a_theorem(equiv(not(equiv(X_27251,X_27251)),and(not(X_27251),X_27251))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_27251,not(X_27251)))),bind(Y,$fot(equiv(not(equiv(X_27251,X_27251)),and(not(X_27251),X_27251))))]]) ).
cnf(refute_0_1267,plain,
( ~ is_a_theorem(or(equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)),and(not(X_27249),X_27249)))
| is_a_theorem(or(and(not(X_27249),X_27249),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))),bind(Q,$fot(and(not(X_27249),X_27249)))]]) ).
cnf(refute_0_1268,plain,
( ~ is_a_theorem(implies(or(equiv(X_27248,X_27248),and(not(X_27248),X_27248)),or(equiv(not(equiv(X_27248,X_27248)),and(not(X_27248),X_27248)),and(not(X_27248),X_27248))))
| ~ is_a_theorem(or(equiv(X_27248,X_27248),and(not(X_27248),X_27248)))
| is_a_theorem(or(equiv(not(equiv(X_27248,X_27248)),and(not(X_27248),X_27248)),and(not(X_27248),X_27248))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(equiv(X_27248,X_27248),and(not(X_27248),X_27248)))),bind(Y,$fot(or(equiv(not(equiv(X_27248,X_27248)),and(not(X_27248),X_27248)),and(not(X_27248),X_27248))))]]) ).
cnf(refute_0_1269,plain,
( ~ is_a_theorem(or(X_2704,implies(or(X_2704,and(X_2705,X_2703)),and(X_2703,X_2705))))
| is_a_theorem(or(implies(or(X_2704,and(X_2705,X_2703)),and(X_2703,X_2705)),X_2704)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_2704)),bind(Q,$fot(implies(or(X_2704,and(X_2705,X_2703)),and(X_2703,X_2705))))]]) ).
cnf(refute_0_1270,plain,
( ~ is_a_theorem(implies(or(X_2558,and(X_2559,X_2557)),or(X_2558,and(X_2557,X_2559))))
| is_a_theorem(or(X_2558,implies(or(X_2558,and(X_2559,X_2557)),and(X_2557,X_2559)))) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(or(X_2558,and(X_2559,X_2557)))),bind(X_68,$fot(X_2558)),bind(X_69,$fot(and(X_2557,X_2559)))]]) ).
cnf(refute_0_1271,plain,
( ~ is_a_theorem(implies(or(P,not(X_17)),implies(X_17,P)))
| is_a_theorem(or(implies(X_17,P),not(or(P,not(X_17))))) ),
inference(subst,[],[refute_0_364:[bind(Q,$fot(implies(X_17,P))),bind(X_17,$fot(or(P,not(X_17))))]]) ).
cnf(refute_0_1272,plain,
is_a_theorem(or(implies(X_17,P),not(or(P,not(X_17))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,not(X_17)),implies(X_17,P))) )],[refute_0_924,refute_0_1271]) ).
cnf(refute_0_1273,plain,
not(or(P,not(X_17))) = and(not(P),X_17),
inference(subst,[],[refute_0_126:[bind(Y,$fot(X_17)),bind(X_9,$fot(P))]]) ).
cnf(refute_0_1274,plain,
or(implies(X_17,P),not(or(P,not(X_17)))) = or(implies(X_17,P),not(or(P,not(X_17)))),
introduced(tautology,[refl,[$fot(or(implies(X_17,P),not(or(P,not(X_17)))))]]) ).
cnf(refute_0_1275,plain,
( not(or(P,not(X_17))) != and(not(P),X_17)
| or(implies(X_17,P),not(or(P,not(X_17)))) != or(implies(X_17,P),not(or(P,not(X_17))))
| or(implies(X_17,P),not(or(P,not(X_17)))) = or(implies(X_17,P),and(not(P),X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_17,P),not(or(P,not(X_17)))),or(implies(X_17,P),not(or(P,not(X_17))))) ),[1,1],$fot(and(not(P),X_17))]]) ).
cnf(refute_0_1276,plain,
( not(or(P,not(X_17))) != and(not(P),X_17)
| or(implies(X_17,P),not(or(P,not(X_17)))) = or(implies(X_17,P),and(not(P),X_17)) ),
inference(resolve,[$cnf( $equal(or(implies(X_17,P),not(or(P,not(X_17)))),or(implies(X_17,P),not(or(P,not(X_17))))) )],[refute_0_1274,refute_0_1275]) ).
cnf(refute_0_1277,plain,
or(implies(X_17,P),not(or(P,not(X_17)))) = or(implies(X_17,P),and(not(P),X_17)),
inference(resolve,[$cnf( $equal(not(or(P,not(X_17))),and(not(P),X_17)) )],[refute_0_1273,refute_0_1276]) ).
cnf(refute_0_1278,plain,
( or(implies(X_17,P),not(or(P,not(X_17)))) != or(implies(X_17,P),and(not(P),X_17))
| ~ is_a_theorem(or(implies(X_17,P),not(or(P,not(X_17)))))
| is_a_theorem(or(implies(X_17,P),and(not(P),X_17))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_17,P),not(or(P,not(X_17))))) ),[0],$fot(or(implies(X_17,P),and(not(P),X_17)))]]) ).
cnf(refute_0_1279,plain,
( ~ is_a_theorem(or(implies(X_17,P),not(or(P,not(X_17)))))
| is_a_theorem(or(implies(X_17,P),and(not(P),X_17))) ),
inference(resolve,[$cnf( $equal(or(implies(X_17,P),not(or(P,not(X_17)))),or(implies(X_17,P),and(not(P),X_17))) )],[refute_0_1277,refute_0_1278]) ).
cnf(refute_0_1280,plain,
is_a_theorem(or(implies(X_17,P),and(not(P),X_17))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_17,P),not(or(P,not(X_17))))) )],[refute_0_1272,refute_0_1279]) ).
cnf(refute_0_1281,plain,
is_a_theorem(or(implies(X_484,not(X_17)),and(not(not(X_17)),X_484))),
inference(subst,[],[refute_0_1280:[bind(P,$fot(not(X_17))),bind(X_17,$fot(X_484))]]) ).
cnf(refute_0_1282,plain,
and(not(not(X_17)),X_484) = and(X_17,X_484),
inference(subst,[],[refute_0_108:[bind(Y,$fot(X_484))]]) ).
cnf(refute_0_1283,plain,
( and(not(not(X_17)),X_484) != and(X_17,X_484)
| ~ is_a_theorem(or(implies(X_484,not(X_17)),and(not(not(X_17)),X_484)))
| is_a_theorem(or(implies(X_484,not(X_17)),and(X_17,X_484))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_484,not(X_17)),and(not(not(X_17)),X_484))) ),[0,1],$fot(and(X_17,X_484))]]) ).
cnf(refute_0_1284,plain,
( ~ is_a_theorem(or(implies(X_484,not(X_17)),and(not(not(X_17)),X_484)))
| is_a_theorem(or(implies(X_484,not(X_17)),and(X_17,X_484))) ),
inference(resolve,[$cnf( $equal(and(not(not(X_17)),X_484),and(X_17,X_484)) )],[refute_0_1282,refute_0_1283]) ).
cnf(refute_0_1285,plain,
is_a_theorem(or(implies(X_484,not(X_17)),and(X_17,X_484))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_484,not(X_17)),and(not(not(X_17)),X_484))) )],[refute_0_1281,refute_0_1284]) ).
cnf(refute_0_1286,plain,
or(implies(X_484,not(X_17)),and(X_17,X_484)) = implies(and(X_484,X_17),and(X_17,X_484)),
inference(subst,[],[refute_0_534:[bind(X,$fot(X_484)),bind(Y,$fot(X_17)),bind(X_10,$fot(and(X_17,X_484)))]]) ).
cnf(refute_0_1287,plain,
( or(implies(X_484,not(X_17)),and(X_17,X_484)) != implies(and(X_484,X_17),and(X_17,X_484))
| ~ is_a_theorem(or(implies(X_484,not(X_17)),and(X_17,X_484)))
| is_a_theorem(implies(and(X_484,X_17),and(X_17,X_484))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_484,not(X_17)),and(X_17,X_484))) ),[0],$fot(implies(and(X_484,X_17),and(X_17,X_484)))]]) ).
cnf(refute_0_1288,plain,
( ~ is_a_theorem(or(implies(X_484,not(X_17)),and(X_17,X_484)))
| is_a_theorem(implies(and(X_484,X_17),and(X_17,X_484))) ),
inference(resolve,[$cnf( $equal(or(implies(X_484,not(X_17)),and(X_17,X_484)),implies(and(X_484,X_17),and(X_17,X_484))) )],[refute_0_1286,refute_0_1287]) ).
cnf(refute_0_1289,plain,
is_a_theorem(implies(and(X_484,X_17),and(X_17,X_484))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_484,not(X_17)),and(X_17,X_484))) )],[refute_0_1285,refute_0_1288]) ).
cnf(refute_0_1290,plain,
( ~ is_a_theorem(implies(and(X_484,X_17),and(X_17,X_484)))
| is_a_theorem(implies(or(X_2334,and(X_484,X_17)),or(X_2334,and(X_17,X_484)))) ),
inference(subst,[],[refute_0_169:[bind(P,$fot(X_2334)),bind(Q,$fot(and(X_484,X_17))),bind(R,$fot(and(X_17,X_484)))]]) ).
cnf(refute_0_1291,plain,
is_a_theorem(implies(or(X_2334,and(X_484,X_17)),or(X_2334,and(X_17,X_484)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_484,X_17),and(X_17,X_484))) )],[refute_0_1289,refute_0_1290]) ).
cnf(refute_0_1292,plain,
is_a_theorem(implies(or(X_2558,and(X_2559,X_2557)),or(X_2558,and(X_2557,X_2559)))),
inference(subst,[],[refute_0_1291:[bind(X_17,$fot(X_2557)),bind(X_2334,$fot(X_2558)),bind(X_484,$fot(X_2559))]]) ).
cnf(refute_0_1293,plain,
is_a_theorem(or(X_2558,implies(or(X_2558,and(X_2559,X_2557)),and(X_2557,X_2559)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_2558,and(X_2559,X_2557)),or(X_2558,and(X_2557,X_2559)))) )],[refute_0_1292,refute_0_1270]) ).
cnf(refute_0_1294,plain,
is_a_theorem(or(X_2704,implies(or(X_2704,and(X_2705,X_2703)),and(X_2703,X_2705)))),
inference(subst,[],[refute_0_1293:[bind(X_2557,$fot(X_2703)),bind(X_2558,$fot(X_2704)),bind(X_2559,$fot(X_2705))]]) ).
cnf(refute_0_1295,plain,
is_a_theorem(or(implies(or(X_2704,and(X_2705,X_2703)),and(X_2703,X_2705)),X_2704)),
inference(resolve,[$cnf( is_a_theorem(or(X_2704,implies(or(X_2704,and(X_2705,X_2703)),and(X_2703,X_2705)))) )],[refute_0_1294,refute_0_1269]) ).
cnf(refute_0_1296,plain,
is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),and(implies(X,Y),implies(Y,X))),X_4443)),
inference(subst,[],[refute_0_1295:[bind(X_2703,$fot(implies(X,Y))),bind(X_2704,$fot(X_4443)),bind(X_2705,$fot(implies(Y,X)))]]) ).
cnf(refute_0_1297,plain,
( and(implies(X,Y),implies(Y,X)) != equiv(X,Y)
| ~ is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),and(implies(X,Y),implies(Y,X))),X_4443))
| is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),and(implies(X,Y),implies(Y,X))),X_4443)) ),[0,0,1],$fot(equiv(X,Y))]]) ).
cnf(refute_0_1298,plain,
( ~ is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),and(implies(X,Y),implies(Y,X))),X_4443))
| is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443)) ),
inference(resolve,[$cnf( $equal(and(implies(X,Y),implies(Y,X)),equiv(X,Y)) )],[refute_0_229,refute_0_1297]) ).
cnf(refute_0_1299,plain,
is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443)),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),and(implies(X,Y),implies(Y,X))),X_4443)) )],[refute_0_1296,refute_0_1298]) ).
cnf(refute_0_1300,plain,
and(implies(Y,X),implies(X,Y)) = equiv(Y,X),
inference(subst,[],[refute_0_229:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_1301,plain,
or(X_4443,and(implies(Y,X),implies(X,Y))) = or(X_4443,and(implies(Y,X),implies(X,Y))),
introduced(tautology,[refl,[$fot(or(X_4443,and(implies(Y,X),implies(X,Y))))]]) ).
cnf(refute_0_1302,plain,
( and(implies(Y,X),implies(X,Y)) != equiv(Y,X)
| or(X_4443,and(implies(Y,X),implies(X,Y))) != or(X_4443,and(implies(Y,X),implies(X,Y)))
| or(X_4443,and(implies(Y,X),implies(X,Y))) = or(X_4443,equiv(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_4443,and(implies(Y,X),implies(X,Y))),or(X_4443,and(implies(Y,X),implies(X,Y)))) ),[1,1],$fot(equiv(Y,X))]]) ).
cnf(refute_0_1303,plain,
( and(implies(Y,X),implies(X,Y)) != equiv(Y,X)
| or(X_4443,and(implies(Y,X),implies(X,Y))) = or(X_4443,equiv(Y,X)) ),
inference(resolve,[$cnf( $equal(or(X_4443,and(implies(Y,X),implies(X,Y))),or(X_4443,and(implies(Y,X),implies(X,Y)))) )],[refute_0_1301,refute_0_1302]) ).
cnf(refute_0_1304,plain,
or(X_4443,and(implies(Y,X),implies(X,Y))) = or(X_4443,equiv(Y,X)),
inference(resolve,[$cnf( $equal(and(implies(Y,X),implies(X,Y)),equiv(Y,X)) )],[refute_0_1300,refute_0_1303]) ).
cnf(refute_0_1305,plain,
implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)) = implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),
introduced(tautology,[refl,[$fot(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)))]]) ).
cnf(refute_0_1306,plain,
( implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)) != implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y))
| or(X_4443,and(implies(Y,X),implies(X,Y))) != or(X_4443,equiv(Y,X))
| implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)) = implies(or(X_4443,equiv(Y,X)),equiv(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y))) ),[1,0],$fot(or(X_4443,equiv(Y,X)))]]) ).
cnf(refute_0_1307,plain,
( or(X_4443,and(implies(Y,X),implies(X,Y))) != or(X_4443,equiv(Y,X))
| implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)) = implies(or(X_4443,equiv(Y,X)),equiv(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y))) )],[refute_0_1305,refute_0_1306]) ).
cnf(refute_0_1308,plain,
implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)) = implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),
inference(resolve,[$cnf( $equal(or(X_4443,and(implies(Y,X),implies(X,Y))),or(X_4443,equiv(Y,X))) )],[refute_0_1304,refute_0_1307]) ).
cnf(refute_0_1309,plain,
or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443) = or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443),
introduced(tautology,[refl,[$fot(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443))]]) ).
cnf(refute_0_1310,plain,
( implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)) != implies(or(X_4443,equiv(Y,X)),equiv(X,Y))
| or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443) != or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443)
| or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443) = or(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),X_4443) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443),or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443)) ),[1,0],$fot(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)))]]) ).
cnf(refute_0_1311,plain,
( implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)) != implies(or(X_4443,equiv(Y,X)),equiv(X,Y))
| or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443) = or(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),X_4443) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443),or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443)) )],[refute_0_1309,refute_0_1310]) ).
cnf(refute_0_1312,plain,
or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443) = or(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),X_4443),
inference(resolve,[$cnf( $equal(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),implies(or(X_4443,equiv(Y,X)),equiv(X,Y))) )],[refute_0_1308,refute_0_1311]) ).
cnf(refute_0_1313,plain,
( or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443) != or(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),X_4443)
| ~ is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443))
| is_a_theorem(or(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),X_4443)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443)) ),[0],$fot(or(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),X_4443))]]) ).
cnf(refute_0_1314,plain,
( ~ is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443))
| is_a_theorem(or(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),X_4443)) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443),or(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),X_4443)) )],[refute_0_1312,refute_0_1313]) ).
cnf(refute_0_1315,plain,
is_a_theorem(or(implies(or(X_4443,equiv(Y,X)),equiv(X,Y)),X_4443)),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(X_4443,and(implies(Y,X),implies(X,Y))),equiv(X,Y)),X_4443)) )],[refute_0_1299,refute_0_1314]) ).
cnf(refute_0_1316,plain,
is_a_theorem(or(implies(or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)),equiv(X_11926,X_11927)),equiv(X_11927,X_11926))),
inference(subst,[],[refute_0_1315:[bind(X,$fot(X_11926)),bind(Y,$fot(X_11927)),bind(X_4443,$fot(equiv(X_11927,X_11926)))]]) ).
cnf(refute_0_1317,plain,
equiv(X_11927,X_11926) = or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(equiv(X_11927,X_11926)))]]) ).
cnf(refute_0_1318,plain,
( equiv(X_11927,X_11926) != or(equiv(X_11927,X_11926),equiv(X_11927,X_11926))
| or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)) = equiv(X_11927,X_11926) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X_11927,X_11926))),bind(Y0,$fot(or(equiv(X_11927,X_11926),equiv(X_11927,X_11926))))]]) ).
cnf(refute_0_1319,plain,
or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)) = equiv(X_11927,X_11926),
inference(resolve,[$cnf( $equal(equiv(X_11927,X_11926),or(equiv(X_11927,X_11926),equiv(X_11927,X_11926))) )],[refute_0_1317,refute_0_1318]) ).
cnf(refute_0_1320,plain,
( or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)) != equiv(X_11927,X_11926)
| ~ is_a_theorem(or(implies(or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)),equiv(X_11926,X_11927)),equiv(X_11927,X_11926)))
| is_a_theorem(or(implies(equiv(X_11927,X_11926),equiv(X_11926,X_11927)),equiv(X_11927,X_11926))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)),equiv(X_11926,X_11927)),equiv(X_11927,X_11926))) ),[0,0,0],$fot(equiv(X_11927,X_11926))]]) ).
cnf(refute_0_1321,plain,
( ~ is_a_theorem(or(implies(or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)),equiv(X_11926,X_11927)),equiv(X_11927,X_11926)))
| is_a_theorem(or(implies(equiv(X_11927,X_11926),equiv(X_11926,X_11927)),equiv(X_11927,X_11926))) ),
inference(resolve,[$cnf( $equal(or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)),equiv(X_11927,X_11926)) )],[refute_0_1319,refute_0_1320]) ).
cnf(refute_0_1322,plain,
is_a_theorem(or(implies(equiv(X_11927,X_11926),equiv(X_11926,X_11927)),equiv(X_11927,X_11926))),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(equiv(X_11927,X_11926),equiv(X_11927,X_11926)),equiv(X_11926,X_11927)),equiv(X_11927,X_11926))) )],[refute_0_1316,refute_0_1321]) ).
cnf(refute_0_1323,plain,
is_a_theorem(implies(implies(not(Y),X_132),implies(implies(X_130,not(Y)),implies(X_130,X_132)))),
inference(subst,[],[refute_0_1191:[bind(X,$fot(X_130)),bind(X_71,$fot(not(Y))),bind(X_72,$fot(X_132))]]) ).
cnf(refute_0_1324,plain,
implies(implies(X_130,not(Y)),implies(X_130,X_132)) = or(and(X_130,Y),implies(X_130,X_132)),
inference(subst,[],[refute_0_67:[bind(X,$fot(X_130)),bind(X_18,$fot(implies(X_130,X_132)))]]) ).
cnf(refute_0_1325,plain,
( implies(implies(X_130,not(Y)),implies(X_130,X_132)) != or(and(X_130,Y),implies(X_130,X_132))
| ~ is_a_theorem(implies(implies(not(Y),X_132),implies(implies(X_130,not(Y)),implies(X_130,X_132))))
| is_a_theorem(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_132),implies(implies(X_130,not(Y)),implies(X_130,X_132)))) ),[0,1],$fot(or(and(X_130,Y),implies(X_130,X_132)))]]) ).
cnf(refute_0_1326,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_132),implies(implies(X_130,not(Y)),implies(X_130,X_132))))
| is_a_theorem(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_130,not(Y)),implies(X_130,X_132)),or(and(X_130,Y),implies(X_130,X_132))) )],[refute_0_1324,refute_0_1325]) ).
cnf(refute_0_1327,plain,
is_a_theorem(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_132),implies(implies(X_130,not(Y)),implies(X_130,X_132)))) )],[refute_0_1323,refute_0_1326]) ).
cnf(refute_0_1328,plain,
implies(not(Y),X_132) = or(Y,X_132),
inference(subst,[],[refute_0_295:[bind(X,$fot(Y)),bind(Y,$fot(X_132))]]) ).
cnf(refute_0_1329,plain,
implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))) = implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))))]]) ).
cnf(refute_0_1330,plain,
( implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))) != implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132)))
| implies(not(Y),X_132) != or(Y,X_132)
| implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))) = implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))),implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132)))) ),[1,0],$fot(or(Y,X_132))]]) ).
cnf(refute_0_1331,plain,
( implies(not(Y),X_132) != or(Y,X_132)
| implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))) = implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))),implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132)))) )],[refute_0_1329,refute_0_1330]) ).
cnf(refute_0_1332,plain,
implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))) = implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132))),
inference(resolve,[$cnf( $equal(implies(not(Y),X_132),or(Y,X_132)) )],[refute_0_1328,refute_0_1331]) ).
cnf(refute_0_1333,plain,
( implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))) != implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132)))
| ~ is_a_theorem(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))))
| is_a_theorem(implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132)))) ),[0],$fot(implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132))))]]) ).
cnf(refute_0_1334,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))))
| is_a_theorem(implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132))),implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132)))) )],[refute_0_1332,refute_0_1333]) ).
cnf(refute_0_1335,plain,
is_a_theorem(implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_132),or(and(X_130,Y),implies(X_130,X_132)))) )],[refute_0_1327,refute_0_1334]) ).
cnf(refute_0_1336,plain,
( ~ is_a_theorem(implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132))))
| ~ is_a_theorem(or(Y,X_132))
| is_a_theorem(or(and(X_130,Y),implies(X_130,X_132))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(Y,X_132))),bind(Y,$fot(or(and(X_130,Y),implies(X_130,X_132))))]]) ).
cnf(refute_0_1337,plain,
( ~ is_a_theorem(or(Y,X_132))
| is_a_theorem(or(and(X_130,Y),implies(X_130,X_132))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(Y,X_132),or(and(X_130,Y),implies(X_130,X_132)))) )],[refute_0_1335,refute_0_1336]) ).
cnf(refute_0_1338,plain,
( ~ is_a_theorem(or(implies(equiv(X_11927,X_11926),equiv(X_11926,X_11927)),equiv(X_11927,X_11926)))
| is_a_theorem(or(and(X_12672,implies(equiv(X_11927,X_11926),equiv(X_11926,X_11927))),implies(X_12672,equiv(X_11927,X_11926)))) ),
inference(subst,[],[refute_0_1337:[bind(Y,$fot(implies(equiv(X_11927,X_11926),equiv(X_11926,X_11927)))),bind(X_130,$fot(X_12672)),bind(X_132,$fot(equiv(X_11927,X_11926)))]]) ).
cnf(refute_0_1339,plain,
is_a_theorem(or(and(X_12672,implies(equiv(X_11927,X_11926),equiv(X_11926,X_11927))),implies(X_12672,equiv(X_11927,X_11926)))),
inference(resolve,[$cnf( is_a_theorem(or(implies(equiv(X_11927,X_11926),equiv(X_11926,X_11927)),equiv(X_11927,X_11926))) )],[refute_0_1322,refute_0_1338]) ).
cnf(refute_0_1340,plain,
is_a_theorem(or(and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))),implies(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),equiv(X_20949,X_20948)))),
inference(subst,[],[refute_0_1339:[bind(X_11926,$fot(X_20948)),bind(X_11927,$fot(X_20949)),bind(X_12672,$fot(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948))))]]) ).
cnf(refute_0_1341,plain,
equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)) = and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))),
inference(subst,[],[refute_0_71:[bind(X,$fot(equiv(X_20948,X_20949))),bind(Y,$fot(equiv(X_20949,X_20948)))]]) ).
cnf(refute_0_1342,plain,
( equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)) != and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949)))
| and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))) = equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)))),bind(Y0,$fot(and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949)))))]]) ).
cnf(refute_0_1343,plain,
and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))) = equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),
inference(resolve,[$cnf( $equal(equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949)))) )],[refute_0_1341,refute_0_1342]) ).
cnf(refute_0_1344,plain,
( and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))) != equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948))
| ~ is_a_theorem(or(and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))),implies(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),equiv(X_20949,X_20948))))
| is_a_theorem(or(equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),equiv(X_20949,X_20948)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))),implies(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),equiv(X_20949,X_20948)))) ),[0,0],$fot(equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)))]]) ).
cnf(refute_0_1345,plain,
( ~ is_a_theorem(or(and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))),implies(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),equiv(X_20949,X_20948))))
| is_a_theorem(or(equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),equiv(X_20949,X_20948)))) ),
inference(resolve,[$cnf( $equal(and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))),equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948))) )],[refute_0_1343,refute_0_1344]) ).
cnf(refute_0_1346,plain,
is_a_theorem(or(equiv(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),equiv(X_20949,X_20948)))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),implies(equiv(X_20949,X_20948),equiv(X_20948,X_20949))),implies(implies(equiv(X_20948,X_20949),equiv(X_20949,X_20948)),equiv(X_20949,X_20948)))) )],[refute_0_1340,refute_0_1345]) ).
cnf(refute_0_1347,plain,
is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),equiv(X_20952,not(X_20952))))),
inference(subst,[],[refute_0_1346:[bind(X_20948,$fot(not(X_20952))),bind(X_20949,$fot(X_20952))]]) ).
cnf(refute_0_1348,plain,
equiv(X_20952,not(X_20952)) = and(not(X_20952),X_20952),
inference(subst,[],[refute_0_1264:[bind(X,$fot(X_20952))]]) ).
cnf(refute_0_1349,plain,
( equiv(X_20952,not(X_20952)) != and(not(X_20952),X_20952)
| ~ is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),equiv(X_20952,not(X_20952)))))
| is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),equiv(X_20952,not(X_20952))))) ),[0,1,1],$fot(and(not(X_20952),X_20952))]]) ).
cnf(refute_0_1350,plain,
( ~ is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),equiv(X_20952,not(X_20952)))))
| is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))) ),
inference(resolve,[$cnf( $equal(equiv(X_20952,not(X_20952)),and(not(X_20952),X_20952)) )],[refute_0_1348,refute_0_1349]) ).
cnf(refute_0_1351,plain,
is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),equiv(X_20952,not(X_20952))))) )],[refute_0_1347,refute_0_1350]) ).
cnf(refute_0_1352,plain,
implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) = or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),
inference(subst,[],[refute_0_295:[bind(X,$fot(equiv(X_20952,X_20952))),bind(Y,$fot(and(not(X_20952),X_20952)))]]) ).
cnf(refute_0_1353,plain,
implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),
introduced(tautology,[refl,[$fot(implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))))]]) ).
cnf(refute_0_1354,plain,
( equiv(X_20952,not(X_20952)) != and(not(X_20952),X_20952)
| implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) != implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))
| implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))) ),[1,1],$fot(and(not(X_20952),X_20952))]]) ).
cnf(refute_0_1355,plain,
( equiv(X_20952,not(X_20952)) != and(not(X_20952),X_20952)
| implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) ),
inference(resolve,[$cnf( $equal(implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))) )],[refute_0_1353,refute_0_1354]) ).
cnf(refute_0_1356,plain,
implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),
inference(resolve,[$cnf( $equal(equiv(X_20952,not(X_20952)),and(not(X_20952),X_20952)) )],[refute_0_1348,refute_0_1355]) ).
cnf(refute_0_1357,plain,
equiv(not(X_1832),not(not(X_1832))) = and(not(not(X_1832)),not(X_1832)),
inference(subst,[],[refute_0_1264:[bind(X,$fot(not(X_1832)))]]) ).
cnf(refute_0_1358,plain,
( equiv(not(X_1832),not(not(X_1832))) != and(not(not(X_1832)),not(X_1832))
| not(not(X_1832)) != X_1832
| equiv(not(X_1832),X_1832) = and(not(not(X_1832)),not(X_1832)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_1832),not(not(X_1832))),and(not(not(X_1832)),not(X_1832))) ),[0,1],$fot(X_1832)]]) ).
cnf(refute_0_1359,plain,
( equiv(not(X_1832),not(not(X_1832))) != and(not(not(X_1832)),not(X_1832))
| equiv(not(X_1832),X_1832) = and(not(not(X_1832)),not(X_1832)) ),
inference(resolve,[$cnf( $equal(not(not(X_1832)),X_1832) )],[refute_0_638,refute_0_1358]) ).
cnf(refute_0_1360,plain,
equiv(not(X_1832),X_1832) = and(not(not(X_1832)),not(X_1832)),
inference(resolve,[$cnf( $equal(equiv(not(X_1832),not(not(X_1832))),and(not(not(X_1832)),not(X_1832))) )],[refute_0_1357,refute_0_1359]) ).
cnf(refute_0_1361,plain,
implies(not(not(X_1832)),X_1832) = or(not(X_1832),X_1832),
inference(subst,[],[refute_0_295:[bind(X,$fot(not(X_1832))),bind(Y,$fot(X_1832))]]) ).
cnf(refute_0_1362,plain,
( implies(not(not(X_1832)),X_1832) != or(not(X_1832),X_1832)
| or(not(X_1832),X_1832) != equiv(X_1832,X_1832)
| implies(not(not(X_1832)),X_1832) = equiv(X_1832,X_1832) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(not(not(X_1832)),X_1832))),bind(Y0,$fot(or(not(X_1832),X_1832))),bind(Z,$fot(equiv(X_1832,X_1832)))]]) ).
cnf(refute_0_1363,plain,
( or(not(X_1832),X_1832) != equiv(X_1832,X_1832)
| implies(not(not(X_1832)),X_1832) = equiv(X_1832,X_1832) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_1832)),X_1832),or(not(X_1832),X_1832)) )],[refute_0_1361,refute_0_1362]) ).
cnf(refute_0_1364,plain,
implies(not(not(X_1832)),X_1832) = equiv(X_1832,X_1832),
inference(resolve,[$cnf( $equal(or(not(X_1832),X_1832),equiv(X_1832,X_1832)) )],[refute_0_1102,refute_0_1363]) ).
cnf(refute_0_1365,plain,
not(implies(not(not(X_1832)),X_1832)) = not(implies(not(not(X_1832)),X_1832)),
introduced(tautology,[refl,[$fot(not(implies(not(not(X_1832)),X_1832)))]]) ).
cnf(refute_0_1366,plain,
( implies(not(not(X_1832)),X_1832) != equiv(X_1832,X_1832)
| not(implies(not(not(X_1832)),X_1832)) != not(implies(not(not(X_1832)),X_1832))
| not(implies(not(not(X_1832)),X_1832)) = not(equiv(X_1832,X_1832)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(X_1832)),X_1832)),not(implies(not(not(X_1832)),X_1832))) ),[1,0],$fot(equiv(X_1832,X_1832))]]) ).
cnf(refute_0_1367,plain,
( implies(not(not(X_1832)),X_1832) != equiv(X_1832,X_1832)
| not(implies(not(not(X_1832)),X_1832)) = not(equiv(X_1832,X_1832)) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(X_1832)),X_1832)),not(implies(not(not(X_1832)),X_1832))) )],[refute_0_1365,refute_0_1366]) ).
cnf(refute_0_1368,plain,
not(implies(not(not(X_1832)),X_1832)) = not(equiv(X_1832,X_1832)),
inference(resolve,[$cnf( $equal(implies(not(not(X_1832)),X_1832),equiv(X_1832,X_1832)) )],[refute_0_1364,refute_0_1367]) ).
cnf(refute_0_1369,plain,
and(not(not(X_1832)),not(X_1832)) = not(implies(not(not(X_1832)),X_1832)),
inference(subst,[],[refute_0_567:[bind(X,$fot(not(not(X_1832)))),bind(X_1833,$fot(X_1832))]]) ).
cnf(refute_0_1370,plain,
( and(not(not(X_1832)),not(X_1832)) != not(implies(not(not(X_1832)),X_1832))
| not(implies(not(not(X_1832)),X_1832)) != not(equiv(X_1832,X_1832))
| and(not(not(X_1832)),not(X_1832)) = not(equiv(X_1832,X_1832)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(not(not(X_1832)),not(X_1832)))),bind(Y0,$fot(not(implies(not(not(X_1832)),X_1832)))),bind(Z,$fot(not(equiv(X_1832,X_1832))))]]) ).
cnf(refute_0_1371,plain,
( not(implies(not(not(X_1832)),X_1832)) != not(equiv(X_1832,X_1832))
| and(not(not(X_1832)),not(X_1832)) = not(equiv(X_1832,X_1832)) ),
inference(resolve,[$cnf( $equal(and(not(not(X_1832)),not(X_1832)),not(implies(not(not(X_1832)),X_1832))) )],[refute_0_1369,refute_0_1370]) ).
cnf(refute_0_1372,plain,
and(not(not(X_1832)),not(X_1832)) = not(equiv(X_1832,X_1832)),
inference(resolve,[$cnf( $equal(not(implies(not(not(X_1832)),X_1832)),not(equiv(X_1832,X_1832))) )],[refute_0_1368,refute_0_1371]) ).
cnf(refute_0_1373,plain,
( and(not(not(X_1832)),not(X_1832)) != not(equiv(X_1832,X_1832))
| equiv(not(X_1832),X_1832) != and(not(not(X_1832)),not(X_1832))
| equiv(not(X_1832),X_1832) = not(equiv(X_1832,X_1832)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_1832),X_1832),and(not(not(X_1832)),not(X_1832))) ),[1],$fot(not(equiv(X_1832,X_1832)))]]) ).
cnf(refute_0_1374,plain,
( equiv(not(X_1832),X_1832) != and(not(not(X_1832)),not(X_1832))
| equiv(not(X_1832),X_1832) = not(equiv(X_1832,X_1832)) ),
inference(resolve,[$cnf( $equal(and(not(not(X_1832)),not(X_1832)),not(equiv(X_1832,X_1832))) )],[refute_0_1372,refute_0_1373]) ).
cnf(refute_0_1375,plain,
equiv(not(X_1832),X_1832) = not(equiv(X_1832,X_1832)),
inference(resolve,[$cnf( $equal(equiv(not(X_1832),X_1832),and(not(not(X_1832)),not(X_1832))) )],[refute_0_1360,refute_0_1374]) ).
cnf(refute_0_1376,plain,
equiv(not(X_20952),X_20952) = not(equiv(X_20952,X_20952)),
inference(subst,[],[refute_0_1375:[bind(X_1832,$fot(X_20952))]]) ).
cnf(refute_0_1377,plain,
implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),
introduced(tautology,[refl,[$fot(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))))]]) ).
cnf(refute_0_1378,plain,
( equiv(not(X_20952),X_20952) != not(equiv(X_20952,X_20952))
| implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) != implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952)))
| implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952)))) ),[1,0],$fot(not(equiv(X_20952,X_20952)))]]) ).
cnf(refute_0_1379,plain,
( equiv(not(X_20952),X_20952) != not(equiv(X_20952,X_20952))
| implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) ),
inference(resolve,[$cnf( $equal(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952)))) )],[refute_0_1377,refute_0_1378]) ).
cnf(refute_0_1380,plain,
implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),
inference(resolve,[$cnf( $equal(equiv(not(X_20952),X_20952),not(equiv(X_20952,X_20952))) )],[refute_0_1376,refute_0_1379]) ).
cnf(refute_0_1381,plain,
( implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) != implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))
| implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) != implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))
| implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))))),bind(Y0,$fot(implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))))),bind(Z,$fot(implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))))]]) ).
cnf(refute_0_1382,plain,
( implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) != implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))
| implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) ),
inference(resolve,[$cnf( $equal(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))) )],[refute_0_1380,refute_0_1381]) ).
cnf(refute_0_1383,plain,
implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),
inference(resolve,[$cnf( $equal(implies(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))) )],[refute_0_1356,refute_0_1382]) ).
cnf(refute_0_1384,plain,
( implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) != implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))
| implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) != or(equiv(X_20952,X_20952),and(not(X_20952),X_20952))
| implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))))),bind(Y0,$fot(implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)))),bind(Z,$fot(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952))))]]) ).
cnf(refute_0_1385,plain,
( implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) != or(equiv(X_20952,X_20952),and(not(X_20952),X_20952))
| implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)) ),
inference(resolve,[$cnf( $equal(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))) )],[refute_0_1383,refute_0_1384]) ).
cnf(refute_0_1386,plain,
implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),
inference(resolve,[$cnf( $equal(implies(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),or(equiv(X_20952,X_20952),and(not(X_20952),X_20952))) )],[refute_0_1352,refute_0_1385]) ).
cnf(refute_0_1387,plain,
implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)) = implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)),
introduced(tautology,[refl,[$fot(implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))]]) ).
cnf(refute_0_1388,plain,
( implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) != or(equiv(X_20952,X_20952),and(not(X_20952),X_20952))
| implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)) != implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))
| implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)) = implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) ),[1,0],$fot(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)))]]) ).
cnf(refute_0_1389,plain,
( implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) != or(equiv(X_20952,X_20952),and(not(X_20952),X_20952))
| implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)) = implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)) ),
inference(resolve,[$cnf( $equal(implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) )],[refute_0_1387,refute_0_1388]) ).
cnf(refute_0_1390,plain,
implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)) = implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)),
inference(resolve,[$cnf( $equal(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),or(equiv(X_20952,X_20952),and(not(X_20952),X_20952))) )],[refute_0_1386,refute_0_1389]) ).
cnf(refute_0_1391,plain,
or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),
introduced(tautology,[refl,[$fot(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))))]]) ).
cnf(refute_0_1392,plain,
( implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)) != implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))
| or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) != or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))
| or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))) ),
introduced(tautology,[equality,[$cnf( $equal(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))) ),[1,1],$fot(implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))]]) ).
cnf(refute_0_1393,plain,
( implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)) != implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))
| or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))) ),
inference(resolve,[$cnf( $equal(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))) )],[refute_0_1391,refute_0_1392]) ).
cnf(refute_0_1394,plain,
or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))),
inference(resolve,[$cnf( $equal(implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))) )],[refute_0_1390,refute_0_1393]) ).
cnf(refute_0_1395,plain,
equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),
introduced(tautology,[refl,[$fot(equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))))]]) ).
cnf(refute_0_1396,plain,
( equiv(X_20952,not(X_20952)) != and(not(X_20952),X_20952)
| equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) != equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))
| equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))) ),[1,1],$fot(and(not(X_20952),X_20952))]]) ).
cnf(refute_0_1397,plain,
( equiv(X_20952,not(X_20952)) != and(not(X_20952),X_20952)
| equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) ),
inference(resolve,[$cnf( $equal(equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))) )],[refute_0_1395,refute_0_1396]) ).
cnf(refute_0_1398,plain,
equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),
inference(resolve,[$cnf( $equal(equiv(X_20952,not(X_20952)),and(not(X_20952),X_20952)) )],[refute_0_1348,refute_0_1397]) ).
cnf(refute_0_1399,plain,
equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),
introduced(tautology,[refl,[$fot(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))))]]) ).
cnf(refute_0_1400,plain,
( equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) != equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952)))
| equiv(not(X_20952),X_20952) != not(equiv(X_20952,X_20952))
| equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952)))) ),[1,0],$fot(not(equiv(X_20952,X_20952)))]]) ).
cnf(refute_0_1401,plain,
( equiv(not(X_20952),X_20952) != not(equiv(X_20952,X_20952))
| equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) ),
inference(resolve,[$cnf( $equal(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952)))) )],[refute_0_1399,refute_0_1400]) ).
cnf(refute_0_1402,plain,
equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),
inference(resolve,[$cnf( $equal(equiv(not(X_20952),X_20952),not(equiv(X_20952,X_20952))) )],[refute_0_1376,refute_0_1401]) ).
cnf(refute_0_1403,plain,
( equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) != equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))
| equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) != equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))
| equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))))),bind(Y0,$fot(equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))))),bind(Z,$fot(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))))]]) ).
cnf(refute_0_1404,plain,
( equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))) != equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))
| equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)) ),
inference(resolve,[$cnf( $equal(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952)))) )],[refute_0_1402,refute_0_1403]) ).
cnf(refute_0_1405,plain,
equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) = equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),
inference(resolve,[$cnf( $equal(equiv(not(equiv(X_20952,X_20952)),equiv(X_20952,not(X_20952))),equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))) )],[refute_0_1398,refute_0_1404]) ).
cnf(refute_0_1406,plain,
or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),
introduced(tautology,[refl,[$fot(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))))]]) ).
cnf(refute_0_1407,plain,
( equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) != equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))
| or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) != or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))
| or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) ),
introduced(tautology,[equality,[$cnf( $equal(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))) ),[1,0],$fot(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)))]]) ).
cnf(refute_0_1408,plain,
( equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))) != equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))
| or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) ),
inference(resolve,[$cnf( $equal(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))) )],[refute_0_1406,refute_0_1407]) ).
cnf(refute_0_1409,plain,
or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),
inference(resolve,[$cnf( $equal(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952))) )],[refute_0_1405,refute_0_1408]) ).
cnf(refute_0_1410,plain,
( or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) != or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))
| or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) != or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))
| or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))))),bind(Y0,$fot(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))))),bind(Z,$fot(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))))]]) ).
cnf(refute_0_1411,plain,
( or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) != or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))
| or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))) ),
inference(resolve,[$cnf( $equal(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))) )],[refute_0_1409,refute_0_1410]) ).
cnf(refute_0_1412,plain,
or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) = or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))),
inference(resolve,[$cnf( $equal(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))) )],[refute_0_1394,refute_0_1411]) ).
cnf(refute_0_1413,plain,
( or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))) != or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))
| ~ is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))))
| is_a_theorem(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))) ),[0],$fot(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))))]]) ).
cnf(refute_0_1414,plain,
( ~ is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))))
| is_a_theorem(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))) ),
inference(resolve,[$cnf( $equal(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952))),or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))) )],[refute_0_1412,refute_0_1413]) ).
cnf(refute_0_1415,plain,
is_a_theorem(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),implies(implies(equiv(not(X_20952),X_20952),equiv(X_20952,not(X_20952))),and(not(X_20952),X_20952)))) )],[refute_0_1351,refute_0_1414]) ).
cnf(refute_0_1416,plain,
( ~ is_a_theorem(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952))))
| is_a_theorem(implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))) ),
inference(subst,[],[refute_0_798:[bind(X,$fot(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)))),bind(X_67,$fot(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)))),bind(X_69,$fot(and(not(X_20952),X_20952)))]]) ).
cnf(refute_0_1417,plain,
is_a_theorem(implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(not(equiv(X_20952,X_20952)),and(not(X_20952),X_20952)),implies(or(equiv(X_20952,X_20952),and(not(X_20952),X_20952)),and(not(X_20952),X_20952)))) )],[refute_0_1415,refute_0_1416]) ).
cnf(refute_0_1418,plain,
is_a_theorem(implies(or(equiv(X_27248,X_27248),and(not(X_27248),X_27248)),or(equiv(not(equiv(X_27248,X_27248)),and(not(X_27248),X_27248)),and(not(X_27248),X_27248)))),
inference(subst,[],[refute_0_1417:[bind(X_20952,$fot(X_27248))]]) ).
cnf(refute_0_1419,plain,
( ~ is_a_theorem(or(equiv(X_27248,X_27248),and(not(X_27248),X_27248)))
| is_a_theorem(or(equiv(not(equiv(X_27248,X_27248)),and(not(X_27248),X_27248)),and(not(X_27248),X_27248))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(equiv(X_27248,X_27248),and(not(X_27248),X_27248)),or(equiv(not(equiv(X_27248,X_27248)),and(not(X_27248),X_27248)),and(not(X_27248),X_27248)))) )],[refute_0_1418,refute_0_1268]) ).
cnf(refute_0_1420,plain,
( ~ is_a_theorem(implies(X_1945,equiv(X_1944,X_1944)))
| is_a_theorem(or(equiv(X_1944,X_1944),not(X_1945))) ),
inference(subst,[],[refute_0_364:[bind(Q,$fot(equiv(X_1944,X_1944))),bind(X_17,$fot(X_1945))]]) ).
cnf(refute_0_1421,plain,
( ~ is_a_theorem(implies(X_1862,X_1862))
| ~ is_a_theorem(implies(implies(X_1862,X_1862),implies(X_1863,equiv(X_1862,X_1862))))
| is_a_theorem(implies(X_1863,equiv(X_1862,X_1862))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_1862,X_1862))),bind(Y,$fot(implies(X_1863,equiv(X_1862,X_1862))))]]) ).
cnf(refute_0_1422,plain,
( ~ is_a_theorem(or(X_469,not(or(X_469,X_469))))
| is_a_theorem(implies(X_17,or(X_469,not(or(X_469,X_469))))) ),
inference(subst,[],[refute_0_679:[bind(X_370,$fot(or(X_469,not(or(X_469,X_469)))))]]) ).
cnf(refute_0_1423,plain,
is_a_theorem(or(X_469,not(or(X_469,X_469)))),
inference(subst,[],[refute_0_406:[bind(X_331,$fot(X_469))]]) ).
cnf(refute_0_1424,plain,
is_a_theorem(implies(X_17,or(X_469,not(or(X_469,X_469))))),
inference(resolve,[$cnf( is_a_theorem(or(X_469,not(or(X_469,X_469)))) )],[refute_0_1423,refute_0_1422]) ).
cnf(refute_0_1425,plain,
is_a_theorem(implies(X_1813,or(X_1814,not(or(X_1814,X_1814))))),
inference(subst,[],[refute_0_1424:[bind(X_17,$fot(X_1813)),bind(X_469,$fot(X_1814))]]) ).
cnf(refute_0_1426,plain,
( ~ is_a_theorem(implies(X_1813,or(X_1814,not(or(X_1814,X_1814)))))
| is_a_theorem(or(X_1814,implies(X_1813,not(or(X_1814,X_1814))))) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(X_1813)),bind(X_68,$fot(X_1814)),bind(X_69,$fot(not(or(X_1814,X_1814))))]]) ).
cnf(refute_0_1427,plain,
is_a_theorem(or(X_1814,implies(X_1813,not(or(X_1814,X_1814))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1813,or(X_1814,not(or(X_1814,X_1814))))) )],[refute_0_1425,refute_0_1426]) ).
cnf(refute_0_1428,plain,
implies(X_1813,not(or(X_1814,X_1814))) = not(and(X_1813,or(X_1814,X_1814))),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_1813)),bind(X_1833,$fot(or(X_1814,X_1814)))]]) ).
cnf(refute_0_1429,plain,
or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))) = or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))),
introduced(tautology,[refl,[$fot(or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))))]]) ).
cnf(refute_0_1430,plain,
( implies(X_1813,not(or(X_1814,X_1814))) != not(and(X_1813,or(X_1814,X_1814)))
| or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))) != or(X_1814,implies(X_1813,not(or(X_1814,X_1814))))
| or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))) = or(X_1814,not(and(X_1813,or(X_1814,X_1814)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))),or(X_1814,implies(X_1813,not(or(X_1814,X_1814))))) ),[1,1],$fot(not(and(X_1813,or(X_1814,X_1814))))]]) ).
cnf(refute_0_1431,plain,
( implies(X_1813,not(or(X_1814,X_1814))) != not(and(X_1813,or(X_1814,X_1814)))
| or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))) = or(X_1814,not(and(X_1813,or(X_1814,X_1814)))) ),
inference(resolve,[$cnf( $equal(or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))),or(X_1814,implies(X_1813,not(or(X_1814,X_1814))))) )],[refute_0_1429,refute_0_1430]) ).
cnf(refute_0_1432,plain,
or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))) = or(X_1814,not(and(X_1813,or(X_1814,X_1814)))),
inference(resolve,[$cnf( $equal(implies(X_1813,not(or(X_1814,X_1814))),not(and(X_1813,or(X_1814,X_1814)))) )],[refute_0_1428,refute_0_1431]) ).
cnf(refute_0_1433,plain,
( or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))) != or(X_1814,not(and(X_1813,or(X_1814,X_1814))))
| ~ is_a_theorem(or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))))
| is_a_theorem(or(X_1814,not(and(X_1813,or(X_1814,X_1814))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_1814,implies(X_1813,not(or(X_1814,X_1814))))) ),[0],$fot(or(X_1814,not(and(X_1813,or(X_1814,X_1814)))))]]) ).
cnf(refute_0_1434,plain,
( ~ is_a_theorem(or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))))
| is_a_theorem(or(X_1814,not(and(X_1813,or(X_1814,X_1814))))) ),
inference(resolve,[$cnf( $equal(or(X_1814,implies(X_1813,not(or(X_1814,X_1814)))),or(X_1814,not(and(X_1813,or(X_1814,X_1814))))) )],[refute_0_1432,refute_0_1433]) ).
cnf(refute_0_1435,plain,
is_a_theorem(or(X_1814,not(and(X_1813,or(X_1814,X_1814))))),
inference(resolve,[$cnf( is_a_theorem(or(X_1814,implies(X_1813,not(or(X_1814,X_1814))))) )],[refute_0_1427,refute_0_1434]) ).
cnf(refute_0_1436,plain,
is_a_theorem(or(not(X),not(and(X_1852,or(not(X),not(X)))))),
inference(subst,[],[refute_0_1435:[bind(X_1813,$fot(X_1852)),bind(X_1814,$fot(not(X)))]]) ).
cnf(refute_0_1437,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(or(not(X),not(and(X_1852,or(not(X),not(X))))))
| is_a_theorem(or(not(X),not(and(X_1852,implies(X,not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),not(and(X_1852,or(not(X),not(X)))))) ),[0,1,0,1],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_1438,plain,
( ~ is_a_theorem(or(not(X),not(and(X_1852,or(not(X),not(X))))))
| is_a_theorem(or(not(X),not(and(X_1852,implies(X,not(X)))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_307,refute_0_1437]) ).
cnf(refute_0_1439,plain,
is_a_theorem(or(not(X),not(and(X_1852,implies(X,not(X)))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(and(X_1852,or(not(X),not(X)))))) )],[refute_0_1436,refute_0_1438]) ).
cnf(refute_0_1440,plain,
not(not(implies(X,implies(X_1852,and(X,X))))) = implies(X,implies(X_1852,and(X,X))),
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(implies(X,implies(X_1852,and(X,X)))))]]) ).
cnf(refute_0_1441,plain,
and(X,not(implies(X_1852,and(X,X)))) = not(implies(X,implies(X_1852,and(X,X)))),
inference(subst,[],[refute_0_567:[bind(X_1833,$fot(implies(X_1852,and(X,X))))]]) ).
cnf(refute_0_1442,plain,
and(X_1852,not(and(X,X))) = not(implies(X_1852,and(X,X))),
inference(subst,[],[refute_0_567:[bind(X,$fot(X_1852)),bind(X_1833,$fot(and(X,X)))]]) ).
cnf(refute_0_1443,plain,
and(X_1852,implies(X,not(X))) = and(X_1852,implies(X,not(X))),
introduced(tautology,[refl,[$fot(and(X_1852,implies(X,not(X))))]]) ).
cnf(refute_0_1444,plain,
( and(X_1852,implies(X,not(X))) != and(X_1852,implies(X,not(X)))
| implies(X,not(X)) != not(and(X,X))
| and(X_1852,implies(X,not(X))) = and(X_1852,not(and(X,X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_1852,implies(X,not(X))),and(X_1852,implies(X,not(X)))) ),[1,1],$fot(not(and(X,X)))]]) ).
cnf(refute_0_1445,plain,
( implies(X,not(X)) != not(and(X,X))
| and(X_1852,implies(X,not(X))) = and(X_1852,not(and(X,X))) ),
inference(resolve,[$cnf( $equal(and(X_1852,implies(X,not(X))),and(X_1852,implies(X,not(X)))) )],[refute_0_1443,refute_0_1444]) ).
cnf(refute_0_1446,plain,
and(X_1852,implies(X,not(X))) = and(X_1852,not(and(X,X))),
inference(resolve,[$cnf( $equal(implies(X,not(X)),not(and(X,X))) )],[refute_0_1254,refute_0_1445]) ).
cnf(refute_0_1447,plain,
( and(X_1852,implies(X,not(X))) != and(X_1852,not(and(X,X)))
| and(X_1852,not(and(X,X))) != not(implies(X_1852,and(X,X)))
| and(X_1852,implies(X,not(X))) = not(implies(X_1852,and(X,X))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(X_1852,implies(X,not(X))))),bind(Y0,$fot(and(X_1852,not(and(X,X))))),bind(Z,$fot(not(implies(X_1852,and(X,X)))))]]) ).
cnf(refute_0_1448,plain,
( and(X_1852,not(and(X,X))) != not(implies(X_1852,and(X,X)))
| and(X_1852,implies(X,not(X))) = not(implies(X_1852,and(X,X))) ),
inference(resolve,[$cnf( $equal(and(X_1852,implies(X,not(X))),and(X_1852,not(and(X,X)))) )],[refute_0_1446,refute_0_1447]) ).
cnf(refute_0_1449,plain,
and(X_1852,implies(X,not(X))) = not(implies(X_1852,and(X,X))),
inference(resolve,[$cnf( $equal(and(X_1852,not(and(X,X))),not(implies(X_1852,and(X,X)))) )],[refute_0_1442,refute_0_1448]) ).
cnf(refute_0_1450,plain,
and(X,and(X_1852,implies(X,not(X)))) = and(X,and(X_1852,implies(X,not(X)))),
introduced(tautology,[refl,[$fot(and(X,and(X_1852,implies(X,not(X)))))]]) ).
cnf(refute_0_1451,plain,
( and(X,and(X_1852,implies(X,not(X)))) != and(X,and(X_1852,implies(X,not(X))))
| and(X_1852,implies(X,not(X))) != not(implies(X_1852,and(X,X)))
| and(X,and(X_1852,implies(X,not(X)))) = and(X,not(implies(X_1852,and(X,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,and(X_1852,implies(X,not(X)))),and(X,and(X_1852,implies(X,not(X))))) ),[1,1],$fot(not(implies(X_1852,and(X,X))))]]) ).
cnf(refute_0_1452,plain,
( and(X_1852,implies(X,not(X))) != not(implies(X_1852,and(X,X)))
| and(X,and(X_1852,implies(X,not(X)))) = and(X,not(implies(X_1852,and(X,X)))) ),
inference(resolve,[$cnf( $equal(and(X,and(X_1852,implies(X,not(X)))),and(X,and(X_1852,implies(X,not(X))))) )],[refute_0_1450,refute_0_1451]) ).
cnf(refute_0_1453,plain,
and(X,and(X_1852,implies(X,not(X)))) = and(X,not(implies(X_1852,and(X,X)))),
inference(resolve,[$cnf( $equal(and(X_1852,implies(X,not(X))),not(implies(X_1852,and(X,X)))) )],[refute_0_1449,refute_0_1452]) ).
cnf(refute_0_1454,plain,
( and(X,and(X_1852,implies(X,not(X)))) != and(X,not(implies(X_1852,and(X,X))))
| and(X,not(implies(X_1852,and(X,X)))) != not(implies(X,implies(X_1852,and(X,X))))
| and(X,and(X_1852,implies(X,not(X)))) = not(implies(X,implies(X_1852,and(X,X)))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(X,and(X_1852,implies(X,not(X)))))),bind(Y0,$fot(and(X,not(implies(X_1852,and(X,X)))))),bind(Z,$fot(not(implies(X,implies(X_1852,and(X,X))))))]]) ).
cnf(refute_0_1455,plain,
( and(X,not(implies(X_1852,and(X,X)))) != not(implies(X,implies(X_1852,and(X,X))))
| and(X,and(X_1852,implies(X,not(X)))) = not(implies(X,implies(X_1852,and(X,X)))) ),
inference(resolve,[$cnf( $equal(and(X,and(X_1852,implies(X,not(X)))),and(X,not(implies(X_1852,and(X,X))))) )],[refute_0_1453,refute_0_1454]) ).
cnf(refute_0_1456,plain,
and(X,and(X_1852,implies(X,not(X)))) = not(implies(X,implies(X_1852,and(X,X)))),
inference(resolve,[$cnf( $equal(and(X,not(implies(X_1852,and(X,X)))),not(implies(X,implies(X_1852,and(X,X))))) )],[refute_0_1441,refute_0_1455]) ).
cnf(refute_0_1457,plain,
not(and(X,and(X_1852,implies(X,not(X))))) = not(and(X,and(X_1852,implies(X,not(X))))),
introduced(tautology,[refl,[$fot(not(and(X,and(X_1852,implies(X,not(X))))))]]) ).
cnf(refute_0_1458,plain,
( and(X,and(X_1852,implies(X,not(X)))) != not(implies(X,implies(X_1852,and(X,X))))
| not(and(X,and(X_1852,implies(X,not(X))))) != not(and(X,and(X_1852,implies(X,not(X)))))
| not(and(X,and(X_1852,implies(X,not(X))))) = not(not(implies(X,implies(X_1852,and(X,X))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X,and(X_1852,implies(X,not(X))))),not(and(X,and(X_1852,implies(X,not(X)))))) ),[1,0],$fot(not(implies(X,implies(X_1852,and(X,X)))))]]) ).
cnf(refute_0_1459,plain,
( and(X,and(X_1852,implies(X,not(X)))) != not(implies(X,implies(X_1852,and(X,X))))
| not(and(X,and(X_1852,implies(X,not(X))))) = not(not(implies(X,implies(X_1852,and(X,X))))) ),
inference(resolve,[$cnf( $equal(not(and(X,and(X_1852,implies(X,not(X))))),not(and(X,and(X_1852,implies(X,not(X)))))) )],[refute_0_1457,refute_0_1458]) ).
cnf(refute_0_1460,plain,
not(and(X,and(X_1852,implies(X,not(X))))) = not(not(implies(X,implies(X_1852,and(X,X))))),
inference(resolve,[$cnf( $equal(and(X,and(X_1852,implies(X,not(X)))),not(implies(X,implies(X_1852,and(X,X))))) )],[refute_0_1456,refute_0_1459]) ).
cnf(refute_0_1461,plain,
( not(and(X,and(X_1852,implies(X,not(X))))) != not(not(implies(X,implies(X_1852,and(X,X)))))
| not(not(implies(X,implies(X_1852,and(X,X))))) != implies(X,implies(X_1852,and(X,X)))
| not(and(X,and(X_1852,implies(X,not(X))))) = implies(X,implies(X_1852,and(X,X))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(and(X,and(X_1852,implies(X,not(X))))))),bind(Y0,$fot(not(not(implies(X,implies(X_1852,and(X,X))))))),bind(Z,$fot(implies(X,implies(X_1852,and(X,X)))))]]) ).
cnf(refute_0_1462,plain,
( not(not(implies(X,implies(X_1852,and(X,X))))) != implies(X,implies(X_1852,and(X,X)))
| not(and(X,and(X_1852,implies(X,not(X))))) = implies(X,implies(X_1852,and(X,X))) ),
inference(resolve,[$cnf( $equal(not(and(X,and(X_1852,implies(X,not(X))))),not(not(implies(X,implies(X_1852,and(X,X)))))) )],[refute_0_1460,refute_0_1461]) ).
cnf(refute_0_1463,plain,
not(and(X,and(X_1852,implies(X,not(X))))) = implies(X,implies(X_1852,and(X,X))),
inference(resolve,[$cnf( $equal(not(not(implies(X,implies(X_1852,and(X,X))))),implies(X,implies(X_1852,and(X,X)))) )],[refute_0_1440,refute_0_1462]) ).
cnf(refute_0_1464,plain,
implies(X,not(and(X_1852,implies(X,not(X))))) = not(and(X,and(X_1852,implies(X,not(X))))),
inference(subst,[],[refute_0_448:[bind(X_1833,$fot(and(X_1852,implies(X,not(X)))))]]) ).
cnf(refute_0_1465,plain,
or(not(X),not(and(X_1852,implies(X,not(X))))) = implies(X,not(and(X_1852,implies(X,not(X))))),
inference(subst,[],[refute_0_37:[bind(Y,$fot(not(and(X_1852,implies(X,not(X))))))]]) ).
cnf(refute_0_1466,plain,
( implies(X,not(and(X_1852,implies(X,not(X))))) != not(and(X,and(X_1852,implies(X,not(X)))))
| or(not(X),not(and(X_1852,implies(X,not(X))))) != implies(X,not(and(X_1852,implies(X,not(X)))))
| or(not(X),not(and(X_1852,implies(X,not(X))))) = not(and(X,and(X_1852,implies(X,not(X))))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(X),not(and(X_1852,implies(X,not(X))))))),bind(Y0,$fot(implies(X,not(and(X_1852,implies(X,not(X))))))),bind(Z,$fot(not(and(X,and(X_1852,implies(X,not(X)))))))]]) ).
cnf(refute_0_1467,plain,
( implies(X,not(and(X_1852,implies(X,not(X))))) != not(and(X,and(X_1852,implies(X,not(X)))))
| or(not(X),not(and(X_1852,implies(X,not(X))))) = not(and(X,and(X_1852,implies(X,not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(and(X_1852,implies(X,not(X))))),implies(X,not(and(X_1852,implies(X,not(X)))))) )],[refute_0_1465,refute_0_1466]) ).
cnf(refute_0_1468,plain,
or(not(X),not(and(X_1852,implies(X,not(X))))) = not(and(X,and(X_1852,implies(X,not(X))))),
inference(resolve,[$cnf( $equal(implies(X,not(and(X_1852,implies(X,not(X))))),not(and(X,and(X_1852,implies(X,not(X)))))) )],[refute_0_1464,refute_0_1467]) ).
cnf(refute_0_1469,plain,
( not(and(X,and(X_1852,implies(X,not(X))))) != implies(X,implies(X_1852,and(X,X)))
| or(not(X),not(and(X_1852,implies(X,not(X))))) != not(and(X,and(X_1852,implies(X,not(X)))))
| or(not(X),not(and(X_1852,implies(X,not(X))))) = implies(X,implies(X_1852,and(X,X))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(X),not(and(X_1852,implies(X,not(X))))))),bind(Y0,$fot(not(and(X,and(X_1852,implies(X,not(X))))))),bind(Z,$fot(implies(X,implies(X_1852,and(X,X)))))]]) ).
cnf(refute_0_1470,plain,
( not(and(X,and(X_1852,implies(X,not(X))))) != implies(X,implies(X_1852,and(X,X)))
| or(not(X),not(and(X_1852,implies(X,not(X))))) = implies(X,implies(X_1852,and(X,X))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(and(X_1852,implies(X,not(X))))),not(and(X,and(X_1852,implies(X,not(X)))))) )],[refute_0_1468,refute_0_1469]) ).
cnf(refute_0_1471,plain,
or(not(X),not(and(X_1852,implies(X,not(X))))) = implies(X,implies(X_1852,and(X,X))),
inference(resolve,[$cnf( $equal(not(and(X,and(X_1852,implies(X,not(X))))),implies(X,implies(X_1852,and(X,X)))) )],[refute_0_1463,refute_0_1470]) ).
cnf(refute_0_1472,plain,
( or(not(X),not(and(X_1852,implies(X,not(X))))) != implies(X,implies(X_1852,and(X,X)))
| ~ is_a_theorem(or(not(X),not(and(X_1852,implies(X,not(X))))))
| is_a_theorem(implies(X,implies(X_1852,and(X,X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),not(and(X_1852,implies(X,not(X)))))) ),[0],$fot(implies(X,implies(X_1852,and(X,X))))]]) ).
cnf(refute_0_1473,plain,
( ~ is_a_theorem(or(not(X),not(and(X_1852,implies(X,not(X))))))
| is_a_theorem(implies(X,implies(X_1852,and(X,X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(and(X_1852,implies(X,not(X))))),implies(X,implies(X_1852,and(X,X)))) )],[refute_0_1471,refute_0_1472]) ).
cnf(refute_0_1474,plain,
is_a_theorem(implies(X,implies(X_1852,and(X,X)))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(and(X_1852,implies(X,not(X)))))) )],[refute_0_1439,refute_0_1473]) ).
cnf(refute_0_1475,plain,
is_a_theorem(implies(implies(X,X),implies(X_1861,and(implies(X,X),implies(X,X))))),
inference(subst,[],[refute_0_1474:[bind(X,$fot(implies(X,X))),bind(X_1852,$fot(X_1861))]]) ).
cnf(refute_0_1476,plain,
( and(implies(X,X),implies(X,X)) != equiv(X,X)
| ~ is_a_theorem(implies(implies(X,X),implies(X_1861,and(implies(X,X),implies(X,X)))))
| is_a_theorem(implies(implies(X,X),implies(X_1861,equiv(X,X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,X),implies(X_1861,and(implies(X,X),implies(X,X))))) ),[0,1,1],$fot(equiv(X,X))]]) ).
cnf(refute_0_1477,plain,
( ~ is_a_theorem(implies(implies(X,X),implies(X_1861,and(implies(X,X),implies(X,X)))))
| is_a_theorem(implies(implies(X,X),implies(X_1861,equiv(X,X)))) ),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),equiv(X,X)) )],[refute_0_1169,refute_0_1476]) ).
cnf(refute_0_1478,plain,
is_a_theorem(implies(implies(X,X),implies(X_1861,equiv(X,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,X),implies(X_1861,and(implies(X,X),implies(X,X))))) )],[refute_0_1475,refute_0_1477]) ).
cnf(refute_0_1479,plain,
is_a_theorem(implies(implies(X_1862,X_1862),implies(X_1863,equiv(X_1862,X_1862)))),
inference(subst,[],[refute_0_1478:[bind(X,$fot(X_1862)),bind(X_1861,$fot(X_1863))]]) ).
cnf(refute_0_1480,plain,
( ~ is_a_theorem(implies(X_1862,X_1862))
| is_a_theorem(implies(X_1863,equiv(X_1862,X_1862))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1862,X_1862),implies(X_1863,equiv(X_1862,X_1862)))) )],[refute_0_1479,refute_0_1421]) ).
cnf(refute_0_1481,plain,
is_a_theorem(implies(X_1862,X_1862)),
inference(subst,[],[refute_0_434:[bind(X_1830,$fot(X_1862))]]) ).
cnf(refute_0_1482,plain,
is_a_theorem(implies(X_1863,equiv(X_1862,X_1862))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1862,X_1862)) )],[refute_0_1481,refute_0_1480]) ).
cnf(refute_0_1483,plain,
is_a_theorem(implies(X_1945,equiv(X_1944,X_1944))),
inference(subst,[],[refute_0_1482:[bind(X_1862,$fot(X_1944)),bind(X_1863,$fot(X_1945))]]) ).
cnf(refute_0_1484,plain,
is_a_theorem(or(equiv(X_1944,X_1944),not(X_1945))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1945,equiv(X_1944,X_1944))) )],[refute_0_1483,refute_0_1420]) ).
cnf(refute_0_1485,plain,
is_a_theorem(or(equiv(X_1946,X_1946),not(not(X_1832)))),
inference(subst,[],[refute_0_1484:[bind(X_1944,$fot(X_1946)),bind(X_1945,$fot(not(X_1832)))]]) ).
cnf(refute_0_1486,plain,
( not(not(X_1832)) != X_1832
| ~ is_a_theorem(or(equiv(X_1946,X_1946),not(not(X_1832))))
| is_a_theorem(or(equiv(X_1946,X_1946),X_1832)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(equiv(X_1946,X_1946),not(not(X_1832)))) ),[0,1],$fot(X_1832)]]) ).
cnf(refute_0_1487,plain,
( ~ is_a_theorem(or(equiv(X_1946,X_1946),not(not(X_1832))))
| is_a_theorem(or(equiv(X_1946,X_1946),X_1832)) ),
inference(resolve,[$cnf( $equal(not(not(X_1832)),X_1832) )],[refute_0_638,refute_0_1486]) ).
cnf(refute_0_1488,plain,
is_a_theorem(or(equiv(X_1946,X_1946),X_1832)),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_1946,X_1946),not(not(X_1832)))) )],[refute_0_1485,refute_0_1487]) ).
cnf(refute_0_1489,plain,
is_a_theorem(or(equiv(X_27248,X_27248),and(not(X_27248),X_27248))),
inference(subst,[],[refute_0_1488:[bind(X_1832,$fot(and(not(X_27248),X_27248))),bind(X_1946,$fot(X_27248))]]) ).
cnf(refute_0_1490,plain,
is_a_theorem(or(equiv(not(equiv(X_27248,X_27248)),and(not(X_27248),X_27248)),and(not(X_27248),X_27248))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_27248,X_27248),and(not(X_27248),X_27248))) )],[refute_0_1489,refute_0_1419]) ).
cnf(refute_0_1491,plain,
is_a_theorem(or(equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)),and(not(X_27249),X_27249))),
inference(subst,[],[refute_0_1490:[bind(X_27248,$fot(X_27249))]]) ).
cnf(refute_0_1492,plain,
is_a_theorem(or(and(not(X_27249),X_27249),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)),and(not(X_27249),X_27249))) )],[refute_0_1491,refute_0_1267]) ).
cnf(refute_0_1493,plain,
or(and(not(X_27249),X_27249),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249))) = implies(or(X_27249,not(X_27249)),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249))),
inference(subst,[],[refute_0_131:[bind(Y,$fot(X_27249)),bind(X_18,$fot(equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))),bind(X_9,$fot(X_27249))]]) ).
cnf(refute_0_1494,plain,
( or(and(not(X_27249),X_27249),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249))) != implies(or(X_27249,not(X_27249)),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))
| ~ is_a_theorem(or(and(not(X_27249),X_27249),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249))))
| is_a_theorem(implies(or(X_27249,not(X_27249)),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_27249),X_27249),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))) ),[0],$fot(implies(or(X_27249,not(X_27249)),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249))))]]) ).
cnf(refute_0_1495,plain,
( ~ is_a_theorem(or(and(not(X_27249),X_27249),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249))))
| is_a_theorem(implies(or(X_27249,not(X_27249)),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_27249),X_27249),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249))),implies(or(X_27249,not(X_27249)),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))) )],[refute_0_1493,refute_0_1494]) ).
cnf(refute_0_1496,plain,
is_a_theorem(implies(or(X_27249,not(X_27249)),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_27249),X_27249),equiv(not(equiv(X_27249,X_27249)),and(not(X_27249),X_27249)))) )],[refute_0_1492,refute_0_1495]) ).
cnf(refute_0_1497,plain,
is_a_theorem(implies(or(X_27251,not(X_27251)),equiv(not(equiv(X_27251,X_27251)),and(not(X_27251),X_27251)))),
inference(subst,[],[refute_0_1496:[bind(X_27249,$fot(X_27251))]]) ).
cnf(refute_0_1498,plain,
( ~ is_a_theorem(or(X_27251,not(X_27251)))
| is_a_theorem(equiv(not(equiv(X_27251,X_27251)),and(not(X_27251),X_27251))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_27251,not(X_27251)),equiv(not(equiv(X_27251,X_27251)),and(not(X_27251),X_27251)))) )],[refute_0_1497,refute_0_1266]) ).
cnf(refute_0_1499,plain,
( ~ is_a_theorem(implies(X_1831,X_1831))
| is_a_theorem(or(X_1831,not(X_1831))) ),
inference(subst,[],[refute_0_364:[bind(Q,$fot(X_1831)),bind(X_17,$fot(X_1831))]]) ).
cnf(refute_0_1500,plain,
is_a_theorem(or(X_1831,not(X_1831))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1831,X_1831)) )],[refute_0_435,refute_0_1499]) ).
cnf(refute_0_1501,plain,
is_a_theorem(or(X_27251,not(X_27251))),
inference(subst,[],[refute_0_1500:[bind(X_1831,$fot(X_27251))]]) ).
cnf(refute_0_1502,plain,
is_a_theorem(equiv(not(equiv(X_27251,X_27251)),and(not(X_27251),X_27251))),
inference(resolve,[$cnf( is_a_theorem(or(X_27251,not(X_27251))) )],[refute_0_1501,refute_0_1498]) ).
cnf(refute_0_1503,plain,
is_a_theorem(equiv(not(equiv(X_27252,X_27252)),and(not(X_27252),X_27252))),
inference(subst,[],[refute_0_1502:[bind(X_27251,$fot(X_27252))]]) ).
cnf(refute_0_1504,plain,
not(equiv(X_27252,X_27252)) = and(not(X_27252),X_27252),
inference(resolve,[$cnf( is_a_theorem(equiv(not(equiv(X_27252,X_27252)),and(not(X_27252),X_27252))) )],[refute_0_1503,refute_0_1265]) ).
cnf(refute_0_1505,plain,
( not(equiv(X_27252,X_27252)) != and(not(X_27252),X_27252)
| and(not(X_27252),X_27252) = not(equiv(X_27252,X_27252)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(not(equiv(X_27252,X_27252)))),bind(Y0,$fot(and(not(X_27252),X_27252)))]]) ).
cnf(refute_0_1506,plain,
and(not(X_27252),X_27252) = not(equiv(X_27252,X_27252)),
inference(resolve,[$cnf( $equal(not(equiv(X_27252,X_27252)),and(not(X_27252),X_27252)) )],[refute_0_1504,refute_0_1505]) ).
cnf(refute_0_1507,plain,
and(not(X),X) = not(equiv(X,X)),
inference(subst,[],[refute_0_1506:[bind(X_27252,$fot(X))]]) ).
cnf(refute_0_1508,plain,
( and(not(X),X) != not(equiv(X,X))
| equiv(X,not(X)) != and(not(X),X)
| equiv(X,not(X)) = not(equiv(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,not(X)),and(not(X),X)) ),[1],$fot(not(equiv(X,X)))]]) ).
cnf(refute_0_1509,plain,
( equiv(X,not(X)) != and(not(X),X)
| equiv(X,not(X)) = not(equiv(X,X)) ),
inference(resolve,[$cnf( $equal(and(not(X),X),not(equiv(X,X))) )],[refute_0_1507,refute_0_1508]) ).
cnf(refute_0_1510,plain,
equiv(X,not(X)) = not(equiv(X,X)),
inference(resolve,[$cnf( $equal(equiv(X,not(X)),and(not(X),X)) )],[refute_0_1264,refute_0_1509]) ).
cnf(refute_0_1511,plain,
equiv(not(X_9),not(not(X_9))) = not(equiv(not(X_9),not(X_9))),
inference(subst,[],[refute_0_1510:[bind(X,$fot(not(X_9)))]]) ).
cnf(refute_0_1512,plain,
( equiv(not(X_9),not(not(X_9))) != not(equiv(not(X_9),not(X_9)))
| implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) != not(equiv(not(X_9),not(not(X_9))))
| implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) = not(not(equiv(not(X_9),not(X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)),not(equiv(not(X_9),not(not(X_9))))) ),[1,0],$fot(not(equiv(not(X_9),not(X_9))))]]) ).
cnf(refute_0_1513,plain,
( implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) != not(equiv(not(X_9),not(not(X_9))))
| implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) = not(not(equiv(not(X_9),not(X_9)))) ),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(not(X_9))),not(equiv(not(X_9),not(X_9)))) )],[refute_0_1511,refute_0_1512]) ).
cnf(refute_0_1514,plain,
implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) = not(not(equiv(not(X_9),not(X_9)))),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)),not(equiv(not(X_9),not(not(X_9))))) )],[refute_0_1240,refute_0_1513]) ).
cnf(refute_0_1515,plain,
not(not(equiv(X_9,X_9))) = equiv(X_9,X_9),
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(equiv(X_9,X_9)))]]) ).
cnf(refute_0_1516,plain,
and(not(X_9),X_9) = not(equiv(X_9,X_9)),
inference(subst,[],[refute_0_1506:[bind(X_27252,$fot(X_9))]]) ).
cnf(refute_0_1517,plain,
not(or(X_9,not(X_9))) = and(not(X_9),X_9),
inference(subst,[],[refute_0_126:[bind(Y,$fot(X_9))]]) ).
cnf(refute_0_1518,plain,
( and(not(X_9),X_9) != not(equiv(X_9,X_9))
| not(or(X_9,not(X_9))) != and(not(X_9),X_9)
| not(or(X_9,not(X_9))) = not(equiv(X_9,X_9)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(or(X_9,not(X_9))))),bind(Y0,$fot(and(not(X_9),X_9))),bind(Z,$fot(not(equiv(X_9,X_9))))]]) ).
cnf(refute_0_1519,plain,
( and(not(X_9),X_9) != not(equiv(X_9,X_9))
| not(or(X_9,not(X_9))) = not(equiv(X_9,X_9)) ),
inference(resolve,[$cnf( $equal(not(or(X_9,not(X_9))),and(not(X_9),X_9)) )],[refute_0_1517,refute_0_1518]) ).
cnf(refute_0_1520,plain,
not(or(X_9,not(X_9))) = not(equiv(X_9,X_9)),
inference(resolve,[$cnf( $equal(and(not(X_9),X_9),not(equiv(X_9,X_9))) )],[refute_0_1516,refute_0_1519]) ).
cnf(refute_0_1521,plain,
equiv(not(X_9),not(X_9)) = or(X_9,not(X_9)),
inference(subst,[],[refute_0_1231:[bind(X_154,$fot(X_9))]]) ).
cnf(refute_0_1522,plain,
not(equiv(not(X_9),not(X_9))) = not(equiv(not(X_9),not(X_9))),
introduced(tautology,[refl,[$fot(not(equiv(not(X_9),not(X_9))))]]) ).
cnf(refute_0_1523,plain,
( equiv(not(X_9),not(X_9)) != or(X_9,not(X_9))
| not(equiv(not(X_9),not(X_9))) != not(equiv(not(X_9),not(X_9)))
| not(equiv(not(X_9),not(X_9))) = not(or(X_9,not(X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(not(equiv(not(X_9),not(X_9))),not(equiv(not(X_9),not(X_9)))) ),[1,0],$fot(or(X_9,not(X_9)))]]) ).
cnf(refute_0_1524,plain,
( equiv(not(X_9),not(X_9)) != or(X_9,not(X_9))
| not(equiv(not(X_9),not(X_9))) = not(or(X_9,not(X_9))) ),
inference(resolve,[$cnf( $equal(not(equiv(not(X_9),not(X_9))),not(equiv(not(X_9),not(X_9)))) )],[refute_0_1522,refute_0_1523]) ).
cnf(refute_0_1525,plain,
not(equiv(not(X_9),not(X_9))) = not(or(X_9,not(X_9))),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(X_9)),or(X_9,not(X_9))) )],[refute_0_1521,refute_0_1524]) ).
cnf(refute_0_1526,plain,
( not(equiv(not(X_9),not(X_9))) != not(or(X_9,not(X_9)))
| not(or(X_9,not(X_9))) != not(equiv(X_9,X_9))
| not(equiv(not(X_9),not(X_9))) = not(equiv(X_9,X_9)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(equiv(not(X_9),not(X_9))))),bind(Y0,$fot(not(or(X_9,not(X_9))))),bind(Z,$fot(not(equiv(X_9,X_9))))]]) ).
cnf(refute_0_1527,plain,
( not(or(X_9,not(X_9))) != not(equiv(X_9,X_9))
| not(equiv(not(X_9),not(X_9))) = not(equiv(X_9,X_9)) ),
inference(resolve,[$cnf( $equal(not(equiv(not(X_9),not(X_9))),not(or(X_9,not(X_9)))) )],[refute_0_1525,refute_0_1526]) ).
cnf(refute_0_1528,plain,
not(equiv(not(X_9),not(X_9))) = not(equiv(X_9,X_9)),
inference(resolve,[$cnf( $equal(not(or(X_9,not(X_9))),not(equiv(X_9,X_9))) )],[refute_0_1520,refute_0_1527]) ).
cnf(refute_0_1529,plain,
( equiv(not(X_9),not(not(X_9))) != not(equiv(not(X_9),not(X_9)))
| not(equiv(not(X_9),not(X_9))) != not(equiv(X_9,X_9))
| equiv(not(X_9),not(not(X_9))) = not(equiv(X_9,X_9)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(equiv(not(X_9),not(not(X_9))))),bind(Y0,$fot(not(equiv(not(X_9),not(X_9))))),bind(Z,$fot(not(equiv(X_9,X_9))))]]) ).
cnf(refute_0_1530,plain,
( not(equiv(not(X_9),not(X_9))) != not(equiv(X_9,X_9))
| equiv(not(X_9),not(not(X_9))) = not(equiv(X_9,X_9)) ),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(not(X_9))),not(equiv(not(X_9),not(X_9)))) )],[refute_0_1511,refute_0_1529]) ).
cnf(refute_0_1531,plain,
equiv(not(X_9),not(not(X_9))) = not(equiv(X_9,X_9)),
inference(resolve,[$cnf( $equal(not(equiv(not(X_9),not(X_9))),not(equiv(X_9,X_9))) )],[refute_0_1528,refute_0_1530]) ).
cnf(refute_0_1532,plain,
not(equiv(not(X_9),not(not(X_9)))) = not(equiv(not(X_9),not(not(X_9)))),
introduced(tautology,[refl,[$fot(not(equiv(not(X_9),not(not(X_9)))))]]) ).
cnf(refute_0_1533,plain,
( equiv(not(X_9),not(not(X_9))) != not(equiv(X_9,X_9))
| not(equiv(not(X_9),not(not(X_9)))) != not(equiv(not(X_9),not(not(X_9))))
| not(equiv(not(X_9),not(not(X_9)))) = not(not(equiv(X_9,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(not(equiv(not(X_9),not(not(X_9)))),not(equiv(not(X_9),not(not(X_9))))) ),[1,0],$fot(not(equiv(X_9,X_9)))]]) ).
cnf(refute_0_1534,plain,
( equiv(not(X_9),not(not(X_9))) != not(equiv(X_9,X_9))
| not(equiv(not(X_9),not(not(X_9)))) = not(not(equiv(X_9,X_9))) ),
inference(resolve,[$cnf( $equal(not(equiv(not(X_9),not(not(X_9)))),not(equiv(not(X_9),not(not(X_9))))) )],[refute_0_1532,refute_0_1533]) ).
cnf(refute_0_1535,plain,
not(equiv(not(X_9),not(not(X_9)))) = not(not(equiv(X_9,X_9))),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(not(X_9))),not(equiv(X_9,X_9))) )],[refute_0_1531,refute_0_1534]) ).
cnf(refute_0_1536,plain,
( not(equiv(not(X_9),not(not(X_9)))) != not(not(equiv(X_9,X_9)))
| not(not(equiv(X_9,X_9))) != equiv(X_9,X_9)
| not(equiv(not(X_9),not(not(X_9)))) = equiv(X_9,X_9) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(equiv(not(X_9),not(not(X_9)))))),bind(Y0,$fot(not(not(equiv(X_9,X_9))))),bind(Z,$fot(equiv(X_9,X_9)))]]) ).
cnf(refute_0_1537,plain,
( not(not(equiv(X_9,X_9))) != equiv(X_9,X_9)
| not(equiv(not(X_9),not(not(X_9)))) = equiv(X_9,X_9) ),
inference(resolve,[$cnf( $equal(not(equiv(not(X_9),not(not(X_9)))),not(not(equiv(X_9,X_9)))) )],[refute_0_1535,refute_0_1536]) ).
cnf(refute_0_1538,plain,
not(equiv(not(X_9),not(not(X_9)))) = equiv(X_9,X_9),
inference(resolve,[$cnf( $equal(not(not(equiv(X_9,X_9))),equiv(X_9,X_9)) )],[refute_0_1515,refute_0_1537]) ).
cnf(refute_0_1539,plain,
( implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) != not(equiv(not(X_9),not(not(X_9))))
| not(equiv(not(X_9),not(not(X_9)))) != equiv(X_9,X_9)
| implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) = equiv(X_9,X_9) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)))),bind(Y0,$fot(not(equiv(not(X_9),not(not(X_9)))))),bind(Z,$fot(equiv(X_9,X_9)))]]) ).
cnf(refute_0_1540,plain,
( not(equiv(not(X_9),not(not(X_9)))) != equiv(X_9,X_9)
| implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) = equiv(X_9,X_9) ),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)),not(equiv(not(X_9),not(not(X_9))))) )],[refute_0_1240,refute_0_1539]) ).
cnf(refute_0_1541,plain,
implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) = equiv(X_9,X_9),
inference(resolve,[$cnf( $equal(not(equiv(not(X_9),not(not(X_9)))),equiv(X_9,X_9)) )],[refute_0_1538,refute_0_1540]) ).
cnf(refute_0_1542,plain,
( implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) != equiv(X_9,X_9)
| implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) != not(not(equiv(not(X_9),not(X_9))))
| equiv(X_9,X_9) = not(not(equiv(not(X_9),not(X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)),not(not(equiv(not(X_9),not(X_9))))) ),[0],$fot(equiv(X_9,X_9))]]) ).
cnf(refute_0_1543,plain,
( implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) != not(not(equiv(not(X_9),not(X_9))))
| equiv(X_9,X_9) = not(not(equiv(not(X_9),not(X_9)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)),equiv(X_9,X_9)) )],[refute_0_1541,refute_0_1542]) ).
cnf(refute_0_1544,plain,
not(not(equiv(not(X_9),not(X_9)))) = equiv(not(X_9),not(X_9)),
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(equiv(not(X_9),not(X_9))))]]) ).
cnf(refute_0_1545,plain,
( equiv(not(X_9),not(X_9)) != or(X_9,not(X_9))
| not(not(equiv(not(X_9),not(X_9)))) != equiv(not(X_9),not(X_9))
| not(not(equiv(not(X_9),not(X_9)))) = or(X_9,not(X_9)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(not(equiv(not(X_9),not(X_9)))))),bind(Y0,$fot(equiv(not(X_9),not(X_9)))),bind(Z,$fot(or(X_9,not(X_9))))]]) ).
cnf(refute_0_1546,plain,
( equiv(not(X_9),not(X_9)) != or(X_9,not(X_9))
| not(not(equiv(not(X_9),not(X_9)))) = or(X_9,not(X_9)) ),
inference(resolve,[$cnf( $equal(not(not(equiv(not(X_9),not(X_9)))),equiv(not(X_9),not(X_9))) )],[refute_0_1544,refute_0_1545]) ).
cnf(refute_0_1547,plain,
not(not(equiv(not(X_9),not(X_9)))) = or(X_9,not(X_9)),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(X_9)),or(X_9,not(X_9))) )],[refute_0_1521,refute_0_1546]) ).
cnf(refute_0_1548,plain,
( equiv(X_9,X_9) != not(not(equiv(not(X_9),not(X_9))))
| not(not(equiv(not(X_9),not(X_9)))) != or(X_9,not(X_9))
| equiv(X_9,X_9) = or(X_9,not(X_9)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(equiv(X_9,X_9),or(X_9,not(X_9))) ),[0],$fot(not(not(equiv(not(X_9),not(X_9)))))]]) ).
cnf(refute_0_1549,plain,
( equiv(X_9,X_9) != not(not(equiv(not(X_9),not(X_9))))
| equiv(X_9,X_9) = or(X_9,not(X_9)) ),
inference(resolve,[$cnf( $equal(not(not(equiv(not(X_9),not(X_9)))),or(X_9,not(X_9))) )],[refute_0_1547,refute_0_1548]) ).
cnf(refute_0_1550,plain,
( implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)) != not(not(equiv(not(X_9),not(X_9))))
| equiv(X_9,X_9) = or(X_9,not(X_9)) ),
inference(resolve,[$cnf( $equal(equiv(X_9,X_9),not(not(equiv(not(X_9),not(X_9))))) )],[refute_0_1543,refute_0_1549]) ).
cnf(refute_0_1551,plain,
equiv(X_9,X_9) = or(X_9,not(X_9)),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(not(X_9))),and(not(not(X_9)),X_9)),not(not(equiv(not(X_9),not(X_9))))) )],[refute_0_1514,refute_0_1550]) ).
cnf(refute_0_1552,plain,
( equiv(X_9,X_9) != or(X_9,not(X_9))
| or(X_9,not(X_9)) = equiv(X_9,X_9) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X_9,X_9))),bind(Y0,$fot(or(X_9,not(X_9))))]]) ).
cnf(refute_0_1553,plain,
or(X_9,not(X_9)) = equiv(X_9,X_9),
inference(resolve,[$cnf( $equal(equiv(X_9,X_9),or(X_9,not(X_9))) )],[refute_0_1551,refute_0_1552]) ).
cnf(refute_0_1554,plain,
or(X_26619,not(X_26619)) = equiv(X_26619,X_26619),
inference(subst,[],[refute_0_1553:[bind(X_9,$fot(X_26619))]]) ).
cnf(refute_0_1555,plain,
implies(or(X_26619,not(X_26619)),X_26621) = implies(or(X_26619,not(X_26619)),X_26621),
introduced(tautology,[refl,[$fot(implies(or(X_26619,not(X_26619)),X_26621))]]) ).
cnf(refute_0_1556,plain,
( implies(or(X_26619,not(X_26619)),X_26621) != implies(or(X_26619,not(X_26619)),X_26621)
| or(X_26619,not(X_26619)) != equiv(X_26619,X_26619)
| implies(or(X_26619,not(X_26619)),X_26621) = implies(equiv(X_26619,X_26619),X_26621) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_26619,not(X_26619)),X_26621),implies(or(X_26619,not(X_26619)),X_26621)) ),[1,0],$fot(equiv(X_26619,X_26619))]]) ).
cnf(refute_0_1557,plain,
( or(X_26619,not(X_26619)) != equiv(X_26619,X_26619)
| implies(or(X_26619,not(X_26619)),X_26621) = implies(equiv(X_26619,X_26619),X_26621) ),
inference(resolve,[$cnf( $equal(implies(or(X_26619,not(X_26619)),X_26621),implies(or(X_26619,not(X_26619)),X_26621)) )],[refute_0_1555,refute_0_1556]) ).
cnf(refute_0_1558,plain,
implies(or(X_26619,not(X_26619)),X_26621) = implies(equiv(X_26619,X_26619),X_26621),
inference(resolve,[$cnf( $equal(or(X_26619,not(X_26619)),equiv(X_26619,X_26619)) )],[refute_0_1554,refute_0_1557]) ).
cnf(refute_0_1559,plain,
implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)) = implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),
introduced(tautology,[refl,[$fot(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)))]]) ).
cnf(refute_0_1560,plain,
( implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)) != implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621))
| implies(or(X_26619,not(X_26619)),X_26621) != implies(equiv(X_26619,X_26619),X_26621)
| implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)) = implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621))) ),[1,0],$fot(implies(equiv(X_26619,X_26619),X_26621))]]) ).
cnf(refute_0_1561,plain,
( implies(or(X_26619,not(X_26619)),X_26621) != implies(equiv(X_26619,X_26619),X_26621)
| implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)) = implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)) ),
inference(resolve,[$cnf( $equal(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621))) )],[refute_0_1559,refute_0_1560]) ).
cnf(refute_0_1562,plain,
implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)) = implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),
inference(resolve,[$cnf( $equal(implies(or(X_26619,not(X_26619)),X_26621),implies(equiv(X_26619,X_26619),X_26621)) )],[refute_0_1558,refute_0_1561]) ).
cnf(refute_0_1563,plain,
and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166) = and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),
introduced(tautology,[refl,[$fot(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166))]]) ).
cnf(refute_0_1564,plain,
( and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166) != and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166)
| implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)) != implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621))
| and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166) = and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166)) ),[1,0],$fot(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)))]]) ).
cnf(refute_0_1565,plain,
( implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)) != implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621))
| and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166) = and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166) ),
inference(resolve,[$cnf( $equal(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166)) )],[refute_0_1563,refute_0_1564]) ).
cnf(refute_0_1566,plain,
and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166) = and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),
inference(resolve,[$cnf( $equal(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621))) )],[refute_0_1562,refute_0_1565]) ).
cnf(refute_0_1567,plain,
or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)) = or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)),
introduced(tautology,[refl,[$fot(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)))]]) ).
cnf(refute_0_1568,plain,
( and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166) != and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166)
| or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)) != or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))
| or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)) = or(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)),or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))) ),[1,0],$fot(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166))]]) ).
cnf(refute_0_1569,plain,
( and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166) != and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166)
| or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)) = or(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)) ),
inference(resolve,[$cnf( $equal(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)),or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))) )],[refute_0_1567,refute_0_1568]) ).
cnf(refute_0_1570,plain,
or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)) = or(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)),
inference(resolve,[$cnf( $equal(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166)) )],[refute_0_1566,refute_0_1569]) ).
cnf(refute_0_1571,plain,
( or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)) != or(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))
| ~ is_a_theorem(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)))
| is_a_theorem(or(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))) ),[0],$fot(or(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)))]]) ).
cnf(refute_0_1572,plain,
( ~ is_a_theorem(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)))
| is_a_theorem(or(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))) ),
inference(resolve,[$cnf( $equal(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166)),or(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))) )],[refute_0_1570,refute_0_1571]) ).
cnf(refute_0_1573,plain,
is_a_theorem(or(and(implies(implies(equiv(X_26619,X_26619),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(implies(or(X_26619,not(X_26619)),X_26621),or(X_26620,X_26621)),X_9166),not(X_9166))) )],[refute_0_1239,refute_0_1572]) ).
cnf(refute_0_1574,plain,
is_a_theorem(or(and(implies(implies(equiv(X_30647,X_30647),X_30649),or(X_30649,X_30649)),X_30650),not(X_30650))),
inference(subst,[],[refute_0_1573:[bind(X_26619,$fot(X_30647)),bind(X_26620,$fot(X_30649)),bind(X_26621,$fot(X_30649)),bind(X_9166,$fot(X_30650))]]) ).
cnf(refute_0_1575,plain,
X_30649 = or(X_30649,X_30649),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(X_30649))]]) ).
cnf(refute_0_1576,plain,
( X_30649 != or(X_30649,X_30649)
| or(X_30649,X_30649) = X_30649 ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(X_30649)),bind(Y0,$fot(or(X_30649,X_30649)))]]) ).
cnf(refute_0_1577,plain,
or(X_30649,X_30649) = X_30649,
inference(resolve,[$cnf( $equal(X_30649,or(X_30649,X_30649)) )],[refute_0_1575,refute_0_1576]) ).
cnf(refute_0_1578,plain,
( or(X_30649,X_30649) != X_30649
| ~ is_a_theorem(or(and(implies(implies(equiv(X_30647,X_30647),X_30649),or(X_30649,X_30649)),X_30650),not(X_30650)))
| is_a_theorem(or(and(implies(implies(equiv(X_30647,X_30647),X_30649),X_30649),X_30650),not(X_30650))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(implies(equiv(X_30647,X_30647),X_30649),or(X_30649,X_30649)),X_30650),not(X_30650))) ),[0,0,0,1],$fot(X_30649)]]) ).
cnf(refute_0_1579,plain,
( ~ is_a_theorem(or(and(implies(implies(equiv(X_30647,X_30647),X_30649),or(X_30649,X_30649)),X_30650),not(X_30650)))
| is_a_theorem(or(and(implies(implies(equiv(X_30647,X_30647),X_30649),X_30649),X_30650),not(X_30650))) ),
inference(resolve,[$cnf( $equal(or(X_30649,X_30649),X_30649) )],[refute_0_1577,refute_0_1578]) ).
cnf(refute_0_1580,plain,
is_a_theorem(or(and(implies(implies(equiv(X_30647,X_30647),X_30649),X_30649),X_30650),not(X_30650))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(implies(equiv(X_30647,X_30647),X_30649),or(X_30649,X_30649)),X_30650),not(X_30650))) )],[refute_0_1574,refute_0_1579]) ).
cnf(refute_0_1581,plain,
is_a_theorem(or(and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653),not(X_30653))),
inference(subst,[],[refute_0_1580:[bind(X_30647,$fot(X_30651)),bind(X_30649,$fot(X_30652)),bind(X_30650,$fot(X_30653))]]) ).
cnf(refute_0_1582,plain,
is_a_theorem(or(not(X_30653),and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653),not(X_30653))) )],[refute_0_1581,refute_0_1127]) ).
cnf(refute_0_1583,plain,
or(not(X_30653),and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653)) = implies(X_30653,and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653)),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_30653)),bind(Y,$fot(and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653)))]]) ).
cnf(refute_0_1584,plain,
( or(not(X_30653),and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653)) != implies(X_30653,and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))
| ~ is_a_theorem(or(not(X_30653),and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653)))
| is_a_theorem(implies(X_30653,and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X_30653),and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))) ),[0],$fot(implies(X_30653,and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653)))]]) ).
cnf(refute_0_1585,plain,
( ~ is_a_theorem(or(not(X_30653),and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653)))
| is_a_theorem(implies(X_30653,and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))) ),
inference(resolve,[$cnf( $equal(or(not(X_30653),and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653)),implies(X_30653,and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))) )],[refute_0_1583,refute_0_1584]) ).
cnf(refute_0_1586,plain,
is_a_theorem(implies(X_30653,and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_30653),and(implies(implies(equiv(X_30651,X_30651),X_30652),X_30652),X_30653))) )],[refute_0_1582,refute_0_1585]) ).
cnf(refute_0_1587,plain,
is_a_theorem(implies(implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)),and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826))))),
inference(subst,[],[refute_0_1586:[bind(X_30651,$fot(X_31825)),bind(X_30652,$fot(X_31826)),bind(X_30653,$fot(implies(X_31826,implies(equiv(X_31825,X_31825),X_31826))))]]) ).
cnf(refute_0_1588,plain,
equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826) = and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826))),
inference(subst,[],[refute_0_71:[bind(X,$fot(implies(equiv(X_31825,X_31825),X_31826))),bind(Y,$fot(X_31826))]]) ).
cnf(refute_0_1589,plain,
( equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826) != and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)))
| and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826))) = equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826))),bind(Y0,$fot(and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)))))]]) ).
cnf(refute_0_1590,plain,
and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826))) = equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826),
inference(resolve,[$cnf( $equal(equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826),and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)))) )],[refute_0_1588,refute_0_1589]) ).
cnf(refute_0_1591,plain,
( and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826))) != equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826)
| ~ is_a_theorem(implies(implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)),and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)))))
| is_a_theorem(implies(implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)),equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)),and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826))))) ),[0,1],$fot(equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826))]]) ).
cnf(refute_0_1592,plain,
( ~ is_a_theorem(implies(implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)),and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)))))
| is_a_theorem(implies(implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)),equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826))) ),
inference(resolve,[$cnf( $equal(and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826))),equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826)) )],[refute_0_1590,refute_0_1591]) ).
cnf(refute_0_1593,plain,
is_a_theorem(implies(implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)),equiv(implies(equiv(X_31825,X_31825),X_31826),X_31826))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_31826,implies(equiv(X_31825,X_31825),X_31826)),and(implies(implies(equiv(X_31825,X_31825),X_31826),X_31826),implies(X_31826,implies(equiv(X_31825,X_31825),X_31826))))) )],[refute_0_1587,refute_0_1592]) ).
cnf(refute_0_1594,plain,
is_a_theorem(implies(implies(X_31829,implies(equiv(X_31828,X_31828),X_31829)),equiv(implies(equiv(X_31828,X_31828),X_31829),X_31829))),
inference(subst,[],[refute_0_1593:[bind(X_31825,$fot(X_31828)),bind(X_31826,$fot(X_31829))]]) ).
cnf(refute_0_1595,plain,
( ~ is_a_theorem(implies(X_31829,implies(equiv(X_31828,X_31828),X_31829)))
| is_a_theorem(equiv(implies(equiv(X_31828,X_31828),X_31829),X_31829)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_31829,implies(equiv(X_31828,X_31828),X_31829)),equiv(implies(equiv(X_31828,X_31828),X_31829),X_31829))) )],[refute_0_1594,refute_0_1126]) ).
cnf(refute_0_1596,plain,
is_a_theorem(implies(X_31829,implies(equiv(X_31828,X_31828),X_31829))),
inference(subst,[],[refute_0_676:[bind(Q,$fot(X_31829)),bind(X_17,$fot(equiv(X_31828,X_31828)))]]) ).
cnf(refute_0_1597,plain,
is_a_theorem(equiv(implies(equiv(X_31828,X_31828),X_31829),X_31829)),
inference(resolve,[$cnf( is_a_theorem(implies(X_31829,implies(equiv(X_31828,X_31828),X_31829))) )],[refute_0_1596,refute_0_1595]) ).
cnf(refute_0_1598,plain,
is_a_theorem(equiv(implies(equiv(X_31830,X_31830),X_31831),X_31831)),
inference(subst,[],[refute_0_1597:[bind(X_31828,$fot(X_31830)),bind(X_31829,$fot(X_31831))]]) ).
cnf(refute_0_1599,plain,
implies(equiv(X_31830,X_31830),X_31831) = X_31831,
inference(resolve,[$cnf( is_a_theorem(equiv(implies(equiv(X_31830,X_31830),X_31831),X_31831)) )],[refute_0_1598,refute_0_1125]) ).
cnf(refute_0_1600,plain,
implies(equiv(X_15433,X_15433),X_15431) = X_15431,
inference(subst,[],[refute_0_1599:[bind(X_31830,$fot(X_15433)),bind(X_31831,$fot(X_15431))]]) ).
cnf(refute_0_1601,plain,
implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)) = implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)),
introduced(tautology,[refl,[$fot(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)))]]) ).
cnf(refute_0_1602,plain,
( implies(equiv(X_15433,X_15433),X_15431) != X_15431
| implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)) != implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431))
| implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)) = implies(X_15431,equiv(equiv(X_15433,X_15433),X_15431)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)),implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431))) ),[1,0],$fot(X_15431)]]) ).
cnf(refute_0_1603,plain,
( implies(equiv(X_15433,X_15433),X_15431) != X_15431
| implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)) = implies(X_15431,equiv(equiv(X_15433,X_15433),X_15431)) ),
inference(resolve,[$cnf( $equal(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)),implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431))) )],[refute_0_1601,refute_0_1602]) ).
cnf(refute_0_1604,plain,
implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)) = implies(X_15431,equiv(equiv(X_15433,X_15433),X_15431)),
inference(resolve,[$cnf( $equal(implies(equiv(X_15433,X_15433),X_15431),X_15431) )],[refute_0_1600,refute_0_1603]) ).
cnf(refute_0_1605,plain,
( implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)) != implies(X_15431,equiv(equiv(X_15433,X_15433),X_15431))
| ~ is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)))
| is_a_theorem(implies(X_15431,equiv(equiv(X_15433,X_15433),X_15431))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431))) ),[0],$fot(implies(X_15431,equiv(equiv(X_15433,X_15433),X_15431)))]]) ).
cnf(refute_0_1606,plain,
( ~ is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)))
| is_a_theorem(implies(X_15431,equiv(equiv(X_15433,X_15433),X_15431))) ),
inference(resolve,[$cnf( $equal(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431)),implies(X_15431,equiv(equiv(X_15433,X_15433),X_15431))) )],[refute_0_1604,refute_0_1605]) ).
cnf(refute_0_1607,plain,
is_a_theorem(implies(X_15431,equiv(equiv(X_15433,X_15433),X_15431))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(equiv(X_15433,X_15433),X_15431),equiv(equiv(X_15433,X_15433),X_15431))) )],[refute_0_1124,refute_0_1606]) ).
cnf(refute_0_1608,plain,
is_a_theorem(implies(equiv(X_31830,X_31830),equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830)))),
inference(subst,[],[refute_0_1607:[bind(X_15431,$fot(equiv(X_31830,X_31830))),bind(X_15433,$fot(X_31837))]]) ).
cnf(refute_0_1609,plain,
implies(equiv(X_31830,X_31830),equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))) = equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830)),
inference(subst,[],[refute_0_1599:[bind(X_31831,$fot(equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))))]]) ).
cnf(refute_0_1610,plain,
( implies(equiv(X_31830,X_31830),equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))) != equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))
| ~ is_a_theorem(implies(equiv(X_31830,X_31830),equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))))
| is_a_theorem(equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(equiv(X_31830,X_31830),equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830)))) ),[0],$fot(equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830)))]]) ).
cnf(refute_0_1611,plain,
( ~ is_a_theorem(implies(equiv(X_31830,X_31830),equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))))
| is_a_theorem(equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))) ),
inference(resolve,[$cnf( $equal(implies(equiv(X_31830,X_31830),equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))),equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))) )],[refute_0_1609,refute_0_1610]) ).
cnf(refute_0_1612,plain,
is_a_theorem(equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830))),
inference(resolve,[$cnf( is_a_theorem(implies(equiv(X_31830,X_31830),equiv(equiv(X_31837,X_31837),equiv(X_31830,X_31830)))) )],[refute_0_1608,refute_0_1611]) ).
cnf(refute_0_1613,plain,
is_a_theorem(equiv(equiv(X_31900,X_31900),equiv(X_31899,X_31899))),
inference(subst,[],[refute_0_1612:[bind(X_31830,$fot(X_31899)),bind(X_31837,$fot(X_31900))]]) ).
cnf(refute_0_1614,plain,
equiv(X_31900,X_31900) = equiv(X_31899,X_31899),
inference(resolve,[$cnf( is_a_theorem(equiv(equiv(X_31900,X_31900),equiv(X_31899,X_31899))) )],[refute_0_1613,refute_0_847]) ).
cnf(refute_0_1615,plain,
equiv(not(X_9),not(X_9)) = equiv(X_31901,X_31901),
inference(subst,[],[refute_0_1614:[bind(X_31899,$fot(X_31901)),bind(X_31900,$fot(not(X_9)))]]) ).
cnf(refute_0_1616,plain,
( equiv(not(X_9),not(X_9)) != equiv(X_31901,X_31901)
| implies(or(X_9,not(X_9)),and(not(X_9),X_9)) != not(equiv(not(X_9),not(X_9)))
| implies(or(X_9,not(X_9)),and(not(X_9),X_9)) = not(equiv(X_31901,X_31901)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_9,not(X_9)),and(not(X_9),X_9)),not(equiv(not(X_9),not(X_9)))) ),[1,0],$fot(equiv(X_31901,X_31901))]]) ).
cnf(refute_0_1617,plain,
( implies(or(X_9,not(X_9)),and(not(X_9),X_9)) != not(equiv(not(X_9),not(X_9)))
| implies(or(X_9,not(X_9)),and(not(X_9),X_9)) = not(equiv(X_31901,X_31901)) ),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(X_9)),equiv(X_31901,X_31901)) )],[refute_0_1615,refute_0_1616]) ).
cnf(refute_0_1618,plain,
implies(or(X_9,not(X_9)),and(not(X_9),X_9)) = not(equiv(X_31901,X_31901)),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(X_9)),and(not(X_9),X_9)),not(equiv(not(X_9),not(X_9)))) )],[refute_0_846,refute_0_1617]) ).
cnf(refute_0_1619,plain,
implies(or(X_9,not(Y)),and(not(X_9),Y)) = or(and(not(X_9),Y),and(not(X_9),Y)),
inference(subst,[],[refute_0_129:[bind(X_18,$fot(and(not(X_9),Y)))]]) ).
cnf(refute_0_1620,plain,
and(not(X_9),Y) = or(and(not(X_9),Y),and(not(X_9),Y)),
inference(subst,[],[refute_0_630:[bind(X_8900,$fot(and(not(X_9),Y)))]]) ).
cnf(refute_0_1621,plain,
( and(not(X_9),Y) != or(and(not(X_9),Y),and(not(X_9),Y))
| or(and(not(X_9),Y),and(not(X_9),Y)) = and(not(X_9),Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(and(not(X_9),Y))),bind(Y0,$fot(or(and(not(X_9),Y),and(not(X_9),Y))))]]) ).
cnf(refute_0_1622,plain,
or(and(not(X_9),Y),and(not(X_9),Y)) = and(not(X_9),Y),
inference(resolve,[$cnf( $equal(and(not(X_9),Y),or(and(not(X_9),Y),and(not(X_9),Y))) )],[refute_0_1620,refute_0_1621]) ).
cnf(refute_0_1623,plain,
( implies(or(X_9,not(Y)),and(not(X_9),Y)) != or(and(not(X_9),Y),and(not(X_9),Y))
| or(and(not(X_9),Y),and(not(X_9),Y)) != and(not(X_9),Y)
| implies(or(X_9,not(Y)),and(not(X_9),Y)) = and(not(X_9),Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(or(X_9,not(Y)),and(not(X_9),Y)),and(not(X_9),Y)) ),[0],$fot(or(and(not(X_9),Y),and(not(X_9),Y)))]]) ).
cnf(refute_0_1624,plain,
( implies(or(X_9,not(Y)),and(not(X_9),Y)) != or(and(not(X_9),Y),and(not(X_9),Y))
| implies(or(X_9,not(Y)),and(not(X_9),Y)) = and(not(X_9),Y) ),
inference(resolve,[$cnf( $equal(or(and(not(X_9),Y),and(not(X_9),Y)),and(not(X_9),Y)) )],[refute_0_1622,refute_0_1623]) ).
cnf(refute_0_1625,plain,
implies(or(X_9,not(Y)),and(not(X_9),Y)) = and(not(X_9),Y),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(Y)),and(not(X_9),Y)),or(and(not(X_9),Y),and(not(X_9),Y))) )],[refute_0_1619,refute_0_1624]) ).
cnf(refute_0_1626,plain,
implies(or(X_9,not(X_9)),and(not(X_9),X_9)) = and(not(X_9),X_9),
inference(subst,[],[refute_0_1625:[bind(Y,$fot(X_9))]]) ).
cnf(refute_0_1627,plain,
( and(not(X_9),X_9) != not(equiv(X_9,X_9))
| implies(or(X_9,not(X_9)),and(not(X_9),X_9)) != and(not(X_9),X_9)
| implies(or(X_9,not(X_9)),and(not(X_9),X_9)) = not(equiv(X_9,X_9)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(or(X_9,not(X_9)),and(not(X_9),X_9)))),bind(Y0,$fot(and(not(X_9),X_9))),bind(Z,$fot(not(equiv(X_9,X_9))))]]) ).
cnf(refute_0_1628,plain,
( and(not(X_9),X_9) != not(equiv(X_9,X_9))
| implies(or(X_9,not(X_9)),and(not(X_9),X_9)) = not(equiv(X_9,X_9)) ),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(X_9)),and(not(X_9),X_9)),and(not(X_9),X_9)) )],[refute_0_1626,refute_0_1627]) ).
cnf(refute_0_1629,plain,
implies(or(X_9,not(X_9)),and(not(X_9),X_9)) = not(equiv(X_9,X_9)),
inference(resolve,[$cnf( $equal(and(not(X_9),X_9),not(equiv(X_9,X_9))) )],[refute_0_1516,refute_0_1628]) ).
cnf(refute_0_1630,plain,
( implies(or(X_9,not(X_9)),and(not(X_9),X_9)) != not(equiv(X_31901,X_31901))
| implies(or(X_9,not(X_9)),and(not(X_9),X_9)) != not(equiv(X_9,X_9))
| not(equiv(X_9,X_9)) = not(equiv(X_31901,X_31901)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_9,not(X_9)),and(not(X_9),X_9)),not(equiv(X_31901,X_31901))) ),[0],$fot(not(equiv(X_9,X_9)))]]) ).
cnf(refute_0_1631,plain,
( implies(or(X_9,not(X_9)),and(not(X_9),X_9)) != not(equiv(X_31901,X_31901))
| not(equiv(X_9,X_9)) = not(equiv(X_31901,X_31901)) ),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(X_9)),and(not(X_9),X_9)),not(equiv(X_9,X_9))) )],[refute_0_1629,refute_0_1630]) ).
cnf(refute_0_1632,plain,
not(equiv(X_9,X_9)) = not(equiv(X_31901,X_31901)),
inference(resolve,[$cnf( $equal(implies(or(X_9,not(X_9)),and(not(X_9),X_9)),not(equiv(X_31901,X_31901))) )],[refute_0_1618,refute_0_1631]) ).
cnf(refute_0_1633,plain,
( not(equiv(X_9,X_9)) != not(equiv(X_31901,X_31901))
| not(equiv(X_31901,X_31901)) = not(equiv(X_9,X_9)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(not(equiv(X_9,X_9)))),bind(Y0,$fot(not(equiv(X_31901,X_31901))))]]) ).
cnf(refute_0_1634,plain,
not(equiv(X_31901,X_31901)) = not(equiv(X_9,X_9)),
inference(resolve,[$cnf( $equal(not(equiv(X_9,X_9)),not(equiv(X_31901,X_31901))) )],[refute_0_1632,refute_0_1633]) ).
cnf(refute_0_1635,plain,
( not(equiv(X_31901,X_31901)) != not(equiv(X_9,X_9))
| ~ is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_31901,X_31901)))))
| is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_31901,X_31901))))) ),[0,1,1],$fot(not(equiv(X_9,X_9)))]]) ).
cnf(refute_0_1636,plain,
( ~ is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_31901,X_31901)))))
| is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9))))) ),
inference(resolve,[$cnf( $equal(not(equiv(X_31901,X_31901)),not(equiv(X_9,X_9))) )],[refute_0_1634,refute_0_1635]) ).
cnf(refute_0_1637,plain,
is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_31901,X_31901))))) )],[refute_0_821,refute_0_1636]) ).
cnf(refute_0_1638,plain,
or(X_9,not(equiv(not(X_9),not(X_9)))) = not(and(not(X_9),equiv(not(X_9),not(X_9)))),
inference(subst,[],[refute_0_456:[bind(Y,$fot(equiv(not(X_9),not(X_9))))]]) ).
cnf(refute_0_1639,plain,
( ~ is_a_theorem(equiv(and(X_47408,equiv(X_47408,X_47408)),X_47408))
| and(X_47408,equiv(X_47408,X_47408)) = X_47408 ),
inference(subst,[],[refute_0_155:[bind(X,$fot(and(X_47408,equiv(X_47408,X_47408)))),bind(Y,$fot(X_47408))]]) ).
cnf(refute_0_1640,plain,
( ~ is_a_theorem(implies(and(X_47407,equiv(X_47407,X_47407)),X_47407))
| ~ is_a_theorem(implies(implies(and(X_47407,equiv(X_47407,X_47407)),X_47407),equiv(and(X_47407,equiv(X_47407,X_47407)),X_47407)))
| is_a_theorem(equiv(and(X_47407,equiv(X_47407,X_47407)),X_47407)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(and(X_47407,equiv(X_47407,X_47407)),X_47407))),bind(Y,$fot(equiv(and(X_47407,equiv(X_47407,X_47407)),X_47407)))]]) ).
cnf(refute_0_1641,plain,
( ~ is_a_theorem(or(equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406),not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406))))
| is_a_theorem(or(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))),bind(Q,$fot(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406))))]]) ).
cnf(refute_0_1642,plain,
( ~ is_a_theorem(implies(X_25598,or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599))))
| is_a_theorem(or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598))) ),
inference(subst,[],[refute_0_364:[bind(Q,$fot(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)))),bind(X_17,$fot(X_25598))]]) ).
cnf(refute_0_1643,plain,
( ~ is_a_theorem(implies(implies(X_8388,or(or(X_8389,X_8389),and(X_8387,or(X_8389,X_8389)))),implies(X_8388,X_8389)))
| is_a_theorem(implies(X_8388,implies(implies(X_8388,or(or(X_8389,X_8389),and(X_8387,or(X_8389,X_8389)))),X_8389))) ),
inference(subst,[],[refute_0_215:[bind(X,$fot(X_8388)),bind(X_205,$fot(implies(X_8388,or(or(X_8389,X_8389),and(X_8387,or(X_8389,X_8389)))))),bind(X_207,$fot(X_8389))]]) ).
cnf(refute_0_1644,plain,
( ~ is_a_theorem(implies(or(or(X_2673,X_2673),and(X_4907,or(X_2673,X_2673))),or(X_2673,X_2673)))
| is_a_theorem(implies(or(or(X_2673,X_2673),and(X_4907,or(X_2673,X_2673))),X_2673)) ),
inference(subst,[],[refute_0_184:[bind(X,$fot(or(or(X_2673,X_2673),and(X_4907,or(X_2673,X_2673)))))]]) ).
cnf(refute_0_1645,plain,
is_a_theorem(implies(not(X),implies(X_25,not(X)))),
inference(subst,[],[refute_0_676:[bind(Q,$fot(not(X))),bind(X_17,$fot(X_25))]]) ).
cnf(refute_0_1646,plain,
or(X,implies(X_25,not(X))) = implies(not(X),implies(X_25,not(X))),
inference(subst,[],[refute_0_84:[bind(Y,$fot(implies(X_25,not(X))))]]) ).
cnf(refute_0_1647,plain,
( or(X,implies(X_25,not(X))) != implies(not(X),implies(X_25,not(X)))
| implies(not(X),implies(X_25,not(X))) = or(X,implies(X_25,not(X))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,implies(X_25,not(X))))),bind(Y0,$fot(implies(not(X),implies(X_25,not(X)))))]]) ).
cnf(refute_0_1648,plain,
implies(not(X),implies(X_25,not(X))) = or(X,implies(X_25,not(X))),
inference(resolve,[$cnf( $equal(or(X,implies(X_25,not(X))),implies(not(X),implies(X_25,not(X)))) )],[refute_0_1646,refute_0_1647]) ).
cnf(refute_0_1649,plain,
( implies(not(X),implies(X_25,not(X))) != or(X,implies(X_25,not(X)))
| ~ is_a_theorem(implies(not(X),implies(X_25,not(X))))
| is_a_theorem(or(X,implies(X_25,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X),implies(X_25,not(X)))) ),[0],$fot(or(X,implies(X_25,not(X))))]]) ).
cnf(refute_0_1650,plain,
( ~ is_a_theorem(implies(not(X),implies(X_25,not(X))))
| is_a_theorem(or(X,implies(X_25,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(X_25,not(X))),or(X,implies(X_25,not(X)))) )],[refute_0_1648,refute_0_1649]) ).
cnf(refute_0_1651,plain,
is_a_theorem(or(X,implies(X_25,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),implies(X_25,not(X)))) )],[refute_0_1645,refute_0_1650]) ).
cnf(refute_0_1652,plain,
is_a_theorem(or(X_854,implies(X_25,not(X_854)))),
inference(subst,[],[refute_0_1651:[bind(X,$fot(X_854))]]) ).
cnf(refute_0_1653,plain,
( ~ is_a_theorem(or(X_854,implies(X_25,not(X_854))))
| is_a_theorem(or(implies(X_25,not(X_854)),X_854)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_854)),bind(Q,$fot(implies(X_25,not(X_854))))]]) ).
cnf(refute_0_1654,plain,
is_a_theorem(or(implies(X_25,not(X_854)),X_854)),
inference(resolve,[$cnf( is_a_theorem(or(X_854,implies(X_25,not(X_854)))) )],[refute_0_1652,refute_0_1653]) ).
cnf(refute_0_1655,plain,
or(implies(X_25,not(X_854)),X_854) = implies(and(X_25,X_854),X_854),
inference(subst,[],[refute_0_534:[bind(X,$fot(X_25)),bind(Y,$fot(X_854)),bind(X_10,$fot(X_854))]]) ).
cnf(refute_0_1656,plain,
( or(implies(X_25,not(X_854)),X_854) != implies(and(X_25,X_854),X_854)
| ~ is_a_theorem(or(implies(X_25,not(X_854)),X_854))
| is_a_theorem(implies(and(X_25,X_854),X_854)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_25,not(X_854)),X_854)) ),[0],$fot(implies(and(X_25,X_854),X_854))]]) ).
cnf(refute_0_1657,plain,
( ~ is_a_theorem(or(implies(X_25,not(X_854)),X_854))
| is_a_theorem(implies(and(X_25,X_854),X_854)) ),
inference(resolve,[$cnf( $equal(or(implies(X_25,not(X_854)),X_854),implies(and(X_25,X_854),X_854)) )],[refute_0_1655,refute_0_1656]) ).
cnf(refute_0_1658,plain,
is_a_theorem(implies(and(X_25,X_854),X_854)),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_25,not(X_854)),X_854)) )],[refute_0_1654,refute_0_1657]) ).
cnf(refute_0_1659,plain,
is_a_theorem(implies(and(X_25,X_2336),X_2336)),
inference(subst,[],[refute_0_1658:[bind(X_854,$fot(X_2336))]]) ).
cnf(refute_0_1660,plain,
( ~ is_a_theorem(implies(and(X_25,X_2336),X_2336))
| is_a_theorem(implies(or(X_2334,and(X_25,X_2336)),or(X_2334,X_2336))) ),
inference(subst,[],[refute_0_169:[bind(P,$fot(X_2334)),bind(Q,$fot(and(X_25,X_2336))),bind(R,$fot(X_2336))]]) ).
cnf(refute_0_1661,plain,
is_a_theorem(implies(or(X_2334,and(X_25,X_2336)),or(X_2334,X_2336))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_25,X_2336),X_2336)) )],[refute_0_1659,refute_0_1660]) ).
cnf(refute_0_1662,plain,
is_a_theorem(implies(or(X_4885,and(X_25,X_4885)),or(X_4885,X_4885))),
inference(subst,[],[refute_0_1661:[bind(X_2334,$fot(X_4885)),bind(X_2336,$fot(X_4885))]]) ).
cnf(refute_0_1663,plain,
( ~ is_a_theorem(implies(or(X_4885,and(X_25,X_4885)),or(X_4885,X_4885)))
| is_a_theorem(implies(or(X_4885,and(X_25,X_4885)),X_4885)) ),
inference(subst,[],[refute_0_184:[bind(X,$fot(or(X_4885,and(X_25,X_4885)))),bind(X_2673,$fot(X_4885))]]) ).
cnf(refute_0_1664,plain,
is_a_theorem(implies(or(X_4885,and(X_25,X_4885)),X_4885)),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_4885,and(X_25,X_4885)),or(X_4885,X_4885))) )],[refute_0_1662,refute_0_1663]) ).
cnf(refute_0_1665,plain,
is_a_theorem(implies(or(or(X_2673,X_2673),and(X_4907,or(X_2673,X_2673))),or(X_2673,X_2673))),
inference(subst,[],[refute_0_1664:[bind(X_25,$fot(X_4907)),bind(X_4885,$fot(or(X_2673,X_2673)))]]) ).
cnf(refute_0_1666,plain,
is_a_theorem(implies(or(or(X_2673,X_2673),and(X_4907,or(X_2673,X_2673))),X_2673)),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_2673,X_2673),and(X_4907,or(X_2673,X_2673))),or(X_2673,X_2673))) )],[refute_0_1665,refute_0_1644]) ).
cnf(refute_0_1667,plain,
is_a_theorem(implies(or(or(X_6811,X_6811),and(X_4907,or(X_6811,X_6811))),X_6811)),
inference(subst,[],[refute_0_1666:[bind(X_2673,$fot(X_6811))]]) ).
cnf(refute_0_1668,plain,
( ~ is_a_theorem(implies(or(or(X_6811,X_6811),and(X_4907,or(X_6811,X_6811))),X_6811))
| is_a_theorem(implies(implies(X_6809,or(or(X_6811,X_6811),and(X_4907,or(X_6811,X_6811)))),implies(X_6809,X_6811))) ),
inference(subst,[],[refute_0_1193:[bind(X,$fot(X_6809)),bind(X_71,$fot(or(or(X_6811,X_6811),and(X_4907,or(X_6811,X_6811))))),bind(X_72,$fot(X_6811))]]) ).
cnf(refute_0_1669,plain,
is_a_theorem(implies(implies(X_6809,or(or(X_6811,X_6811),and(X_4907,or(X_6811,X_6811)))),implies(X_6809,X_6811))),
inference(resolve,[$cnf( is_a_theorem(implies(or(or(X_6811,X_6811),and(X_4907,or(X_6811,X_6811))),X_6811)) )],[refute_0_1667,refute_0_1668]) ).
cnf(refute_0_1670,plain,
is_a_theorem(implies(implies(X_8388,or(or(X_8389,X_8389),and(X_8387,or(X_8389,X_8389)))),implies(X_8388,X_8389))),
inference(subst,[],[refute_0_1669:[bind(X_4907,$fot(X_8387)),bind(X_6809,$fot(X_8388)),bind(X_6811,$fot(X_8389))]]) ).
cnf(refute_0_1671,plain,
is_a_theorem(implies(X_8388,implies(implies(X_8388,or(or(X_8389,X_8389),and(X_8387,or(X_8389,X_8389)))),X_8389))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_8388,or(or(X_8389,X_8389),and(X_8387,or(X_8389,X_8389)))),implies(X_8388,X_8389))) )],[refute_0_1670,refute_0_1643]) ).
cnf(refute_0_1672,plain,
is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))))),not(X_9)))),
inference(subst,[],[refute_0_1671:[bind(X_8387,$fot(or(X_9,not(not(X_9))))),bind(X_8388,$fot(X_8393)),bind(X_8389,$fot(not(X_9)))]]) ).
cnf(refute_0_1673,plain,
equiv(not(X_9),not(not(X_9))) = and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))),
inference(subst,[],[refute_0_1226:[bind(X_154,$fot(not(X_9)))]]) ).
cnf(refute_0_1674,plain,
( equiv(not(X_9),not(not(X_9))) != and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9)))
| and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))) = equiv(not(X_9),not(not(X_9))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(not(X_9),not(not(X_9))))),bind(Y0,$fot(and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9)))))]]) ).
cnf(refute_0_1675,plain,
and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))) = equiv(not(X_9),not(not(X_9))),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(not(X_9))),and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9)))) )],[refute_0_1673,refute_0_1674]) ).
cnf(refute_0_1676,plain,
( and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))) != equiv(not(X_9),not(not(X_9)))
| ~ is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))))),not(X_9))))
| is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))))),not(X_9)))) ),[0,1,0,1,1],$fot(equiv(not(X_9),not(not(X_9))))]]) ).
cnf(refute_0_1677,plain,
( ~ is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))))),not(X_9))))
| is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)))) ),
inference(resolve,[$cnf( $equal(and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))),equiv(not(X_9),not(not(X_9)))) )],[refute_0_1675,refute_0_1676]) ).
cnf(refute_0_1678,plain,
is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),and(or(X_9,not(not(X_9))),or(not(X_9),not(X_9))))),not(X_9)))) )],[refute_0_1672,refute_0_1677]) ).
cnf(refute_0_1679,plain,
implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) = not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_8393)),bind(X_1833,$fot(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))]]) ).
cnf(refute_0_1680,plain,
not(not(X_9)) = X_9,
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(X_9))]]) ).
cnf(refute_0_1681,plain,
equiv(not(X_9),not(not(X_9))) = equiv(not(X_9),not(not(X_9))),
introduced(tautology,[refl,[$fot(equiv(not(X_9),not(not(X_9))))]]) ).
cnf(refute_0_1682,plain,
( equiv(not(X_9),not(not(X_9))) != equiv(not(X_9),not(not(X_9)))
| not(not(X_9)) != X_9
| equiv(not(X_9),not(not(X_9))) = equiv(not(X_9),X_9) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_9),not(not(X_9))),equiv(not(X_9),not(not(X_9)))) ),[1,1],$fot(X_9)]]) ).
cnf(refute_0_1683,plain,
( not(not(X_9)) != X_9
| equiv(not(X_9),not(not(X_9))) = equiv(not(X_9),X_9) ),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(not(X_9))),equiv(not(X_9),not(not(X_9)))) )],[refute_0_1681,refute_0_1682]) ).
cnf(refute_0_1684,plain,
equiv(not(X_9),not(not(X_9))) = equiv(not(X_9),X_9),
inference(resolve,[$cnf( $equal(not(not(X_9)),X_9) )],[refute_0_1680,refute_0_1683]) ).
cnf(refute_0_1685,plain,
implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))),
introduced(tautology,[refl,[$fot(implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))))]]) ).
cnf(refute_0_1686,plain,
( equiv(not(X_9),not(not(X_9))) != equiv(not(X_9),X_9)
| implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))) != implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9))))
| implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))),implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9))))) ),[1,1],$fot(equiv(not(X_9),X_9))]]) ).
cnf(refute_0_1687,plain,
( equiv(not(X_9),not(not(X_9))) != equiv(not(X_9),X_9)
| implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),X_9)) ),
inference(resolve,[$cnf( $equal(implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))),implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9))))) )],[refute_0_1685,refute_0_1686]) ).
cnf(refute_0_1688,plain,
implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),X_9)),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(not(X_9))),equiv(not(X_9),X_9)) )],[refute_0_1684,refute_0_1687]) ).
cnf(refute_0_1689,plain,
and(not(not(X_9)),X_9) = and(not(not(X_9)),X_9),
introduced(tautology,[refl,[$fot(and(not(not(X_9)),X_9))]]) ).
cnf(refute_0_1690,plain,
( and(not(not(X_9)),X_9) != and(not(not(X_9)),X_9)
| not(not(X_9)) != X_9
| and(not(not(X_9)),X_9) = and(X_9,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X_9)),X_9),and(not(not(X_9)),X_9)) ),[1,0],$fot(X_9)]]) ).
cnf(refute_0_1691,plain,
( not(not(X_9)) != X_9
| and(not(not(X_9)),X_9) = and(X_9,X_9) ),
inference(resolve,[$cnf( $equal(and(not(not(X_9)),X_9),and(not(not(X_9)),X_9)) )],[refute_0_1689,refute_0_1690]) ).
cnf(refute_0_1692,plain,
and(not(not(X_9)),X_9) = and(X_9,X_9),
inference(resolve,[$cnf( $equal(not(not(X_9)),X_9) )],[refute_0_1680,refute_0_1691]) ).
cnf(refute_0_1693,plain,
implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))),
introduced(tautology,[refl,[$fot(implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))))]]) ).
cnf(refute_0_1694,plain,
( and(not(not(X_9)),X_9) != and(X_9,X_9)
| implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) != implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9))))
| implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))),implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9))))) ),[1,0],$fot(and(X_9,X_9))]]) ).
cnf(refute_0_1695,plain,
( and(not(not(X_9)),X_9) != and(X_9,X_9)
| implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))),implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9))))) )],[refute_0_1693,refute_0_1694]) ).
cnf(refute_0_1696,plain,
implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))),
inference(resolve,[$cnf( $equal(and(not(not(X_9)),X_9),and(X_9,X_9)) )],[refute_0_1692,refute_0_1695]) ).
cnf(refute_0_1697,plain,
( implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))) != implies(and(X_9,X_9),equiv(not(X_9),X_9))
| implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) != implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9))))
| implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),X_9)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))))),bind(Y0,$fot(implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))))),bind(Z,$fot(implies(and(X_9,X_9),equiv(not(X_9),X_9))))]]) ).
cnf(refute_0_1698,plain,
( implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))) != implies(and(X_9,X_9),equiv(not(X_9),X_9))
| implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),X_9)) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))),implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9))))) )],[refute_0_1696,refute_0_1697]) ).
cnf(refute_0_1699,plain,
implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),X_9)),
inference(resolve,[$cnf( $equal(implies(and(X_9,X_9),equiv(not(X_9),not(not(X_9)))),implies(and(X_9,X_9),equiv(not(X_9),X_9))) )],[refute_0_1688,refute_0_1698]) ).
cnf(refute_0_1700,plain,
or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))) = implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))),
inference(subst,[],[refute_0_1034:[bind(Y,$fot(equiv(not(X_9),not(not(X_9))))),bind(X_11,$fot(X_9)),bind(X_12,$fot(not(X_9)))]]) ).
cnf(refute_0_1701,plain,
( implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) != implies(and(X_9,X_9),equiv(not(X_9),X_9))
| or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))) != implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9))))
| or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),X_9)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))))),bind(Y0,$fot(implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))))),bind(Z,$fot(implies(and(X_9,X_9),equiv(not(X_9),X_9))))]]) ).
cnf(refute_0_1702,plain,
( implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))) != implies(and(X_9,X_9),equiv(not(X_9),X_9))
| or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),X_9)) ),
inference(resolve,[$cnf( $equal(or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))),implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9))))) )],[refute_0_1700,refute_0_1701]) ).
cnf(refute_0_1703,plain,
or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))) = implies(and(X_9,X_9),equiv(not(X_9),X_9)),
inference(resolve,[$cnf( $equal(implies(and(not(not(X_9)),X_9),equiv(not(X_9),not(not(X_9)))),implies(and(X_9,X_9),equiv(not(X_9),X_9))) )],[refute_0_1699,refute_0_1702]) ).
cnf(refute_0_1704,plain,
implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))) = implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),
introduced(tautology,[refl,[$fot(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))))]]) ).
cnf(refute_0_1705,plain,
( implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))) != implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))))
| or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))) != implies(and(X_9,X_9),equiv(not(X_9),X_9))
| implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))) = implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))))) ),[1,1],$fot(implies(and(X_9,X_9),equiv(not(X_9),X_9)))]]) ).
cnf(refute_0_1706,plain,
( or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))) != implies(and(X_9,X_9),equiv(not(X_9),X_9))
| implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))) = implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) ),
inference(resolve,[$cnf( $equal(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))))) )],[refute_0_1704,refute_0_1705]) ).
cnf(refute_0_1707,plain,
implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))) = implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),
inference(resolve,[$cnf( $equal(or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9)))),implies(and(X_9,X_9),equiv(not(X_9),X_9))) )],[refute_0_1703,refute_0_1706]) ).
cnf(refute_0_1708,plain,
and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9) = and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9),
introduced(tautology,[refl,[$fot(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9))]]) ).
cnf(refute_0_1709,plain,
( and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9) != and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)
| implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))) != implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9)))
| and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9) = and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9),and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)) ),[1,0],$fot(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))))]]) ).
cnf(refute_0_1710,plain,
( implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))) != implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9)))
| and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9) = and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9) ),
inference(resolve,[$cnf( $equal(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9),and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)) )],[refute_0_1708,refute_0_1709]) ).
cnf(refute_0_1711,plain,
and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9) = and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9),
inference(resolve,[$cnf( $equal(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9)))) )],[refute_0_1707,refute_0_1710]) ).
cnf(refute_0_1712,plain,
not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)) = not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)),
introduced(tautology,[refl,[$fot(not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)))]]) ).
cnf(refute_0_1713,plain,
( and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9) != and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)
| not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)) != not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9))
| not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)) = not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)),not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9))) ),[1,0],$fot(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))]]) ).
cnf(refute_0_1714,plain,
( and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9) != and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)
| not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)) = not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)),not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9))) )],[refute_0_1712,refute_0_1713]) ).
cnf(refute_0_1715,plain,
not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)) = not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)),
inference(resolve,[$cnf( $equal(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9),and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) )],[refute_0_1711,refute_0_1714]) ).
cnf(refute_0_1716,plain,
implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)) = not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)),
inference(subst,[],[refute_0_448:[bind(X,$fot(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))))),bind(X_1833,$fot(X_9))]]) ).
cnf(refute_0_1717,plain,
( implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)) != not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9))
| not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)) != not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))
| implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)) = not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)))),bind(Y0,$fot(not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)))),bind(Z,$fot(not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))))]]) ).
cnf(refute_0_1718,plain,
( not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)) != not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))
| implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)) = not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)),not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9))) )],[refute_0_1716,refute_0_1717]) ).
cnf(refute_0_1719,plain,
implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)) = not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)),
inference(resolve,[$cnf( $equal(not(and(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),X_9)),not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) )],[refute_0_1715,refute_0_1718]) ).
cnf(refute_0_1720,plain,
implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) = implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))),
introduced(tautology,[refl,[$fot(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))))]]) ).
cnf(refute_0_1721,plain,
( implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) != implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)))
| implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)) != not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))
| implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) = implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))),implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)))) ),[1,1],$fot(not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))]]) ).
cnf(refute_0_1722,plain,
( implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)) != not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))
| implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) = implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) ),
inference(resolve,[$cnf( $equal(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))),implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)))) )],[refute_0_1720,refute_0_1721]) ).
cnf(refute_0_1723,plain,
implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) = implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))),
inference(resolve,[$cnf( $equal(implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)),not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) )],[refute_0_1719,refute_0_1722]) ).
cnf(refute_0_1724,plain,
( implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) != implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))
| implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) != not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))
| implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) = not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))))),bind(Y0,$fot(implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))))),bind(Z,$fot(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))))]]) ).
cnf(refute_0_1725,plain,
( implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) != not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))
| implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) = not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) ),
inference(resolve,[$cnf( $equal(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))),implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))) )],[refute_0_1723,refute_0_1724]) ).
cnf(refute_0_1726,plain,
implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) = not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))),
inference(resolve,[$cnf( $equal(implies(X_8393,not(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))),not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))) )],[refute_0_1679,refute_0_1725]) ).
cnf(refute_0_1727,plain,
( implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))) != not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))
| ~ is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))))
| is_a_theorem(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)))) ),[0],$fot(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))))]]) ).
cnf(refute_0_1728,plain,
( ~ is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))))
| is_a_theorem(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))) ),
inference(resolve,[$cnf( $equal(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9))),not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))) )],[refute_0_1726,refute_0_1727]) ).
cnf(refute_0_1729,plain,
is_a_theorem(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_8393,implies(implies(X_8393,or(or(not(X_9),not(X_9)),equiv(not(X_9),not(not(X_9))))),not(X_9)))) )],[refute_0_1678,refute_0_1728]) ).
cnf(refute_0_1730,plain,
( implies(X,or(X_12,not(X_11))) != not(and(X,and(not(X_12),X_11)))
| not(and(X,and(not(X_12),X_11))) = implies(X,or(X_12,not(X_11))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,or(X_12,not(X_11))))),bind(Y0,$fot(not(and(X,and(not(X_12),X_11)))))]]) ).
cnf(refute_0_1731,plain,
not(and(X,and(not(X_12),X_11))) = implies(X,or(X_12,not(X_11))),
inference(resolve,[$cnf( $equal(implies(X,or(X_12,not(X_11))),not(and(X,and(not(X_12),X_11)))) )],[refute_0_958,refute_0_1730]) ).
cnf(refute_0_1732,plain,
not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))) = implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9))),
inference(subst,[],[refute_0_1731:[bind(X,$fot(X_8393)),bind(X_11,$fot(X_9)),bind(X_12,$fot(and(X_8393,and(X_9,equiv(X_9,X_9)))))]]) ).
cnf(refute_0_1733,plain,
implies(X_8393,not(and(X_9,equiv(X_9,X_9)))) = not(and(X_8393,and(X_9,equiv(X_9,X_9)))),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_8393)),bind(X_1833,$fot(and(X_9,equiv(X_9,X_9))))]]) ).
cnf(refute_0_1734,plain,
implies(X_9,not(equiv(X_9,X_9))) = not(and(X_9,equiv(X_9,X_9))),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_9)),bind(X_1833,$fot(equiv(X_9,X_9)))]]) ).
cnf(refute_0_1735,plain,
equiv(not(X_9),X_9) = not(equiv(X_9,X_9)),
inference(subst,[],[refute_0_1375:[bind(X_1832,$fot(X_9))]]) ).
cnf(refute_0_1736,plain,
implies(X_9,equiv(not(X_9),X_9)) = implies(X_9,equiv(not(X_9),X_9)),
introduced(tautology,[refl,[$fot(implies(X_9,equiv(not(X_9),X_9)))]]) ).
cnf(refute_0_1737,plain,
( equiv(not(X_9),X_9) != not(equiv(X_9,X_9))
| implies(X_9,equiv(not(X_9),X_9)) != implies(X_9,equiv(not(X_9),X_9))
| implies(X_9,equiv(not(X_9),X_9)) = implies(X_9,not(equiv(X_9,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_9,equiv(not(X_9),X_9)),implies(X_9,equiv(not(X_9),X_9))) ),[1,1],$fot(not(equiv(X_9,X_9)))]]) ).
cnf(refute_0_1738,plain,
( equiv(not(X_9),X_9) != not(equiv(X_9,X_9))
| implies(X_9,equiv(not(X_9),X_9)) = implies(X_9,not(equiv(X_9,X_9))) ),
inference(resolve,[$cnf( $equal(implies(X_9,equiv(not(X_9),X_9)),implies(X_9,equiv(not(X_9),X_9))) )],[refute_0_1736,refute_0_1737]) ).
cnf(refute_0_1739,plain,
implies(X_9,equiv(not(X_9),X_9)) = implies(X_9,not(equiv(X_9,X_9))),
inference(resolve,[$cnf( $equal(equiv(not(X_9),X_9),not(equiv(X_9,X_9))) )],[refute_0_1735,refute_0_1738]) ).
cnf(refute_0_1740,plain,
and(X_9,X_9) = X_9,
inference(subst,[],[refute_0_649:[bind(Y,$fot(X_9))]]) ).
cnf(refute_0_1741,plain,
implies(and(X_9,X_9),equiv(not(X_9),X_9)) = implies(and(X_9,X_9),equiv(not(X_9),X_9)),
introduced(tautology,[refl,[$fot(implies(and(X_9,X_9),equiv(not(X_9),X_9)))]]) ).
cnf(refute_0_1742,plain,
( and(X_9,X_9) != X_9
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) != implies(and(X_9,X_9),equiv(not(X_9),X_9))
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) = implies(X_9,equiv(not(X_9),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(X_9,X_9),equiv(not(X_9),X_9)),implies(and(X_9,X_9),equiv(not(X_9),X_9))) ),[1,0],$fot(X_9)]]) ).
cnf(refute_0_1743,plain,
( and(X_9,X_9) != X_9
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) = implies(X_9,equiv(not(X_9),X_9)) ),
inference(resolve,[$cnf( $equal(implies(and(X_9,X_9),equiv(not(X_9),X_9)),implies(and(X_9,X_9),equiv(not(X_9),X_9))) )],[refute_0_1741,refute_0_1742]) ).
cnf(refute_0_1744,plain,
implies(and(X_9,X_9),equiv(not(X_9),X_9)) = implies(X_9,equiv(not(X_9),X_9)),
inference(resolve,[$cnf( $equal(and(X_9,X_9),X_9) )],[refute_0_1740,refute_0_1743]) ).
cnf(refute_0_1745,plain,
( implies(X_9,equiv(not(X_9),X_9)) != implies(X_9,not(equiv(X_9,X_9)))
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) != implies(X_9,equiv(not(X_9),X_9))
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) = implies(X_9,not(equiv(X_9,X_9))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(and(X_9,X_9),equiv(not(X_9),X_9)))),bind(Y0,$fot(implies(X_9,equiv(not(X_9),X_9)))),bind(Z,$fot(implies(X_9,not(equiv(X_9,X_9)))))]]) ).
cnf(refute_0_1746,plain,
( implies(X_9,equiv(not(X_9),X_9)) != implies(X_9,not(equiv(X_9,X_9)))
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) = implies(X_9,not(equiv(X_9,X_9))) ),
inference(resolve,[$cnf( $equal(implies(and(X_9,X_9),equiv(not(X_9),X_9)),implies(X_9,equiv(not(X_9),X_9))) )],[refute_0_1744,refute_0_1745]) ).
cnf(refute_0_1747,plain,
implies(and(X_9,X_9),equiv(not(X_9),X_9)) = implies(X_9,not(equiv(X_9,X_9))),
inference(resolve,[$cnf( $equal(implies(X_9,equiv(not(X_9),X_9)),implies(X_9,not(equiv(X_9,X_9)))) )],[refute_0_1739,refute_0_1746]) ).
cnf(refute_0_1748,plain,
( implies(X_9,not(equiv(X_9,X_9))) != not(and(X_9,equiv(X_9,X_9)))
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) != implies(X_9,not(equiv(X_9,X_9)))
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) = not(and(X_9,equiv(X_9,X_9))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(and(X_9,X_9),equiv(not(X_9),X_9)))),bind(Y0,$fot(implies(X_9,not(equiv(X_9,X_9))))),bind(Z,$fot(not(and(X_9,equiv(X_9,X_9)))))]]) ).
cnf(refute_0_1749,plain,
( implies(X_9,not(equiv(X_9,X_9))) != not(and(X_9,equiv(X_9,X_9)))
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) = not(and(X_9,equiv(X_9,X_9))) ),
inference(resolve,[$cnf( $equal(implies(and(X_9,X_9),equiv(not(X_9),X_9)),implies(X_9,not(equiv(X_9,X_9)))) )],[refute_0_1747,refute_0_1748]) ).
cnf(refute_0_1750,plain,
implies(and(X_9,X_9),equiv(not(X_9),X_9)) = not(and(X_9,equiv(X_9,X_9))),
inference(resolve,[$cnf( $equal(implies(X_9,not(equiv(X_9,X_9))),not(and(X_9,equiv(X_9,X_9)))) )],[refute_0_1734,refute_0_1749]) ).
cnf(refute_0_1751,plain,
implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) = implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),
introduced(tautology,[refl,[$fot(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))))]]) ).
cnf(refute_0_1752,plain,
( implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) != implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9)))
| implies(and(X_9,X_9),equiv(not(X_9),X_9)) != not(and(X_9,equiv(X_9,X_9)))
| implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) = implies(X_8393,not(and(X_9,equiv(X_9,X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9)))) ),[1,1],$fot(not(and(X_9,equiv(X_9,X_9))))]]) ).
cnf(refute_0_1753,plain,
( implies(and(X_9,X_9),equiv(not(X_9),X_9)) != not(and(X_9,equiv(X_9,X_9)))
| implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) = implies(X_8393,not(and(X_9,equiv(X_9,X_9)))) ),
inference(resolve,[$cnf( $equal(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9)))) )],[refute_0_1751,refute_0_1752]) ).
cnf(refute_0_1754,plain,
implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) = implies(X_8393,not(and(X_9,equiv(X_9,X_9)))),
inference(resolve,[$cnf( $equal(implies(and(X_9,X_9),equiv(not(X_9),X_9)),not(and(X_9,equiv(X_9,X_9)))) )],[refute_0_1750,refute_0_1753]) ).
cnf(refute_0_1755,plain,
( implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) != implies(X_8393,not(and(X_9,equiv(X_9,X_9))))
| implies(X_8393,not(and(X_9,equiv(X_9,X_9)))) != not(and(X_8393,and(X_9,equiv(X_9,X_9))))
| implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) = not(and(X_8393,and(X_9,equiv(X_9,X_9)))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))))),bind(Y0,$fot(implies(X_8393,not(and(X_9,equiv(X_9,X_9)))))),bind(Z,$fot(not(and(X_8393,and(X_9,equiv(X_9,X_9))))))]]) ).
cnf(refute_0_1756,plain,
( implies(X_8393,not(and(X_9,equiv(X_9,X_9)))) != not(and(X_8393,and(X_9,equiv(X_9,X_9))))
| implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) = not(and(X_8393,and(X_9,equiv(X_9,X_9)))) ),
inference(resolve,[$cnf( $equal(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),implies(X_8393,not(and(X_9,equiv(X_9,X_9))))) )],[refute_0_1754,refute_0_1755]) ).
cnf(refute_0_1757,plain,
implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) = not(and(X_8393,and(X_9,equiv(X_9,X_9)))),
inference(resolve,[$cnf( $equal(implies(X_8393,not(and(X_9,equiv(X_9,X_9)))),not(and(X_8393,and(X_9,equiv(X_9,X_9))))) )],[refute_0_1733,refute_0_1756]) ).
cnf(refute_0_1758,plain,
and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9) = and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9),
introduced(tautology,[refl,[$fot(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))]]) ).
cnf(refute_0_1759,plain,
( and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9) != and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)
| implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) != not(and(X_8393,and(X_9,equiv(X_9,X_9))))
| and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9) = and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9),and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) ),[1,0],$fot(not(and(X_8393,and(X_9,equiv(X_9,X_9)))))]]) ).
cnf(refute_0_1760,plain,
( implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))) != not(and(X_8393,and(X_9,equiv(X_9,X_9))))
| and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9) = and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9) ),
inference(resolve,[$cnf( $equal(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9),and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) )],[refute_0_1758,refute_0_1759]) ).
cnf(refute_0_1761,plain,
and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9) = and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9),
inference(resolve,[$cnf( $equal(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),not(and(X_8393,and(X_9,equiv(X_9,X_9))))) )],[refute_0_1757,refute_0_1760]) ).
cnf(refute_0_1762,plain,
and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) = and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)),
introduced(tautology,[refl,[$fot(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))]]) ).
cnf(refute_0_1763,plain,
( and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) != and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))
| and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9) != and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9)
| and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) = and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)),and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) ),[1,1],$fot(and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))]]) ).
cnf(refute_0_1764,plain,
( and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9) != and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9)
| and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) = and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9)) ),
inference(resolve,[$cnf( $equal(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)),and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) )],[refute_0_1762,refute_0_1763]) ).
cnf(refute_0_1765,plain,
and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) = and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9)),
inference(resolve,[$cnf( $equal(and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9),and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9)) )],[refute_0_1761,refute_0_1764]) ).
cnf(refute_0_1766,plain,
not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) = not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))),
introduced(tautology,[refl,[$fot(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))))]]) ).
cnf(refute_0_1767,plain,
( and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) != and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))
| not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) != not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))
| not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) = not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))),not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))) ),[1,0],$fot(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9)))]]) ).
cnf(refute_0_1768,plain,
( and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)) != and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))
| not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) = not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))) ),
inference(resolve,[$cnf( $equal(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))),not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))) )],[refute_0_1766,refute_0_1767]) ).
cnf(refute_0_1769,plain,
not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) = not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))),
inference(resolve,[$cnf( $equal(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)),and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))) )],[refute_0_1765,refute_0_1768]) ).
cnf(refute_0_1770,plain,
( not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) != not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9)))
| not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))) != implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9)))
| not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) = implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))))),bind(Y0,$fot(not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))))),bind(Z,$fot(implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9)))))]]) ).
cnf(refute_0_1771,plain,
( not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))) != implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9)))
| not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) = implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9))) ),
inference(resolve,[$cnf( $equal(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))),not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9)))) )],[refute_0_1769,refute_0_1770]) ).
cnf(refute_0_1772,plain,
not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) = implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9))),
inference(resolve,[$cnf( $equal(not(and(X_8393,and(not(and(X_8393,and(X_9,equiv(X_9,X_9)))),X_9))),implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9)))) )],[refute_0_1732,refute_0_1771]) ).
cnf(refute_0_1773,plain,
( not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))) != implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9)))
| ~ is_a_theorem(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))))
| is_a_theorem(implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))) ),[0],$fot(implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9))))]]) ).
cnf(refute_0_1774,plain,
( ~ is_a_theorem(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))))
| is_a_theorem(implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9)))) ),
inference(resolve,[$cnf( $equal(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9))),implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9)))) )],[refute_0_1772,refute_0_1773]) ).
cnf(refute_0_1775,plain,
is_a_theorem(implies(X_8393,or(and(X_8393,and(X_9,equiv(X_9,X_9))),not(X_9)))),
inference(resolve,[$cnf( is_a_theorem(not(and(X_8393,and(implies(X_8393,implies(and(X_9,X_9),equiv(not(X_9),X_9))),X_9)))) )],[refute_0_1729,refute_0_1774]) ).
cnf(refute_0_1776,plain,
is_a_theorem(implies(X_25598,or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)))),
inference(subst,[],[refute_0_1775:[bind(X_8393,$fot(X_25598)),bind(X_9,$fot(X_25599))]]) ).
cnf(refute_0_1777,plain,
is_a_theorem(or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598))),
inference(resolve,[$cnf( is_a_theorem(implies(X_25598,or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)))) )],[refute_0_1776,refute_0_1642]) ).
cnf(refute_0_1778,plain,
implies(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),not(X_25598)) = not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598)),
inference(subst,[],[refute_0_448:[bind(X,$fot(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599))),bind(X_1833,$fot(X_25598))]]) ).
cnf(refute_0_1779,plain,
or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)) = implies(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),not(X_25598)),
inference(subst,[],[refute_0_1034:[bind(Y,$fot(not(X_25598))),bind(X_11,$fot(X_25599)),bind(X_12,$fot(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))))]]) ).
cnf(refute_0_1780,plain,
( implies(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),not(X_25598)) != not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))
| or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)) != implies(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),not(X_25598))
| or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)) = not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)))),bind(Y0,$fot(implies(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),not(X_25598)))),bind(Z,$fot(not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))))]]) ).
cnf(refute_0_1781,plain,
( implies(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),not(X_25598)) != not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))
| or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)) = not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598)) ),
inference(resolve,[$cnf( $equal(or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)),implies(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),not(X_25598))) )],[refute_0_1779,refute_0_1780]) ).
cnf(refute_0_1782,plain,
or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)) = not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598)),
inference(resolve,[$cnf( $equal(implies(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),not(X_25598)),not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))) )],[refute_0_1778,refute_0_1781]) ).
cnf(refute_0_1783,plain,
( or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)) != not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))
| ~ is_a_theorem(or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)))
| is_a_theorem(not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598))) ),[0],$fot(not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598)))]]) ).
cnf(refute_0_1784,plain,
( ~ is_a_theorem(or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)))
| is_a_theorem(not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))) ),
inference(resolve,[$cnf( $equal(or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598)),not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))) )],[refute_0_1782,refute_0_1783]) ).
cnf(refute_0_1785,plain,
is_a_theorem(not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))),
inference(resolve,[$cnf( is_a_theorem(or(or(and(X_25598,and(X_25599,equiv(X_25599,X_25599))),not(X_25599)),not(X_25598))) )],[refute_0_1777,refute_0_1784]) ).
cnf(refute_0_1786,plain,
is_a_theorem(or(X_2798,not(and(implies(X_17,X_2798),X_17)))),
inference(subst,[],[refute_0_692:[bind(X_1814,$fot(X_2798))]]) ).
cnf(refute_0_1787,plain,
( ~ is_a_theorem(implies(not(X),X_371))
| ~ is_a_theorem(not(X))
| is_a_theorem(X_371) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(not(X))),bind(Y,$fot(X_371))]]) ).
cnf(refute_0_1788,plain,
or(X,X_371) = implies(not(X),X_371),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_371))]]) ).
cnf(refute_0_1789,plain,
( or(X,X_371) != implies(not(X),X_371)
| implies(not(X),X_371) = or(X,X_371) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,X_371))),bind(Y0,$fot(implies(not(X),X_371)))]]) ).
cnf(refute_0_1790,plain,
implies(not(X),X_371) = or(X,X_371),
inference(resolve,[$cnf( $equal(or(X,X_371),implies(not(X),X_371)) )],[refute_0_1788,refute_0_1789]) ).
cnf(refute_0_1791,plain,
( implies(not(X),X_371) != or(X,X_371)
| ~ is_a_theorem(or(X,X_371))
| is_a_theorem(implies(not(X),X_371)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(not(X),X_371)) ),[0],$fot(or(X,X_371))]]) ).
cnf(refute_0_1792,plain,
( ~ is_a_theorem(or(X,X_371))
| is_a_theorem(implies(not(X),X_371)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_371),or(X,X_371)) )],[refute_0_1790,refute_0_1791]) ).
cnf(refute_0_1793,plain,
( ~ is_a_theorem(not(X))
| ~ is_a_theorem(or(X,X_371))
| is_a_theorem(X_371) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),X_371)) )],[refute_0_1792,refute_0_1787]) ).
cnf(refute_0_1794,plain,
( ~ is_a_theorem(not(X_2798))
| ~ is_a_theorem(or(X_2798,not(and(implies(X_17,X_2798),X_17))))
| is_a_theorem(not(and(implies(X_17,X_2798),X_17))) ),
inference(subst,[],[refute_0_1793:[bind(X,$fot(X_2798)),bind(X_371,$fot(not(and(implies(X_17,X_2798),X_17))))]]) ).
cnf(refute_0_1795,plain,
( ~ is_a_theorem(not(X_2798))
| is_a_theorem(not(and(implies(X_17,X_2798),X_17))) ),
inference(resolve,[$cnf( is_a_theorem(or(X_2798,not(and(implies(X_17,X_2798),X_17)))) )],[refute_0_1786,refute_0_1794]) ).
cnf(refute_0_1796,plain,
( ~ is_a_theorem(not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598)))
| is_a_theorem(not(and(implies(X_47151,and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598)),X_47151))) ),
inference(subst,[],[refute_0_1795:[bind(X_17,$fot(X_47151)),bind(X_2798,$fot(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598)))]]) ).
cnf(refute_0_1797,plain,
is_a_theorem(not(and(implies(X_47151,and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598)),X_47151))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(not(and(X_25598,and(X_25599,equiv(X_25599,X_25599)))),X_25599),X_25598))) )],[refute_0_1785,refute_0_1796]) ).
cnf(refute_0_1798,plain,
is_a_theorem(not(and(implies(X_47403,and(and(not(and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402)))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))),
inference(subst,[],[refute_0_1797:[bind(X_25598,$fot(not(and(X_47402,equiv(X_47402,X_47402))))),bind(X_25599,$fot(X_47402)),bind(X_47151,$fot(X_47403))]]) ).
cnf(refute_0_1799,plain,
not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))) = and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402))),
inference(subst,[],[refute_0_1504:[bind(X_27252,$fot(and(X_47402,equiv(X_47402,X_47402))))]]) ).
cnf(refute_0_1800,plain,
( not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))) != and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402)))
| and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402))) = not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))))),bind(Y0,$fot(and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402)))))]]) ).
cnf(refute_0_1801,plain,
and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402))) = not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))),
inference(resolve,[$cnf( $equal(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))),and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402)))) )],[refute_0_1799,refute_0_1800]) ).
cnf(refute_0_1802,plain,
( and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402))) != not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))
| ~ is_a_theorem(not(and(implies(X_47403,and(and(not(and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402)))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)))
| is_a_theorem(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(implies(X_47403,and(and(not(and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402)))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))) ),[0,0,0,1,0,0,0],$fot(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))))]]) ).
cnf(refute_0_1803,plain,
( ~ is_a_theorem(not(and(implies(X_47403,and(and(not(and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402)))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)))
| is_a_theorem(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))) ),
inference(resolve,[$cnf( $equal(and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402))),not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))) )],[refute_0_1801,refute_0_1802]) ).
cnf(refute_0_1804,plain,
is_a_theorem(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(X_47403,and(and(not(and(not(and(X_47402,equiv(X_47402,X_47402))),and(X_47402,equiv(X_47402,X_47402)))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))) )],[refute_0_1798,refute_0_1803]) ).
cnf(refute_0_1805,plain,
not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)) = or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403)),
inference(subst,[],[refute_0_458:[bind(Y,$fot(X_47403)),bind(X_9,$fot(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))))]]) ).
cnf(refute_0_1806,plain,
implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))) = not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_47403)),bind(X_1833,$fot(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))]]) ).
cnf(refute_0_1807,plain,
and(equiv(X_31856,X_31856),X_31855) = not(not(and(equiv(X_31856,X_31856),X_31855))),
inference(subst,[],[refute_0_442:[bind(X_1832,$fot(and(equiv(X_31856,X_31856),X_31855)))]]) ).
cnf(refute_0_1808,plain,
implies(equiv(X_31832,X_31832),not(X_1833)) = not(and(equiv(X_31832,X_31832),X_1833)),
inference(subst,[],[refute_0_448:[bind(X,$fot(equiv(X_31832,X_31832)))]]) ).
cnf(refute_0_1809,plain,
implies(equiv(X_31832,X_31832),not(X_1833)) = not(X_1833),
inference(subst,[],[refute_0_1599:[bind(X_31830,$fot(X_31832)),bind(X_31831,$fot(not(X_1833)))]]) ).
cnf(refute_0_1810,plain,
( implies(equiv(X_31832,X_31832),not(X_1833)) != not(X_1833)
| implies(equiv(X_31832,X_31832),not(X_1833)) != not(and(equiv(X_31832,X_31832),X_1833))
| not(X_1833) = not(and(equiv(X_31832,X_31832),X_1833)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(equiv(X_31832,X_31832),not(X_1833)),not(and(equiv(X_31832,X_31832),X_1833))) ),[0],$fot(not(X_1833))]]) ).
cnf(refute_0_1811,plain,
( implies(equiv(X_31832,X_31832),not(X_1833)) != not(and(equiv(X_31832,X_31832),X_1833))
| not(X_1833) = not(and(equiv(X_31832,X_31832),X_1833)) ),
inference(resolve,[$cnf( $equal(implies(equiv(X_31832,X_31832),not(X_1833)),not(X_1833)) )],[refute_0_1809,refute_0_1810]) ).
cnf(refute_0_1812,plain,
not(X_1833) = not(and(equiv(X_31832,X_31832),X_1833)),
inference(resolve,[$cnf( $equal(implies(equiv(X_31832,X_31832),not(X_1833)),not(and(equiv(X_31832,X_31832),X_1833))) )],[refute_0_1808,refute_0_1811]) ).
cnf(refute_0_1813,plain,
not(X_31855) = not(and(equiv(X_31856,X_31856),X_31855)),
inference(subst,[],[refute_0_1812:[bind(X_1833,$fot(X_31855)),bind(X_31832,$fot(X_31856))]]) ).
cnf(refute_0_1814,plain,
( not(X_31855) != not(and(equiv(X_31856,X_31856),X_31855))
| not(and(equiv(X_31856,X_31856),X_31855)) = not(X_31855) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(not(X_31855))),bind(Y0,$fot(not(and(equiv(X_31856,X_31856),X_31855))))]]) ).
cnf(refute_0_1815,plain,
not(and(equiv(X_31856,X_31856),X_31855)) = not(X_31855),
inference(resolve,[$cnf( $equal(not(X_31855),not(and(equiv(X_31856,X_31856),X_31855))) )],[refute_0_1813,refute_0_1814]) ).
cnf(refute_0_1816,plain,
( and(equiv(X_31856,X_31856),X_31855) != not(not(and(equiv(X_31856,X_31856),X_31855)))
| not(and(equiv(X_31856,X_31856),X_31855)) != not(X_31855)
| and(equiv(X_31856,X_31856),X_31855) = not(not(X_31855)) ),
introduced(tautology,[equality,[$cnf( $equal(and(equiv(X_31856,X_31856),X_31855),not(not(and(equiv(X_31856,X_31856),X_31855)))) ),[1,0],$fot(not(X_31855))]]) ).
cnf(refute_0_1817,plain,
( and(equiv(X_31856,X_31856),X_31855) != not(not(and(equiv(X_31856,X_31856),X_31855)))
| and(equiv(X_31856,X_31856),X_31855) = not(not(X_31855)) ),
inference(resolve,[$cnf( $equal(not(and(equiv(X_31856,X_31856),X_31855)),not(X_31855)) )],[refute_0_1815,refute_0_1816]) ).
cnf(refute_0_1818,plain,
and(equiv(X_31856,X_31856),X_31855) = not(not(X_31855)),
inference(resolve,[$cnf( $equal(and(equiv(X_31856,X_31856),X_31855),not(not(and(equiv(X_31856,X_31856),X_31855)))) )],[refute_0_1807,refute_0_1817]) ).
cnf(refute_0_1819,plain,
not(not(X_31855)) = X_31855,
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(X_31855))]]) ).
cnf(refute_0_1820,plain,
( and(equiv(X_31856,X_31856),X_31855) != not(not(X_31855))
| not(not(X_31855)) != X_31855
| and(equiv(X_31856,X_31856),X_31855) = X_31855 ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(equiv(X_31856,X_31856),X_31855),X_31855) ),[0],$fot(not(not(X_31855)))]]) ).
cnf(refute_0_1821,plain,
( and(equiv(X_31856,X_31856),X_31855) != not(not(X_31855))
| and(equiv(X_31856,X_31856),X_31855) = X_31855 ),
inference(resolve,[$cnf( $equal(not(not(X_31855)),X_31855) )],[refute_0_1819,refute_0_1820]) ).
cnf(refute_0_1822,plain,
and(equiv(X_31856,X_31856),X_31855) = X_31855,
inference(resolve,[$cnf( $equal(and(equiv(X_31856,X_31856),X_31855),not(not(X_31855))) )],[refute_0_1818,refute_0_1821]) ).
cnf(refute_0_1823,plain,
and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402) = X_47402,
inference(subst,[],[refute_0_1822:[bind(X_31855,$fot(X_47402)),bind(X_31856,$fot(and(X_47402,equiv(X_47402,X_47402))))]]) ).
cnf(refute_0_1824,plain,
not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))) = equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))))]]) ).
cnf(refute_0_1825,plain,
and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) = and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),
introduced(tautology,[refl,[$fot(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402))]]) ).
cnf(refute_0_1826,plain,
( and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) != and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402)
| not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))) != equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))
| and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) = and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402)) ),[1,0],$fot(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))]]) ).
cnf(refute_0_1827,plain,
( not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))) != equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))
| and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) = and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402) ),
inference(resolve,[$cnf( $equal(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402)) )],[refute_0_1825,refute_0_1826]) ).
cnf(refute_0_1828,plain,
and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) = and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402),
inference(resolve,[$cnf( $equal(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402)))) )],[refute_0_1824,refute_0_1827]) ).
cnf(refute_0_1829,plain,
( and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402) != X_47402
| and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) != and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402)
| and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) = X_47402 ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402))),bind(Y0,$fot(and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402))),bind(Z,$fot(X_47402))]]) ).
cnf(refute_0_1830,plain,
( and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402) != X_47402
| and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) = X_47402 ),
inference(resolve,[$cnf( $equal(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402)) )],[refute_0_1828,refute_0_1829]) ).
cnf(refute_0_1831,plain,
and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) = X_47402,
inference(resolve,[$cnf( $equal(and(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))),X_47402),X_47402) )],[refute_0_1823,refute_0_1830]) ).
cnf(refute_0_1832,plain,
implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))) = implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))),
introduced(tautology,[refl,[$fot(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))))]]) ).
cnf(refute_0_1833,plain,
( and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) != X_47402
| implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))) != implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))
| implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))) = implies(X_47402,and(X_47402,equiv(X_47402,X_47402))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))),implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))) ),[1,0],$fot(X_47402)]]) ).
cnf(refute_0_1834,plain,
( and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402) != X_47402
| implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))) = implies(X_47402,and(X_47402,equiv(X_47402,X_47402))) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))),implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))) )],[refute_0_1832,refute_0_1833]) ).
cnf(refute_0_1835,plain,
implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))) = implies(X_47402,and(X_47402,equiv(X_47402,X_47402))),
inference(resolve,[$cnf( $equal(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),X_47402) )],[refute_0_1831,refute_0_1834]) ).
cnf(refute_0_1836,plain,
not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))) = not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))),
introduced(tautology,[refl,[$fot(not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))))]]) ).
cnf(refute_0_1837,plain,
( implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))) != implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))
| not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))) != not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))))
| not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))) = not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))),not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))))) ),[1,0],$fot(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))]]) ).
cnf(refute_0_1838,plain,
( implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))) != implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))
| not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))) = not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))) ),
inference(resolve,[$cnf( $equal(not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))),not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))))) )],[refute_0_1836,refute_0_1837]) ).
cnf(refute_0_1839,plain,
not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))) = not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),
inference(resolve,[$cnf( $equal(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))),implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))) )],[refute_0_1835,refute_0_1838]) ).
cnf(refute_0_1840,plain,
and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))) = not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))),
inference(subst,[],[refute_0_567:[bind(X,$fot(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402))),bind(X_1833,$fot(and(X_47402,equiv(X_47402,X_47402))))]]) ).
cnf(refute_0_1841,plain,
( and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))) != not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))))
| not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))) != not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))
| and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))) = not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))))),bind(Y0,$fot(not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))))),bind(Z,$fot(not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))))]]) ).
cnf(refute_0_1842,plain,
( not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))) != not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))
| and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))) = not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))) ),
inference(resolve,[$cnf( $equal(and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))),not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402))))) )],[refute_0_1840,refute_0_1841]) ).
cnf(refute_0_1843,plain,
and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))) = not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),
inference(resolve,[$cnf( $equal(not(implies(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),and(X_47402,equiv(X_47402,X_47402)))),not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))) )],[refute_0_1839,refute_0_1842]) ).
cnf(refute_0_1844,plain,
implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) = implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),
introduced(tautology,[refl,[$fot(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))))]]) ).
cnf(refute_0_1845,plain,
( and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))) != not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))
| implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) != implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))))
| implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) = implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))))) ),[1,1],$fot(not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))]]) ).
cnf(refute_0_1846,plain,
( and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))) != not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))
| implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) = implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))) ),
inference(resolve,[$cnf( $equal(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))))) )],[refute_0_1844,refute_0_1845]) ).
cnf(refute_0_1847,plain,
implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) = implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),
inference(resolve,[$cnf( $equal(and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402)))),not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))) )],[refute_0_1843,refute_0_1846]) ).
cnf(refute_0_1848,plain,
( implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) != implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))
| implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))) != not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))
| implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) = not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))))),bind(Y0,$fot(implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))))),bind(Z,$fot(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))))]]) ).
cnf(refute_0_1849,plain,
( implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))) != not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))
| implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) = not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))) ),
inference(resolve,[$cnf( $equal(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))) )],[refute_0_1847,refute_0_1848]) ).
cnf(refute_0_1850,plain,
implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) = not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),
inference(resolve,[$cnf( $equal(implies(X_47403,not(implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))) )],[refute_0_1806,refute_0_1849]) ).
cnf(refute_0_1851,plain,
and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403) = and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403),
introduced(tautology,[refl,[$fot(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))]]) ).
cnf(refute_0_1852,plain,
( and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403) != and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)
| implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) != not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))
| and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403) = and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403),and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) ),[1,0],$fot(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))))]]) ).
cnf(refute_0_1853,plain,
( implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))) != not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))
| and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403) = and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403) ),
inference(resolve,[$cnf( $equal(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403),and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) )],[refute_0_1851,refute_0_1852]) ).
cnf(refute_0_1854,plain,
and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403) = and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403),
inference(resolve,[$cnf( $equal(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))))) )],[refute_0_1850,refute_0_1853]) ).
cnf(refute_0_1855,plain,
not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) = not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)),
introduced(tautology,[refl,[$fot(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)))]]) ).
cnf(refute_0_1856,plain,
( and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403) != and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)
| not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) != not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))
| not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) = not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)),not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))) ),[1,0],$fot(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403))]]) ).
cnf(refute_0_1857,plain,
( and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403) != and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)
| not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) = not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)),not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))) )],[refute_0_1855,refute_0_1856]) ).
cnf(refute_0_1858,plain,
not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) = not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)),
inference(resolve,[$cnf( $equal(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403),and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)) )],[refute_0_1854,refute_0_1857]) ).
cnf(refute_0_1859,plain,
( not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) != not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403))
| not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)) != or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403))
| not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) = or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)))),bind(Y0,$fot(not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)))),bind(Z,$fot(or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403))))]]) ).
cnf(refute_0_1860,plain,
( not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)) != or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403))
| not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) = or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)),not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403))) )],[refute_0_1858,refute_0_1859]) ).
cnf(refute_0_1861,plain,
not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) = or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403)),
inference(resolve,[$cnf( $equal(not(and(not(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402))))),X_47403)),or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403))) )],[refute_0_1805,refute_0_1860]) ).
cnf(refute_0_1862,plain,
( not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)) != or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403))
| ~ is_a_theorem(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)))
| is_a_theorem(or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))) ),[0],$fot(or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403)))]]) ).
cnf(refute_0_1863,plain,
( ~ is_a_theorem(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)))
| is_a_theorem(or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403))) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403)),or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403))) )],[refute_0_1861,refute_0_1862]) ).
cnf(refute_0_1864,plain,
is_a_theorem(or(and(X_47403,implies(X_47402,and(X_47402,equiv(X_47402,X_47402)))),not(X_47403))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(X_47403,and(and(not(not(equiv(and(X_47402,equiv(X_47402,X_47402)),and(X_47402,equiv(X_47402,X_47402))))),X_47402),not(and(X_47402,equiv(X_47402,X_47402))))),X_47403))) )],[refute_0_1804,refute_0_1863]) ).
cnf(refute_0_1865,plain,
is_a_theorem(or(and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))),not(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404)))),
inference(subst,[],[refute_0_1864:[bind(X_47402,$fot(X_47404)),bind(X_47403,$fot(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404)))]]) ).
cnf(refute_0_1866,plain,
equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404) = and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))),
inference(subst,[],[refute_0_71:[bind(X,$fot(and(X_47404,equiv(X_47404,X_47404)))),bind(Y,$fot(X_47404))]]) ).
cnf(refute_0_1867,plain,
( equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404) != and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404))))
| and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))) = equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404))),bind(Y0,$fot(and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404))))))]]) ).
cnf(refute_0_1868,plain,
and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))) = equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404),
inference(resolve,[$cnf( $equal(equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404),and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404))))) )],[refute_0_1866,refute_0_1867]) ).
cnf(refute_0_1869,plain,
( and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))) != equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404)
| ~ is_a_theorem(or(and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))),not(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404))))
| is_a_theorem(or(equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404),not(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))),not(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404)))) ),[0,0],$fot(equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404))]]) ).
cnf(refute_0_1870,plain,
( ~ is_a_theorem(or(and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))),not(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404))))
| is_a_theorem(or(equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404),not(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404)))) ),
inference(resolve,[$cnf( $equal(and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))),equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404)) )],[refute_0_1868,refute_0_1869]) ).
cnf(refute_0_1871,plain,
is_a_theorem(or(equiv(and(X_47404,equiv(X_47404,X_47404)),X_47404),not(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404)))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404),implies(X_47404,and(X_47404,equiv(X_47404,X_47404)))),not(implies(and(X_47404,equiv(X_47404,X_47404)),X_47404)))) )],[refute_0_1865,refute_0_1870]) ).
cnf(refute_0_1872,plain,
is_a_theorem(or(equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406),not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)))),
inference(subst,[],[refute_0_1871:[bind(X_47404,$fot(X_47406))]]) ).
cnf(refute_0_1873,plain,
is_a_theorem(or(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406),not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)))) )],[refute_0_1872,refute_0_1641]) ).
cnf(refute_0_1874,plain,
or(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406)) = implies(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406)),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406))),bind(Y,$fot(equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406)))]]) ).
cnf(refute_0_1875,plain,
( or(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406)) != implies(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))
| ~ is_a_theorem(or(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406)))
| is_a_theorem(implies(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))) ),[0],$fot(implies(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406)))]]) ).
cnf(refute_0_1876,plain,
( ~ is_a_theorem(or(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406)))
| is_a_theorem(implies(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))) ),
inference(resolve,[$cnf( $equal(or(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406)),implies(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))) )],[refute_0_1874,refute_0_1875]) ).
cnf(refute_0_1877,plain,
is_a_theorem(implies(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))),
inference(resolve,[$cnf( is_a_theorem(or(not(implies(and(X_47406,equiv(X_47406,X_47406)),X_47406)),equiv(and(X_47406,equiv(X_47406,X_47406)),X_47406))) )],[refute_0_1873,refute_0_1876]) ).
cnf(refute_0_1878,plain,
is_a_theorem(implies(implies(and(X_47407,equiv(X_47407,X_47407)),X_47407),equiv(and(X_47407,equiv(X_47407,X_47407)),X_47407))),
inference(subst,[],[refute_0_1877:[bind(X_47406,$fot(X_47407))]]) ).
cnf(refute_0_1879,plain,
( ~ is_a_theorem(implies(and(X_47407,equiv(X_47407,X_47407)),X_47407))
| is_a_theorem(equiv(and(X_47407,equiv(X_47407,X_47407)),X_47407)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_47407,equiv(X_47407,X_47407)),X_47407),equiv(and(X_47407,equiv(X_47407,X_47407)),X_47407))) )],[refute_0_1878,refute_0_1640]) ).
cnf(refute_0_1880,plain,
is_a_theorem(or(implies(not(X),X_483),and(not(X_483),not(X)))),
inference(subst,[],[refute_0_1280:[bind(P,$fot(X_483)),bind(X_17,$fot(not(X)))]]) ).
cnf(refute_0_1881,plain,
or(X,X_483) = implies(not(X),X_483),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_483))]]) ).
cnf(refute_0_1882,plain,
( or(X,X_483) != implies(not(X),X_483)
| implies(not(X),X_483) = or(X,X_483) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,X_483))),bind(Y0,$fot(implies(not(X),X_483)))]]) ).
cnf(refute_0_1883,plain,
implies(not(X),X_483) = or(X,X_483),
inference(resolve,[$cnf( $equal(or(X,X_483),implies(not(X),X_483)) )],[refute_0_1881,refute_0_1882]) ).
cnf(refute_0_1884,plain,
( implies(not(X),X_483) != or(X,X_483)
| ~ is_a_theorem(or(implies(not(X),X_483),and(not(X_483),not(X))))
| is_a_theorem(or(or(X,X_483),and(not(X_483),not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(not(X),X_483),and(not(X_483),not(X)))) ),[0,0],$fot(or(X,X_483))]]) ).
cnf(refute_0_1885,plain,
( ~ is_a_theorem(or(implies(not(X),X_483),and(not(X_483),not(X))))
| is_a_theorem(or(or(X,X_483),and(not(X_483),not(X)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_483),or(X,X_483)) )],[refute_0_1883,refute_0_1884]) ).
cnf(refute_0_1886,plain,
is_a_theorem(or(or(X,X_483),and(not(X_483),not(X)))),
inference(resolve,[$cnf( is_a_theorem(or(implies(not(X),X_483),and(not(X_483),not(X)))) )],[refute_0_1880,refute_0_1885]) ).
cnf(refute_0_1887,plain,
or(X,and(X_91,not(X_92))) = implies(not(X),and(X_91,not(X_92))),
inference(subst,[],[refute_0_84:[bind(Y,$fot(and(X_91,not(X_92))))]]) ).
cnf(refute_0_1888,plain,
implies(not(X),and(X_91,not(X_92))) = not(and(not(X),implies(X_91,X_92))),
inference(subst,[],[refute_0_950:[bind(X,$fot(not(X))),bind(X_7,$fot(X_91)),bind(X_8,$fot(X_92))]]) ).
cnf(refute_0_1889,plain,
( implies(not(X),and(X_91,not(X_92))) != not(and(not(X),implies(X_91,X_92)))
| or(X,and(X_91,not(X_92))) != implies(not(X),and(X_91,not(X_92)))
| or(X,and(X_91,not(X_92))) = not(and(not(X),implies(X_91,X_92))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,and(X_91,not(X_92))),implies(not(X),and(X_91,not(X_92)))) ),[1],$fot(not(and(not(X),implies(X_91,X_92))))]]) ).
cnf(refute_0_1890,plain,
( or(X,and(X_91,not(X_92))) != implies(not(X),and(X_91,not(X_92)))
| or(X,and(X_91,not(X_92))) = not(and(not(X),implies(X_91,X_92))) ),
inference(resolve,[$cnf( $equal(implies(not(X),and(X_91,not(X_92))),not(and(not(X),implies(X_91,X_92)))) )],[refute_0_1888,refute_0_1889]) ).
cnf(refute_0_1891,plain,
or(X,and(X_91,not(X_92))) = not(and(not(X),implies(X_91,X_92))),
inference(resolve,[$cnf( $equal(or(X,and(X_91,not(X_92))),implies(not(X),and(X_91,not(X_92)))) )],[refute_0_1887,refute_0_1890]) ).
cnf(refute_0_1892,plain,
or(X_312,and(not(X),not(X_314))) = not(and(not(X_312),implies(not(X),X_314))),
inference(subst,[],[refute_0_1891:[bind(X,$fot(X_312)),bind(X_91,$fot(not(X))),bind(X_92,$fot(X_314))]]) ).
cnf(refute_0_1893,plain,
or(X,X_314) = implies(not(X),X_314),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_314))]]) ).
cnf(refute_0_1894,plain,
( or(X,X_314) != implies(not(X),X_314)
| implies(not(X),X_314) = or(X,X_314) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,X_314))),bind(Y0,$fot(implies(not(X),X_314)))]]) ).
cnf(refute_0_1895,plain,
implies(not(X),X_314) = or(X,X_314),
inference(resolve,[$cnf( $equal(or(X,X_314),implies(not(X),X_314)) )],[refute_0_1893,refute_0_1894]) ).
cnf(refute_0_1896,plain,
( implies(not(X),X_314) != or(X,X_314)
| or(X_312,and(not(X),not(X_314))) != not(and(not(X_312),implies(not(X),X_314)))
| or(X_312,and(not(X),not(X_314))) = not(and(not(X_312),or(X,X_314))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_312,and(not(X),not(X_314))),not(and(not(X_312),implies(not(X),X_314)))) ),[1,0,1],$fot(or(X,X_314))]]) ).
cnf(refute_0_1897,plain,
( or(X_312,and(not(X),not(X_314))) != not(and(not(X_312),implies(not(X),X_314)))
| or(X_312,and(not(X),not(X_314))) = not(and(not(X_312),or(X,X_314))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_314),or(X,X_314)) )],[refute_0_1895,refute_0_1896]) ).
cnf(refute_0_1898,plain,
or(X_312,and(not(X),not(X_314))) = not(and(not(X_312),or(X,X_314))),
inference(resolve,[$cnf( $equal(or(X_312,and(not(X),not(X_314))),not(and(not(X_312),implies(not(X),X_314)))) )],[refute_0_1892,refute_0_1897]) ).
cnf(refute_0_1899,plain,
or(or(X,X_483),and(not(X_483),not(X))) = not(and(not(or(X,X_483)),or(X_483,X))),
inference(subst,[],[refute_0_1898:[bind(X,$fot(X_483)),bind(X_312,$fot(or(X,X_483))),bind(X_314,$fot(X))]]) ).
cnf(refute_0_1900,plain,
( or(or(X,X_483),and(not(X_483),not(X))) != not(and(not(or(X,X_483)),or(X_483,X)))
| ~ is_a_theorem(or(or(X,X_483),and(not(X_483),not(X))))
| is_a_theorem(not(and(not(or(X,X_483)),or(X_483,X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(X,X_483),and(not(X_483),not(X)))) ),[0],$fot(not(and(not(or(X,X_483)),or(X_483,X))))]]) ).
cnf(refute_0_1901,plain,
( ~ is_a_theorem(or(or(X,X_483),and(not(X_483),not(X))))
| is_a_theorem(not(and(not(or(X,X_483)),or(X_483,X)))) ),
inference(resolve,[$cnf( $equal(or(or(X,X_483),and(not(X_483),not(X))),not(and(not(or(X,X_483)),or(X_483,X)))) )],[refute_0_1899,refute_0_1900]) ).
cnf(refute_0_1902,plain,
is_a_theorem(not(and(not(or(X,X_483)),or(X_483,X)))),
inference(resolve,[$cnf( is_a_theorem(or(or(X,X_483),and(not(X_483),not(X)))) )],[refute_0_1886,refute_0_1901]) ).
cnf(refute_0_1903,plain,
is_a_theorem(not(and(not(or(X_555,not(X))),or(not(X),X_555)))),
inference(subst,[],[refute_0_1902:[bind(X,$fot(X_555)),bind(X_483,$fot(not(X)))]]) ).
cnf(refute_0_1904,plain,
implies(X,X_555) = or(not(X),X_555),
inference(subst,[],[refute_0_26:[bind(Y,$fot(X_555))]]) ).
cnf(refute_0_1905,plain,
( implies(X,X_555) != or(not(X),X_555)
| or(not(X),X_555) = implies(X,X_555) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,X_555))),bind(Y0,$fot(or(not(X),X_555)))]]) ).
cnf(refute_0_1906,plain,
or(not(X),X_555) = implies(X,X_555),
inference(resolve,[$cnf( $equal(implies(X,X_555),or(not(X),X_555)) )],[refute_0_1904,refute_0_1905]) ).
cnf(refute_0_1907,plain,
( or(not(X),X_555) != implies(X,X_555)
| ~ is_a_theorem(not(and(not(or(X_555,not(X))),or(not(X),X_555))))
| is_a_theorem(not(and(not(or(X_555,not(X))),implies(X,X_555)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(not(or(X_555,not(X))),or(not(X),X_555)))) ),[0,0,1],$fot(implies(X,X_555))]]) ).
cnf(refute_0_1908,plain,
( ~ is_a_theorem(not(and(not(or(X_555,not(X))),or(not(X),X_555))))
| is_a_theorem(not(and(not(or(X_555,not(X))),implies(X,X_555)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_555),implies(X,X_555)) )],[refute_0_1906,refute_0_1907]) ).
cnf(refute_0_1909,plain,
is_a_theorem(not(and(not(or(X_555,not(X))),implies(X,X_555)))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(or(X_555,not(X))),or(not(X),X_555)))) )],[refute_0_1903,refute_0_1908]) ).
cnf(refute_0_1910,plain,
implies(and(not(X_555),X),and(X,not(X_555))) = not(and(and(not(X_555),X),implies(X,X_555))),
inference(subst,[],[refute_0_950:[bind(X,$fot(and(not(X_555),X))),bind(X_7,$fot(X)),bind(X_8,$fot(X_555))]]) ).
cnf(refute_0_1911,plain,
or(or(X_555,not(X)),and(X,not(X_555))) = implies(and(not(X_555),X),and(X,not(X_555))),
inference(subst,[],[refute_0_1034:[bind(Y,$fot(and(X,not(X_555)))),bind(X_11,$fot(X)),bind(X_12,$fot(X_555))]]) ).
cnf(refute_0_1912,plain,
( implies(and(not(X_555),X),and(X,not(X_555))) != not(and(and(not(X_555),X),implies(X,X_555)))
| or(or(X_555,not(X)),and(X,not(X_555))) != implies(and(not(X_555),X),and(X,not(X_555)))
| or(or(X_555,not(X)),and(X,not(X_555))) = not(and(and(not(X_555),X),implies(X,X_555))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(or(X_555,not(X)),and(X,not(X_555))))),bind(Y0,$fot(implies(and(not(X_555),X),and(X,not(X_555))))),bind(Z,$fot(not(and(and(not(X_555),X),implies(X,X_555)))))]]) ).
cnf(refute_0_1913,plain,
( implies(and(not(X_555),X),and(X,not(X_555))) != not(and(and(not(X_555),X),implies(X,X_555)))
| or(or(X_555,not(X)),and(X,not(X_555))) = not(and(and(not(X_555),X),implies(X,X_555))) ),
inference(resolve,[$cnf( $equal(or(or(X_555,not(X)),and(X,not(X_555))),implies(and(not(X_555),X),and(X,not(X_555)))) )],[refute_0_1911,refute_0_1912]) ).
cnf(refute_0_1914,plain,
or(or(X_555,not(X)),and(X,not(X_555))) = not(and(and(not(X_555),X),implies(X,X_555))),
inference(resolve,[$cnf( $equal(implies(and(not(X_555),X),and(X,not(X_555))),not(and(and(not(X_555),X),implies(X,X_555)))) )],[refute_0_1910,refute_0_1913]) ).
cnf(refute_0_1915,plain,
( or(X,and(X_91,not(X_92))) != not(and(not(X),implies(X_91,X_92)))
| not(and(not(X),implies(X_91,X_92))) = or(X,and(X_91,not(X_92))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X,and(X_91,not(X_92))))),bind(Y0,$fot(not(and(not(X),implies(X_91,X_92)))))]]) ).
cnf(refute_0_1916,plain,
not(and(not(X),implies(X_91,X_92))) = or(X,and(X_91,not(X_92))),
inference(resolve,[$cnf( $equal(or(X,and(X_91,not(X_92))),not(and(not(X),implies(X_91,X_92)))) )],[refute_0_1891,refute_0_1915]) ).
cnf(refute_0_1917,plain,
not(and(not(or(X_555,not(X))),implies(X,X_555))) = or(or(X_555,not(X)),and(X,not(X_555))),
inference(subst,[],[refute_0_1916:[bind(X,$fot(or(X_555,not(X)))),bind(X_91,$fot(X)),bind(X_92,$fot(X_555))]]) ).
cnf(refute_0_1918,plain,
( not(and(not(or(X_555,not(X))),implies(X,X_555))) != or(or(X_555,not(X)),and(X,not(X_555)))
| or(or(X_555,not(X)),and(X,not(X_555))) != not(and(and(not(X_555),X),implies(X,X_555)))
| not(and(not(or(X_555,not(X))),implies(X,X_555))) = not(and(and(not(X_555),X),implies(X,X_555))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(and(not(or(X_555,not(X))),implies(X,X_555))))),bind(Y0,$fot(or(or(X_555,not(X)),and(X,not(X_555))))),bind(Z,$fot(not(and(and(not(X_555),X),implies(X,X_555)))))]]) ).
cnf(refute_0_1919,plain,
( or(or(X_555,not(X)),and(X,not(X_555))) != not(and(and(not(X_555),X),implies(X,X_555)))
| not(and(not(or(X_555,not(X))),implies(X,X_555))) = not(and(and(not(X_555),X),implies(X,X_555))) ),
inference(resolve,[$cnf( $equal(not(and(not(or(X_555,not(X))),implies(X,X_555))),or(or(X_555,not(X)),and(X,not(X_555)))) )],[refute_0_1917,refute_0_1918]) ).
cnf(refute_0_1920,plain,
not(and(not(or(X_555,not(X))),implies(X,X_555))) = not(and(and(not(X_555),X),implies(X,X_555))),
inference(resolve,[$cnf( $equal(or(or(X_555,not(X)),and(X,not(X_555))),not(and(and(not(X_555),X),implies(X,X_555)))) )],[refute_0_1914,refute_0_1919]) ).
cnf(refute_0_1921,plain,
( not(and(not(or(X_555,not(X))),implies(X,X_555))) != not(and(and(not(X_555),X),implies(X,X_555)))
| ~ is_a_theorem(not(and(not(or(X_555,not(X))),implies(X,X_555))))
| is_a_theorem(not(and(and(not(X_555),X),implies(X,X_555)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(not(or(X_555,not(X))),implies(X,X_555)))) ),[0],$fot(not(and(and(not(X_555),X),implies(X,X_555))))]]) ).
cnf(refute_0_1922,plain,
( ~ is_a_theorem(not(and(not(or(X_555,not(X))),implies(X,X_555))))
| is_a_theorem(not(and(and(not(X_555),X),implies(X,X_555)))) ),
inference(resolve,[$cnf( $equal(not(and(not(or(X_555,not(X))),implies(X,X_555))),not(and(and(not(X_555),X),implies(X,X_555)))) )],[refute_0_1920,refute_0_1921]) ).
cnf(refute_0_1923,plain,
is_a_theorem(not(and(and(not(X_555),X),implies(X,X_555)))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(or(X_555,not(X))),implies(X,X_555)))) )],[refute_0_1909,refute_0_1922]) ).
cnf(refute_0_1924,plain,
is_a_theorem(not(and(and(not(X_555),equiv(X_31832,X_31832)),implies(equiv(X_31832,X_31832),X_555)))),
inference(subst,[],[refute_0_1923:[bind(X,$fot(equiv(X_31832,X_31832)))]]) ).
cnf(refute_0_1925,plain,
implies(equiv(X_31832,X_31832),X_555) = X_555,
inference(subst,[],[refute_0_1599:[bind(X_31830,$fot(X_31832)),bind(X_31831,$fot(X_555))]]) ).
cnf(refute_0_1926,plain,
( implies(equiv(X_31832,X_31832),X_555) != X_555
| ~ is_a_theorem(not(and(and(not(X_555),equiv(X_31832,X_31832)),implies(equiv(X_31832,X_31832),X_555))))
| is_a_theorem(not(and(and(not(X_555),equiv(X_31832,X_31832)),X_555))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(and(not(X_555),equiv(X_31832,X_31832)),implies(equiv(X_31832,X_31832),X_555)))) ),[0,0,1],$fot(X_555)]]) ).
cnf(refute_0_1927,plain,
( ~ is_a_theorem(not(and(and(not(X_555),equiv(X_31832,X_31832)),implies(equiv(X_31832,X_31832),X_555))))
| is_a_theorem(not(and(and(not(X_555),equiv(X_31832,X_31832)),X_555))) ),
inference(resolve,[$cnf( $equal(implies(equiv(X_31832,X_31832),X_555),X_555) )],[refute_0_1925,refute_0_1926]) ).
cnf(refute_0_1928,plain,
is_a_theorem(not(and(and(not(X_555),equiv(X_31832,X_31832)),X_555))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(not(X_555),equiv(X_31832,X_31832)),implies(equiv(X_31832,X_31832),X_555)))) )],[refute_0_1924,refute_0_1927]) ).
cnf(refute_0_1929,plain,
is_a_theorem(not(and(and(not(not(X_1832)),equiv(X_31885,X_31885)),not(X_1832)))),
inference(subst,[],[refute_0_1928:[bind(X_31832,$fot(X_31885)),bind(X_555,$fot(not(X_1832)))]]) ).
cnf(refute_0_1930,plain,
( not(not(X_1832)) != X_1832
| ~ is_a_theorem(not(and(and(not(not(X_1832)),equiv(X_31885,X_31885)),not(X_1832))))
| is_a_theorem(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(and(not(not(X_1832)),equiv(X_31885,X_31885)),not(X_1832)))) ),[0,0,0,0],$fot(X_1832)]]) ).
cnf(refute_0_1931,plain,
( ~ is_a_theorem(not(and(and(not(not(X_1832)),equiv(X_31885,X_31885)),not(X_1832))))
| is_a_theorem(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)))) ),
inference(resolve,[$cnf( $equal(not(not(X_1832)),X_1832) )],[refute_0_638,refute_0_1930]) ).
cnf(refute_0_1932,plain,
is_a_theorem(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)))),
inference(resolve,[$cnf( is_a_theorem(not(and(and(not(not(X_1832)),equiv(X_31885,X_31885)),not(X_1832)))) )],[refute_0_1929,refute_0_1931]) ).
cnf(refute_0_1933,plain,
not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))) = implies(and(X_1832,equiv(X_31885,X_31885)),X_1832),
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)))]]) ).
cnf(refute_0_1934,plain,
and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)) = not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)),
inference(subst,[],[refute_0_567:[bind(X,$fot(and(X_1832,equiv(X_31885,X_31885)))),bind(X_1833,$fot(X_1832))]]) ).
cnf(refute_0_1935,plain,
not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) = not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))),
introduced(tautology,[refl,[$fot(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))))]]) ).
cnf(refute_0_1936,plain,
( and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)) != not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))
| not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) != not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)))
| not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) = not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))),not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)))) ),[1,0],$fot(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)))]]) ).
cnf(refute_0_1937,plain,
( and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)) != not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))
| not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) = not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))) ),
inference(resolve,[$cnf( $equal(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))),not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)))) )],[refute_0_1935,refute_0_1936]) ).
cnf(refute_0_1938,plain,
not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) = not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))),
inference(resolve,[$cnf( $equal(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)),not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))) )],[refute_0_1934,refute_0_1937]) ).
cnf(refute_0_1939,plain,
( not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) != not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)))
| not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))) != implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)
| not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) = implies(and(X_1832,equiv(X_31885,X_31885)),X_1832) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))))),bind(Y0,$fot(not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))))),bind(Z,$fot(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)))]]) ).
cnf(refute_0_1940,plain,
( not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))) != implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)
| not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) = implies(and(X_1832,equiv(X_31885,X_31885)),X_1832) ),
inference(resolve,[$cnf( $equal(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))),not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)))) )],[refute_0_1938,refute_0_1939]) ).
cnf(refute_0_1941,plain,
not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) = implies(and(X_1832,equiv(X_31885,X_31885)),X_1832),
inference(resolve,[$cnf( $equal(not(not(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))),implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)) )],[refute_0_1933,refute_0_1940]) ).
cnf(refute_0_1942,plain,
( not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))) != implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)
| ~ is_a_theorem(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))))
| is_a_theorem(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)))) ),[0],$fot(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832))]]) ).
cnf(refute_0_1943,plain,
( ~ is_a_theorem(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))))
| is_a_theorem(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)) ),
inference(resolve,[$cnf( $equal(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832))),implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)) )],[refute_0_1941,refute_0_1942]) ).
cnf(refute_0_1944,plain,
is_a_theorem(implies(and(X_1832,equiv(X_31885,X_31885)),X_1832)),
inference(resolve,[$cnf( is_a_theorem(not(and(and(X_1832,equiv(X_31885,X_31885)),not(X_1832)))) )],[refute_0_1932,refute_0_1943]) ).
cnf(refute_0_1945,plain,
is_a_theorem(implies(and(X_47407,equiv(X_47407,X_47407)),X_47407)),
inference(subst,[],[refute_0_1944:[bind(X_1832,$fot(X_47407)),bind(X_31885,$fot(X_47407))]]) ).
cnf(refute_0_1946,plain,
is_a_theorem(equiv(and(X_47407,equiv(X_47407,X_47407)),X_47407)),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_47407,equiv(X_47407,X_47407)),X_47407)) )],[refute_0_1945,refute_0_1879]) ).
cnf(refute_0_1947,plain,
is_a_theorem(equiv(and(X_47408,equiv(X_47408,X_47408)),X_47408)),
inference(subst,[],[refute_0_1946:[bind(X_47407,$fot(X_47408))]]) ).
cnf(refute_0_1948,plain,
and(X_47408,equiv(X_47408,X_47408)) = X_47408,
inference(resolve,[$cnf( is_a_theorem(equiv(and(X_47408,equiv(X_47408,X_47408)),X_47408)) )],[refute_0_1947,refute_0_1639]) ).
cnf(refute_0_1949,plain,
and(not(X_9),equiv(not(X_9),not(X_9))) = not(X_9),
inference(subst,[],[refute_0_1948:[bind(X_47408,$fot(not(X_9)))]]) ).
cnf(refute_0_1950,plain,
( and(not(X_9),equiv(not(X_9),not(X_9))) != not(X_9)
| or(X_9,not(equiv(not(X_9),not(X_9)))) != not(and(not(X_9),equiv(not(X_9),not(X_9))))
| or(X_9,not(equiv(not(X_9),not(X_9)))) = not(not(X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_9,not(equiv(not(X_9),not(X_9)))),not(and(not(X_9),equiv(not(X_9),not(X_9))))) ),[1,0],$fot(not(X_9))]]) ).
cnf(refute_0_1951,plain,
( or(X_9,not(equiv(not(X_9),not(X_9)))) != not(and(not(X_9),equiv(not(X_9),not(X_9))))
| or(X_9,not(equiv(not(X_9),not(X_9)))) = not(not(X_9)) ),
inference(resolve,[$cnf( $equal(and(not(X_9),equiv(not(X_9),not(X_9))),not(X_9)) )],[refute_0_1949,refute_0_1950]) ).
cnf(refute_0_1952,plain,
or(X_9,not(equiv(not(X_9),not(X_9)))) = not(not(X_9)),
inference(resolve,[$cnf( $equal(or(X_9,not(equiv(not(X_9),not(X_9)))),not(and(not(X_9),equiv(not(X_9),not(X_9))))) )],[refute_0_1638,refute_0_1951]) ).
cnf(refute_0_1953,plain,
or(X_9,not(equiv(not(X_9),not(X_9)))) = or(X_9,not(equiv(not(X_9),not(X_9)))),
introduced(tautology,[refl,[$fot(or(X_9,not(equiv(not(X_9),not(X_9)))))]]) ).
cnf(refute_0_1954,plain,
( not(equiv(not(X_9),not(X_9))) != not(equiv(X_9,X_9))
| or(X_9,not(equiv(not(X_9),not(X_9)))) != or(X_9,not(equiv(not(X_9),not(X_9))))
| or(X_9,not(equiv(not(X_9),not(X_9)))) = or(X_9,not(equiv(X_9,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_9,not(equiv(not(X_9),not(X_9)))),or(X_9,not(equiv(not(X_9),not(X_9))))) ),[1,1],$fot(not(equiv(X_9,X_9)))]]) ).
cnf(refute_0_1955,plain,
( not(equiv(not(X_9),not(X_9))) != not(equiv(X_9,X_9))
| or(X_9,not(equiv(not(X_9),not(X_9)))) = or(X_9,not(equiv(X_9,X_9))) ),
inference(resolve,[$cnf( $equal(or(X_9,not(equiv(not(X_9),not(X_9)))),or(X_9,not(equiv(not(X_9),not(X_9))))) )],[refute_0_1953,refute_0_1954]) ).
cnf(refute_0_1956,plain,
or(X_9,not(equiv(not(X_9),not(X_9)))) = or(X_9,not(equiv(X_9,X_9))),
inference(resolve,[$cnf( $equal(not(equiv(not(X_9),not(X_9))),not(equiv(X_9,X_9))) )],[refute_0_1528,refute_0_1955]) ).
cnf(refute_0_1957,plain,
( or(X_9,not(equiv(not(X_9),not(X_9)))) != not(not(X_9))
| or(X_9,not(equiv(not(X_9),not(X_9)))) != or(X_9,not(equiv(X_9,X_9)))
| or(X_9,not(equiv(X_9,X_9))) = not(not(X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_9,not(equiv(not(X_9),not(X_9)))),not(not(X_9))) ),[0],$fot(or(X_9,not(equiv(X_9,X_9))))]]) ).
cnf(refute_0_1958,plain,
( or(X_9,not(equiv(not(X_9),not(X_9)))) != not(not(X_9))
| or(X_9,not(equiv(X_9,X_9))) = not(not(X_9)) ),
inference(resolve,[$cnf( $equal(or(X_9,not(equiv(not(X_9),not(X_9)))),or(X_9,not(equiv(X_9,X_9)))) )],[refute_0_1956,refute_0_1957]) ).
cnf(refute_0_1959,plain,
( not(not(X_9)) != X_9
| or(X_9,not(equiv(X_9,X_9))) != not(not(X_9))
| or(X_9,not(equiv(X_9,X_9))) = X_9 ),
introduced(tautology,[equality,[$cnf( $equal(or(X_9,not(equiv(X_9,X_9))),not(not(X_9))) ),[1],$fot(X_9)]]) ).
cnf(refute_0_1960,plain,
( or(X_9,not(equiv(X_9,X_9))) != not(not(X_9))
| or(X_9,not(equiv(X_9,X_9))) = X_9 ),
inference(resolve,[$cnf( $equal(not(not(X_9)),X_9) )],[refute_0_1680,refute_0_1959]) ).
cnf(refute_0_1961,plain,
( or(X_9,not(equiv(not(X_9),not(X_9)))) != not(not(X_9))
| or(X_9,not(equiv(X_9,X_9))) = X_9 ),
inference(resolve,[$cnf( $equal(or(X_9,not(equiv(X_9,X_9))),not(not(X_9))) )],[refute_0_1958,refute_0_1960]) ).
cnf(refute_0_1962,plain,
or(X_9,not(equiv(X_9,X_9))) = X_9,
inference(resolve,[$cnf( $equal(or(X_9,not(equiv(not(X_9),not(X_9)))),not(not(X_9))) )],[refute_0_1952,refute_0_1961]) ).
cnf(refute_0_1963,plain,
or(X_47412,not(equiv(X_47412,X_47412))) = X_47412,
inference(subst,[],[refute_0_1962:[bind(X_9,$fot(X_47412))]]) ).
cnf(refute_0_1964,plain,
equiv(X_31900,X_31900) = equiv(X_47412,X_47412),
inference(subst,[],[refute_0_1614:[bind(X_31899,$fot(X_47412))]]) ).
cnf(refute_0_1965,plain,
( equiv(X_31900,X_31900) != equiv(X_47412,X_47412)
| equiv(X_47412,X_47412) = equiv(X_31900,X_31900) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X_31900,X_31900))),bind(Y0,$fot(equiv(X_47412,X_47412)))]]) ).
cnf(refute_0_1966,plain,
equiv(X_47412,X_47412) = equiv(X_31900,X_31900),
inference(resolve,[$cnf( $equal(equiv(X_31900,X_31900),equiv(X_47412,X_47412)) )],[refute_0_1964,refute_0_1965]) ).
cnf(refute_0_1967,plain,
( equiv(X_47412,X_47412) != equiv(X_31900,X_31900)
| or(X_47412,not(equiv(X_47412,X_47412))) != X_47412
| or(X_47412,not(equiv(X_31900,X_31900))) = X_47412 ),
introduced(tautology,[equality,[$cnf( $equal(or(X_47412,not(equiv(X_47412,X_47412))),X_47412) ),[0,1,0],$fot(equiv(X_31900,X_31900))]]) ).
cnf(refute_0_1968,plain,
( or(X_47412,not(equiv(X_47412,X_47412))) != X_47412
| or(X_47412,not(equiv(X_31900,X_31900))) = X_47412 ),
inference(resolve,[$cnf( $equal(equiv(X_47412,X_47412),equiv(X_31900,X_31900)) )],[refute_0_1966,refute_0_1967]) ).
cnf(refute_0_1969,plain,
or(X_47412,not(equiv(X_31900,X_31900))) = X_47412,
inference(resolve,[$cnf( $equal(or(X_47412,not(equiv(X_47412,X_47412))),X_47412) )],[refute_0_1963,refute_0_1968]) ).
cnf(refute_0_1970,plain,
or(X_56002,not(equiv(X_9,X_9))) = X_56002,
inference(subst,[],[refute_0_1969:[bind(X_31900,$fot(X_9)),bind(X_47412,$fot(X_56002))]]) ).
cnf(refute_0_1971,plain,
implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))),
introduced(tautology,[refl,[$fot(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))))]]) ).
cnf(refute_0_1972,plain,
( implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))) != implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9))))
| or(X_56002,not(equiv(X_9,X_9))) != X_56002
| implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))),implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9))))) ),[1,1],$fot(X_56002)]]) ).
cnf(refute_0_1973,plain,
( or(X_56002,not(equiv(X_9,X_9))) != X_56002
| implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002) ),
inference(resolve,[$cnf( $equal(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))),implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9))))) )],[refute_0_1971,refute_0_1972]) ).
cnf(refute_0_1974,plain,
implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002),
inference(resolve,[$cnf( $equal(or(X_56002,not(equiv(X_9,X_9))),X_56002) )],[refute_0_1970,refute_0_1973]) ).
cnf(refute_0_1975,plain,
and(X_47409,equiv(X_47409,X_47409)) = X_47409,
inference(subst,[],[refute_0_1948:[bind(X_47408,$fot(X_47409))]]) ).
cnf(refute_0_1976,plain,
equiv(X_31900,X_31900) = equiv(X_47409,X_47409),
inference(subst,[],[refute_0_1614:[bind(X_31899,$fot(X_47409))]]) ).
cnf(refute_0_1977,plain,
( equiv(X_31900,X_31900) != equiv(X_47409,X_47409)
| equiv(X_47409,X_47409) = equiv(X_31900,X_31900) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X_31900,X_31900))),bind(Y0,$fot(equiv(X_47409,X_47409)))]]) ).
cnf(refute_0_1978,plain,
equiv(X_47409,X_47409) = equiv(X_31900,X_31900),
inference(resolve,[$cnf( $equal(equiv(X_31900,X_31900),equiv(X_47409,X_47409)) )],[refute_0_1976,refute_0_1977]) ).
cnf(refute_0_1979,plain,
( and(X_47409,equiv(X_47409,X_47409)) != X_47409
| equiv(X_47409,X_47409) != equiv(X_31900,X_31900)
| and(X_47409,equiv(X_31900,X_31900)) = X_47409 ),
introduced(tautology,[equality,[$cnf( $equal(and(X_47409,equiv(X_47409,X_47409)),X_47409) ),[0,1],$fot(equiv(X_31900,X_31900))]]) ).
cnf(refute_0_1980,plain,
( and(X_47409,equiv(X_47409,X_47409)) != X_47409
| and(X_47409,equiv(X_31900,X_31900)) = X_47409 ),
inference(resolve,[$cnf( $equal(equiv(X_47409,X_47409),equiv(X_31900,X_31900)) )],[refute_0_1978,refute_0_1979]) ).
cnf(refute_0_1981,plain,
and(X_47409,equiv(X_31900,X_31900)) = X_47409,
inference(resolve,[$cnf( $equal(and(X_47409,equiv(X_47409,X_47409)),X_47409) )],[refute_0_1975,refute_0_1980]) ).
cnf(refute_0_1982,plain,
and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)) = implies(or(X_55999,X_56000),or(X_56000,X_55999)),
inference(subst,[],[refute_0_1981:[bind(X_31900,$fot(X_31901)),bind(X_47409,$fot(implies(or(X_55999,X_56000),or(X_56000,X_55999))))]]) ).
cnf(refute_0_1983,plain,
not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))) = not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))),
introduced(tautology,[refl,[$fot(not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))))]]) ).
cnf(refute_0_1984,plain,
( and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)) != implies(or(X_55999,X_56000),or(X_56000,X_55999))
| not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))) != not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))
| not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))) = not(implies(or(X_55999,X_56000),or(X_56000,X_55999))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))),not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))) ),[1,0],$fot(implies(or(X_55999,X_56000),or(X_56000,X_55999)))]]) ).
cnf(refute_0_1985,plain,
( and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)) != implies(or(X_55999,X_56000),or(X_56000,X_55999))
| not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))) = not(implies(or(X_55999,X_56000),or(X_56000,X_55999))) ),
inference(resolve,[$cnf( $equal(not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))),not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))) )],[refute_0_1983,refute_0_1984]) ).
cnf(refute_0_1986,plain,
not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))) = not(implies(or(X_55999,X_56000),or(X_56000,X_55999))),
inference(resolve,[$cnf( $equal(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)),implies(or(X_55999,X_56000),or(X_56000,X_55999))) )],[refute_0_1982,refute_0_1985]) ).
cnf(refute_0_1987,plain,
or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))) = or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),
introduced(tautology,[refl,[$fot(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))))]]) ).
cnf(refute_0_1988,plain,
( not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))) != not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))
| or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))) != or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))))
| or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))) = or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))))) ),[1,1],$fot(not(implies(or(X_55999,X_56000),or(X_56000,X_55999))))]]) ).
cnf(refute_0_1989,plain,
( not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))) != not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))
| or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))) = or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))) ),
inference(resolve,[$cnf( $equal(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))))) )],[refute_0_1987,refute_0_1988]) ).
cnf(refute_0_1990,plain,
or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))) = or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),
inference(resolve,[$cnf( $equal(not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901))),not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))) )],[refute_0_1986,refute_0_1989]) ).
cnf(refute_0_1991,plain,
implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))),
introduced(tautology,[refl,[$fot(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))))]]) ).
cnf(refute_0_1992,plain,
( implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) != implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9))))
| or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))) != or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999))))
| implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))),implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9))))) ),[1,0],$fot(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))))]]) ).
cnf(refute_0_1993,plain,
( or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))) != or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999))))
| implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))),implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9))))) )],[refute_0_1991,refute_0_1992]) ).
cnf(refute_0_1994,plain,
implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))),
inference(resolve,[$cnf( $equal(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999))))) )],[refute_0_1990,refute_0_1993]) ).
cnf(refute_0_1995,plain,
( implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) != implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9))))
| implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))) != implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002)
| implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))))),bind(Y0,$fot(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))))),bind(Z,$fot(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002)))]]) ).
cnf(refute_0_1996,plain,
( implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))) != implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002)
| implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002) ),
inference(resolve,[$cnf( $equal(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))),implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9))))) )],[refute_0_1994,refute_0_1995]) ).
cnf(refute_0_1997,plain,
implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) = implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002),
inference(resolve,[$cnf( $equal(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),or(X_56002,not(equiv(X_9,X_9)))),implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002)) )],[refute_0_1974,refute_0_1996]) ).
cnf(refute_0_1998,plain,
( implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))) != implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002)
| ~ is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))))
| is_a_theorem(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9))))) ),[0],$fot(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002))]]) ).
cnf(refute_0_1999,plain,
( ~ is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))))
| is_a_theorem(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002)) ),
inference(resolve,[$cnf( $equal(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9)))),implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002)) )],[refute_0_1997,refute_0_1998]) ).
cnf(refute_0_2000,plain,
is_a_theorem(implies(or(X_56002,not(implies(or(X_55999,X_56000),or(X_56000,X_55999)))),X_56002)),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_56002,not(and(implies(or(X_55999,X_56000),or(X_56000,X_55999)),equiv(X_31901,X_31901)))),or(X_56002,not(equiv(X_9,X_9))))) )],[refute_0_1637,refute_0_1999]) ).
cnf(refute_0_2001,plain,
is_a_theorem(implies(or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X))),
inference(subst,[],[refute_0_2000:[bind(X_55999,$fot(X_58917)),bind(X_56000,$fot(X_58918)),bind(X_56002,$fot(not(X)))]]) ).
cnf(refute_0_2002,plain,
implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))) = or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),
inference(subst,[],[refute_0_26:[bind(Y,$fot(not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))))]]) ).
cnf(refute_0_2003,plain,
( implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))) != or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917))))
| or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))) = implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))))),bind(Y0,$fot(or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917))))))]]) ).
cnf(refute_0_2004,plain,
or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))) = implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917))))) )],[refute_0_2002,refute_0_2003]) ).
cnf(refute_0_2005,plain,
( or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))) != implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917))))
| ~ is_a_theorem(implies(or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)))
| is_a_theorem(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X))) ),[0,0],$fot(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))))]]) ).
cnf(refute_0_2006,plain,
( ~ is_a_theorem(implies(or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)))
| is_a_theorem(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917))))) )],[refute_0_2004,refute_0_2005]) ).
cnf(refute_0_2007,plain,
is_a_theorem(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X))) )],[refute_0_2001,refute_0_2006]) ).
cnf(refute_0_2008,plain,
not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) = or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X)),
inference(subst,[],[refute_0_458:[bind(Y,$fot(X)),bind(X_9,$fot(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))))]]) ).
cnf(refute_0_2009,plain,
implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))) = not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),
inference(subst,[],[refute_0_448:[bind(X_1833,$fot(implies(or(X_58917,X_58918),or(X_58918,X_58917))))]]) ).
cnf(refute_0_2010,plain,
and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X) = and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X),
introduced(tautology,[refl,[$fot(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X))]]) ).
cnf(refute_0_2011,plain,
( and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X) != and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)
| implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))) != not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))))
| and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X) = and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X),and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) ),[1,0],$fot(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))))]]) ).
cnf(refute_0_2012,plain,
( implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))) != not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))))
| and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X) = and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X) ),
inference(resolve,[$cnf( $equal(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X),and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) )],[refute_0_2010,refute_0_2011]) ).
cnf(refute_0_2013,plain,
and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X) = and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X),
inference(resolve,[$cnf( $equal(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))))) )],[refute_0_2009,refute_0_2012]) ).
cnf(refute_0_2014,plain,
not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) = not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)),
introduced(tautology,[refl,[$fot(not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)))]]) ).
cnf(refute_0_2015,plain,
( and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X) != and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)
| not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) != not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X))
| not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) = not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)),not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X))) ),[1,0],$fot(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X))]]) ).
cnf(refute_0_2016,plain,
( and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X) != and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)
| not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) = not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)),not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X))) )],[refute_0_2014,refute_0_2015]) ).
cnf(refute_0_2017,plain,
not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) = not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)),
inference(resolve,[$cnf( $equal(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X),and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) )],[refute_0_2013,refute_0_2016]) ).
cnf(refute_0_2018,plain,
( not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) != not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X))
| not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) != or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))
| not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) = or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)))),bind(Y0,$fot(not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)))),bind(Z,$fot(or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))))]]) ).
cnf(refute_0_2019,plain,
( not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) != or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))
| not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) = or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)),not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X))) )],[refute_0_2017,refute_0_2018]) ).
cnf(refute_0_2020,plain,
not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) = or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X)),
inference(resolve,[$cnf( $equal(not(and(not(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)),or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))) )],[refute_0_2008,refute_0_2019]) ).
cnf(refute_0_2021,plain,
implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)) = not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)),
inference(subst,[],[refute_0_448:[bind(X,$fot(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))))),bind(X_1833,$fot(X))]]) ).
cnf(refute_0_2022,plain,
( implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)) != not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X))
| not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) != or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))
| implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)) = or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)))),bind(Y0,$fot(not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)))),bind(Z,$fot(or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))))]]) ).
cnf(refute_0_2023,plain,
( not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)) != or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))
| implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)) = or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)),not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X))) )],[refute_0_2021,refute_0_2022]) ).
cnf(refute_0_2024,plain,
implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)) = or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X)),
inference(resolve,[$cnf( $equal(not(and(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),X)),or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))) )],[refute_0_2020,refute_0_2023]) ).
cnf(refute_0_2025,plain,
( implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)) != or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))
| ~ is_a_theorem(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)))
| is_a_theorem(or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X))) ),[0],$fot(or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X)))]]) ).
cnf(refute_0_2026,plain,
( ~ is_a_theorem(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)))
| is_a_theorem(or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X)),or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))) )],[refute_0_2024,refute_0_2025]) ).
cnf(refute_0_2027,plain,
is_a_theorem(or(and(X,implies(or(X_58917,X_58918),or(X_58918,X_58917))),not(X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(implies(or(X_58917,X_58918),or(X_58918,X_58917)))),not(X))) )],[refute_0_2007,refute_0_2026]) ).
cnf(refute_0_2028,plain,
is_a_theorem(or(and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))),not(implies(or(X_58928,X_58927),or(X_58927,X_58928))))),
inference(subst,[],[refute_0_2027:[bind(X,$fot(implies(or(X_58928,X_58927),or(X_58927,X_58928)))),bind(X_58917,$fot(X_58927)),bind(X_58918,$fot(X_58928))]]) ).
cnf(refute_0_2029,plain,
equiv(or(X_58928,X_58927),or(X_58927,X_58928)) = and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))),
inference(subst,[],[refute_0_71:[bind(X,$fot(or(X_58928,X_58927))),bind(Y,$fot(or(X_58927,X_58928)))]]) ).
cnf(refute_0_2030,plain,
( equiv(or(X_58928,X_58927),or(X_58927,X_58928)) != and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927)))
| and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))) = equiv(or(X_58928,X_58927),or(X_58927,X_58928)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(or(X_58928,X_58927),or(X_58927,X_58928)))),bind(Y0,$fot(and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927)))))]]) ).
cnf(refute_0_2031,plain,
and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))) = equiv(or(X_58928,X_58927),or(X_58927,X_58928)),
inference(resolve,[$cnf( $equal(equiv(or(X_58928,X_58927),or(X_58927,X_58928)),and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927)))) )],[refute_0_2029,refute_0_2030]) ).
cnf(refute_0_2032,plain,
( and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))) != equiv(or(X_58928,X_58927),or(X_58927,X_58928))
| ~ is_a_theorem(or(and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))),not(implies(or(X_58928,X_58927),or(X_58927,X_58928)))))
| is_a_theorem(or(equiv(or(X_58928,X_58927),or(X_58927,X_58928)),not(implies(or(X_58928,X_58927),or(X_58927,X_58928))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))),not(implies(or(X_58928,X_58927),or(X_58927,X_58928))))) ),[0,0],$fot(equiv(or(X_58928,X_58927),or(X_58927,X_58928)))]]) ).
cnf(refute_0_2033,plain,
( ~ is_a_theorem(or(and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))),not(implies(or(X_58928,X_58927),or(X_58927,X_58928)))))
| is_a_theorem(or(equiv(or(X_58928,X_58927),or(X_58927,X_58928)),not(implies(or(X_58928,X_58927),or(X_58927,X_58928))))) ),
inference(resolve,[$cnf( $equal(and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))),equiv(or(X_58928,X_58927),or(X_58927,X_58928))) )],[refute_0_2031,refute_0_2032]) ).
cnf(refute_0_2034,plain,
is_a_theorem(or(equiv(or(X_58928,X_58927),or(X_58927,X_58928)),not(implies(or(X_58928,X_58927),or(X_58927,X_58928))))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(or(X_58928,X_58927),or(X_58927,X_58928)),implies(or(X_58927,X_58928),or(X_58928,X_58927))),not(implies(or(X_58928,X_58927),or(X_58927,X_58928))))) )],[refute_0_2028,refute_0_2033]) ).
cnf(refute_0_2035,plain,
is_a_theorem(or(equiv(or(X_58930,X_58929),or(X_58929,X_58930)),not(implies(or(X_58930,X_58929),or(X_58929,X_58930))))),
inference(subst,[],[refute_0_2034:[bind(X_58927,$fot(X_58929)),bind(X_58928,$fot(X_58930))]]) ).
cnf(refute_0_2036,plain,
is_a_theorem(or(not(implies(or(X_58930,X_58929),or(X_58929,X_58930))),equiv(or(X_58930,X_58929),or(X_58929,X_58930)))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(or(X_58930,X_58929),or(X_58929,X_58930)),not(implies(or(X_58930,X_58929),or(X_58929,X_58930))))) )],[refute_0_2035,refute_0_158]) ).
cnf(refute_0_2037,plain,
or(not(implies(or(X_58930,X_58929),or(X_58929,X_58930))),equiv(or(X_58930,X_58929),or(X_58929,X_58930))) = implies(implies(or(X_58930,X_58929),or(X_58929,X_58930)),equiv(or(X_58930,X_58929),or(X_58929,X_58930))),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(or(X_58930,X_58929),or(X_58929,X_58930)))),bind(Y,$fot(equiv(or(X_58930,X_58929),or(X_58929,X_58930))))]]) ).
cnf(refute_0_2038,plain,
( or(not(implies(or(X_58930,X_58929),or(X_58929,X_58930))),equiv(or(X_58930,X_58929),or(X_58929,X_58930))) != implies(implies(or(X_58930,X_58929),or(X_58929,X_58930)),equiv(or(X_58930,X_58929),or(X_58929,X_58930)))
| ~ is_a_theorem(or(not(implies(or(X_58930,X_58929),or(X_58929,X_58930))),equiv(or(X_58930,X_58929),or(X_58929,X_58930))))
| is_a_theorem(implies(implies(or(X_58930,X_58929),or(X_58929,X_58930)),equiv(or(X_58930,X_58929),or(X_58929,X_58930)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(implies(or(X_58930,X_58929),or(X_58929,X_58930))),equiv(or(X_58930,X_58929),or(X_58929,X_58930)))) ),[0],$fot(implies(implies(or(X_58930,X_58929),or(X_58929,X_58930)),equiv(or(X_58930,X_58929),or(X_58929,X_58930))))]]) ).
cnf(refute_0_2039,plain,
( ~ is_a_theorem(or(not(implies(or(X_58930,X_58929),or(X_58929,X_58930))),equiv(or(X_58930,X_58929),or(X_58929,X_58930))))
| is_a_theorem(implies(implies(or(X_58930,X_58929),or(X_58929,X_58930)),equiv(or(X_58930,X_58929),or(X_58929,X_58930)))) ),
inference(resolve,[$cnf( $equal(or(not(implies(or(X_58930,X_58929),or(X_58929,X_58930))),equiv(or(X_58930,X_58929),or(X_58929,X_58930))),implies(implies(or(X_58930,X_58929),or(X_58929,X_58930)),equiv(or(X_58930,X_58929),or(X_58929,X_58930)))) )],[refute_0_2037,refute_0_2038]) ).
cnf(refute_0_2040,plain,
is_a_theorem(implies(implies(or(X_58930,X_58929),or(X_58929,X_58930)),equiv(or(X_58930,X_58929),or(X_58929,X_58930)))),
inference(resolve,[$cnf( is_a_theorem(or(not(implies(or(X_58930,X_58929),or(X_58929,X_58930))),equiv(or(X_58930,X_58929),or(X_58929,X_58930)))) )],[refute_0_2036,refute_0_2039]) ).
cnf(refute_0_2041,plain,
is_a_theorem(implies(implies(or(X_58932,X_58931),or(X_58931,X_58932)),equiv(or(X_58932,X_58931),or(X_58931,X_58932)))),
inference(subst,[],[refute_0_2040:[bind(X_58929,$fot(X_58931)),bind(X_58930,$fot(X_58932))]]) ).
cnf(refute_0_2042,plain,
( ~ is_a_theorem(implies(or(X_58932,X_58931),or(X_58931,X_58932)))
| is_a_theorem(equiv(or(X_58932,X_58931),or(X_58931,X_58932))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_58932,X_58931),or(X_58931,X_58932)),equiv(or(X_58932,X_58931),or(X_58931,X_58932)))) )],[refute_0_2041,refute_0_157]) ).
cnf(refute_0_2043,plain,
is_a_theorem(implies(or(X_58932,X_58931),or(X_58931,X_58932))),
inference(subst,[],[refute_0_5:[bind(P,$fot(X_58932)),bind(Q,$fot(X_58931))]]) ).
cnf(refute_0_2044,plain,
is_a_theorem(equiv(or(X_58932,X_58931),or(X_58931,X_58932))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_58932,X_58931),or(X_58931,X_58932))) )],[refute_0_2043,refute_0_2042]) ).
cnf(refute_0_2045,plain,
is_a_theorem(equiv(or(X_58934,X_58933),or(X_58933,X_58934))),
inference(subst,[],[refute_0_2044:[bind(X_58931,$fot(X_58933)),bind(X_58932,$fot(X_58934))]]) ).
cnf(refute_0_2046,plain,
or(X_58934,X_58933) = or(X_58933,X_58934),
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_58934,X_58933),or(X_58933,X_58934))) )],[refute_0_2045,refute_0_156]) ).
cnf(refute_0_2047,plain,
( or(X_58934,X_58933) != or(X_58933,X_58934)
| or(X_58933,X_58934) = or(X_58934,X_58933) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(or(X_58934,X_58933))),bind(Y0,$fot(or(X_58933,X_58934)))]]) ).
cnf(refute_0_2048,plain,
or(X_58933,X_58934) = or(X_58934,X_58933),
inference(resolve,[$cnf( $equal(or(X_58934,X_58933),or(X_58933,X_58934)) )],[refute_0_2046,refute_0_2047]) ).
cnf(refute_0_2049,plain,
or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420)) = or(and(X_4419,X_4420),equiv(X_4419,not(X_4420))),
inference(subst,[],[refute_0_2048:[bind(X_58933,$fot(equiv(X_4419,not(X_4420)))),bind(X_58934,$fot(and(X_4419,X_4420)))]]) ).
cnf(refute_0_2050,plain,
implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))) = implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),
introduced(tautology,[refl,[$fot(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))))]]) ).
cnf(refute_0_2051,plain,
( implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))) != implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420)))
| or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420)) != or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))
| implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))) = implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420)))) ),[1,1],$fot(or(and(X_4419,X_4420),equiv(X_4419,not(X_4420))))]]) ).
cnf(refute_0_2052,plain,
( or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420)) != or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))
| implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))) = implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420)))) )],[refute_0_2050,refute_0_2051]) ).
cnf(refute_0_2053,plain,
implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))) = implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),
inference(resolve,[$cnf( $equal(or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420)),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))) )],[refute_0_2049,refute_0_2052]) ).
cnf(refute_0_2054,plain,
or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418) = or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418),
introduced(tautology,[refl,[$fot(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418))]]) ).
cnf(refute_0_2055,plain,
( implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))) != implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420))))
| or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418) != or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418)
| or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418) = or(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),X_4418) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418),or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418)) ),[1,0],$fot(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))))]]) ).
cnf(refute_0_2056,plain,
( implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))) != implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420))))
| or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418) = or(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),X_4418) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418),or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418)) )],[refute_0_2054,refute_0_2055]) ).
cnf(refute_0_2057,plain,
or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418) = or(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),X_4418),
inference(resolve,[$cnf( $equal(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420))))) )],[refute_0_2053,refute_0_2056]) ).
cnf(refute_0_2058,plain,
( or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418) != or(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),X_4418)
| ~ is_a_theorem(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418))
| is_a_theorem(or(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),X_4418)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418)) ),[0],$fot(or(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),X_4418))]]) ).
cnf(refute_0_2059,plain,
( ~ is_a_theorem(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418))
| is_a_theorem(or(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),X_4418)) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418),or(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),X_4418)) )],[refute_0_2057,refute_0_2058]) ).
cnf(refute_0_2060,plain,
is_a_theorem(or(implies(or(X_4420,X_4419),or(and(X_4419,X_4420),equiv(X_4419,not(X_4420)))),X_4418)),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(X_4420,X_4419),or(equiv(X_4419,not(X_4420)),and(X_4419,X_4420))),X_4418)) )],[refute_0_152,refute_0_2059]) ).
cnf(refute_0_2061,plain,
is_a_theorem(or(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),and(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),X_1833))),
inference(subst,[],[refute_0_2060:[bind(X_4418,$fot(and(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),X_1833))),bind(X_4419,$fot(X_61738)),bind(X_4420,$fot(X_61739))]]) ).
cnf(refute_0_2062,plain,
( ~ is_a_theorem(equiv(or(X_52957,and(X_52956,X_52957)),X_52957))
| or(X_52957,and(X_52956,X_52957)) = X_52957 ),
inference(subst,[],[refute_0_155:[bind(X,$fot(or(X_52957,and(X_52956,X_52957)))),bind(Y,$fot(X_52957))]]) ).
cnf(refute_0_2063,plain,
( ~ is_a_theorem(implies(X_52955,or(X_52955,and(X_52954,X_52955))))
| ~ is_a_theorem(implies(implies(X_52955,or(X_52955,and(X_52954,X_52955))),equiv(or(X_52955,and(X_52954,X_52955)),X_52955)))
| is_a_theorem(equiv(or(X_52955,and(X_52954,X_52955)),X_52955)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_52955,or(X_52955,and(X_52954,X_52955))))),bind(Y,$fot(equiv(or(X_52955,and(X_52954,X_52955)),X_52955)))]]) ).
cnf(refute_0_2064,plain,
( ~ is_a_theorem(or(equiv(or(X_52947,and(X_52946,X_52947)),X_52947),not(implies(X_52947,or(X_52947,and(X_52946,X_52947))))))
| is_a_theorem(or(not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947))) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(equiv(or(X_52947,and(X_52946,X_52947)),X_52947))),bind(Q,$fot(not(implies(X_52947,or(X_52947,and(X_52946,X_52947))))))]]) ).
cnf(refute_0_2065,plain,
is_a_theorem(implies(or(X_52943,and(X_25,X_52943)),X_52943)),
inference(subst,[],[refute_0_1664:[bind(X_4885,$fot(X_52943))]]) ).
cnf(refute_0_2066,plain,
( ~ is_a_theorem(implies(X_9168,X_9169))
| ~ is_a_theorem(implies(implies(X_9168,X_9169),or(equiv(X_9168,X_9169),not(implies(X_9169,X_9168)))))
| is_a_theorem(or(equiv(X_9168,X_9169),not(implies(X_9169,X_9168)))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_9168,X_9169))),bind(Y,$fot(or(equiv(X_9168,X_9169),not(implies(X_9169,X_9168)))))]]) ).
cnf(refute_0_2067,plain,
is_a_theorem(implies(implies(X,Y),or(and(implies(X,Y),implies(Y,X)),not(implies(Y,X))))),
inference(subst,[],[refute_0_668:[bind(X_1833,$fot(implies(Y,X))),bind(X_5087,$fot(implies(X,Y)))]]) ).
cnf(refute_0_2068,plain,
( and(implies(X,Y),implies(Y,X)) != equiv(X,Y)
| ~ is_a_theorem(implies(implies(X,Y),or(and(implies(X,Y),implies(Y,X)),not(implies(Y,X)))))
| is_a_theorem(implies(implies(X,Y),or(equiv(X,Y),not(implies(Y,X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,Y),or(and(implies(X,Y),implies(Y,X)),not(implies(Y,X))))) ),[0,1,0],$fot(equiv(X,Y))]]) ).
cnf(refute_0_2069,plain,
( ~ is_a_theorem(implies(implies(X,Y),or(and(implies(X,Y),implies(Y,X)),not(implies(Y,X)))))
| is_a_theorem(implies(implies(X,Y),or(equiv(X,Y),not(implies(Y,X))))) ),
inference(resolve,[$cnf( $equal(and(implies(X,Y),implies(Y,X)),equiv(X,Y)) )],[refute_0_229,refute_0_2068]) ).
cnf(refute_0_2070,plain,
is_a_theorem(implies(implies(X,Y),or(equiv(X,Y),not(implies(Y,X))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),or(and(implies(X,Y),implies(Y,X)),not(implies(Y,X))))) )],[refute_0_2067,refute_0_2069]) ).
cnf(refute_0_2071,plain,
is_a_theorem(implies(implies(X_9168,X_9169),or(equiv(X_9168,X_9169),not(implies(X_9169,X_9168))))),
inference(subst,[],[refute_0_2070:[bind(X,$fot(X_9168)),bind(Y,$fot(X_9169))]]) ).
cnf(refute_0_2072,plain,
( ~ is_a_theorem(implies(X_9168,X_9169))
| is_a_theorem(or(equiv(X_9168,X_9169),not(implies(X_9169,X_9168)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_9168,X_9169),or(equiv(X_9168,X_9169),not(implies(X_9169,X_9168))))) )],[refute_0_2071,refute_0_2066]) ).
cnf(refute_0_2073,plain,
( ~ is_a_theorem(implies(or(X_52943,and(X_25,X_52943)),X_52943))
| is_a_theorem(or(equiv(or(X_52943,and(X_25,X_52943)),X_52943),not(implies(X_52943,or(X_52943,and(X_25,X_52943)))))) ),
inference(subst,[],[refute_0_2072:[bind(X_9168,$fot(or(X_52943,and(X_25,X_52943)))),bind(X_9169,$fot(X_52943))]]) ).
cnf(refute_0_2074,plain,
is_a_theorem(or(equiv(or(X_52943,and(X_25,X_52943)),X_52943),not(implies(X_52943,or(X_52943,and(X_25,X_52943)))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_52943,and(X_25,X_52943)),X_52943)) )],[refute_0_2065,refute_0_2073]) ).
cnf(refute_0_2075,plain,
is_a_theorem(or(equiv(or(X_52947,and(X_52946,X_52947)),X_52947),not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))))),
inference(subst,[],[refute_0_2074:[bind(X_25,$fot(X_52946)),bind(X_52943,$fot(X_52947))]]) ).
cnf(refute_0_2076,plain,
is_a_theorem(or(not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947))),
inference(resolve,[$cnf( is_a_theorem(or(equiv(or(X_52947,and(X_52946,X_52947)),X_52947),not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))))) )],[refute_0_2075,refute_0_2064]) ).
cnf(refute_0_2077,plain,
or(not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947)) = implies(implies(X_52947,or(X_52947,and(X_52946,X_52947))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947)),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(X_52947,or(X_52947,and(X_52946,X_52947))))),bind(Y,$fot(equiv(or(X_52947,and(X_52946,X_52947)),X_52947)))]]) ).
cnf(refute_0_2078,plain,
( or(not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947)) != implies(implies(X_52947,or(X_52947,and(X_52946,X_52947))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947))
| ~ is_a_theorem(or(not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947)))
| is_a_theorem(implies(implies(X_52947,or(X_52947,and(X_52946,X_52947))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947))) ),[0],$fot(implies(implies(X_52947,or(X_52947,and(X_52946,X_52947))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947)))]]) ).
cnf(refute_0_2079,plain,
( ~ is_a_theorem(or(not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947)))
| is_a_theorem(implies(implies(X_52947,or(X_52947,and(X_52946,X_52947))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947))) ),
inference(resolve,[$cnf( $equal(or(not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947)),implies(implies(X_52947,or(X_52947,and(X_52946,X_52947))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947))) )],[refute_0_2077,refute_0_2078]) ).
cnf(refute_0_2080,plain,
is_a_theorem(implies(implies(X_52947,or(X_52947,and(X_52946,X_52947))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947))),
inference(resolve,[$cnf( is_a_theorem(or(not(implies(X_52947,or(X_52947,and(X_52946,X_52947)))),equiv(or(X_52947,and(X_52946,X_52947)),X_52947))) )],[refute_0_2076,refute_0_2079]) ).
cnf(refute_0_2081,plain,
is_a_theorem(implies(implies(X_52955,or(X_52955,and(X_52954,X_52955))),equiv(or(X_52955,and(X_52954,X_52955)),X_52955))),
inference(subst,[],[refute_0_2080:[bind(X_52946,$fot(X_52954)),bind(X_52947,$fot(X_52955))]]) ).
cnf(refute_0_2082,plain,
( ~ is_a_theorem(implies(X_52955,or(X_52955,and(X_52954,X_52955))))
| is_a_theorem(equiv(or(X_52955,and(X_52954,X_52955)),X_52955)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_52955,or(X_52955,and(X_52954,X_52955))),equiv(or(X_52955,and(X_52954,X_52955)),X_52955))) )],[refute_0_2081,refute_0_2063]) ).
cnf(refute_0_2083,plain,
( ~ is_a_theorem(implies(X_4011,or(implies(or(X_4012,X_4013),X_4012),X_4013)))
| is_a_theorem(or(or(implies(or(X_4012,X_4013),X_4012),X_4013),not(X_4011))) ),
inference(subst,[],[refute_0_364:[bind(Q,$fot(or(implies(or(X_4012,X_4013),X_4012),X_4013))),bind(X_17,$fot(X_4011))]]) ).
cnf(refute_0_2084,plain,
is_a_theorem(implies(X_4011,or(implies(or(X_4012,X_4013),X_4012),X_4013))),
inference(subst,[],[refute_0_719:[bind(X_17,$fot(X_4011)),bind(X_1963,$fot(X_4012)),bind(X_1964,$fot(X_4013))]]) ).
cnf(refute_0_2085,plain,
is_a_theorem(or(or(implies(or(X_4012,X_4013),X_4012),X_4013),not(X_4011))),
inference(resolve,[$cnf( is_a_theorem(implies(X_4011,or(implies(or(X_4012,X_4013),X_4012),X_4013))) )],[refute_0_2084,refute_0_2083]) ).
cnf(refute_0_2086,plain,
is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),not(not(X_1832)))),
inference(subst,[],[refute_0_2085:[bind(X_4011,$fot(not(X_1832))),bind(X_4012,$fot(X_4809)),bind(X_4013,$fot(X_4810))]]) ).
cnf(refute_0_2087,plain,
( not(not(X_1832)) != X_1832
| ~ is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),not(not(X_1832))))
| is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),X_1832)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),not(not(X_1832)))) ),[0,1],$fot(X_1832)]]) ).
cnf(refute_0_2088,plain,
( ~ is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),not(not(X_1832))))
| is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),X_1832)) ),
inference(resolve,[$cnf( $equal(not(not(X_1832)),X_1832) )],[refute_0_638,refute_0_2087]) ).
cnf(refute_0_2089,plain,
is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),X_1832)),
inference(resolve,[$cnf( is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),not(not(X_1832)))) )],[refute_0_2086,refute_0_2088]) ).
cnf(refute_0_2090,plain,
is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),X_12673)),
inference(subst,[],[refute_0_2089:[bind(X_1832,$fot(X_12673))]]) ).
cnf(refute_0_2091,plain,
( ~ is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),X_12673))
| is_a_theorem(or(and(X_12672,or(implies(or(X_4809,X_4810),X_4809),X_4810)),implies(X_12672,X_12673))) ),
inference(subst,[],[refute_0_1337:[bind(Y,$fot(or(implies(or(X_4809,X_4810),X_4809),X_4810))),bind(X_130,$fot(X_12672)),bind(X_132,$fot(X_12673))]]) ).
cnf(refute_0_2092,plain,
is_a_theorem(or(and(X_12672,or(implies(or(X_4809,X_4810),X_4809),X_4810)),implies(X_12672,X_12673))),
inference(resolve,[$cnf( is_a_theorem(or(or(implies(or(X_4809,X_4810),X_4809),X_4810),X_12673)) )],[refute_0_2090,refute_0_2091]) ).
cnf(refute_0_2093,plain,
is_a_theorem(or(and(X_12856,or(implies(or(not(X),X_12859),not(X)),X_12859)),implies(X_12856,X_12857))),
inference(subst,[],[refute_0_2092:[bind(X_12672,$fot(X_12856)),bind(X_12673,$fot(X_12857)),bind(X_4809,$fot(not(X))),bind(X_4810,$fot(X_12859))]]) ).
cnf(refute_0_2094,plain,
implies(X,X_12859) = or(not(X),X_12859),
inference(subst,[],[refute_0_26:[bind(Y,$fot(X_12859))]]) ).
cnf(refute_0_2095,plain,
( implies(X,X_12859) != or(not(X),X_12859)
| or(not(X),X_12859) = implies(X,X_12859) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,X_12859))),bind(Y0,$fot(or(not(X),X_12859)))]]) ).
cnf(refute_0_2096,plain,
or(not(X),X_12859) = implies(X,X_12859),
inference(resolve,[$cnf( $equal(implies(X,X_12859),or(not(X),X_12859)) )],[refute_0_2094,refute_0_2095]) ).
cnf(refute_0_2097,plain,
( or(not(X),X_12859) != implies(X,X_12859)
| ~ is_a_theorem(or(and(X_12856,or(implies(or(not(X),X_12859),not(X)),X_12859)),implies(X_12856,X_12857)))
| is_a_theorem(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_12856,or(implies(or(not(X),X_12859),not(X)),X_12859)),implies(X_12856,X_12857))) ),[0,0,1,0,0],$fot(implies(X,X_12859))]]) ).
cnf(refute_0_2098,plain,
( ~ is_a_theorem(or(and(X_12856,or(implies(or(not(X),X_12859),not(X)),X_12859)),implies(X_12856,X_12857)))
| is_a_theorem(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_12859),implies(X,X_12859)) )],[refute_0_2096,refute_0_2097]) ).
cnf(refute_0_2099,plain,
is_a_theorem(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_12856,or(implies(or(not(X),X_12859),not(X)),X_12859)),implies(X_12856,X_12857))) )],[refute_0_2093,refute_0_2098]) ).
cnf(refute_0_2100,plain,
or(not(and(implies(X,X_12859),X)),X_12859) = implies(and(implies(X,X_12859),X),X_12859),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(implies(X,X_12859),X))),bind(Y,$fot(X_12859))]]) ).
cnf(refute_0_2101,plain,
implies(implies(X,X_12859),not(X)) = not(and(implies(X,X_12859),X)),
inference(subst,[],[refute_0_448:[bind(X,$fot(implies(X,X_12859))),bind(X_1833,$fot(X))]]) ).
cnf(refute_0_2102,plain,
or(implies(implies(X,X_12859),not(X)),X_12859) = or(implies(implies(X,X_12859),not(X)),X_12859),
introduced(tautology,[refl,[$fot(or(implies(implies(X,X_12859),not(X)),X_12859))]]) ).
cnf(refute_0_2103,plain,
( implies(implies(X,X_12859),not(X)) != not(and(implies(X,X_12859),X))
| or(implies(implies(X,X_12859),not(X)),X_12859) != or(implies(implies(X,X_12859),not(X)),X_12859)
| or(implies(implies(X,X_12859),not(X)),X_12859) = or(not(and(implies(X,X_12859),X)),X_12859) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(implies(X,X_12859),not(X)),X_12859),or(implies(implies(X,X_12859),not(X)),X_12859)) ),[1,0],$fot(not(and(implies(X,X_12859),X)))]]) ).
cnf(refute_0_2104,plain,
( implies(implies(X,X_12859),not(X)) != not(and(implies(X,X_12859),X))
| or(implies(implies(X,X_12859),not(X)),X_12859) = or(not(and(implies(X,X_12859),X)),X_12859) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,X_12859),not(X)),X_12859),or(implies(implies(X,X_12859),not(X)),X_12859)) )],[refute_0_2102,refute_0_2103]) ).
cnf(refute_0_2105,plain,
or(implies(implies(X,X_12859),not(X)),X_12859) = or(not(and(implies(X,X_12859),X)),X_12859),
inference(resolve,[$cnf( $equal(implies(implies(X,X_12859),not(X)),not(and(implies(X,X_12859),X))) )],[refute_0_2101,refute_0_2104]) ).
cnf(refute_0_2106,plain,
( or(implies(implies(X,X_12859),not(X)),X_12859) != or(not(and(implies(X,X_12859),X)),X_12859)
| or(not(and(implies(X,X_12859),X)),X_12859) != implies(and(implies(X,X_12859),X),X_12859)
| or(implies(implies(X,X_12859),not(X)),X_12859) = implies(and(implies(X,X_12859),X),X_12859) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(implies(implies(X,X_12859),not(X)),X_12859))),bind(Y0,$fot(or(not(and(implies(X,X_12859),X)),X_12859))),bind(Z,$fot(implies(and(implies(X,X_12859),X),X_12859)))]]) ).
cnf(refute_0_2107,plain,
( or(not(and(implies(X,X_12859),X)),X_12859) != implies(and(implies(X,X_12859),X),X_12859)
| or(implies(implies(X,X_12859),not(X)),X_12859) = implies(and(implies(X,X_12859),X),X_12859) ),
inference(resolve,[$cnf( $equal(or(implies(implies(X,X_12859),not(X)),X_12859),or(not(and(implies(X,X_12859),X)),X_12859)) )],[refute_0_2105,refute_0_2106]) ).
cnf(refute_0_2108,plain,
or(implies(implies(X,X_12859),not(X)),X_12859) = implies(and(implies(X,X_12859),X),X_12859),
inference(resolve,[$cnf( $equal(or(not(and(implies(X,X_12859),X)),X_12859),implies(and(implies(X,X_12859),X),X_12859)) )],[refute_0_2100,refute_0_2107]) ).
cnf(refute_0_2109,plain,
and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)) = and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),
introduced(tautology,[refl,[$fot(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)))]]) ).
cnf(refute_0_2110,plain,
( and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)) != and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859))
| or(implies(implies(X,X_12859),not(X)),X_12859) != implies(and(implies(X,X_12859),X),X_12859)
| and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)) = and(X_12856,implies(and(implies(X,X_12859),X),X_12859)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859))) ),[1,1],$fot(implies(and(implies(X,X_12859),X),X_12859))]]) ).
cnf(refute_0_2111,plain,
( or(implies(implies(X,X_12859),not(X)),X_12859) != implies(and(implies(X,X_12859),X),X_12859)
| and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)) = and(X_12856,implies(and(implies(X,X_12859),X),X_12859)) ),
inference(resolve,[$cnf( $equal(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859))) )],[refute_0_2109,refute_0_2110]) ).
cnf(refute_0_2112,plain,
and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)) = and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),
inference(resolve,[$cnf( $equal(or(implies(implies(X,X_12859),not(X)),X_12859),implies(and(implies(X,X_12859),X),X_12859)) )],[refute_0_2108,refute_0_2111]) ).
cnf(refute_0_2113,plain,
or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)) = or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)),
introduced(tautology,[refl,[$fot(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)))]]) ).
cnf(refute_0_2114,plain,
( and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)) != and(X_12856,implies(and(implies(X,X_12859),X),X_12859))
| or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)) != or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857))
| or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)) = or(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),implies(X_12856,X_12857)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)),or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857))) ),[1,0],$fot(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)))]]) ).
cnf(refute_0_2115,plain,
( and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)) != and(X_12856,implies(and(implies(X,X_12859),X),X_12859))
| or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)) = or(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),implies(X_12856,X_12857)) ),
inference(resolve,[$cnf( $equal(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)),or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857))) )],[refute_0_2113,refute_0_2114]) ).
cnf(refute_0_2116,plain,
or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)) = or(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),implies(X_12856,X_12857)),
inference(resolve,[$cnf( $equal(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),and(X_12856,implies(and(implies(X,X_12859),X),X_12859))) )],[refute_0_2112,refute_0_2115]) ).
cnf(refute_0_2117,plain,
( or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)) != or(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),implies(X_12856,X_12857))
| ~ is_a_theorem(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)))
| is_a_theorem(or(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),implies(X_12856,X_12857))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857))) ),[0],$fot(or(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),implies(X_12856,X_12857)))]]) ).
cnf(refute_0_2118,plain,
( ~ is_a_theorem(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)))
| is_a_theorem(or(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),implies(X_12856,X_12857))) ),
inference(resolve,[$cnf( $equal(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857)),or(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),implies(X_12856,X_12857))) )],[refute_0_2116,refute_0_2117]) ).
cnf(refute_0_2119,plain,
is_a_theorem(or(and(X_12856,implies(and(implies(X,X_12859),X),X_12859)),implies(X_12856,X_12857))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_12856,or(implies(implies(X,X_12859),not(X)),X_12859)),implies(X_12856,X_12857))) )],[refute_0_2099,refute_0_2118]) ).
cnf(refute_0_2120,plain,
is_a_theorem(or(and(X_26283,implies(and(implies(X,X_12859),X),X_12859)),implies(X_26283,X_26285))),
inference(subst,[],[refute_0_2119:[bind(X_12856,$fot(X_26283)),bind(X_12857,$fot(X_26285))]]) ).
cnf(refute_0_2121,plain,
( ~ is_a_theorem(or(and(X_26283,implies(and(implies(X,X_12859),X),X_12859)),implies(X_26283,X_26285)))
| is_a_theorem(implies(X_26283,or(and(X_26283,implies(and(implies(X,X_12859),X),X_12859)),X_26285))) ),
inference(subst,[],[refute_0_798:[bind(X,$fot(X_26283)),bind(X_67,$fot(and(X_26283,implies(and(implies(X,X_12859),X),X_12859)))),bind(X_69,$fot(X_26285))]]) ).
cnf(refute_0_2122,plain,
is_a_theorem(implies(X_26283,or(and(X_26283,implies(and(implies(X,X_12859),X),X_12859)),X_26285))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_26283,implies(and(implies(X,X_12859),X),X_12859)),implies(X_26283,X_26285))) )],[refute_0_2120,refute_0_2121]) ).
cnf(refute_0_2123,plain,
is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(implies(X_26678,not(X_1833)),X_26678),not(X_1833))),X_26681))),
inference(subst,[],[refute_0_2122:[bind(X,$fot(X_26678)),bind(X_12859,$fot(not(X_1833))),bind(X_26283,$fot(X_26680)),bind(X_26285,$fot(X_26681))]]) ).
cnf(refute_0_2124,plain,
implies(X_26678,not(X_1833)) = not(and(X_26678,X_1833)),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_26678))]]) ).
cnf(refute_0_2125,plain,
( implies(X_26678,not(X_1833)) != not(and(X_26678,X_1833))
| ~ is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(implies(X_26678,not(X_1833)),X_26678),not(X_1833))),X_26681)))
| is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(implies(X_26678,not(X_1833)),X_26678),not(X_1833))),X_26681))) ),[0,1,0,1,0,0],$fot(not(and(X_26678,X_1833)))]]) ).
cnf(refute_0_2126,plain,
( ~ is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(implies(X_26678,not(X_1833)),X_26678),not(X_1833))),X_26681)))
| is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))) ),
inference(resolve,[$cnf( $equal(implies(X_26678,not(X_1833)),not(and(X_26678,X_1833))) )],[refute_0_2124,refute_0_2125]) ).
cnf(refute_0_2127,plain,
is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))),
inference(resolve,[$cnf( is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(implies(X_26678,not(X_1833)),X_26678),not(X_1833))),X_26681))) )],[refute_0_2123,refute_0_2126]) ).
cnf(refute_0_2128,plain,
or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681) = implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))),bind(Y,$fot(X_26681))]]) ).
cnf(refute_0_2129,plain,
and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))) = not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),
inference(subst,[],[refute_0_567:[bind(X,$fot(X_26680)),bind(X_1833,$fot(and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))]]) ).
cnf(refute_0_2130,plain,
implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833)) = not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),
inference(subst,[],[refute_0_448:[bind(X,$fot(and(not(and(X_26678,X_1833)),X_26678)))]]) ).
cnf(refute_0_2131,plain,
and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) = and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),
introduced(tautology,[refl,[$fot(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))))]]) ).
cnf(refute_0_2132,plain,
( and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) != and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833)))
| implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833)) != not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))
| and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) = and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833)))) ),[1,1],$fot(not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))]]) ).
cnf(refute_0_2133,plain,
( implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833)) != not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))
| and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) = and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))) ),
inference(resolve,[$cnf( $equal(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833)))) )],[refute_0_2131,refute_0_2132]) ).
cnf(refute_0_2134,plain,
and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) = and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),
inference(resolve,[$cnf( $equal(implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833)),not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))) )],[refute_0_2130,refute_0_2133]) ).
cnf(refute_0_2135,plain,
( and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) != and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))
| and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))) != not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))
| and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) = not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))))),bind(Y0,$fot(and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))))),bind(Z,$fot(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))))]]) ).
cnf(refute_0_2136,plain,
( and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))) != not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))
| and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) = not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))) ),
inference(resolve,[$cnf( $equal(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))) )],[refute_0_2134,refute_0_2135]) ).
cnf(refute_0_2137,plain,
and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) = not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),
inference(resolve,[$cnf( $equal(and(X_26680,not(and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))) )],[refute_0_2129,refute_0_2136]) ).
cnf(refute_0_2138,plain,
or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) = or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681),
introduced(tautology,[refl,[$fot(or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))]]) ).
cnf(refute_0_2139,plain,
( and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) != not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))
| or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) != or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)
| or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) = or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681),or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)) ),[1,0],$fot(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))))]]) ).
cnf(refute_0_2140,plain,
( and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))) != not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))
| or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) = or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681) ),
inference(resolve,[$cnf( $equal(or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681),or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)) )],[refute_0_2138,refute_0_2139]) ).
cnf(refute_0_2141,plain,
or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) = or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681),
inference(resolve,[$cnf( $equal(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)))) )],[refute_0_2137,refute_0_2140]) ).
cnf(refute_0_2142,plain,
( or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) != or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681)
| or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681) != implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)
| or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) = implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))),bind(Y0,$fot(or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681))),bind(Z,$fot(implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)))]]) ).
cnf(refute_0_2143,plain,
( or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681) != implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)
| or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) = implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681) ),
inference(resolve,[$cnf( $equal(or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681),or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681)) )],[refute_0_2141,refute_0_2142]) ).
cnf(refute_0_2144,plain,
or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) = implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681),
inference(resolve,[$cnf( $equal(or(not(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833))),X_26681),implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)) )],[refute_0_2128,refute_0_2143]) ).
cnf(refute_0_2145,plain,
implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)) = implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)),
introduced(tautology,[refl,[$fot(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)))]]) ).
cnf(refute_0_2146,plain,
( implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)) != implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))
| or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) != implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)
| implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)) = implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)),implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))) ),[1,1],$fot(implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681))]]) ).
cnf(refute_0_2147,plain,
( or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681) != implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)
| implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)) = implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)) ),
inference(resolve,[$cnf( $equal(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)),implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))) )],[refute_0_2145,refute_0_2146]) ).
cnf(refute_0_2148,plain,
implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)) = implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)),
inference(resolve,[$cnf( $equal(or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681),implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)) )],[refute_0_2144,refute_0_2147]) ).
cnf(refute_0_2149,plain,
( implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)) != implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681))
| ~ is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)))
| is_a_theorem(implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))) ),[0],$fot(implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681)))]]) ).
cnf(refute_0_2150,plain,
( ~ is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)))
| is_a_theorem(implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681))) ),
inference(resolve,[$cnf( $equal(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681)),implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681))) )],[refute_0_2148,refute_0_2149]) ).
cnf(refute_0_2151,plain,
is_a_theorem(implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,X_1833)),X_26678),X_1833)),X_26681))),
inference(resolve,[$cnf( is_a_theorem(implies(X_26680,or(and(X_26680,implies(and(not(and(X_26678,X_1833)),X_26678),not(X_1833))),X_26681))) )],[refute_0_2127,refute_0_2150]) ).
cnf(refute_0_2152,plain,
is_a_theorem(implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),equiv(X_47419,X_47419))),X_26681))),
inference(subst,[],[refute_0_2151:[bind(X_1833,$fot(equiv(X_47419,X_47419)))]]) ).
cnf(refute_0_2153,plain,
and(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),equiv(X_47419,X_47419)) = and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),
inference(subst,[],[refute_0_1981:[bind(X_31900,$fot(X_47419)),bind(X_47409,$fot(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)))]]) ).
cnf(refute_0_2154,plain,
( and(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),equiv(X_47419,X_47419)) != and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)
| ~ is_a_theorem(implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),equiv(X_47419,X_47419))),X_26681)))
| is_a_theorem(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),equiv(X_47419,X_47419))),X_26681))) ),[0,1,0,1],$fot(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678))]]) ).
cnf(refute_0_2155,plain,
( ~ is_a_theorem(implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),equiv(X_47419,X_47419))),X_26681)))
| is_a_theorem(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))) ),
inference(resolve,[$cnf( $equal(and(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),equiv(X_47419,X_47419)),and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) )],[refute_0_2153,refute_0_2154]) ).
cnf(refute_0_2156,plain,
is_a_theorem(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))),
inference(resolve,[$cnf( is_a_theorem(implies(X_26680,implies(implies(X_26680,and(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),equiv(X_47419,X_47419))),X_26681))) )],[refute_0_2152,refute_0_2155]) ).
cnf(refute_0_2157,plain,
implies(not(X_26680),X_26681) = or(X_26680,X_26681),
inference(subst,[],[refute_0_295:[bind(X,$fot(X_26680)),bind(Y,$fot(X_26681))]]) ).
cnf(refute_0_2158,plain,
and(X_26680,equiv(X_26678,X_26678)) = X_26680,
inference(subst,[],[refute_0_1981:[bind(X_31900,$fot(X_26678)),bind(X_47409,$fot(X_26680))]]) ).
cnf(refute_0_2159,plain,
not(and(X_26680,equiv(X_26678,X_26678))) = not(and(X_26680,equiv(X_26678,X_26678))),
introduced(tautology,[refl,[$fot(not(and(X_26680,equiv(X_26678,X_26678))))]]) ).
cnf(refute_0_2160,plain,
( and(X_26680,equiv(X_26678,X_26678)) != X_26680
| not(and(X_26680,equiv(X_26678,X_26678))) != not(and(X_26680,equiv(X_26678,X_26678)))
| not(and(X_26680,equiv(X_26678,X_26678))) = not(X_26680) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X_26680,equiv(X_26678,X_26678))),not(and(X_26680,equiv(X_26678,X_26678)))) ),[1,0],$fot(X_26680)]]) ).
cnf(refute_0_2161,plain,
( and(X_26680,equiv(X_26678,X_26678)) != X_26680
| not(and(X_26680,equiv(X_26678,X_26678))) = not(X_26680) ),
inference(resolve,[$cnf( $equal(not(and(X_26680,equiv(X_26678,X_26678))),not(and(X_26680,equiv(X_26678,X_26678)))) )],[refute_0_2159,refute_0_2160]) ).
cnf(refute_0_2162,plain,
not(and(X_26680,equiv(X_26678,X_26678))) = not(X_26680),
inference(resolve,[$cnf( $equal(and(X_26680,equiv(X_26678,X_26678)),X_26680) )],[refute_0_2158,refute_0_2161]) ).
cnf(refute_0_2163,plain,
implies(X_26680,not(equiv(X_26678,X_26678))) = not(and(X_26680,equiv(X_26678,X_26678))),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_26680)),bind(X_1833,$fot(equiv(X_26678,X_26678)))]]) ).
cnf(refute_0_2164,plain,
( implies(X_26680,not(equiv(X_26678,X_26678))) != not(and(X_26680,equiv(X_26678,X_26678)))
| not(and(X_26680,equiv(X_26678,X_26678))) != not(X_26680)
| implies(X_26680,not(equiv(X_26678,X_26678))) = not(X_26680) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(X_26680,not(equiv(X_26678,X_26678))))),bind(Y0,$fot(not(and(X_26680,equiv(X_26678,X_26678))))),bind(Z,$fot(not(X_26680)))]]) ).
cnf(refute_0_2165,plain,
( not(and(X_26680,equiv(X_26678,X_26678))) != not(X_26680)
| implies(X_26680,not(equiv(X_26678,X_26678))) = not(X_26680) ),
inference(resolve,[$cnf( $equal(implies(X_26680,not(equiv(X_26678,X_26678))),not(and(X_26680,equiv(X_26678,X_26678)))) )],[refute_0_2163,refute_0_2164]) ).
cnf(refute_0_2166,plain,
implies(X_26680,not(equiv(X_26678,X_26678))) = not(X_26680),
inference(resolve,[$cnf( $equal(not(and(X_26680,equiv(X_26678,X_26678))),not(X_26680)) )],[refute_0_2162,refute_0_2165]) ).
cnf(refute_0_2167,plain,
and(not(X_26678),X_26678) = not(equiv(X_26678,X_26678)),
inference(subst,[],[refute_0_1506:[bind(X_27252,$fot(X_26678))]]) ).
cnf(refute_0_2168,plain,
and(X_26678,equiv(X_47419,X_47419)) = X_26678,
inference(subst,[],[refute_0_1981:[bind(X_31900,$fot(X_47419)),bind(X_47409,$fot(X_26678))]]) ).
cnf(refute_0_2169,plain,
not(and(X_26678,equiv(X_47419,X_47419))) = not(and(X_26678,equiv(X_47419,X_47419))),
introduced(tautology,[refl,[$fot(not(and(X_26678,equiv(X_47419,X_47419))))]]) ).
cnf(refute_0_2170,plain,
( and(X_26678,equiv(X_47419,X_47419)) != X_26678
| not(and(X_26678,equiv(X_47419,X_47419))) != not(and(X_26678,equiv(X_47419,X_47419)))
| not(and(X_26678,equiv(X_47419,X_47419))) = not(X_26678) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X_26678,equiv(X_47419,X_47419))),not(and(X_26678,equiv(X_47419,X_47419)))) ),[1,0],$fot(X_26678)]]) ).
cnf(refute_0_2171,plain,
( and(X_26678,equiv(X_47419,X_47419)) != X_26678
| not(and(X_26678,equiv(X_47419,X_47419))) = not(X_26678) ),
inference(resolve,[$cnf( $equal(not(and(X_26678,equiv(X_47419,X_47419))),not(and(X_26678,equiv(X_47419,X_47419)))) )],[refute_0_2169,refute_0_2170]) ).
cnf(refute_0_2172,plain,
not(and(X_26678,equiv(X_47419,X_47419))) = not(X_26678),
inference(resolve,[$cnf( $equal(and(X_26678,equiv(X_47419,X_47419)),X_26678) )],[refute_0_2168,refute_0_2171]) ).
cnf(refute_0_2173,plain,
and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) = and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),
introduced(tautology,[refl,[$fot(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678))]]) ).
cnf(refute_0_2174,plain,
( and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) != and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)
| not(and(X_26678,equiv(X_47419,X_47419))) != not(X_26678)
| and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) = and(not(X_26678),X_26678) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) ),[1,0],$fot(not(X_26678))]]) ).
cnf(refute_0_2175,plain,
( not(and(X_26678,equiv(X_47419,X_47419))) != not(X_26678)
| and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) = and(not(X_26678),X_26678) ),
inference(resolve,[$cnf( $equal(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) )],[refute_0_2173,refute_0_2174]) ).
cnf(refute_0_2176,plain,
and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) = and(not(X_26678),X_26678),
inference(resolve,[$cnf( $equal(not(and(X_26678,equiv(X_47419,X_47419))),not(X_26678)) )],[refute_0_2172,refute_0_2175]) ).
cnf(refute_0_2177,plain,
( and(not(X_26678),X_26678) != not(equiv(X_26678,X_26678))
| and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) != and(not(X_26678),X_26678)
| and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) = not(equiv(X_26678,X_26678)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678))),bind(Y0,$fot(and(not(X_26678),X_26678))),bind(Z,$fot(not(equiv(X_26678,X_26678))))]]) ).
cnf(refute_0_2178,plain,
( and(not(X_26678),X_26678) != not(equiv(X_26678,X_26678))
| and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) = not(equiv(X_26678,X_26678)) ),
inference(resolve,[$cnf( $equal(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),and(not(X_26678),X_26678)) )],[refute_0_2176,refute_0_2177]) ).
cnf(refute_0_2179,plain,
and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) = not(equiv(X_26678,X_26678)),
inference(resolve,[$cnf( $equal(and(not(X_26678),X_26678),not(equiv(X_26678,X_26678))) )],[refute_0_2167,refute_0_2178]) ).
cnf(refute_0_2180,plain,
implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) = implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),
introduced(tautology,[refl,[$fot(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)))]]) ).
cnf(refute_0_2181,plain,
( and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) != not(equiv(X_26678,X_26678))
| implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) != implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678))
| implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) = implies(X_26680,not(equiv(X_26678,X_26678))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678))) ),[1,1],$fot(not(equiv(X_26678,X_26678)))]]) ).
cnf(refute_0_2182,plain,
( and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678) != not(equiv(X_26678,X_26678))
| implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) = implies(X_26680,not(equiv(X_26678,X_26678))) ),
inference(resolve,[$cnf( $equal(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678))) )],[refute_0_2180,refute_0_2181]) ).
cnf(refute_0_2183,plain,
implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) = implies(X_26680,not(equiv(X_26678,X_26678))),
inference(resolve,[$cnf( $equal(and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678),not(equiv(X_26678,X_26678))) )],[refute_0_2179,refute_0_2182]) ).
cnf(refute_0_2184,plain,
( implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) != implies(X_26680,not(equiv(X_26678,X_26678)))
| implies(X_26680,not(equiv(X_26678,X_26678))) != not(X_26680)
| implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) = not(X_26680) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)))),bind(Y0,$fot(implies(X_26680,not(equiv(X_26678,X_26678))))),bind(Z,$fot(not(X_26680)))]]) ).
cnf(refute_0_2185,plain,
( implies(X_26680,not(equiv(X_26678,X_26678))) != not(X_26680)
| implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) = not(X_26680) ),
inference(resolve,[$cnf( $equal(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),implies(X_26680,not(equiv(X_26678,X_26678)))) )],[refute_0_2183,refute_0_2184]) ).
cnf(refute_0_2186,plain,
implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) = not(X_26680),
inference(resolve,[$cnf( $equal(implies(X_26680,not(equiv(X_26678,X_26678))),not(X_26680)) )],[refute_0_2166,refute_0_2185]) ).
cnf(refute_0_2187,plain,
implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) = implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681),
introduced(tautology,[refl,[$fot(implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))]]) ).
cnf(refute_0_2188,plain,
( implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) != not(X_26680)
| implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) != implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)
| implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) = implies(not(X_26680),X_26681) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681),implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)) ),[1,0],$fot(not(X_26680))]]) ).
cnf(refute_0_2189,plain,
( implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)) != not(X_26680)
| implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) = implies(not(X_26680),X_26681) ),
inference(resolve,[$cnf( $equal(implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681),implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)) )],[refute_0_2187,refute_0_2188]) ).
cnf(refute_0_2190,plain,
implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) = implies(not(X_26680),X_26681),
inference(resolve,[$cnf( $equal(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),not(X_26680)) )],[refute_0_2186,refute_0_2189]) ).
cnf(refute_0_2191,plain,
( implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) != implies(not(X_26680),X_26681)
| implies(not(X_26680),X_26681) != or(X_26680,X_26681)
| implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) = or(X_26680,X_26681) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))),bind(Y0,$fot(implies(not(X_26680),X_26681))),bind(Z,$fot(or(X_26680,X_26681)))]]) ).
cnf(refute_0_2192,plain,
( implies(not(X_26680),X_26681) != or(X_26680,X_26681)
| implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) = or(X_26680,X_26681) ),
inference(resolve,[$cnf( $equal(implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681),implies(not(X_26680),X_26681)) )],[refute_0_2190,refute_0_2191]) ).
cnf(refute_0_2193,plain,
implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) = or(X_26680,X_26681),
inference(resolve,[$cnf( $equal(implies(not(X_26680),X_26681),or(X_26680,X_26681)) )],[refute_0_2157,refute_0_2192]) ).
cnf(refute_0_2194,plain,
implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)) = implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)),
introduced(tautology,[refl,[$fot(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)))]]) ).
cnf(refute_0_2195,plain,
( implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)) != implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))
| implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) != or(X_26680,X_26681)
| implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)) = implies(X_26680,or(X_26680,X_26681)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)),implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))) ),[1,1],$fot(or(X_26680,X_26681))]]) ).
cnf(refute_0_2196,plain,
( implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681) != or(X_26680,X_26681)
| implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)) = implies(X_26680,or(X_26680,X_26681)) ),
inference(resolve,[$cnf( $equal(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)),implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))) )],[refute_0_2194,refute_0_2195]) ).
cnf(refute_0_2197,plain,
implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)) = implies(X_26680,or(X_26680,X_26681)),
inference(resolve,[$cnf( $equal(implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681),or(X_26680,X_26681)) )],[refute_0_2193,refute_0_2196]) ).
cnf(refute_0_2198,plain,
( implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)) != implies(X_26680,or(X_26680,X_26681))
| ~ is_a_theorem(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)))
| is_a_theorem(implies(X_26680,or(X_26680,X_26681))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))) ),[0],$fot(implies(X_26680,or(X_26680,X_26681)))]]) ).
cnf(refute_0_2199,plain,
( ~ is_a_theorem(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)))
| is_a_theorem(implies(X_26680,or(X_26680,X_26681))) ),
inference(resolve,[$cnf( $equal(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681)),implies(X_26680,or(X_26680,X_26681))) )],[refute_0_2197,refute_0_2198]) ).
cnf(refute_0_2200,plain,
is_a_theorem(implies(X_26680,or(X_26680,X_26681))),
inference(resolve,[$cnf( is_a_theorem(implies(X_26680,implies(implies(X_26680,and(not(and(X_26678,equiv(X_47419,X_47419))),X_26678)),X_26681))) )],[refute_0_2156,refute_0_2199]) ).
cnf(refute_0_2201,plain,
is_a_theorem(implies(X_52955,or(X_52955,and(X_52954,X_52955)))),
inference(subst,[],[refute_0_2200:[bind(X_26680,$fot(X_52955)),bind(X_26681,$fot(and(X_52954,X_52955)))]]) ).
cnf(refute_0_2202,plain,
is_a_theorem(equiv(or(X_52955,and(X_52954,X_52955)),X_52955)),
inference(resolve,[$cnf( is_a_theorem(implies(X_52955,or(X_52955,and(X_52954,X_52955)))) )],[refute_0_2201,refute_0_2082]) ).
cnf(refute_0_2203,plain,
is_a_theorem(equiv(or(X_52957,and(X_52956,X_52957)),X_52957)),
inference(subst,[],[refute_0_2202:[bind(X_52954,$fot(X_52956)),bind(X_52955,$fot(X_52957))]]) ).
cnf(refute_0_2204,plain,
or(X_52957,and(X_52956,X_52957)) = X_52957,
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_52957,and(X_52956,X_52957)),X_52957)) )],[refute_0_2203,refute_0_2062]) ).
cnf(refute_0_2205,plain,
or(X_52957,and(not(X_58960),X_52957)) = X_52957,
inference(subst,[],[refute_0_2204:[bind(X_52956,$fot(not(X_58960)))]]) ).
cnf(refute_0_2206,plain,
or(X_9,not(Y)) = or(not(Y),X_9),
inference(subst,[],[refute_0_2046:[bind(X_58933,$fot(not(Y))),bind(X_58934,$fot(X_9))]]) ).
cnf(refute_0_2207,plain,
( and(not(X_9),Y) != not(or(X_9,not(Y)))
| or(X_9,not(Y)) != or(not(Y),X_9)
| and(not(X_9),Y) = not(or(not(Y),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X_9),Y),not(or(X_9,not(Y)))) ),[1,0],$fot(or(not(Y),X_9))]]) ).
cnf(refute_0_2208,plain,
( and(not(X_9),Y) != not(or(X_9,not(Y)))
| and(not(X_9),Y) = not(or(not(Y),X_9)) ),
inference(resolve,[$cnf( $equal(or(X_9,not(Y)),or(not(Y),X_9)) )],[refute_0_2206,refute_0_2207]) ).
cnf(refute_0_2209,plain,
and(not(X_9),Y) = not(or(not(Y),X_9)),
inference(resolve,[$cnf( $equal(and(not(X_9),Y),not(or(X_9,not(Y)))) )],[refute_0_97,refute_0_2208]) ).
cnf(refute_0_2210,plain,
or(not(Y),X_9) = implies(Y,X_9),
inference(subst,[],[refute_0_37:[bind(X,$fot(Y)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_2211,plain,
not(or(not(Y),X_9)) = not(or(not(Y),X_9)),
introduced(tautology,[refl,[$fot(not(or(not(Y),X_9)))]]) ).
cnf(refute_0_2212,plain,
( not(or(not(Y),X_9)) != not(or(not(Y),X_9))
| or(not(Y),X_9) != implies(Y,X_9)
| not(or(not(Y),X_9)) = not(implies(Y,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(Y),X_9)),not(or(not(Y),X_9))) ),[1,0],$fot(implies(Y,X_9))]]) ).
cnf(refute_0_2213,plain,
( or(not(Y),X_9) != implies(Y,X_9)
| not(or(not(Y),X_9)) = not(implies(Y,X_9)) ),
inference(resolve,[$cnf( $equal(not(or(not(Y),X_9)),not(or(not(Y),X_9))) )],[refute_0_2211,refute_0_2212]) ).
cnf(refute_0_2214,plain,
not(or(not(Y),X_9)) = not(implies(Y,X_9)),
inference(resolve,[$cnf( $equal(or(not(Y),X_9),implies(Y,X_9)) )],[refute_0_2210,refute_0_2213]) ).
cnf(refute_0_2215,plain,
( and(not(X_9),Y) != not(or(not(Y),X_9))
| not(or(not(Y),X_9)) != not(implies(Y,X_9))
| and(not(X_9),Y) = not(implies(Y,X_9)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(X_9),Y),not(implies(Y,X_9))) ),[0],$fot(not(or(not(Y),X_9)))]]) ).
cnf(refute_0_2216,plain,
( and(not(X_9),Y) != not(or(not(Y),X_9))
| and(not(X_9),Y) = not(implies(Y,X_9)) ),
inference(resolve,[$cnf( $equal(not(or(not(Y),X_9)),not(implies(Y,X_9))) )],[refute_0_2214,refute_0_2215]) ).
cnf(refute_0_2217,plain,
and(not(X_9),Y) = not(implies(Y,X_9)),
inference(resolve,[$cnf( $equal(and(not(X_9),Y),not(or(not(Y),X_9))) )],[refute_0_2209,refute_0_2216]) ).
cnf(refute_0_2218,plain,
and(not(X_58960),X_52957) = not(implies(X_52957,X_58960)),
inference(subst,[],[refute_0_2217:[bind(Y,$fot(X_52957)),bind(X_9,$fot(X_58960))]]) ).
cnf(refute_0_2219,plain,
( and(not(X_58960),X_52957) != not(implies(X_52957,X_58960))
| or(X_52957,and(not(X_58960),X_52957)) != X_52957
| or(X_52957,not(implies(X_52957,X_58960))) = X_52957 ),
introduced(tautology,[equality,[$cnf( $equal(or(X_52957,and(not(X_58960),X_52957)),X_52957) ),[0,1],$fot(not(implies(X_52957,X_58960)))]]) ).
cnf(refute_0_2220,plain,
( or(X_52957,and(not(X_58960),X_52957)) != X_52957
| or(X_52957,not(implies(X_52957,X_58960))) = X_52957 ),
inference(resolve,[$cnf( $equal(and(not(X_58960),X_52957),not(implies(X_52957,X_58960))) )],[refute_0_2218,refute_0_2219]) ).
cnf(refute_0_2221,plain,
or(X_52957,not(implies(X_52957,X_58960))) = X_52957,
inference(resolve,[$cnf( $equal(or(X_52957,and(not(X_58960),X_52957)),X_52957) )],[refute_0_2205,refute_0_2220]) ).
cnf(refute_0_2222,plain,
or(not(X),Y) = or(Y,not(X)),
inference(subst,[],[refute_0_2046:[bind(X_58933,$fot(Y)),bind(X_58934,$fot(not(X)))]]) ).
cnf(refute_0_2223,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) != or(Y,not(X))
| implies(X,Y) = or(Y,not(X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,Y),or(Y,not(X))) ),[0],$fot(or(not(X),Y))]]) ).
cnf(refute_0_2224,plain,
( implies(X,Y) != or(not(X),Y)
| implies(X,Y) = or(Y,not(X)) ),
inference(resolve,[$cnf( $equal(or(not(X),Y),or(Y,not(X))) )],[refute_0_2222,refute_0_2223]) ).
cnf(refute_0_2225,plain,
implies(X,Y) = or(Y,not(X)),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_26,refute_0_2224]) ).
cnf(refute_0_2226,plain,
( implies(X,Y) != or(Y,not(X))
| or(Y,not(X)) = implies(X,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(Y,not(X))))]]) ).
cnf(refute_0_2227,plain,
or(Y,not(X)) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(Y,not(X))) )],[refute_0_2225,refute_0_2226]) ).
cnf(refute_0_2228,plain,
or(X_52957,not(implies(X_52957,X_58960))) = implies(implies(X_52957,X_58960),X_52957),
inference(subst,[],[refute_0_2227:[bind(X,$fot(implies(X_52957,X_58960))),bind(Y,$fot(X_52957))]]) ).
cnf(refute_0_2229,plain,
( or(X_52957,not(implies(X_52957,X_58960))) != X_52957
| or(X_52957,not(implies(X_52957,X_58960))) != implies(implies(X_52957,X_58960),X_52957)
| implies(implies(X_52957,X_58960),X_52957) = X_52957 ),
introduced(tautology,[equality,[$cnf( $equal(or(X_52957,not(implies(X_52957,X_58960))),X_52957) ),[0],$fot(implies(implies(X_52957,X_58960),X_52957))]]) ).
cnf(refute_0_2230,plain,
( or(X_52957,not(implies(X_52957,X_58960))) != X_52957
| implies(implies(X_52957,X_58960),X_52957) = X_52957 ),
inference(resolve,[$cnf( $equal(or(X_52957,not(implies(X_52957,X_58960))),implies(implies(X_52957,X_58960),X_52957)) )],[refute_0_2228,refute_0_2229]) ).
cnf(refute_0_2231,plain,
implies(implies(X_52957,X_58960),X_52957) = X_52957,
inference(resolve,[$cnf( $equal(or(X_52957,not(implies(X_52957,X_58960))),X_52957) )],[refute_0_2221,refute_0_2230]) ).
cnf(refute_0_2232,plain,
implies(implies(X_58961,not(X_1833)),X_58961) = X_58961,
inference(subst,[],[refute_0_2231:[bind(X_52957,$fot(X_58961)),bind(X_58960,$fot(not(X_1833)))]]) ).
cnf(refute_0_2233,plain,
implies(X_58961,not(X_1833)) = not(and(X_58961,X_1833)),
inference(subst,[],[refute_0_448:[bind(X,$fot(X_58961))]]) ).
cnf(refute_0_2234,plain,
( implies(X_58961,not(X_1833)) != not(and(X_58961,X_1833))
| implies(implies(X_58961,not(X_1833)),X_58961) != X_58961
| implies(not(and(X_58961,X_1833)),X_58961) = X_58961 ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_58961,not(X_1833)),X_58961),X_58961) ),[0,0],$fot(not(and(X_58961,X_1833)))]]) ).
cnf(refute_0_2235,plain,
( implies(implies(X_58961,not(X_1833)),X_58961) != X_58961
| implies(not(and(X_58961,X_1833)),X_58961) = X_58961 ),
inference(resolve,[$cnf( $equal(implies(X_58961,not(X_1833)),not(and(X_58961,X_1833))) )],[refute_0_2233,refute_0_2234]) ).
cnf(refute_0_2236,plain,
implies(not(and(X_58961,X_1833)),X_58961) = X_58961,
inference(resolve,[$cnf( $equal(implies(implies(X_58961,not(X_1833)),X_58961),X_58961) )],[refute_0_2232,refute_0_2235]) ).
cnf(refute_0_2237,plain,
or(and(X_58961,X_1833),X_58961) = or(X_58961,and(X_58961,X_1833)),
inference(subst,[],[refute_0_2048:[bind(X_58933,$fot(and(X_58961,X_1833))),bind(X_58934,$fot(X_58961))]]) ).
cnf(refute_0_2238,plain,
implies(not(and(X_58961,X_1833)),X_58961) = or(and(X_58961,X_1833),X_58961),
inference(subst,[],[refute_0_295:[bind(X,$fot(and(X_58961,X_1833))),bind(Y,$fot(X_58961))]]) ).
cnf(refute_0_2239,plain,
( implies(not(and(X_58961,X_1833)),X_58961) != or(and(X_58961,X_1833),X_58961)
| or(and(X_58961,X_1833),X_58961) != or(X_58961,and(X_58961,X_1833))
| implies(not(and(X_58961,X_1833)),X_58961) = or(X_58961,and(X_58961,X_1833)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(not(and(X_58961,X_1833)),X_58961))),bind(Y0,$fot(or(and(X_58961,X_1833),X_58961))),bind(Z,$fot(or(X_58961,and(X_58961,X_1833))))]]) ).
cnf(refute_0_2240,plain,
( or(and(X_58961,X_1833),X_58961) != or(X_58961,and(X_58961,X_1833))
| implies(not(and(X_58961,X_1833)),X_58961) = or(X_58961,and(X_58961,X_1833)) ),
inference(resolve,[$cnf( $equal(implies(not(and(X_58961,X_1833)),X_58961),or(and(X_58961,X_1833),X_58961)) )],[refute_0_2238,refute_0_2239]) ).
cnf(refute_0_2241,plain,
implies(not(and(X_58961,X_1833)),X_58961) = or(X_58961,and(X_58961,X_1833)),
inference(resolve,[$cnf( $equal(or(and(X_58961,X_1833),X_58961),or(X_58961,and(X_58961,X_1833))) )],[refute_0_2237,refute_0_2240]) ).
cnf(refute_0_2242,plain,
( implies(not(and(X_58961,X_1833)),X_58961) != X_58961
| implies(not(and(X_58961,X_1833)),X_58961) != or(X_58961,and(X_58961,X_1833))
| or(X_58961,and(X_58961,X_1833)) = X_58961 ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(and(X_58961,X_1833)),X_58961),X_58961) ),[0],$fot(or(X_58961,and(X_58961,X_1833)))]]) ).
cnf(refute_0_2243,plain,
( implies(not(and(X_58961,X_1833)),X_58961) != X_58961
| or(X_58961,and(X_58961,X_1833)) = X_58961 ),
inference(resolve,[$cnf( $equal(implies(not(and(X_58961,X_1833)),X_58961),or(X_58961,and(X_58961,X_1833))) )],[refute_0_2241,refute_0_2242]) ).
cnf(refute_0_2244,plain,
or(X_58961,and(X_58961,X_1833)) = X_58961,
inference(resolve,[$cnf( $equal(implies(not(and(X_58961,X_1833)),X_58961),X_58961) )],[refute_0_2236,refute_0_2243]) ).
cnf(refute_0_2245,plain,
or(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),and(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),X_1833)) = implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),
inference(subst,[],[refute_0_2244:[bind(X_58961,$fot(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739))))))]]) ).
cnf(refute_0_2246,plain,
( or(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),and(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),X_1833)) != implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739))))
| ~ is_a_theorem(or(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),and(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),X_1833)))
| is_a_theorem(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),and(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),X_1833))) ),[0],$fot(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))))]]) ).
cnf(refute_0_2247,plain,
( ~ is_a_theorem(or(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),and(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),X_1833)))
| is_a_theorem(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739))))) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),and(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),X_1833)),implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739))))) )],[refute_0_2245,refute_0_2246]) ).
cnf(refute_0_2248,plain,
is_a_theorem(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739))))),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),and(implies(or(X_61739,X_61738),or(and(X_61738,X_61739),equiv(X_61738,not(X_61739)))),X_1833))) )],[refute_0_2061,refute_0_2247]) ).
cnf(refute_0_2249,plain,
is_a_theorem(implies(or(X_61741,not(X_9)),or(and(not(X_9),X_61741),equiv(not(X_9),not(X_61741))))),
inference(subst,[],[refute_0_2248:[bind(X_61738,$fot(not(X_9))),bind(X_61739,$fot(X_61741))]]) ).
cnf(refute_0_2250,plain,
and(not(X_9),X_61741) = not(implies(X_61741,X_9)),
inference(subst,[],[refute_0_2217:[bind(Y,$fot(X_61741))]]) ).
cnf(refute_0_2251,plain,
( and(not(X_9),X_61741) != not(implies(X_61741,X_9))
| ~ is_a_theorem(implies(or(X_61741,not(X_9)),or(and(not(X_9),X_61741),equiv(not(X_9),not(X_61741)))))
| is_a_theorem(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_61741,not(X_9)),or(and(not(X_9),X_61741),equiv(not(X_9),not(X_61741))))) ),[0,1,0],$fot(not(implies(X_61741,X_9)))]]) ).
cnf(refute_0_2252,plain,
( ~ is_a_theorem(implies(or(X_61741,not(X_9)),or(and(not(X_9),X_61741),equiv(not(X_9),not(X_61741)))))
| is_a_theorem(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))) ),
inference(resolve,[$cnf( $equal(and(not(X_9),X_61741),not(implies(X_61741,X_9))) )],[refute_0_2250,refute_0_2251]) ).
cnf(refute_0_2253,plain,
is_a_theorem(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_61741,not(X_9)),or(and(not(X_9),X_61741),equiv(not(X_9),not(X_61741))))) )],[refute_0_2249,refute_0_2252]) ).
cnf(refute_0_2254,plain,
not(not(X_61741)) = X_61741,
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(X_61741))]]) ).
cnf(refute_0_2255,plain,
equiv(X_9,not(not(X_61741))) = equiv(X_9,not(not(X_61741))),
introduced(tautology,[refl,[$fot(equiv(X_9,not(not(X_61741))))]]) ).
cnf(refute_0_2256,plain,
( equiv(X_9,not(not(X_61741))) != equiv(X_9,not(not(X_61741)))
| not(not(X_61741)) != X_61741
| equiv(X_9,not(not(X_61741))) = equiv(X_9,X_61741) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_9,not(not(X_61741))),equiv(X_9,not(not(X_61741)))) ),[1,1],$fot(X_61741)]]) ).
cnf(refute_0_2257,plain,
( not(not(X_61741)) != X_61741
| equiv(X_9,not(not(X_61741))) = equiv(X_9,X_61741) ),
inference(resolve,[$cnf( $equal(equiv(X_9,not(not(X_61741))),equiv(X_9,not(not(X_61741)))) )],[refute_0_2255,refute_0_2256]) ).
cnf(refute_0_2258,plain,
equiv(X_9,not(not(X_61741))) = equiv(X_9,X_61741),
inference(resolve,[$cnf( $equal(not(not(X_61741)),X_61741) )],[refute_0_2254,refute_0_2257]) ).
cnf(refute_0_2259,plain,
not(not(equiv(not(X_9),X))) = equiv(not(X_9),X),
inference(subst,[],[refute_0_638:[bind(X_1832,$fot(equiv(not(X_9),X)))]]) ).
cnf(refute_0_2260,plain,
implies(or(X_9,X),and(X,X_9)) = not(equiv(not(X_9),X)),
inference(subst,[],[refute_0_845:[bind(Y,$fot(X))]]) ).
cnf(refute_0_2261,plain,
not(implies(or(X_9,X),and(X,X_9))) = not(implies(or(X_9,X),and(X,X_9))),
introduced(tautology,[refl,[$fot(not(implies(or(X_9,X),and(X,X_9))))]]) ).
cnf(refute_0_2262,plain,
( implies(or(X_9,X),and(X,X_9)) != not(equiv(not(X_9),X))
| not(implies(or(X_9,X),and(X,X_9))) != not(implies(or(X_9,X),and(X,X_9)))
| not(implies(or(X_9,X),and(X,X_9))) = not(not(equiv(not(X_9),X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(or(X_9,X),and(X,X_9))),not(implies(or(X_9,X),and(X,X_9)))) ),[1,0],$fot(not(equiv(not(X_9),X)))]]) ).
cnf(refute_0_2263,plain,
( implies(or(X_9,X),and(X,X_9)) != not(equiv(not(X_9),X))
| not(implies(or(X_9,X),and(X,X_9))) = not(not(equiv(not(X_9),X))) ),
inference(resolve,[$cnf( $equal(not(implies(or(X_9,X),and(X,X_9))),not(implies(or(X_9,X),and(X,X_9)))) )],[refute_0_2261,refute_0_2262]) ).
cnf(refute_0_2264,plain,
not(implies(or(X_9,X),and(X,X_9))) = not(not(equiv(not(X_9),X))),
inference(resolve,[$cnf( $equal(implies(or(X_9,X),and(X,X_9)),not(equiv(not(X_9),X))) )],[refute_0_2260,refute_0_2263]) ).
cnf(refute_0_2265,plain,
( not(implies(or(X_9,X),and(X,X_9))) != not(not(equiv(not(X_9),X)))
| not(not(equiv(not(X_9),X))) != equiv(not(X_9),X)
| not(implies(or(X_9,X),and(X,X_9))) = equiv(not(X_9),X) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(not(implies(or(X_9,X),and(X,X_9))))),bind(Y0,$fot(not(not(equiv(not(X_9),X))))),bind(Z,$fot(equiv(not(X_9),X)))]]) ).
cnf(refute_0_2266,plain,
( not(not(equiv(not(X_9),X))) != equiv(not(X_9),X)
| not(implies(or(X_9,X),and(X,X_9))) = equiv(not(X_9),X) ),
inference(resolve,[$cnf( $equal(not(implies(or(X_9,X),and(X,X_9))),not(not(equiv(not(X_9),X)))) )],[refute_0_2264,refute_0_2265]) ).
cnf(refute_0_2267,plain,
not(implies(or(X_9,X),and(X,X_9))) = equiv(not(X_9),X),
inference(resolve,[$cnf( $equal(not(not(equiv(not(X_9),X))),equiv(not(X_9),X)) )],[refute_0_2259,refute_0_2266]) ).
cnf(refute_0_2268,plain,
and(not(and(X,X_9)),or(X_9,X)) = not(implies(or(X_9,X),and(X,X_9))),
inference(subst,[],[refute_0_2217:[bind(Y,$fot(or(X_9,X))),bind(X_9,$fot(and(X,X_9)))]]) ).
cnf(refute_0_2269,plain,
( and(not(and(X,X_9)),or(X_9,X)) != not(implies(or(X_9,X),and(X,X_9)))
| not(implies(or(X_9,X),and(X,X_9))) != equiv(not(X_9),X)
| and(not(and(X,X_9)),or(X_9,X)) = equiv(not(X_9),X) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(not(and(X,X_9)),or(X_9,X)))),bind(Y0,$fot(not(implies(or(X_9,X),and(X,X_9))))),bind(Z,$fot(equiv(not(X_9),X)))]]) ).
cnf(refute_0_2270,plain,
( not(implies(or(X_9,X),and(X,X_9))) != equiv(not(X_9),X)
| and(not(and(X,X_9)),or(X_9,X)) = equiv(not(X_9),X) ),
inference(resolve,[$cnf( $equal(and(not(and(X,X_9)),or(X_9,X)),not(implies(or(X_9,X),and(X,X_9)))) )],[refute_0_2268,refute_0_2269]) ).
cnf(refute_0_2271,plain,
and(not(and(X,X_9)),or(X_9,X)) = equiv(not(X_9),X),
inference(resolve,[$cnf( $equal(not(implies(or(X_9,X),and(X,X_9))),equiv(not(X_9),X)) )],[refute_0_2267,refute_0_2270]) ).
cnf(refute_0_2272,plain,
( and(not(and(X,X_9)),or(X_9,X)) != equiv(not(X_9),X)
| equiv(X,not(X_9)) != and(not(and(X,X_9)),or(X_9,X))
| equiv(X,not(X_9)) = equiv(not(X_9),X) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X,not(X_9)),and(not(and(X,X_9)),or(X_9,X))) ),[1],$fot(equiv(not(X_9),X))]]) ).
cnf(refute_0_2273,plain,
( equiv(X,not(X_9)) != and(not(and(X,X_9)),or(X_9,X))
| equiv(X,not(X_9)) = equiv(not(X_9),X) ),
inference(resolve,[$cnf( $equal(and(not(and(X,X_9)),or(X_9,X)),equiv(not(X_9),X)) )],[refute_0_2271,refute_0_2272]) ).
cnf(refute_0_2274,plain,
equiv(X,not(X_9)) = equiv(not(X_9),X),
inference(resolve,[$cnf( $equal(equiv(X,not(X_9)),and(not(and(X,X_9)),or(X_9,X))) )],[refute_0_118,refute_0_2273]) ).
cnf(refute_0_2275,plain,
or(X_9,not(X_154)) = or(not(X_154),X_9),
inference(subst,[],[refute_0_2046:[bind(X_58933,$fot(not(X_154))),bind(X_58934,$fot(X_9))]]) ).
cnf(refute_0_2276,plain,
( equiv(not(X_9),not(X_154)) != and(or(X_9,not(X_154)),or(X_154,not(X_9)))
| or(X_9,not(X_154)) != or(not(X_154),X_9)
| equiv(not(X_9),not(X_154)) = and(or(not(X_154),X_9),or(X_154,not(X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_9),not(X_154)),and(or(X_9,not(X_154)),or(X_154,not(X_9)))) ),[1,0],$fot(or(not(X_154),X_9))]]) ).
cnf(refute_0_2277,plain,
( equiv(not(X_9),not(X_154)) != and(or(X_9,not(X_154)),or(X_154,not(X_9)))
| equiv(not(X_9),not(X_154)) = and(or(not(X_154),X_9),or(X_154,not(X_9))) ),
inference(resolve,[$cnf( $equal(or(X_9,not(X_154)),or(not(X_154),X_9)) )],[refute_0_2275,refute_0_2276]) ).
cnf(refute_0_2278,plain,
equiv(not(X_9),not(X_154)) = and(or(not(X_154),X_9),or(X_154,not(X_9))),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(X_154)),and(or(X_9,not(X_154)),or(X_154,not(X_9)))) )],[refute_0_1226,refute_0_2277]) ).
cnf(refute_0_2279,plain,
and(implies(X_154,X_9),implies(X_9,X_154)) = equiv(X_154,X_9),
inference(subst,[],[refute_0_229:[bind(X,$fot(X_154)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_2280,plain,
or(X_154,not(X_9)) = implies(X_9,X_154),
inference(subst,[],[refute_0_2227:[bind(X,$fot(X_9)),bind(Y,$fot(X_154))]]) ).
cnf(refute_0_2281,plain,
and(implies(X_154,X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),or(X_154,not(X_9))),
introduced(tautology,[refl,[$fot(and(implies(X_154,X_9),or(X_154,not(X_9))))]]) ).
cnf(refute_0_2282,plain,
( and(implies(X_154,X_9),or(X_154,not(X_9))) != and(implies(X_154,X_9),or(X_154,not(X_9)))
| or(X_154,not(X_9)) != implies(X_9,X_154)
| and(implies(X_154,X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),implies(X_9,X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_154,X_9),or(X_154,not(X_9))),and(implies(X_154,X_9),or(X_154,not(X_9)))) ),[1,1],$fot(implies(X_9,X_154))]]) ).
cnf(refute_0_2283,plain,
( or(X_154,not(X_9)) != implies(X_9,X_154)
| and(implies(X_154,X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),implies(X_9,X_154)) ),
inference(resolve,[$cnf( $equal(and(implies(X_154,X_9),or(X_154,not(X_9))),and(implies(X_154,X_9),or(X_154,not(X_9)))) )],[refute_0_2281,refute_0_2282]) ).
cnf(refute_0_2284,plain,
and(implies(X_154,X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),implies(X_9,X_154)),
inference(resolve,[$cnf( $equal(or(X_154,not(X_9)),implies(X_9,X_154)) )],[refute_0_2280,refute_0_2283]) ).
cnf(refute_0_2285,plain,
or(not(X_154),X_9) = implies(X_154,X_9),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_154)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_2286,plain,
and(or(not(X_154),X_9),or(X_154,not(X_9))) = and(or(not(X_154),X_9),or(X_154,not(X_9))),
introduced(tautology,[refl,[$fot(and(or(not(X_154),X_9),or(X_154,not(X_9))))]]) ).
cnf(refute_0_2287,plain,
( and(or(not(X_154),X_9),or(X_154,not(X_9))) != and(or(not(X_154),X_9),or(X_154,not(X_9)))
| or(not(X_154),X_9) != implies(X_154,X_9)
| and(or(not(X_154),X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),or(X_154,not(X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(not(X_154),X_9),or(X_154,not(X_9))),and(or(not(X_154),X_9),or(X_154,not(X_9)))) ),[1,0],$fot(implies(X_154,X_9))]]) ).
cnf(refute_0_2288,plain,
( or(not(X_154),X_9) != implies(X_154,X_9)
| and(or(not(X_154),X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),or(X_154,not(X_9))) ),
inference(resolve,[$cnf( $equal(and(or(not(X_154),X_9),or(X_154,not(X_9))),and(or(not(X_154),X_9),or(X_154,not(X_9)))) )],[refute_0_2286,refute_0_2287]) ).
cnf(refute_0_2289,plain,
and(or(not(X_154),X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),or(X_154,not(X_9))),
inference(resolve,[$cnf( $equal(or(not(X_154),X_9),implies(X_154,X_9)) )],[refute_0_2285,refute_0_2288]) ).
cnf(refute_0_2290,plain,
( and(implies(X_154,X_9),or(X_154,not(X_9))) != and(implies(X_154,X_9),implies(X_9,X_154))
| and(or(not(X_154),X_9),or(X_154,not(X_9))) != and(implies(X_154,X_9),or(X_154,not(X_9)))
| and(or(not(X_154),X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),implies(X_9,X_154)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(or(not(X_154),X_9),or(X_154,not(X_9))))),bind(Y0,$fot(and(implies(X_154,X_9),or(X_154,not(X_9))))),bind(Z,$fot(and(implies(X_154,X_9),implies(X_9,X_154))))]]) ).
cnf(refute_0_2291,plain,
( and(implies(X_154,X_9),or(X_154,not(X_9))) != and(implies(X_154,X_9),implies(X_9,X_154))
| and(or(not(X_154),X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),implies(X_9,X_154)) ),
inference(resolve,[$cnf( $equal(and(or(not(X_154),X_9),or(X_154,not(X_9))),and(implies(X_154,X_9),or(X_154,not(X_9)))) )],[refute_0_2289,refute_0_2290]) ).
cnf(refute_0_2292,plain,
and(or(not(X_154),X_9),or(X_154,not(X_9))) = and(implies(X_154,X_9),implies(X_9,X_154)),
inference(resolve,[$cnf( $equal(and(implies(X_154,X_9),or(X_154,not(X_9))),and(implies(X_154,X_9),implies(X_9,X_154))) )],[refute_0_2284,refute_0_2291]) ).
cnf(refute_0_2293,plain,
( and(implies(X_154,X_9),implies(X_9,X_154)) != equiv(X_154,X_9)
| and(or(not(X_154),X_9),or(X_154,not(X_9))) != and(implies(X_154,X_9),implies(X_9,X_154))
| and(or(not(X_154),X_9),or(X_154,not(X_9))) = equiv(X_154,X_9) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(and(or(not(X_154),X_9),or(X_154,not(X_9))))),bind(Y0,$fot(and(implies(X_154,X_9),implies(X_9,X_154)))),bind(Z,$fot(equiv(X_154,X_9)))]]) ).
cnf(refute_0_2294,plain,
( and(implies(X_154,X_9),implies(X_9,X_154)) != equiv(X_154,X_9)
| and(or(not(X_154),X_9),or(X_154,not(X_9))) = equiv(X_154,X_9) ),
inference(resolve,[$cnf( $equal(and(or(not(X_154),X_9),or(X_154,not(X_9))),and(implies(X_154,X_9),implies(X_9,X_154))) )],[refute_0_2292,refute_0_2293]) ).
cnf(refute_0_2295,plain,
and(or(not(X_154),X_9),or(X_154,not(X_9))) = equiv(X_154,X_9),
inference(resolve,[$cnf( $equal(and(implies(X_154,X_9),implies(X_9,X_154)),equiv(X_154,X_9)) )],[refute_0_2279,refute_0_2294]) ).
cnf(refute_0_2296,plain,
( and(or(not(X_154),X_9),or(X_154,not(X_9))) != equiv(X_154,X_9)
| equiv(not(X_9),not(X_154)) != and(or(not(X_154),X_9),or(X_154,not(X_9)))
| equiv(not(X_9),not(X_154)) = equiv(X_154,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_9),not(X_154)),and(or(not(X_154),X_9),or(X_154,not(X_9)))) ),[1],$fot(equiv(X_154,X_9))]]) ).
cnf(refute_0_2297,plain,
( equiv(not(X_9),not(X_154)) != and(or(not(X_154),X_9),or(X_154,not(X_9)))
| equiv(not(X_9),not(X_154)) = equiv(X_154,X_9) ),
inference(resolve,[$cnf( $equal(and(or(not(X_154),X_9),or(X_154,not(X_9))),equiv(X_154,X_9)) )],[refute_0_2295,refute_0_2296]) ).
cnf(refute_0_2298,plain,
equiv(not(X_9),not(X_154)) = equiv(X_154,X_9),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(X_154)),and(or(not(X_154),X_9),or(X_154,not(X_9)))) )],[refute_0_2278,refute_0_2297]) ).
cnf(refute_0_2299,plain,
equiv(not(X_58958),not(not(X_1832))) = equiv(not(X_1832),X_58958),
inference(subst,[],[refute_0_2298:[bind(X_154,$fot(not(X_1832))),bind(X_9,$fot(X_58958))]]) ).
cnf(refute_0_2300,plain,
( equiv(not(X_58958),not(not(X_1832))) != equiv(not(X_1832),X_58958)
| not(not(X_1832)) != X_1832
| equiv(not(X_58958),X_1832) = equiv(not(X_1832),X_58958) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X_58958),not(not(X_1832))),equiv(not(X_1832),X_58958)) ),[0,1],$fot(X_1832)]]) ).
cnf(refute_0_2301,plain,
( equiv(not(X_58958),not(not(X_1832))) != equiv(not(X_1832),X_58958)
| equiv(not(X_58958),X_1832) = equiv(not(X_1832),X_58958) ),
inference(resolve,[$cnf( $equal(not(not(X_1832)),X_1832) )],[refute_0_638,refute_0_2300]) ).
cnf(refute_0_2302,plain,
equiv(not(X_58958),X_1832) = equiv(not(X_1832),X_58958),
inference(resolve,[$cnf( $equal(equiv(not(X_58958),not(not(X_1832))),equiv(not(X_1832),X_58958)) )],[refute_0_2299,refute_0_2301]) ).
cnf(refute_0_2303,plain,
equiv(not(X_9),X) = equiv(not(X),X_9),
inference(subst,[],[refute_0_2302:[bind(X_1832,$fot(X)),bind(X_58958,$fot(X_9))]]) ).
cnf(refute_0_2304,plain,
( equiv(X,not(X_9)) != equiv(not(X_9),X)
| equiv(not(X_9),X) != equiv(not(X),X_9)
| equiv(X,not(X_9)) = equiv(not(X),X_9) ),
introduced(tautology,[equality,[$cnf( ~ $equal(equiv(X,not(X_9)),equiv(not(X),X_9)) ),[0],$fot(equiv(not(X_9),X))]]) ).
cnf(refute_0_2305,plain,
( equiv(X,not(X_9)) != equiv(not(X_9),X)
| equiv(X,not(X_9)) = equiv(not(X),X_9) ),
inference(resolve,[$cnf( $equal(equiv(not(X_9),X),equiv(not(X),X_9)) )],[refute_0_2303,refute_0_2304]) ).
cnf(refute_0_2306,plain,
equiv(X,not(X_9)) = equiv(not(X),X_9),
inference(resolve,[$cnf( $equal(equiv(X,not(X_9)),equiv(not(X_9),X)) )],[refute_0_2274,refute_0_2305]) ).
cnf(refute_0_2307,plain,
( equiv(X,not(X_9)) != equiv(not(X),X_9)
| equiv(not(X),X_9) = equiv(X,not(X_9)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(equiv(X,not(X_9)))),bind(Y0,$fot(equiv(not(X),X_9)))]]) ).
cnf(refute_0_2308,plain,
equiv(not(X),X_9) = equiv(X,not(X_9)),
inference(resolve,[$cnf( $equal(equiv(X,not(X_9)),equiv(not(X),X_9)) )],[refute_0_2306,refute_0_2307]) ).
cnf(refute_0_2309,plain,
equiv(not(X_9),not(X_61741)) = equiv(X_9,not(not(X_61741))),
inference(subst,[],[refute_0_2308:[bind(X,$fot(X_9)),bind(X_9,$fot(not(X_61741)))]]) ).
cnf(refute_0_2310,plain,
( equiv(X_9,not(not(X_61741))) != equiv(X_9,X_61741)
| equiv(not(X_9),not(X_61741)) != equiv(X_9,not(not(X_61741)))
| equiv(not(X_9),not(X_61741)) = equiv(X_9,X_61741) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(equiv(not(X_9),not(X_61741)))),bind(Y0,$fot(equiv(X_9,not(not(X_61741))))),bind(Z,$fot(equiv(X_9,X_61741)))]]) ).
cnf(refute_0_2311,plain,
( equiv(X_9,not(not(X_61741))) != equiv(X_9,X_61741)
| equiv(not(X_9),not(X_61741)) = equiv(X_9,X_61741) ),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(X_61741)),equiv(X_9,not(not(X_61741)))) )],[refute_0_2309,refute_0_2310]) ).
cnf(refute_0_2312,plain,
equiv(not(X_9),not(X_61741)) = equiv(X_9,X_61741),
inference(resolve,[$cnf( $equal(equiv(X_9,not(not(X_61741))),equiv(X_9,X_61741)) )],[refute_0_2258,refute_0_2311]) ).
cnf(refute_0_2313,plain,
implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))) = implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))),
introduced(tautology,[refl,[$fot(implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))))]]) ).
cnf(refute_0_2314,plain,
( equiv(not(X_9),not(X_61741)) != equiv(X_9,X_61741)
| implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))) != implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741)))
| implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))) = implies(implies(X_61741,X_9),equiv(X_9,X_61741)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))),implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741)))) ),[1,1],$fot(equiv(X_9,X_61741))]]) ).
cnf(refute_0_2315,plain,
( equiv(not(X_9),not(X_61741)) != equiv(X_9,X_61741)
| implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))) = implies(implies(X_61741,X_9),equiv(X_9,X_61741)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))),implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741)))) )],[refute_0_2313,refute_0_2314]) ).
cnf(refute_0_2316,plain,
implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))) = implies(implies(X_61741,X_9),equiv(X_9,X_61741)),
inference(resolve,[$cnf( $equal(equiv(not(X_9),not(X_61741)),equiv(X_9,X_61741)) )],[refute_0_2312,refute_0_2315]) ).
cnf(refute_0_2317,plain,
or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))) = implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(X_61741,X_9))),bind(Y,$fot(equiv(not(X_9),not(X_61741))))]]) ).
cnf(refute_0_2318,plain,
( implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))) != implies(implies(X_61741,X_9),equiv(X_9,X_61741))
| or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))) != implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741)))
| or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))) = implies(implies(X_61741,X_9),equiv(X_9,X_61741)) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))),bind(Y0,$fot(implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))))),bind(Z,$fot(implies(implies(X_61741,X_9),equiv(X_9,X_61741))))]]) ).
cnf(refute_0_2319,plain,
( implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))) != implies(implies(X_61741,X_9),equiv(X_9,X_61741))
| or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))) = implies(implies(X_61741,X_9),equiv(X_9,X_61741)) ),
inference(resolve,[$cnf( $equal(or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))),implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741)))) )],[refute_0_2317,refute_0_2318]) ).
cnf(refute_0_2320,plain,
or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))) = implies(implies(X_61741,X_9),equiv(X_9,X_61741)),
inference(resolve,[$cnf( $equal(implies(implies(X_61741,X_9),equiv(not(X_9),not(X_61741))),implies(implies(X_61741,X_9),equiv(X_9,X_61741))) )],[refute_0_2316,refute_0_2319]) ).
cnf(refute_0_2321,plain,
implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),
introduced(tautology,[refl,[$fot(implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))))]]) ).
cnf(refute_0_2322,plain,
( implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) != implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))
| or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))) != implies(implies(X_61741,X_9),equiv(X_9,X_61741))
| implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))) ),[1,1],$fot(implies(implies(X_61741,X_9),equiv(X_9,X_61741)))]]) ).
cnf(refute_0_2323,plain,
( or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))) != implies(implies(X_61741,X_9),equiv(X_9,X_61741))
| implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))) )],[refute_0_2321,refute_0_2322]) ).
cnf(refute_0_2324,plain,
implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741))),
inference(resolve,[$cnf( $equal(or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))),implies(implies(X_61741,X_9),equiv(X_9,X_61741))) )],[refute_0_2320,refute_0_2323]) ).
cnf(refute_0_2325,plain,
or(X_61741,not(X_9)) = implies(X_9,X_61741),
inference(subst,[],[refute_0_2227:[bind(X,$fot(X_9)),bind(Y,$fot(X_61741))]]) ).
cnf(refute_0_2326,plain,
implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),
introduced(tautology,[refl,[$fot(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))))]]) ).
cnf(refute_0_2327,plain,
( implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) != implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))
| or(X_61741,not(X_9)) != implies(X_9,X_61741)
| implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))) ),[1,0],$fot(implies(X_9,X_61741))]]) ).
cnf(refute_0_2328,plain,
( or(X_61741,not(X_9)) != implies(X_9,X_61741)
| implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))) )],[refute_0_2326,refute_0_2327]) ).
cnf(refute_0_2329,plain,
implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),
inference(resolve,[$cnf( $equal(or(X_61741,not(X_9)),implies(X_9,X_61741)) )],[refute_0_2325,refute_0_2328]) ).
cnf(refute_0_2330,plain,
( implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) != implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741)))
| implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) != implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))
| implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741))) ),
inference(subst,[],[refute_0_134:[bind(X0,$fot(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))))),bind(Y0,$fot(implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))))),bind(Z,$fot(implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741)))))]]) ).
cnf(refute_0_2331,plain,
( implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) != implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741)))
| implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741))) ),
inference(resolve,[$cnf( $equal(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))) )],[refute_0_2329,refute_0_2330]) ).
cnf(refute_0_2332,plain,
implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) = implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741))),
inference(resolve,[$cnf( $equal(implies(implies(X_9,X_61741),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741)))) )],[refute_0_2324,refute_0_2331]) ).
cnf(refute_0_2333,plain,
( implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))) != implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741)))
| ~ is_a_theorem(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))))
| is_a_theorem(implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))) ),[0],$fot(implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741))))]]) ).
cnf(refute_0_2334,plain,
( ~ is_a_theorem(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))))
| is_a_theorem(implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741)))),implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741)))) )],[refute_0_2332,refute_0_2333]) ).
cnf(refute_0_2335,plain,
is_a_theorem(implies(implies(X_9,X_61741),implies(implies(X_61741,X_9),equiv(X_9,X_61741)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_61741,not(X_9)),or(not(implies(X_61741,X_9)),equiv(not(X_9),not(X_61741))))) )],[refute_0_2253,refute_0_2334]) ).
cnf(refute_0_2336,plain,
is_a_theorem(implies(implies(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14),implies(implies(skolemFOFtoCNF_Y_14,skolemFOFtoCNF_X_14),equiv(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14)))),
inference(subst,[],[refute_0_2335:[bind(X_61741,$fot(skolemFOFtoCNF_Y_14)),bind(X_9,$fot(skolemFOFtoCNF_X_14))]]) ).
cnf(refute_0_2337,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14),implies(implies(skolemFOFtoCNF_Y_14,skolemFOFtoCNF_X_14),equiv(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14)))) )],[refute_0_2336,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL495+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.33 % CPULimit : 300
% 0.19/0.34 % WCLimit : 600
% 0.19/0.34 % DateTime : Sat Jul 2 16:43:54 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 251.96/252.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 251.96/252.17
% 251.96/252.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 252.26/252.40
%------------------------------------------------------------------------------