TSTP Solution File: LCL485+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL485+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:52:35 EDT 2022
% Result : Theorem 58.93s 59.16s
% Output : CNFRefutation 59.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 97
% Number of leaves : 184
% Syntax : Number of formulae : 922 ( 475 unt; 0 def)
% Number of atoms : 1568 ( 926 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 1271 ( 625 ~; 608 |; 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 : 1691 ( 27 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(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(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_implies_2,conjecture,
implies_2 ).
fof(subgoal_0,plain,
implies_2,
inference(strip,[],[hilbert_implies_2]) ).
fof(negate_0_0,plain,
~ implies_2,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ implies_2
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[implies_2]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)))
| implies_2 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)))
| implies_2 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ implies_2,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_5,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8)))
| r3 )
& ( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P,Q] :
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
r3,
inference(canonicalize,[],[principia_r3]) ).
fof(normalize_0_8,plain,
( ~ modus_ponens
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y)
| modus_ponens )
& ( is_a_theorem(implies(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| modus_ponens )
& ( is_a_theorem(skolemFOFtoCNF_X)
| modus_ponens )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
modus_ponens,
inference(canonicalize,[],[principia_modus_ponens]) ).
fof(normalize_0_12,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_15,plain,
( ~ r4
<=> ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[r4]) ).
fof(normalize_0_16,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_15]) ).
fof(normalize_0_17,plain,
! [P,Q,R] :
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
r4,
inference(canonicalize,[],[principia_r4]) ).
fof(normalize_0_19,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_22,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_25,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_29,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_30,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
op_equiv,
inference(canonicalize,[],[hilbert_op_equiv]) ).
fof(normalize_0_32,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_33,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_35,plain,
( ~ r1
<=> ? [P] : ~ is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[r1]) ).
fof(normalize_0_36,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_35]) ).
fof(normalize_0_37,plain,
! [P] :
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(conjunct,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
r1,
inference(canonicalize,[],[principia_r1]) ).
fof(normalize_0_39,plain,
( ~ r2
<=> ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[r2]) ).
fof(normalize_0_40,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_39]) ).
fof(normalize_0_41,plain,
! [P,Q] :
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(conjunct,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
r2,
inference(canonicalize,[],[principia_r2]) ).
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_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)))
| implies_2 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ implies_2,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4))),
inference(resolve,[$cnf( implies_2 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r3,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$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(or(X_5108,X_5109),not(or(X_5109,or(X_5108,X_5109)))))
| is_a_theorem(or(not(or(X_5109,or(X_5108,X_5109))),or(X_5108,X_5109))) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(or(X_5108,X_5109))),bind(Q,$fot(not(or(X_5109,or(X_5108,X_5109)))))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7)))),
inference(subst,[],[refute_0_5:[bind(P,$fot(not(X_7)))]]) ).
cnf(refute_0_13,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_15,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
implies(X_7,Q) = or(not(X_7),Q),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_7)),bind(Y,$fot(Q))]]) ).
cnf(refute_0_17,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_18,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_19,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( implies(X_7,Q) != or(not(X_7),Q)
| or(not(X_7),Q) = implies(X_7,Q) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X_7,Q))),bind(Y0,$fot(or(not(X_7),Q)))]]) ).
cnf(refute_0_21,plain,
or(not(X_7),Q) = implies(X_7,Q),
inference(resolve,[$cnf( $equal(implies(X_7,Q),or(not(X_7),Q)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( or(not(X_7),Q) != implies(X_7,Q)
| ~ is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7))))
| is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7)))) ),[0,0],$fot(implies(X_7,Q))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7))))
| is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7)))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),Q),implies(X_7,Q)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_7),Q),or(Q,not(X_7)))) )],[refute_0_12,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(X_7,Q))
| ~ is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7))))
| is_a_theorem(or(Q,not(X_7))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_7,Q))),bind(Y,$fot(or(Q,not(X_7))))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(X_7,Q))
| is_a_theorem(or(Q,not(X_7))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(X_642,implies(X_641,X_643)),implies(X_641,implies(X_642,X_643))))
| is_a_theorem(or(implies(X_641,implies(X_642,X_643)),not(implies(X_642,implies(X_641,X_643))))) ),
inference(subst,[],[refute_0_26:[bind(Q,$fot(implies(X_641,implies(X_642,X_643)))),bind(X_7,$fot(implies(X_642,implies(X_641,X_643))))]]) ).
cnf(refute_0_28,plain,
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_29,plain,
r4,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))),
inference(resolve,[$cnf( r4 )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,or(not(X),X_132)))),
inference(subst,[],[refute_0_30:[bind(P,$fot(not(X))),bind(Q,$fot(X_131)),bind(R,$fot(X_132))]]) ).
cnf(refute_0_32,plain,
implies(X,X_132) = or(not(X),X_132),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_132))]]) ).
cnf(refute_0_33,plain,
( implies(X,X_132) != or(not(X),X_132)
| or(not(X),X_132) = implies(X,X_132) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,X_132))),bind(Y0,$fot(or(not(X),X_132)))]]) ).
cnf(refute_0_34,plain,
or(not(X),X_132) = implies(X,X_132),
inference(resolve,[$cnf( $equal(implies(X,X_132),or(not(X),X_132)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( or(not(X),X_132) != implies(X,X_132)
| ~ is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,or(not(X),X_132))))
| is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,or(not(X),X_132)))) ),[0,1,1],$fot(implies(X,X_132))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,or(not(X),X_132))))
| is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_132),implies(X,X_132)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,or(not(X),X_132)))) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_39,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_15,refute_0_38]) ).
cnf(refute_0_40,plain,
or(not(X),or(X_131,X_132)) = implies(X,or(X_131,X_132)),
inference(subst,[],[refute_0_39:[bind(Y,$fot(or(X_131,X_132)))]]) ).
cnf(refute_0_41,plain,
implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))) = implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))))]]) ).
cnf(refute_0_42,plain,
( implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))) != implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132)))
| or(not(X),or(X_131,X_132)) != implies(X,or(X_131,X_132))
| implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))) = implies(implies(X,or(X_131,X_132)),or(X_131,implies(X,X_132))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))),implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132)))) ),[1,0],$fot(implies(X,or(X_131,X_132)))]]) ).
cnf(refute_0_43,plain,
( or(not(X),or(X_131,X_132)) != implies(X,or(X_131,X_132))
| implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))) = implies(implies(X,or(X_131,X_132)),or(X_131,implies(X,X_132))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))),implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))) = implies(implies(X,or(X_131,X_132)),or(X_131,implies(X,X_132))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_131,X_132)),implies(X,or(X_131,X_132))) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))) != implies(implies(X,or(X_131,X_132)),or(X_131,implies(X,X_132)))
| ~ is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))))
| is_a_theorem(implies(implies(X,or(X_131,X_132)),or(X_131,implies(X,X_132)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132)))) ),[0],$fot(implies(implies(X,or(X_131,X_132)),or(X_131,implies(X,X_132))))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))))
| is_a_theorem(implies(implies(X,or(X_131,X_132)),or(X_131,implies(X,X_132)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132))),implies(implies(X,or(X_131,X_132)),or(X_131,implies(X,X_132)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(implies(X,or(X_131,X_132)),or(X_131,implies(X,X_132)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_131,X_132)),or(X_131,implies(X,X_132)))) )],[refute_0_37,refute_0_46]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(X_160,or(not(X),X_162)),or(not(X),implies(X_160,X_162)))),
inference(subst,[],[refute_0_47:[bind(X,$fot(X_160)),bind(X_131,$fot(not(X))),bind(X_132,$fot(X_162))]]) ).
cnf(refute_0_49,plain,
implies(X,implies(X_160,X_162)) = or(not(X),implies(X_160,X_162)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(implies(X_160,X_162)))]]) ).
cnf(refute_0_50,plain,
( implies(X,implies(X_160,X_162)) != or(not(X),implies(X_160,X_162))
| or(not(X),implies(X_160,X_162)) = implies(X,implies(X_160,X_162)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,implies(X_160,X_162)))),bind(Y0,$fot(or(not(X),implies(X_160,X_162))))]]) ).
cnf(refute_0_51,plain,
or(not(X),implies(X_160,X_162)) = implies(X,implies(X_160,X_162)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_160,X_162)),or(not(X),implies(X_160,X_162))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( or(not(X),implies(X_160,X_162)) != implies(X,implies(X_160,X_162))
| ~ is_a_theorem(implies(implies(X_160,or(not(X),X_162)),or(not(X),implies(X_160,X_162))))
| is_a_theorem(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_160,or(not(X),X_162)),or(not(X),implies(X_160,X_162)))) ),[0,1],$fot(implies(X,implies(X_160,X_162)))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(implies(implies(X_160,or(not(X),X_162)),or(not(X),implies(X_160,X_162))))
| is_a_theorem(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_160,X_162)),implies(X,implies(X_160,X_162))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_160,or(not(X),X_162)),or(not(X),implies(X_160,X_162)))) )],[refute_0_48,refute_0_53]) ).
cnf(refute_0_55,plain,
or(not(X),X_162) = implies(X,X_162),
inference(subst,[],[refute_0_39:[bind(Y,$fot(X_162))]]) ).
cnf(refute_0_56,plain,
implies(X_160,or(not(X),X_162)) = implies(X_160,or(not(X),X_162)),
introduced(tautology,[refl,[$fot(implies(X_160,or(not(X),X_162)))]]) ).
cnf(refute_0_57,plain,
( implies(X_160,or(not(X),X_162)) != implies(X_160,or(not(X),X_162))
| or(not(X),X_162) != implies(X,X_162)
| implies(X_160,or(not(X),X_162)) = implies(X_160,implies(X,X_162)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_160,or(not(X),X_162)),implies(X_160,or(not(X),X_162))) ),[1,1],$fot(implies(X,X_162))]]) ).
cnf(refute_0_58,plain,
( or(not(X),X_162) != implies(X,X_162)
| implies(X_160,or(not(X),X_162)) = implies(X_160,implies(X,X_162)) ),
inference(resolve,[$cnf( $equal(implies(X_160,or(not(X),X_162)),implies(X_160,or(not(X),X_162))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
implies(X_160,or(not(X),X_162)) = implies(X_160,implies(X,X_162)),
inference(resolve,[$cnf( $equal(or(not(X),X_162),implies(X,X_162)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))) = implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))),
introduced(tautology,[refl,[$fot(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))))]]) ).
cnf(refute_0_61,plain,
( implies(X_160,or(not(X),X_162)) != implies(X_160,implies(X,X_162))
| implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))) != implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162)))
| implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))) = implies(implies(X_160,implies(X,X_162)),implies(X,implies(X_160,X_162))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))),implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162)))) ),[1,0],$fot(implies(X_160,implies(X,X_162)))]]) ).
cnf(refute_0_62,plain,
( implies(X_160,or(not(X),X_162)) != implies(X_160,implies(X,X_162))
| implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))) = implies(implies(X_160,implies(X,X_162)),implies(X,implies(X_160,X_162))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))),implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162)))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))) = implies(implies(X_160,implies(X,X_162)),implies(X,implies(X_160,X_162))),
inference(resolve,[$cnf( $equal(implies(X_160,or(not(X),X_162)),implies(X_160,implies(X,X_162))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))) != implies(implies(X_160,implies(X,X_162)),implies(X,implies(X_160,X_162)))
| ~ is_a_theorem(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))))
| is_a_theorem(implies(implies(X_160,implies(X,X_162)),implies(X,implies(X_160,X_162)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162)))) ),[0],$fot(implies(implies(X_160,implies(X,X_162)),implies(X,implies(X_160,X_162))))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))))
| is_a_theorem(implies(implies(X_160,implies(X,X_162)),implies(X,implies(X_160,X_162)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162))),implies(implies(X_160,implies(X,X_162)),implies(X,implies(X_160,X_162)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(X_160,implies(X,X_162)),implies(X,implies(X_160,X_162)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_160,or(not(X),X_162)),implies(X,implies(X_160,X_162)))) )],[refute_0_54,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(X_642,implies(X_641,X_643)),implies(X_641,implies(X_642,X_643)))),
inference(subst,[],[refute_0_66:[bind(X,$fot(X_641)),bind(X_160,$fot(X_642)),bind(X_162,$fot(X_643))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(or(implies(X_641,implies(X_642,X_643)),not(implies(X_642,implies(X_641,X_643))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_642,implies(X_641,X_643)),implies(X_641,implies(X_642,X_643)))) )],[refute_0_67,refute_0_27]) ).
cnf(refute_0_69,plain,
is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(implies(X_750,implies(X_749,not(Y)))))),
inference(subst,[],[refute_0_68:[bind(X_641,$fot(X_749)),bind(X_642,$fot(X_750)),bind(X_643,$fot(not(Y)))]]) ).
cnf(refute_0_70,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_71,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_72,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_71,refute_0_70]) ).
cnf(refute_0_73,plain,
implies(X_28,implies(X,not(Y))) = not(and(X_28,not(implies(X,not(Y))))),
inference(subst,[],[refute_0_72:[bind(X,$fot(X_28)),bind(Y,$fot(implies(X,not(Y))))]]) ).
cnf(refute_0_74,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_75,plain,
op_and,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_76,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_75,refute_0_74]) ).
cnf(refute_0_77,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_39:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_78,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_79,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_80,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_83,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_76,refute_0_83]) ).
cnf(refute_0_85,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_86,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( implies(X_28,implies(X,not(Y))) != not(and(X_28,not(implies(X,not(Y)))))
| not(implies(X,not(Y))) != and(X,Y)
| implies(X_28,implies(X,not(Y))) = not(and(X_28,and(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_28,implies(X,not(Y))),not(and(X_28,not(implies(X,not(Y)))))) ),[1,0,1],$fot(and(X,Y))]]) ).
cnf(refute_0_88,plain,
( implies(X_28,implies(X,not(Y))) != not(and(X_28,not(implies(X,not(Y)))))
| implies(X_28,implies(X,not(Y))) = not(and(X_28,and(X,Y))) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(X_28,implies(X,not(Y))) = not(and(X_28,and(X,Y))),
inference(resolve,[$cnf( $equal(implies(X_28,implies(X,not(Y))),not(and(X_28,not(implies(X,not(Y)))))) )],[refute_0_73,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(X_750,implies(X_749,not(Y))) = not(and(X_750,and(X_749,Y))),
inference(subst,[],[refute_0_89:[bind(X,$fot(X_749)),bind(X_28,$fot(X_750))]]) ).
cnf(refute_0_91,plain,
( implies(X_750,implies(X_749,not(Y))) != not(and(X_750,and(X_749,Y)))
| ~ is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(implies(X_750,implies(X_749,not(Y))))))
| is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(implies(X_750,implies(X_749,not(Y)))))) ),[0,1,0],$fot(not(and(X_750,and(X_749,Y))))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(implies(X_750,implies(X_749,not(Y))))))
| is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y)))))) ),
inference(resolve,[$cnf( $equal(implies(X_750,implies(X_749,not(Y))),not(and(X_750,and(X_749,Y)))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y)))))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(implies(X_750,implies(X_749,not(Y)))))) )],[refute_0_69,refute_0_92]) ).
cnf(refute_0_94,plain,
or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y))))) = implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y))))),
inference(subst,[],[refute_0_39:[bind(X,$fot(and(X_749,and(X_750,Y)))),bind(Y,$fot(not(not(and(X_750,and(X_749,Y))))))]]) ).
cnf(refute_0_95,plain,
implies(X_749,implies(X_750,not(Y))) = not(and(X_749,and(X_750,Y))),
inference(subst,[],[refute_0_89:[bind(X,$fot(X_750)),bind(X_28,$fot(X_749))]]) ).
cnf(refute_0_96,plain,
or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) = or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))),
introduced(tautology,[refl,[$fot(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))))]]) ).
cnf(refute_0_97,plain,
( implies(X_749,implies(X_750,not(Y))) != not(and(X_749,and(X_750,Y)))
| or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) != or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y)))))
| or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) = or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))),or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y)))))) ),[1,0],$fot(not(and(X_749,and(X_750,Y))))]]) ).
cnf(refute_0_98,plain,
( implies(X_749,implies(X_750,not(Y))) != not(and(X_749,and(X_750,Y)))
| or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) = or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y))))) ),
inference(resolve,[$cnf( $equal(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))),or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y)))))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) = or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y))))),
inference(resolve,[$cnf( $equal(implies(X_749,implies(X_750,not(Y))),not(and(X_749,and(X_750,Y)))) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_101,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_19,refute_0_100]) ).
cnf(refute_0_102,plain,
( or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) != or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y)))))
| or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y))))) != implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y)))))
| or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) = implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y))))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))))),bind(Y0,$fot(or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y))))))),bind(Z,$fot(implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y)))))))]]) ).
cnf(refute_0_103,plain,
( or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y))))) != implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y)))))
| or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) = implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y))))) ),
inference(resolve,[$cnf( $equal(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))),or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y)))))) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) = implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y))))),
inference(resolve,[$cnf( $equal(or(not(and(X_749,and(X_750,Y))),not(not(and(X_750,and(X_749,Y))))),implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y)))))) )],[refute_0_94,refute_0_103]) ).
cnf(refute_0_105,plain,
( or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))) != implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y)))))
| ~ is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))))
| is_a_theorem(implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y)))))) ),[0],$fot(implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y))))))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))))
| is_a_theorem(implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y)))))) ),
inference(resolve,[$cnf( $equal(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y))))),implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y)))))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(and(X_749,and(X_750,Y)),not(not(and(X_750,and(X_749,Y)))))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_749,implies(X_750,not(Y))),not(not(and(X_750,and(X_749,Y)))))) )],[refute_0_93,refute_0_106]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(and(X_2488,and(not(Y),not(Y))),not(not(and(not(Y),and(X_2488,not(Y))))))),
inference(subst,[],[refute_0_107:[bind(Y,$fot(not(Y))),bind(X_749,$fot(X_2488)),bind(X_750,$fot(not(Y)))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_110,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_111,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_110,refute_0_109]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(equiv(X_118,not(not(X))))
| X_118 = not(not(X)) ),
inference(subst,[],[refute_0_111:[bind(X,$fot(X_118)),bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_113,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_114,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_115,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_114,refute_0_113]) ).
cnf(refute_0_116,plain,
equiv(X_43,not(X)) = and(implies(X_43,not(X)),implies(not(X),X_43)),
inference(subst,[],[refute_0_115:[bind(X,$fot(X_43)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_117,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_118,plain,
op_or,
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_119,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_118,refute_0_117]) ).
cnf(refute_0_120,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_121,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_72,refute_0_120]) ).
cnf(refute_0_122,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_121:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_123,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_124,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_119,refute_0_124]) ).
cnf(refute_0_126,plain,
or(X,X_43) = implies(not(X),X_43),
inference(subst,[],[refute_0_125:[bind(Y,$fot(X_43))]]) ).
cnf(refute_0_127,plain,
( or(X,X_43) != implies(not(X),X_43)
| implies(not(X),X_43) = or(X,X_43) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,X_43))),bind(Y0,$fot(implies(not(X),X_43)))]]) ).
cnf(refute_0_128,plain,
implies(not(X),X_43) = or(X,X_43),
inference(resolve,[$cnf( $equal(or(X,X_43),implies(not(X),X_43)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
( equiv(X_43,not(X)) != and(implies(X_43,not(X)),implies(not(X),X_43))
| implies(not(X),X_43) != or(X,X_43)
| equiv(X_43,not(X)) = and(implies(X_43,not(X)),or(X,X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_43,not(X)),and(implies(X_43,not(X)),implies(not(X),X_43))) ),[1,1],$fot(or(X,X_43))]]) ).
cnf(refute_0_130,plain,
( equiv(X_43,not(X)) != and(implies(X_43,not(X)),implies(not(X),X_43))
| equiv(X_43,not(X)) = and(implies(X_43,not(X)),or(X,X_43)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_43),or(X,X_43)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
equiv(X_43,not(X)) = and(implies(X_43,not(X)),or(X,X_43)),
inference(resolve,[$cnf( $equal(equiv(X_43,not(X)),and(implies(X_43,not(X)),implies(not(X),X_43))) )],[refute_0_116,refute_0_130]) ).
cnf(refute_0_132,plain,
equiv(X_49,not(not(X))) = and(implies(X_49,not(not(X))),or(not(X),X_49)),
inference(subst,[],[refute_0_131:[bind(X,$fot(not(X))),bind(X_43,$fot(X_49))]]) ).
cnf(refute_0_133,plain,
implies(X,X_49) = or(not(X),X_49),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_49))]]) ).
cnf(refute_0_134,plain,
( implies(X,X_49) != or(not(X),X_49)
| or(not(X),X_49) = implies(X,X_49) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,X_49))),bind(Y0,$fot(or(not(X),X_49)))]]) ).
cnf(refute_0_135,plain,
or(not(X),X_49) = implies(X,X_49),
inference(resolve,[$cnf( $equal(implies(X,X_49),or(not(X),X_49)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
( equiv(X_49,not(not(X))) != and(implies(X_49,not(not(X))),or(not(X),X_49))
| or(not(X),X_49) != implies(X,X_49)
| equiv(X_49,not(not(X))) = and(implies(X_49,not(not(X))),implies(X,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_49,not(not(X))),and(implies(X_49,not(not(X))),or(not(X),X_49))) ),[1,1],$fot(implies(X,X_49))]]) ).
cnf(refute_0_137,plain,
( equiv(X_49,not(not(X))) != and(implies(X_49,not(not(X))),or(not(X),X_49))
| equiv(X_49,not(not(X))) = and(implies(X_49,not(not(X))),implies(X,X_49)) ),
inference(resolve,[$cnf( $equal(or(not(X),X_49),implies(X,X_49)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
equiv(X_49,not(not(X))) = and(implies(X_49,not(not(X))),implies(X,X_49)),
inference(resolve,[$cnf( $equal(equiv(X_49,not(not(X))),and(implies(X_49,not(not(X))),or(not(X),X_49))) )],[refute_0_132,refute_0_137]) ).
cnf(refute_0_139,plain,
( equiv(X,Y) != and(implies(X,Y),implies(Y,X))
| and(implies(X,Y),implies(Y,X)) = equiv(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_140,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_115,refute_0_139]) ).
cnf(refute_0_141,plain,
and(implies(X_49,X),implies(X,X_49)) = equiv(X_49,X),
inference(subst,[],[refute_0_140:[bind(X,$fot(X_49)),bind(Y,$fot(X))]]) ).
cnf(refute_0_142,plain,
not(and(X_49,not(X))) = implies(X_49,X),
inference(subst,[],[refute_0_121:[bind(X,$fot(X_49)),bind(Y,$fot(X))]]) ).
cnf(refute_0_143,plain,
and(not(and(X_49,not(X))),implies(X,X_49)) = and(not(and(X_49,not(X))),implies(X,X_49)),
introduced(tautology,[refl,[$fot(and(not(and(X_49,not(X))),implies(X,X_49)))]]) ).
cnf(refute_0_144,plain,
( and(not(and(X_49,not(X))),implies(X,X_49)) != and(not(and(X_49,not(X))),implies(X,X_49))
| not(and(X_49,not(X))) != implies(X_49,X)
| and(not(and(X_49,not(X))),implies(X,X_49)) = and(implies(X_49,X),implies(X,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_49,not(X))),implies(X,X_49)),and(not(and(X_49,not(X))),implies(X,X_49))) ),[1,0],$fot(implies(X_49,X))]]) ).
cnf(refute_0_145,plain,
( not(and(X_49,not(X))) != implies(X_49,X)
| and(not(and(X_49,not(X))),implies(X,X_49)) = and(implies(X_49,X),implies(X,X_49)) ),
inference(resolve,[$cnf( $equal(and(not(and(X_49,not(X))),implies(X,X_49)),and(not(and(X_49,not(X))),implies(X,X_49))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
and(not(and(X_49,not(X))),implies(X,X_49)) = and(implies(X_49,X),implies(X,X_49)),
inference(resolve,[$cnf( $equal(not(and(X_49,not(X))),implies(X_49,X)) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
( and(implies(X_49,X),implies(X,X_49)) != equiv(X_49,X)
| and(not(and(X_49,not(X))),implies(X,X_49)) != and(implies(X_49,X),implies(X,X_49))
| and(not(and(X_49,not(X))),implies(X,X_49)) = equiv(X_49,X) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(and(not(and(X_49,not(X))),implies(X,X_49)))),bind(Y0,$fot(and(implies(X_49,X),implies(X,X_49)))),bind(Z,$fot(equiv(X_49,X)))]]) ).
cnf(refute_0_148,plain,
( and(implies(X_49,X),implies(X,X_49)) != equiv(X_49,X)
| and(not(and(X_49,not(X))),implies(X,X_49)) = equiv(X_49,X) ),
inference(resolve,[$cnf( $equal(and(not(and(X_49,not(X))),implies(X,X_49)),and(implies(X_49,X),implies(X,X_49))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
and(not(and(X_49,not(X))),implies(X,X_49)) = equiv(X_49,X),
inference(resolve,[$cnf( $equal(and(implies(X_49,X),implies(X,X_49)),equiv(X_49,X)) )],[refute_0_141,refute_0_148]) ).
cnf(refute_0_150,plain,
and(implies(X_57,not(X_58)),Y) = not(implies(implies(X_57,not(X_58)),not(Y))),
inference(subst,[],[refute_0_84:[bind(X,$fot(implies(X_57,not(X_58))))]]) ).
cnf(refute_0_151,plain,
implies(implies(X_14,not(X_15)),Y) = or(not(implies(X_14,not(X_15))),Y),
inference(subst,[],[refute_0_15:[bind(X,$fot(implies(X_14,not(X_15))))]]) ).
cnf(refute_0_152,plain,
and(X_14,X_15) = not(implies(X_14,not(X_15))),
inference(subst,[],[refute_0_84:[bind(X,$fot(X_14)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_153,plain,
( and(X_14,X_15) != not(implies(X_14,not(X_15)))
| not(implies(X_14,not(X_15))) = and(X_14,X_15) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(and(X_14,X_15))),bind(Y0,$fot(not(implies(X_14,not(X_15)))))]]) ).
cnf(refute_0_154,plain,
not(implies(X_14,not(X_15))) = and(X_14,X_15),
inference(resolve,[$cnf( $equal(and(X_14,X_15),not(implies(X_14,not(X_15)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( implies(implies(X_14,not(X_15)),Y) != or(not(implies(X_14,not(X_15))),Y)
| not(implies(X_14,not(X_15))) != and(X_14,X_15)
| implies(implies(X_14,not(X_15)),Y) = or(and(X_14,X_15),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,not(X_15)),Y),or(not(implies(X_14,not(X_15))),Y)) ),[1,0],$fot(and(X_14,X_15))]]) ).
cnf(refute_0_156,plain,
( implies(implies(X_14,not(X_15)),Y) != or(not(implies(X_14,not(X_15))),Y)
| implies(implies(X_14,not(X_15)),Y) = or(and(X_14,X_15),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_14,not(X_15))),and(X_14,X_15)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
implies(implies(X_14,not(X_15)),Y) = or(and(X_14,X_15),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_14,not(X_15)),Y),or(not(implies(X_14,not(X_15))),Y)) )],[refute_0_151,refute_0_156]) ).
cnf(refute_0_158,plain,
implies(implies(X_57,not(X_58)),not(Y)) = or(and(X_57,X_58),not(Y)),
inference(subst,[],[refute_0_157:[bind(Y,$fot(not(Y))),bind(X_14,$fot(X_57)),bind(X_15,$fot(X_58))]]) ).
cnf(refute_0_159,plain,
( and(implies(X_57,not(X_58)),Y) != not(implies(implies(X_57,not(X_58)),not(Y)))
| implies(implies(X_57,not(X_58)),not(Y)) != or(and(X_57,X_58),not(Y))
| and(implies(X_57,not(X_58)),Y) = not(or(and(X_57,X_58),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_57,not(X_58)),Y),not(implies(implies(X_57,not(X_58)),not(Y)))) ),[1,0],$fot(or(and(X_57,X_58),not(Y)))]]) ).
cnf(refute_0_160,plain,
( and(implies(X_57,not(X_58)),Y) != not(implies(implies(X_57,not(X_58)),not(Y)))
| and(implies(X_57,not(X_58)),Y) = not(or(and(X_57,X_58),not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_57,not(X_58)),not(Y)),or(and(X_57,X_58),not(Y))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
and(implies(X_57,not(X_58)),Y) = not(or(and(X_57,X_58),not(Y))),
inference(resolve,[$cnf( $equal(and(implies(X_57,not(X_58)),Y),not(implies(implies(X_57,not(X_58)),not(Y)))) )],[refute_0_150,refute_0_160]) ).
cnf(refute_0_162,plain,
and(not(X),X_15) = not(implies(not(X),not(X_15))),
inference(subst,[],[refute_0_84:[bind(X,$fot(not(X))),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_163,plain,
or(X,not(X_15)) = implies(not(X),not(X_15)),
inference(subst,[],[refute_0_125:[bind(Y,$fot(not(X_15)))]]) ).
cnf(refute_0_164,plain,
( or(X,not(X_15)) != implies(not(X),not(X_15))
| implies(not(X),not(X_15)) = or(X,not(X_15)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,not(X_15)))),bind(Y0,$fot(implies(not(X),not(X_15))))]]) ).
cnf(refute_0_165,plain,
implies(not(X),not(X_15)) = or(X,not(X_15)),
inference(resolve,[$cnf( $equal(or(X,not(X_15)),implies(not(X),not(X_15))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
( and(not(X),X_15) != not(implies(not(X),not(X_15)))
| implies(not(X),not(X_15)) != or(X,not(X_15))
| and(not(X),X_15) = not(or(X,not(X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X),X_15),not(implies(not(X),not(X_15)))) ),[1,0],$fot(or(X,not(X_15)))]]) ).
cnf(refute_0_167,plain,
( and(not(X),X_15) != not(implies(not(X),not(X_15)))
| and(not(X),X_15) = not(or(X,not(X_15))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_15)),or(X,not(X_15))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
and(not(X),X_15) = not(or(X,not(X_15))),
inference(resolve,[$cnf( $equal(and(not(X),X_15),not(implies(not(X),not(X_15)))) )],[refute_0_162,refute_0_167]) ).
cnf(refute_0_169,plain,
( and(not(X),X_15) != not(or(X,not(X_15)))
| not(or(X,not(X_15))) = and(not(X),X_15) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(and(not(X),X_15))),bind(Y0,$fot(not(or(X,not(X_15)))))]]) ).
cnf(refute_0_170,plain,
not(or(X,not(X_15))) = and(not(X),X_15),
inference(resolve,[$cnf( $equal(and(not(X),X_15),not(or(X,not(X_15)))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
not(or(and(X_57,X_58),not(Y))) = and(not(and(X_57,X_58)),Y),
inference(subst,[],[refute_0_170:[bind(X,$fot(and(X_57,X_58))),bind(X_15,$fot(Y))]]) ).
cnf(refute_0_172,plain,
( and(implies(X_57,not(X_58)),Y) != not(or(and(X_57,X_58),not(Y)))
| not(or(and(X_57,X_58),not(Y))) != and(not(and(X_57,X_58)),Y)
| and(implies(X_57,not(X_58)),Y) = and(not(and(X_57,X_58)),Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(implies(X_57,not(X_58)),Y),and(not(and(X_57,X_58)),Y)) ),[0],$fot(not(or(and(X_57,X_58),not(Y))))]]) ).
cnf(refute_0_173,plain,
( and(implies(X_57,not(X_58)),Y) != not(or(and(X_57,X_58),not(Y)))
| and(implies(X_57,not(X_58)),Y) = and(not(and(X_57,X_58)),Y) ),
inference(resolve,[$cnf( $equal(not(or(and(X_57,X_58),not(Y))),and(not(and(X_57,X_58)),Y)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
and(implies(X_57,not(X_58)),Y) = and(not(and(X_57,X_58)),Y),
inference(resolve,[$cnf( $equal(and(implies(X_57,not(X_58)),Y),not(or(and(X_57,X_58),not(Y)))) )],[refute_0_161,refute_0_173]) ).
cnf(refute_0_175,plain,
and(implies(X_49,not(not(X))),implies(X,X_49)) = and(not(and(X_49,not(X))),implies(X,X_49)),
inference(subst,[],[refute_0_174:[bind(Y,$fot(implies(X,X_49))),bind(X_57,$fot(X_49)),bind(X_58,$fot(not(X)))]]) ).
cnf(refute_0_176,plain,
( and(implies(X_49,not(not(X))),implies(X,X_49)) != and(not(and(X_49,not(X))),implies(X,X_49))
| and(not(and(X_49,not(X))),implies(X,X_49)) != equiv(X_49,X)
| and(implies(X_49,not(not(X))),implies(X,X_49)) = equiv(X_49,X) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(and(implies(X_49,not(not(X))),implies(X,X_49)))),bind(Y0,$fot(and(not(and(X_49,not(X))),implies(X,X_49)))),bind(Z,$fot(equiv(X_49,X)))]]) ).
cnf(refute_0_177,plain,
( and(not(and(X_49,not(X))),implies(X,X_49)) != equiv(X_49,X)
| and(implies(X_49,not(not(X))),implies(X,X_49)) = equiv(X_49,X) ),
inference(resolve,[$cnf( $equal(and(implies(X_49,not(not(X))),implies(X,X_49)),and(not(and(X_49,not(X))),implies(X,X_49))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
and(implies(X_49,not(not(X))),implies(X,X_49)) = equiv(X_49,X),
inference(resolve,[$cnf( $equal(and(not(and(X_49,not(X))),implies(X,X_49)),equiv(X_49,X)) )],[refute_0_149,refute_0_177]) ).
cnf(refute_0_179,plain,
( and(implies(X_49,not(not(X))),implies(X,X_49)) != equiv(X_49,X)
| equiv(X_49,not(not(X))) != and(implies(X_49,not(not(X))),implies(X,X_49))
| equiv(X_49,not(not(X))) = equiv(X_49,X) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_49,not(not(X))),and(implies(X_49,not(not(X))),implies(X,X_49))) ),[1],$fot(equiv(X_49,X))]]) ).
cnf(refute_0_180,plain,
( equiv(X_49,not(not(X))) != and(implies(X_49,not(not(X))),implies(X,X_49))
| equiv(X_49,not(not(X))) = equiv(X_49,X) ),
inference(resolve,[$cnf( $equal(and(implies(X_49,not(not(X))),implies(X,X_49)),equiv(X_49,X)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
equiv(X_49,not(not(X))) = equiv(X_49,X),
inference(resolve,[$cnf( $equal(equiv(X_49,not(not(X))),and(implies(X_49,not(not(X))),implies(X,X_49))) )],[refute_0_138,refute_0_180]) ).
cnf(refute_0_182,plain,
equiv(X_118,not(not(X))) = equiv(X_118,X),
inference(subst,[],[refute_0_181:[bind(X_49,$fot(X_118))]]) ).
cnf(refute_0_183,plain,
( equiv(X_118,not(not(X))) != equiv(X_118,X)
| ~ is_a_theorem(equiv(X_118,X))
| is_a_theorem(equiv(X_118,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(equiv(X_118,not(not(X)))) ),[0],$fot(equiv(X_118,X))]]) ).
cnf(refute_0_184,plain,
( ~ is_a_theorem(equiv(X_118,X))
| is_a_theorem(equiv(X_118,not(not(X)))) ),
inference(resolve,[$cnf( $equal(equiv(X_118,not(not(X))),equiv(X_118,X)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
( ~ is_a_theorem(equiv(X_118,X))
| X_118 = not(not(X)) ),
inference(resolve,[$cnf( is_a_theorem(equiv(X_118,not(not(X)))) )],[refute_0_184,refute_0_112]) ).
cnf(refute_0_186,plain,
( ~ is_a_theorem(equiv(and(X_1801,X_1801),and(X_1801,X_1801)))
| and(X_1801,X_1801) = not(not(and(X_1801,X_1801))) ),
inference(subst,[],[refute_0_185:[bind(X,$fot(and(X_1801,X_1801))),bind(X_118,$fot(and(X_1801,X_1801)))]]) ).
cnf(refute_0_187,plain,
( ~ is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7))))
| is_a_theorem(or(or(Q,not(X_7)),not(implies(X_7,Q)))) ),
inference(subst,[],[refute_0_26:[bind(Q,$fot(or(Q,not(X_7)))),bind(X_7,$fot(implies(X_7,Q)))]]) ).
cnf(refute_0_188,plain,
is_a_theorem(or(or(Q,not(X_7)),not(implies(X_7,Q)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_7,Q),or(Q,not(X_7)))) )],[refute_0_24,refute_0_187]) ).
cnf(refute_0_189,plain,
or(or(X_41,not(X_42)),Y) = implies(not(or(X_41,not(X_42))),Y),
inference(subst,[],[refute_0_125:[bind(X,$fot(or(X_41,not(X_42))))]]) ).
cnf(refute_0_190,plain,
and(not(X_41),X_42) = not(or(X_41,not(X_42))),
inference(subst,[],[refute_0_168:[bind(X,$fot(X_41)),bind(X_15,$fot(X_42))]]) ).
cnf(refute_0_191,plain,
( and(not(X_41),X_42) != not(or(X_41,not(X_42)))
| not(or(X_41,not(X_42))) = and(not(X_41),X_42) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(and(not(X_41),X_42))),bind(Y0,$fot(not(or(X_41,not(X_42)))))]]) ).
cnf(refute_0_192,plain,
not(or(X_41,not(X_42))) = and(not(X_41),X_42),
inference(resolve,[$cnf( $equal(and(not(X_41),X_42),not(or(X_41,not(X_42)))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
( not(or(X_41,not(X_42))) != and(not(X_41),X_42)
| or(or(X_41,not(X_42)),Y) != implies(not(or(X_41,not(X_42))),Y)
| or(or(X_41,not(X_42)),Y) = implies(and(not(X_41),X_42),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X_41,not(X_42)),Y),implies(not(or(X_41,not(X_42))),Y)) ),[1,0],$fot(and(not(X_41),X_42))]]) ).
cnf(refute_0_194,plain,
( or(or(X_41,not(X_42)),Y) != implies(not(or(X_41,not(X_42))),Y)
| or(or(X_41,not(X_42)),Y) = implies(and(not(X_41),X_42),Y) ),
inference(resolve,[$cnf( $equal(not(or(X_41,not(X_42))),and(not(X_41),X_42)) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
or(or(X_41,not(X_42)),Y) = implies(and(not(X_41),X_42),Y),
inference(resolve,[$cnf( $equal(or(or(X_41,not(X_42)),Y),implies(not(or(X_41,not(X_42))),Y)) )],[refute_0_189,refute_0_194]) ).
cnf(refute_0_196,plain,
or(or(Q,not(X_7)),not(implies(X_7,Q))) = implies(and(not(Q),X_7),not(implies(X_7,Q))),
inference(subst,[],[refute_0_195:[bind(Y,$fot(not(implies(X_7,Q)))),bind(X_41,$fot(Q)),bind(X_42,$fot(X_7))]]) ).
cnf(refute_0_197,plain,
( or(or(Q,not(X_7)),not(implies(X_7,Q))) != implies(and(not(Q),X_7),not(implies(X_7,Q)))
| ~ is_a_theorem(or(or(Q,not(X_7)),not(implies(X_7,Q))))
| is_a_theorem(implies(and(not(Q),X_7),not(implies(X_7,Q)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(Q,not(X_7)),not(implies(X_7,Q)))) ),[0],$fot(implies(and(not(Q),X_7),not(implies(X_7,Q))))]]) ).
cnf(refute_0_198,plain,
( ~ is_a_theorem(or(or(Q,not(X_7)),not(implies(X_7,Q))))
| is_a_theorem(implies(and(not(Q),X_7),not(implies(X_7,Q)))) ),
inference(resolve,[$cnf( $equal(or(or(Q,not(X_7)),not(implies(X_7,Q))),implies(and(not(Q),X_7),not(implies(X_7,Q)))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
is_a_theorem(implies(and(not(Q),X_7),not(implies(X_7,Q)))),
inference(resolve,[$cnf( is_a_theorem(or(or(Q,not(X_7)),not(implies(X_7,Q)))) )],[refute_0_188,refute_0_198]) ).
cnf(refute_0_200,plain,
is_a_theorem(implies(and(not(not(Y)),X_483),not(implies(X_483,not(Y))))),
inference(subst,[],[refute_0_199:[bind(Q,$fot(not(Y))),bind(X_7,$fot(X_483))]]) ).
cnf(refute_0_201,plain,
and(X_483,Y) = not(implies(X_483,not(Y))),
inference(subst,[],[refute_0_84:[bind(X,$fot(X_483))]]) ).
cnf(refute_0_202,plain,
( and(X_483,Y) != not(implies(X_483,not(Y)))
| not(implies(X_483,not(Y))) = and(X_483,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(and(X_483,Y))),bind(Y0,$fot(not(implies(X_483,not(Y)))))]]) ).
cnf(refute_0_203,plain,
not(implies(X_483,not(Y))) = and(X_483,Y),
inference(resolve,[$cnf( $equal(and(X_483,Y),not(implies(X_483,not(Y)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
( not(implies(X_483,not(Y))) != and(X_483,Y)
| ~ is_a_theorem(implies(and(not(not(Y)),X_483),not(implies(X_483,not(Y)))))
| is_a_theorem(implies(and(not(not(Y)),X_483),and(X_483,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(not(Y)),X_483),not(implies(X_483,not(Y))))) ),[0,1],$fot(and(X_483,Y))]]) ).
cnf(refute_0_205,plain,
( ~ is_a_theorem(implies(and(not(not(Y)),X_483),not(implies(X_483,not(Y)))))
| is_a_theorem(implies(and(not(not(Y)),X_483),and(X_483,Y))) ),
inference(resolve,[$cnf( $equal(not(implies(X_483,not(Y))),and(X_483,Y)) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
is_a_theorem(implies(and(not(not(Y)),X_483),and(X_483,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(not(Y)),X_483),not(implies(X_483,not(Y))))) )],[refute_0_200,refute_0_205]) ).
cnf(refute_0_207,plain,
and(not(not(X)),X_42) = not(or(not(X),not(X_42))),
inference(subst,[],[refute_0_168:[bind(X,$fot(not(X))),bind(X_15,$fot(X_42))]]) ).
cnf(refute_0_208,plain,
implies(X,not(X_42)) = or(not(X),not(X_42)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(not(X_42)))]]) ).
cnf(refute_0_209,plain,
( implies(X,not(X_42)) != or(not(X),not(X_42))
| or(not(X),not(X_42)) = implies(X,not(X_42)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,not(X_42)))),bind(Y0,$fot(or(not(X),not(X_42))))]]) ).
cnf(refute_0_210,plain,
or(not(X),not(X_42)) = implies(X,not(X_42)),
inference(resolve,[$cnf( $equal(implies(X,not(X_42)),or(not(X),not(X_42))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
( and(not(not(X)),X_42) != not(or(not(X),not(X_42)))
| or(not(X),not(X_42)) != implies(X,not(X_42))
| and(not(not(X)),X_42) = not(implies(X,not(X_42))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X)),X_42),not(or(not(X),not(X_42)))) ),[1,0],$fot(implies(X,not(X_42)))]]) ).
cnf(refute_0_212,plain,
( and(not(not(X)),X_42) != not(or(not(X),not(X_42)))
| and(not(not(X)),X_42) = not(implies(X,not(X_42))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_42)),implies(X,not(X_42))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
and(not(not(X)),X_42) = not(implies(X,not(X_42))),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_42),not(or(not(X),not(X_42)))) )],[refute_0_207,refute_0_212]) ).
cnf(refute_0_214,plain,
not(implies(X,not(X_42))) = and(X,X_42),
inference(subst,[],[refute_0_86:[bind(Y,$fot(X_42))]]) ).
cnf(refute_0_215,plain,
( and(not(not(X)),X_42) != not(implies(X,not(X_42)))
| not(implies(X,not(X_42))) != and(X,X_42)
| and(not(not(X)),X_42) = and(X,X_42) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(not(X)),X_42),and(X,X_42)) ),[0],$fot(not(implies(X,not(X_42))))]]) ).
cnf(refute_0_216,plain,
( and(not(not(X)),X_42) != not(implies(X,not(X_42)))
| and(not(not(X)),X_42) = and(X,X_42) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(X_42))),and(X,X_42)) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
and(not(not(X)),X_42) = and(X,X_42),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_42),not(implies(X,not(X_42)))) )],[refute_0_213,refute_0_216]) ).
cnf(refute_0_218,plain,
and(not(not(Y)),X_483) = and(Y,X_483),
inference(subst,[],[refute_0_217:[bind(X,$fot(Y)),bind(X_42,$fot(X_483))]]) ).
cnf(refute_0_219,plain,
implies(and(not(not(Y)),X_483),and(X_483,Y)) = implies(and(not(not(Y)),X_483),and(X_483,Y)),
introduced(tautology,[refl,[$fot(implies(and(not(not(Y)),X_483),and(X_483,Y)))]]) ).
cnf(refute_0_220,plain,
( and(not(not(Y)),X_483) != and(Y,X_483)
| implies(and(not(not(Y)),X_483),and(X_483,Y)) != implies(and(not(not(Y)),X_483),and(X_483,Y))
| implies(and(not(not(Y)),X_483),and(X_483,Y)) = implies(and(Y,X_483),and(X_483,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(not(Y)),X_483),and(X_483,Y)),implies(and(not(not(Y)),X_483),and(X_483,Y))) ),[1,0],$fot(and(Y,X_483))]]) ).
cnf(refute_0_221,plain,
( and(not(not(Y)),X_483) != and(Y,X_483)
| implies(and(not(not(Y)),X_483),and(X_483,Y)) = implies(and(Y,X_483),and(X_483,Y)) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(Y)),X_483),and(X_483,Y)),implies(and(not(not(Y)),X_483),and(X_483,Y))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
implies(and(not(not(Y)),X_483),and(X_483,Y)) = implies(and(Y,X_483),and(X_483,Y)),
inference(resolve,[$cnf( $equal(and(not(not(Y)),X_483),and(Y,X_483)) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
( implies(and(not(not(Y)),X_483),and(X_483,Y)) != implies(and(Y,X_483),and(X_483,Y))
| ~ is_a_theorem(implies(and(not(not(Y)),X_483),and(X_483,Y)))
| is_a_theorem(implies(and(Y,X_483),and(X_483,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(not(Y)),X_483),and(X_483,Y))) ),[0],$fot(implies(and(Y,X_483),and(X_483,Y)))]]) ).
cnf(refute_0_224,plain,
( ~ is_a_theorem(implies(and(not(not(Y)),X_483),and(X_483,Y)))
| is_a_theorem(implies(and(Y,X_483),and(X_483,Y))) ),
inference(resolve,[$cnf( $equal(implies(and(not(not(Y)),X_483),and(X_483,Y)),implies(and(Y,X_483),and(X_483,Y))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
is_a_theorem(implies(and(Y,X_483),and(X_483,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(not(Y)),X_483),and(X_483,Y))) )],[refute_0_206,refute_0_224]) ).
cnf(refute_0_226,plain,
is_a_theorem(implies(and(Y,Y),and(Y,Y))),
inference(subst,[],[refute_0_225:[bind(X_483,$fot(Y))]]) ).
cnf(refute_0_227,plain,
( ~ is_a_theorem(implies(X_480,X_480))
| ~ is_a_theorem(implies(implies(X_480,X_480),equiv(X_480,X_480)))
| is_a_theorem(equiv(X_480,X_480)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_480,X_480))),bind(Y,$fot(equiv(X_480,X_480)))]]) ).
cnf(refute_0_228,plain,
( ~ r1
| is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_229,plain,
r1,
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_230,plain,
is_a_theorem(implies(or(P,P),P)),
inference(resolve,[$cnf( r1 )],[refute_0_229,refute_0_228]) ).
cnf(refute_0_231,plain,
is_a_theorem(implies(or(not(X_7),not(X_7)),not(X_7))),
inference(subst,[],[refute_0_230:[bind(P,$fot(not(X_7)))]]) ).
cnf(refute_0_232,plain,
implies(X_7,not(X_7)) = or(not(X_7),not(X_7)),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_7)),bind(Y,$fot(not(X_7)))]]) ).
cnf(refute_0_233,plain,
( implies(X_7,not(X_7)) != or(not(X_7),not(X_7))
| or(not(X_7),not(X_7)) = implies(X_7,not(X_7)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X_7,not(X_7)))),bind(Y0,$fot(or(not(X_7),not(X_7))))]]) ).
cnf(refute_0_234,plain,
or(not(X_7),not(X_7)) = implies(X_7,not(X_7)),
inference(resolve,[$cnf( $equal(implies(X_7,not(X_7)),or(not(X_7),not(X_7))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
( or(not(X_7),not(X_7)) != implies(X_7,not(X_7))
| ~ is_a_theorem(implies(or(not(X_7),not(X_7)),not(X_7)))
| is_a_theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_7),not(X_7)),not(X_7))) ),[0,0],$fot(implies(X_7,not(X_7)))]]) ).
cnf(refute_0_236,plain,
( ~ is_a_theorem(implies(or(not(X_7),not(X_7)),not(X_7)))
| is_a_theorem(implies(implies(X_7,not(X_7)),not(X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),not(X_7)),implies(X_7,not(X_7))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
is_a_theorem(implies(implies(X_7,not(X_7)),not(X_7))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_7),not(X_7)),not(X_7))) )],[refute_0_231,refute_0_236]) ).
cnf(refute_0_238,plain,
is_a_theorem(implies(implies(not(X),not(not(X))),not(not(X)))),
inference(subst,[],[refute_0_237:[bind(X_7,$fot(not(X)))]]) ).
cnf(refute_0_239,plain,
or(X,not(not(X))) = implies(not(X),not(not(X))),
inference(subst,[],[refute_0_125:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_240,plain,
( or(X,not(not(X))) != implies(not(X),not(not(X)))
| implies(not(X),not(not(X))) = or(X,not(not(X))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,not(not(X))))),bind(Y0,$fot(implies(not(X),not(not(X)))))]]) ).
cnf(refute_0_241,plain,
implies(not(X),not(not(X))) = or(X,not(not(X))),
inference(resolve,[$cnf( $equal(or(X,not(not(X))),implies(not(X),not(not(X)))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
( implies(not(X),not(not(X))) != or(X,not(not(X)))
| ~ is_a_theorem(implies(implies(not(X),not(not(X))),not(not(X))))
| is_a_theorem(implies(or(X,not(not(X))),not(not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),not(not(X))),not(not(X)))) ),[0,0],$fot(or(X,not(not(X))))]]) ).
cnf(refute_0_243,plain,
( ~ is_a_theorem(implies(implies(not(X),not(not(X))),not(not(X))))
| is_a_theorem(implies(or(X,not(not(X))),not(not(X)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(not(X))),or(X,not(not(X)))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
is_a_theorem(implies(or(X,not(not(X))),not(not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(not(X))),not(not(X)))) )],[refute_0_238,refute_0_243]) ).
cnf(refute_0_245,plain,
is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X))))),
inference(subst,[],[refute_0_244:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_246,plain,
implies(X,not(not(not(X)))) = or(not(X),not(not(not(X)))),
inference(subst,[],[refute_0_15:[bind(Y,$fot(not(not(not(X)))))]]) ).
cnf(refute_0_247,plain,
( implies(X,not(not(not(X)))) != or(not(X),not(not(not(X))))
| or(not(X),not(not(not(X)))) = implies(X,not(not(not(X)))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,not(not(not(X)))))),bind(Y0,$fot(or(not(X),not(not(not(X))))))]]) ).
cnf(refute_0_248,plain,
or(not(X),not(not(not(X)))) = implies(X,not(not(not(X)))),
inference(resolve,[$cnf( $equal(implies(X,not(not(not(X)))),or(not(X),not(not(not(X))))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
( or(not(X),not(not(not(X)))) != implies(X,not(not(not(X))))
| ~ is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X))))) ),[0,0],$fot(implies(X,not(not(not(X)))))]]) ).
cnf(refute_0_250,plain,
( ~ is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(not(X)))),implies(X,not(not(not(X))))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(not(not(X)))),not(not(not(X))))) )],[refute_0_245,refute_0_250]) ).
cnf(refute_0_252,plain,
implies(implies(X,not(not(not(X)))),not(not(not(X)))) = or(and(X,not(not(X))),not(not(not(X)))),
inference(subst,[],[refute_0_157:[bind(Y,$fot(not(not(not(X))))),bind(X_14,$fot(X)),bind(X_15,$fot(not(not(X))))]]) ).
cnf(refute_0_253,plain,
( implies(implies(X,not(not(not(X)))),not(not(not(X)))) != or(and(X,not(not(X))),not(not(not(X))))
| ~ is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) ),[0],$fot(or(and(X,not(not(X))),not(not(not(X)))))]]) ).
cnf(refute_0_254,plain,
( ~ is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X)))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(X))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(not(not(X)))),not(not(not(X)))),or(and(X,not(not(X))),not(not(not(X))))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
is_a_theorem(or(and(X,not(not(X))),not(not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(not(not(X)))),not(not(not(X))))) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
implies(implies(X,not(X)),not(not(not(X)))) = or(and(X,X),not(not(not(X)))),
inference(subst,[],[refute_0_157:[bind(Y,$fot(not(not(not(X))))),bind(X_14,$fot(X)),bind(X_15,$fot(X))]]) ).
cnf(refute_0_257,plain,
or(and(X_28,not(X_29)),Y) = implies(not(and(X_28,not(X_29))),Y),
inference(subst,[],[refute_0_125:[bind(X,$fot(and(X_28,not(X_29))))]]) ).
cnf(refute_0_258,plain,
implies(X_28,X_29) = not(and(X_28,not(X_29))),
inference(subst,[],[refute_0_72:[bind(X,$fot(X_28)),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_259,plain,
( implies(X_28,X_29) != not(and(X_28,not(X_29)))
| not(and(X_28,not(X_29))) = implies(X_28,X_29) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X_28,X_29))),bind(Y0,$fot(not(and(X_28,not(X_29)))))]]) ).
cnf(refute_0_260,plain,
not(and(X_28,not(X_29))) = implies(X_28,X_29),
inference(resolve,[$cnf( $equal(implies(X_28,X_29),not(and(X_28,not(X_29)))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
( not(and(X_28,not(X_29))) != implies(X_28,X_29)
| or(and(X_28,not(X_29)),Y) != implies(not(and(X_28,not(X_29))),Y)
| or(and(X_28,not(X_29)),Y) = implies(implies(X_28,X_29),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_28,not(X_29)),Y),implies(not(and(X_28,not(X_29))),Y)) ),[1,0],$fot(implies(X_28,X_29))]]) ).
cnf(refute_0_262,plain,
( or(and(X_28,not(X_29)),Y) != implies(not(and(X_28,not(X_29))),Y)
| or(and(X_28,not(X_29)),Y) = implies(implies(X_28,X_29),Y) ),
inference(resolve,[$cnf( $equal(not(and(X_28,not(X_29))),implies(X_28,X_29)) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
or(and(X_28,not(X_29)),Y) = implies(implies(X_28,X_29),Y),
inference(resolve,[$cnf( $equal(or(and(X_28,not(X_29)),Y),implies(not(and(X_28,not(X_29))),Y)) )],[refute_0_257,refute_0_262]) ).
cnf(refute_0_264,plain,
or(and(X,not(not(X))),not(not(not(X)))) = implies(implies(X,not(X)),not(not(not(X)))),
inference(subst,[],[refute_0_263:[bind(Y,$fot(not(not(not(X))))),bind(X_28,$fot(X)),bind(X_29,$fot(not(X)))]]) ).
cnf(refute_0_265,plain,
( implies(implies(X,not(X)),not(not(not(X)))) != or(and(X,X),not(not(not(X))))
| or(and(X,not(not(X))),not(not(not(X)))) != implies(implies(X,not(X)),not(not(not(X))))
| or(and(X,not(not(X))),not(not(not(X)))) = or(and(X,X),not(not(not(X)))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(and(X,not(not(X))),not(not(not(X)))))),bind(Y0,$fot(implies(implies(X,not(X)),not(not(not(X)))))),bind(Z,$fot(or(and(X,X),not(not(not(X))))))]]) ).
cnf(refute_0_266,plain,
( implies(implies(X,not(X)),not(not(not(X)))) != or(and(X,X),not(not(not(X))))
| or(and(X,not(not(X))),not(not(not(X)))) = or(and(X,X),not(not(not(X)))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(X)))),implies(implies(X,not(X)),not(not(not(X))))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
or(and(X,not(not(X))),not(not(not(X)))) = or(and(X,X),not(not(not(X)))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(X)))),or(and(X,X),not(not(not(X))))) )],[refute_0_256,refute_0_266]) ).
cnf(refute_0_268,plain,
( or(and(X,not(not(X))),not(not(not(X)))) != or(and(X,X),not(not(not(X))))
| ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(X)))))
| is_a_theorem(or(and(X,X),not(not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(X))))) ),[0],$fot(or(and(X,X),not(not(not(X)))))]]) ).
cnf(refute_0_269,plain,
( ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(X)))))
| is_a_theorem(or(and(X,X),not(not(not(X))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(X)))),or(and(X,X),not(not(not(X))))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
is_a_theorem(or(and(X,X),not(not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(X))))) )],[refute_0_255,refute_0_269]) ).
cnf(refute_0_271,plain,
is_a_theorem(or(and(not(not(X_108)),not(not(X_108))),not(not(not(not(not(X_108))))))),
inference(subst,[],[refute_0_270:[bind(X,$fot(not(not(X_108))))]]) ).
cnf(refute_0_272,plain,
and(not(not(X_108)),not(not(X_108))) = and(X_108,not(not(X_108))),
inference(subst,[],[refute_0_217:[bind(X,$fot(X_108)),bind(X_42,$fot(not(not(X_108))))]]) ).
cnf(refute_0_273,plain,
( and(not(not(X_108)),not(not(X_108))) != and(X_108,not(not(X_108)))
| ~ is_a_theorem(or(and(not(not(X_108)),not(not(X_108))),not(not(not(not(not(X_108)))))))
| is_a_theorem(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(X_108)),not(not(X_108))),not(not(not(not(not(X_108))))))) ),[0,0],$fot(and(X_108,not(not(X_108))))]]) ).
cnf(refute_0_274,plain,
( ~ is_a_theorem(or(and(not(not(X_108)),not(not(X_108))),not(not(not(not(not(X_108)))))))
| is_a_theorem(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108))))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X_108)),not(not(X_108))),and(X_108,not(not(X_108)))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
is_a_theorem(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(X_108)),not(not(X_108))),not(not(not(not(not(X_108))))))) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
implies(implies(X_108,not(X_108)),not(not(not(not(not(X_108)))))) = or(and(X_108,X_108),not(not(not(not(not(X_108)))))),
inference(subst,[],[refute_0_157:[bind(Y,$fot(not(not(not(not(not(X_108))))))),bind(X_14,$fot(X_108)),bind(X_15,$fot(X_108))]]) ).
cnf(refute_0_277,plain,
or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))) = implies(implies(X_108,not(X_108)),not(not(not(not(not(X_108)))))),
inference(subst,[],[refute_0_263:[bind(Y,$fot(not(not(not(not(not(X_108))))))),bind(X_28,$fot(X_108)),bind(X_29,$fot(not(X_108)))]]) ).
cnf(refute_0_278,plain,
( implies(implies(X_108,not(X_108)),not(not(not(not(not(X_108)))))) != or(and(X_108,X_108),not(not(not(not(not(X_108))))))
| or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))) != implies(implies(X_108,not(X_108)),not(not(not(not(not(X_108))))))
| or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))) = or(and(X_108,X_108),not(not(not(not(not(X_108)))))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))))),bind(Y0,$fot(implies(implies(X_108,not(X_108)),not(not(not(not(not(X_108)))))))),bind(Z,$fot(or(and(X_108,X_108),not(not(not(not(not(X_108))))))))]]) ).
cnf(refute_0_279,plain,
( implies(implies(X_108,not(X_108)),not(not(not(not(not(X_108)))))) != or(and(X_108,X_108),not(not(not(not(not(X_108))))))
| or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))) = or(and(X_108,X_108),not(not(not(not(not(X_108)))))) ),
inference(resolve,[$cnf( $equal(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))),implies(implies(X_108,not(X_108)),not(not(not(not(not(X_108))))))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))) = or(and(X_108,X_108),not(not(not(not(not(X_108)))))),
inference(resolve,[$cnf( $equal(implies(implies(X_108,not(X_108)),not(not(not(not(not(X_108)))))),or(and(X_108,X_108),not(not(not(not(not(X_108))))))) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
( or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))) != or(and(X_108,X_108),not(not(not(not(not(X_108))))))
| ~ is_a_theorem(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))))
| is_a_theorem(or(and(X_108,X_108),not(not(not(not(not(X_108))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108))))))) ),[0],$fot(or(and(X_108,X_108),not(not(not(not(not(X_108)))))))]]) ).
cnf(refute_0_282,plain,
( ~ is_a_theorem(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))))
| is_a_theorem(or(and(X_108,X_108),not(not(not(not(not(X_108))))))) ),
inference(resolve,[$cnf( $equal(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108)))))),or(and(X_108,X_108),not(not(not(not(not(X_108))))))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
is_a_theorem(or(and(X_108,X_108),not(not(not(not(not(X_108))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_108,not(not(X_108))),not(not(not(not(not(X_108))))))) )],[refute_0_275,refute_0_282]) ).
cnf(refute_0_284,plain,
is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X))))))))),
inference(subst,[],[refute_0_283:[bind(X_108,$fot(not(not(X))))]]) ).
cnf(refute_0_285,plain,
and(not(not(X)),not(not(X))) = and(X,not(not(X))),
inference(subst,[],[refute_0_217:[bind(X_42,$fot(not(not(X))))]]) ).
cnf(refute_0_286,plain,
( and(not(not(X)),not(not(X))) != and(X,not(not(X)))
| ~ is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X))))))))) ),[0,0],$fot(and(X,not(not(X))))]]) ).
cnf(refute_0_287,plain,
( ~ is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),not(not(X))),and(X,not(not(X)))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(X)),not(not(X))),not(not(not(not(not(not(not(X))))))))) )],[refute_0_284,refute_0_287]) ).
cnf(refute_0_289,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_157:[bind(Y,$fot(not(not(not(not(not(not(not(X))))))))),bind(X_14,$fot(X)),bind(X_15,$fot(X))]]) ).
cnf(refute_0_290,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))),
inference(subst,[],[refute_0_263:[bind(Y,$fot(not(not(not(not(not(not(not(X))))))))),bind(X_28,$fot(X)),bind(X_29,$fot(not(X)))]]) ).
cnf(refute_0_291,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))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) != implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))
| or(and(X,not(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_101:[bind(X0,$fot(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))))),bind(Y0,$fot(implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))))),bind(Z,$fot(or(and(X,X),not(not(not(not(not(not(not(X))))))))))]]) ).
cnf(refute_0_292,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))) != or(and(X,X),not(not(not(not(not(not(not(X))))))))
| or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = or(and(X,X),not(not(not(not(not(not(not(X)))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))),implies(implies(X,not(X)),not(not(not(not(not(not(not(X))))))))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) = or(and(X,X),not(not(not(not(not(not(not(X)))))))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(not(not(X)))))))),or(and(X,X),not(not(not(not(not(not(not(X))))))))) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
( or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))) != or(and(X,X),not(not(not(not(not(not(not(X))))))))
| ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(not(not(X)))))))))]]) ).
cnf(refute_0_295,plain,
( ~ is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))) ),
inference(resolve,[$cnf( $equal(or(and(X,not(not(X))),not(not(not(not(not(not(not(X)))))))),or(and(X,X),not(not(not(not(not(not(not(X))))))))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(X))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X,not(not(X))),not(not(not(not(not(not(not(X))))))))) )],[refute_0_288,refute_0_295]) ).
cnf(refute_0_297,plain,
is_a_theorem(or(and(not(X_151),not(X_151)),not(not(not(not(not(not(not(not(X_151)))))))))),
inference(subst,[],[refute_0_296:[bind(X,$fot(not(X_151)))]]) ).
cnf(refute_0_298,plain,
or(and(not(X_151),not(X_151)),not(not(not(not(not(not(not(not(X_151))))))))) = implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))),
inference(subst,[],[refute_0_263:[bind(Y,$fot(not(not(not(not(not(not(not(not(X_151)))))))))),bind(X_28,$fot(not(X_151))),bind(X_29,$fot(X_151))]]) ).
cnf(refute_0_299,plain,
( or(and(not(X_151),not(X_151)),not(not(not(not(not(not(not(not(X_151))))))))) != implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))
| ~ is_a_theorem(or(and(not(X_151),not(X_151)),not(not(not(not(not(not(not(not(X_151))))))))))
| is_a_theorem(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_151),not(X_151)),not(not(not(not(not(not(not(not(X_151)))))))))) ),[0],$fot(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))))]]) ).
cnf(refute_0_300,plain,
( ~ is_a_theorem(or(and(not(X_151),not(X_151)),not(not(not(not(not(not(not(not(X_151))))))))))
| is_a_theorem(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_151),not(X_151)),not(not(not(not(not(not(not(not(X_151))))))))),implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
is_a_theorem(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_151),not(X_151)),not(not(not(not(not(not(not(not(X_151)))))))))) )],[refute_0_297,refute_0_300]) ).
cnf(refute_0_302,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_303,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_125,refute_0_302]) ).
cnf(refute_0_304,plain,
implies(not(X_151),X_151) = or(X_151,X_151),
inference(subst,[],[refute_0_303:[bind(X,$fot(X_151)),bind(Y,$fot(X_151))]]) ).
cnf(refute_0_305,plain,
implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))) = implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))),
introduced(tautology,[refl,[$fot(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))))]]) ).
cnf(refute_0_306,plain,
( implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))) != implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))
| implies(not(X_151),X_151) != or(X_151,X_151)
| implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))) = implies(or(X_151,X_151),not(not(not(not(not(not(not(not(X_151))))))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))),implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))) ),[1,0],$fot(or(X_151,X_151))]]) ).
cnf(refute_0_307,plain,
( implies(not(X_151),X_151) != or(X_151,X_151)
| implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))) = implies(or(X_151,X_151),not(not(not(not(not(not(not(not(X_151))))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))),implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))) = implies(or(X_151,X_151),not(not(not(not(not(not(not(not(X_151))))))))),
inference(resolve,[$cnf( $equal(implies(not(X_151),X_151),or(X_151,X_151)) )],[refute_0_304,refute_0_307]) ).
cnf(refute_0_309,plain,
( implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))) != implies(or(X_151,X_151),not(not(not(not(not(not(not(not(X_151)))))))))
| ~ is_a_theorem(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))))
| is_a_theorem(implies(or(X_151,X_151),not(not(not(not(not(not(not(not(X_151)))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))) ),[0],$fot(implies(or(X_151,X_151),not(not(not(not(not(not(not(not(X_151))))))))))]]) ).
cnf(refute_0_310,plain,
( ~ is_a_theorem(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))))
| is_a_theorem(implies(or(X_151,X_151),not(not(not(not(not(not(not(not(X_151)))))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151))))))))),implies(or(X_151,X_151),not(not(not(not(not(not(not(not(X_151)))))))))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
is_a_theorem(implies(or(X_151,X_151),not(not(not(not(not(not(not(not(X_151)))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_151),X_151),not(not(not(not(not(not(not(not(X_151)))))))))) )],[refute_0_301,refute_0_310]) ).
cnf(refute_0_312,plain,
is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(not(not(X))))))))))),
inference(subst,[],[refute_0_311:[bind(X_151,$fot(not(X)))]]) ).
cnf(refute_0_313,plain,
implies(X,not(X)) = or(not(X),not(X)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_314,plain,
( implies(X,not(X)) != or(not(X),not(X))
| or(not(X),not(X)) = implies(X,not(X)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,not(X)))),bind(Y0,$fot(or(not(X),not(X))))]]) ).
cnf(refute_0_315,plain,
or(not(X),not(X)) = implies(X,not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(X)),or(not(X),not(X))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(not(not(X)))))))))))
| is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(not(not(X))))))))))) ),[0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_317,plain,
( ~ is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(not(not(X)))))))))))
| is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X))))))))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X))))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(X)),not(not(not(not(not(not(not(not(not(X))))))))))) )],[refute_0_312,refute_0_317]) ).
cnf(refute_0_319,plain,
implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))) = or(and(X,X),not(not(not(not(not(not(not(not(not(X)))))))))),
inference(subst,[],[refute_0_157:[bind(Y,$fot(not(not(not(not(not(not(not(not(not(X))))))))))),bind(X_14,$fot(X)),bind(X_15,$fot(X))]]) ).
cnf(refute_0_320,plain,
( implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))) != or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))
| ~ is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X))))))))))) ),[0],$fot(or(and(X,X),not(not(not(not(not(not(not(not(not(X)))))))))))]]) ).
cnf(refute_0_321,plain,
( ~ is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))))
| is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X)))))))))),or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
is_a_theorem(or(and(X,X),not(not(not(not(not(not(not(not(not(X))))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(X)),not(not(not(not(not(not(not(not(not(X))))))))))) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
is_a_theorem(or(and(not(X_29),not(X_29)),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))),
inference(subst,[],[refute_0_322:[bind(X,$fot(not(X_29)))]]) ).
cnf(refute_0_324,plain,
or(and(not(X_29),not(X_29)),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) = implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))),
inference(subst,[],[refute_0_263:[bind(Y,$fot(not(not(not(not(not(not(not(not(not(not(X_29)))))))))))),bind(X_28,$fot(not(X_29)))]]) ).
cnf(refute_0_325,plain,
( or(and(not(X_29),not(X_29)),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) != implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))
| ~ is_a_theorem(or(and(not(X_29),not(X_29)),not(not(not(not(not(not(not(not(not(not(X_29))))))))))))
| is_a_theorem(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_29),not(X_29)),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) ),[0],$fot(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))))]]) ).
cnf(refute_0_326,plain,
( ~ is_a_theorem(or(and(not(X_29),not(X_29)),not(not(not(not(not(not(not(not(not(not(X_29))))))))))))
| is_a_theorem(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_29),not(X_29)),not(not(not(not(not(not(not(not(not(not(X_29))))))))))),implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
is_a_theorem(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_29),not(X_29)),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) )],[refute_0_323,refute_0_326]) ).
cnf(refute_0_328,plain,
implies(not(X_29),X_29) = or(X_29,X_29),
inference(subst,[],[refute_0_303:[bind(X,$fot(X_29)),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_329,plain,
implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) = implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))),
introduced(tautology,[refl,[$fot(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))))]]) ).
cnf(refute_0_330,plain,
( implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) != implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))
| implies(not(X_29),X_29) != or(X_29,X_29)
| implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) = implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))),implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) ),[1,0],$fot(or(X_29,X_29))]]) ).
cnf(refute_0_331,plain,
( implies(not(X_29),X_29) != or(X_29,X_29)
| implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) = implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))),implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) = implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))),
inference(resolve,[$cnf( $equal(implies(not(X_29),X_29),or(X_29,X_29)) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
( implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))) != implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))
| ~ is_a_theorem(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))))
| is_a_theorem(implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) ),[0],$fot(implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))))]]) ).
cnf(refute_0_334,plain,
( ~ is_a_theorem(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))))
| is_a_theorem(implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))),implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
is_a_theorem(implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_29),X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) )],[refute_0_327,refute_0_334]) ).
cnf(refute_0_336,plain,
( ~ is_a_theorem(implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29))))))))))))
| is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29)))) ),
inference(subst,[],[refute_0_26:[bind(Q,$fot(not(not(not(not(not(not(not(not(not(not(X_29)))))))))))),bind(X_7,$fot(or(X_29,X_29)))]]) ).
cnf(refute_0_337,plain,
is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_29,X_29),not(not(not(not(not(not(not(not(not(not(X_29)))))))))))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
implies(not(X_29),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(subst,[],[refute_0_303:[bind(X,$fot(X_29)),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_339,plain,
or(not(not(X_29)),not(or(X_29,X_29))) = implies(not(X_29),not(or(X_29,X_29))),
inference(subst,[],[refute_0_39:[bind(X,$fot(not(X_29))),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_340,plain,
( implies(not(X_29),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(X_29)),not(or(X_29,X_29))) != implies(not(X_29),not(or(X_29,X_29)))
| or(not(not(X_29)),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(not(not(X_29)),not(or(X_29,X_29))))),bind(Y0,$fot(implies(not(X_29),not(or(X_29,X_29))))),bind(Z,$fot(or(X_29,not(or(X_29,X_29)))))]]) ).
cnf(refute_0_341,plain,
( implies(not(X_29),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(X_29)),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(resolve,[$cnf( $equal(or(not(not(X_29)),not(or(X_29,X_29))),implies(not(X_29),not(or(X_29,X_29)))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
or(not(not(X_29)),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(resolve,[$cnf( $equal(implies(not(X_29),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_338,refute_0_341]) ).
cnf(refute_0_343,plain,
implies(not(not(not(X_29))),not(or(X_29,X_29))) = or(not(not(X_29)),not(or(X_29,X_29))),
inference(subst,[],[refute_0_303:[bind(X,$fot(not(not(X_29)))),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_344,plain,
( implies(not(not(not(X_29))),not(or(X_29,X_29))) != or(not(not(X_29)),not(or(X_29,X_29)))
| or(not(not(X_29)),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| implies(not(not(not(X_29))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(implies(not(not(not(X_29))),not(or(X_29,X_29))))),bind(Y0,$fot(or(not(not(X_29)),not(or(X_29,X_29))))),bind(Z,$fot(or(X_29,not(or(X_29,X_29)))))]]) ).
cnf(refute_0_345,plain,
( or(not(not(X_29)),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| implies(not(not(not(X_29))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_29))),not(or(X_29,X_29))),or(not(not(X_29)),not(or(X_29,X_29)))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
implies(not(not(not(X_29))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(resolve,[$cnf( $equal(or(not(not(X_29)),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
or(not(not(not(not(X_29)))),not(or(X_29,X_29))) = implies(not(not(not(X_29))),not(or(X_29,X_29))),
inference(subst,[],[refute_0_39:[bind(X,$fot(not(not(not(X_29))))),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_348,plain,
( implies(not(not(not(X_29))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(not(not(X_29)))),not(or(X_29,X_29))) != implies(not(not(not(X_29))),not(or(X_29,X_29)))
| or(not(not(not(not(X_29)))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(not(not(not(not(X_29)))),not(or(X_29,X_29))))),bind(Y0,$fot(implies(not(not(not(X_29))),not(or(X_29,X_29))))),bind(Z,$fot(or(X_29,not(or(X_29,X_29)))))]]) ).
cnf(refute_0_349,plain,
( implies(not(not(not(X_29))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(not(not(X_29)))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(X_29)))),not(or(X_29,X_29))),implies(not(not(not(X_29))),not(or(X_29,X_29)))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
or(not(not(not(not(X_29)))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_29))),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_346,refute_0_349]) ).
cnf(refute_0_351,plain,
implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))) = or(not(not(not(not(X_29)))),not(or(X_29,X_29))),
inference(subst,[],[refute_0_303:[bind(X,$fot(not(not(not(not(X_29)))))),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_352,plain,
( implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))) != or(not(not(not(not(X_29)))),not(or(X_29,X_29)))
| or(not(not(not(not(X_29)))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))))),bind(Y0,$fot(or(not(not(not(not(X_29)))),not(or(X_29,X_29))))),bind(Z,$fot(or(X_29,not(or(X_29,X_29)))))]]) ).
cnf(refute_0_353,plain,
( or(not(not(not(not(X_29)))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))),or(not(not(not(not(X_29)))),not(or(X_29,X_29)))) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(X_29)))),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_350,refute_0_353]) ).
cnf(refute_0_355,plain,
or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))) = implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))),
inference(subst,[],[refute_0_39:[bind(X,$fot(not(not(not(not(not(X_29))))))),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_356,plain,
( implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))) != implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29)))
| or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))))),bind(Y0,$fot(implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))))),bind(Z,$fot(or(X_29,not(or(X_29,X_29)))))]]) ).
cnf(refute_0_357,plain,
( implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))),implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29)))) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(X_29))))),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_354,refute_0_357]) ).
cnf(refute_0_359,plain,
implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))) = or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))),
inference(subst,[],[refute_0_303:[bind(X,$fot(not(not(not(not(not(not(X_29)))))))),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_360,plain,
( implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))) != or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29)))
| or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))))),bind(Y0,$fot(or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))))),bind(Z,$fot(or(X_29,not(or(X_29,X_29)))))]]) ).
cnf(refute_0_361,plain,
( or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))),or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29)))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(X_29)))))),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_358,refute_0_361]) ).
cnf(refute_0_363,plain,
or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))) = implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))),
inference(subst,[],[refute_0_39:[bind(X,$fot(not(not(not(not(not(not(not(X_29))))))))),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_364,plain,
( implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))) != implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29)))
| or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))))),bind(Y0,$fot(implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))))),bind(Z,$fot(or(X_29,not(or(X_29,X_29)))))]]) ).
cnf(refute_0_365,plain,
( implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))),implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(X_29))))))),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))) = or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))),
inference(subst,[],[refute_0_303:[bind(X,$fot(not(not(not(not(not(not(not(not(X_29)))))))))),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_368,plain,
( implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))) != or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29)))
| or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))))),bind(Y0,$fot(or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))))),bind(Z,$fot(or(X_29,not(or(X_29,X_29)))))]]) ).
cnf(refute_0_369,plain,
( or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))),or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29)))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(X_29)))))))),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_366,refute_0_369]) ).
cnf(refute_0_371,plain,
or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))) = implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))),
inference(subst,[],[refute_0_39:[bind(X,$fot(not(not(not(not(not(not(not(not(not(X_29))))))))))),bind(Y,$fot(not(or(X_29,X_29))))]]) ).
cnf(refute_0_372,plain,
( implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))) != implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29)))
| or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))))),bind(Y0,$fot(implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))))),bind(Z,$fot(or(X_29,not(or(X_29,X_29)))))]]) ).
cnf(refute_0_373,plain,
( implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))),implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29)))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))) = or(X_29,not(or(X_29,X_29))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(not(not(X_29))))))))),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_370,refute_0_373]) ).
cnf(refute_0_375,plain,
( or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))) != or(X_29,not(or(X_29,X_29)))
| ~ is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))))
| is_a_theorem(or(X_29,not(or(X_29,X_29)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29)))) ),[0],$fot(or(X_29,not(or(X_29,X_29))))]]) ).
cnf(refute_0_376,plain,
( ~ is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))))
| is_a_theorem(or(X_29,not(or(X_29,X_29)))) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29))),or(X_29,not(or(X_29,X_29)))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
is_a_theorem(or(X_29,not(or(X_29,X_29)))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(not(not(not(not(not(not(not(not(X_29)))))))))),not(or(X_29,X_29)))) )],[refute_0_337,refute_0_376]) ).
cnf(refute_0_378,plain,
is_a_theorem(or(not(X),not(or(not(X),not(X))))),
inference(subst,[],[refute_0_377:[bind(X_29,$fot(not(X)))]]) ).
cnf(refute_0_379,plain,
( or(not(X),not(X)) != implies(X,not(X))
| ~ is_a_theorem(or(not(X),not(or(not(X),not(X)))))
| is_a_theorem(or(not(X),not(implies(X,not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),not(or(not(X),not(X))))) ),[0,1,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_380,plain,
( ~ is_a_theorem(or(not(X),not(or(not(X),not(X)))))
| is_a_theorem(or(not(X),not(implies(X,not(X))))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_315,refute_0_379]) ).
cnf(refute_0_381,plain,
is_a_theorem(or(not(X),not(implies(X,not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(or(not(X),not(X))))) )],[refute_0_378,refute_0_380]) ).
cnf(refute_0_382,plain,
not(implies(X,not(X))) = and(X,X),
inference(subst,[],[refute_0_86:[bind(Y,$fot(X))]]) ).
cnf(refute_0_383,plain,
implies(X,not(implies(X,not(X)))) = implies(X,not(implies(X,not(X)))),
introduced(tautology,[refl,[$fot(implies(X,not(implies(X,not(X)))))]]) ).
cnf(refute_0_384,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_385,plain,
( not(implies(X,not(X))) != and(X,X)
| implies(X,not(implies(X,not(X)))) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(X)))),implies(X,not(implies(X,not(X))))) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
implies(X,not(implies(X,not(X)))) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X))),and(X,X)) )],[refute_0_382,refute_0_385]) ).
cnf(refute_0_387,plain,
or(not(X),not(implies(X,not(X)))) = implies(X,not(implies(X,not(X)))),
inference(subst,[],[refute_0_39:[bind(Y,$fot(not(implies(X,not(X)))))]]) ).
cnf(refute_0_388,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_101:[bind(X0,$fot(or(not(X),not(implies(X,not(X)))))),bind(Y0,$fot(implies(X,not(implies(X,not(X)))))),bind(Z,$fot(implies(X,and(X,X))))]]) ).
cnf(refute_0_389,plain,
( implies(X,not(implies(X,not(X)))) != implies(X,and(X,X))
| or(not(X),not(implies(X,not(X)))) = implies(X,and(X,X)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(implies(X,not(X)))),implies(X,not(implies(X,not(X))))) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
or(not(X),not(implies(X,not(X)))) = implies(X,and(X,X)),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(X)))),implies(X,and(X,X))) )],[refute_0_386,refute_0_389]) ).
cnf(refute_0_391,plain,
( or(not(X),not(implies(X,not(X)))) != implies(X,and(X,X))
| ~ is_a_theorem(or(not(X),not(implies(X,not(X)))))
| is_a_theorem(implies(X,and(X,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),not(implies(X,not(X))))) ),[0],$fot(implies(X,and(X,X)))]]) ).
cnf(refute_0_392,plain,
( ~ is_a_theorem(or(not(X),not(implies(X,not(X)))))
| is_a_theorem(implies(X,and(X,X))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(implies(X,not(X)))),implies(X,and(X,X))) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
is_a_theorem(implies(X,and(X,X))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),not(implies(X,not(X))))) )],[refute_0_381,refute_0_392]) ).
cnf(refute_0_394,plain,
is_a_theorem(implies(implies(X,X),and(implies(X,X),implies(X,X)))),
inference(subst,[],[refute_0_393:[bind(X,$fot(implies(X,X)))]]) ).
cnf(refute_0_395,plain,
equiv(X,X) = and(implies(X,X),implies(X,X)),
inference(subst,[],[refute_0_115:[bind(Y,$fot(X))]]) ).
cnf(refute_0_396,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_19:[bind(X0,$fot(equiv(X,X))),bind(Y0,$fot(and(implies(X,X),implies(X,X))))]]) ).
cnf(refute_0_397,plain,
and(implies(X,X),implies(X,X)) = equiv(X,X),
inference(resolve,[$cnf( $equal(equiv(X,X),and(implies(X,X),implies(X,X))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
( and(implies(X,X),implies(X,X)) != equiv(X,X)
| ~ is_a_theorem(implies(implies(X,X),and(implies(X,X),implies(X,X))))
| is_a_theorem(implies(implies(X,X),equiv(X,X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,X),and(implies(X,X),implies(X,X)))) ),[0,1],$fot(equiv(X,X))]]) ).
cnf(refute_0_399,plain,
( ~ is_a_theorem(implies(implies(X,X),and(implies(X,X),implies(X,X))))
| is_a_theorem(implies(implies(X,X),equiv(X,X))) ),
inference(resolve,[$cnf( $equal(and(implies(X,X),implies(X,X)),equiv(X,X)) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
is_a_theorem(implies(implies(X,X),equiv(X,X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,X),and(implies(X,X),implies(X,X)))) )],[refute_0_394,refute_0_399]) ).
cnf(refute_0_401,plain,
is_a_theorem(implies(implies(X_480,X_480),equiv(X_480,X_480))),
inference(subst,[],[refute_0_400:[bind(X,$fot(X_480))]]) ).
cnf(refute_0_402,plain,
( ~ is_a_theorem(implies(X_480,X_480))
| is_a_theorem(equiv(X_480,X_480)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_480,X_480),equiv(X_480,X_480))) )],[refute_0_401,refute_0_227]) ).
cnf(refute_0_403,plain,
( ~ is_a_theorem(implies(and(Y,Y),and(Y,Y)))
| is_a_theorem(equiv(and(Y,Y),and(Y,Y))) ),
inference(subst,[],[refute_0_402:[bind(X_480,$fot(and(Y,Y)))]]) ).
cnf(refute_0_404,plain,
is_a_theorem(equiv(and(Y,Y),and(Y,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(and(Y,Y),and(Y,Y))) )],[refute_0_226,refute_0_403]) ).
cnf(refute_0_405,plain,
is_a_theorem(equiv(and(X_1801,X_1801),and(X_1801,X_1801))),
inference(subst,[],[refute_0_404:[bind(Y,$fot(X_1801))]]) ).
cnf(refute_0_406,plain,
and(X_1801,X_1801) = not(not(and(X_1801,X_1801))),
inference(resolve,[$cnf( is_a_theorem(equiv(and(X_1801,X_1801),and(X_1801,X_1801))) )],[refute_0_405,refute_0_186]) ).
cnf(refute_0_407,plain,
and(not(Y),not(Y)) = not(not(and(not(Y),not(Y)))),
inference(subst,[],[refute_0_406:[bind(X_1801,$fot(not(Y)))]]) ).
cnf(refute_0_408,plain,
implies(not(Y),Y) = not(and(not(Y),not(Y))),
inference(subst,[],[refute_0_72:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_409,plain,
( implies(not(Y),Y) != not(and(not(Y),not(Y)))
| not(and(not(Y),not(Y))) = implies(not(Y),Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(not(Y),Y))),bind(Y0,$fot(not(and(not(Y),not(Y)))))]]) ).
cnf(refute_0_410,plain,
not(and(not(Y),not(Y))) = implies(not(Y),Y),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),not(and(not(Y),not(Y)))) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
( and(not(Y),not(Y)) != not(not(and(not(Y),not(Y))))
| not(and(not(Y),not(Y))) != implies(not(Y),Y)
| and(not(Y),not(Y)) = not(implies(not(Y),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(Y),not(Y)),not(not(and(not(Y),not(Y))))) ),[1,0],$fot(implies(not(Y),Y))]]) ).
cnf(refute_0_412,plain,
( and(not(Y),not(Y)) != not(not(and(not(Y),not(Y))))
| and(not(Y),not(Y)) = not(implies(not(Y),Y)) ),
inference(resolve,[$cnf( $equal(not(and(not(Y),not(Y))),implies(not(Y),Y)) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
and(not(Y),not(Y)) = not(implies(not(Y),Y)),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(not(and(not(Y),not(Y))))) )],[refute_0_407,refute_0_412]) ).
cnf(refute_0_414,plain,
implies(not(Y),Y) = or(Y,Y),
inference(subst,[],[refute_0_303:[bind(X,$fot(Y))]]) ).
cnf(refute_0_415,plain,
not(implies(not(Y),Y)) = not(implies(not(Y),Y)),
introduced(tautology,[refl,[$fot(not(implies(not(Y),Y)))]]) ).
cnf(refute_0_416,plain,
( implies(not(Y),Y) != or(Y,Y)
| not(implies(not(Y),Y)) != not(implies(not(Y),Y))
| not(implies(not(Y),Y)) = not(or(Y,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(Y),Y)),not(implies(not(Y),Y))) ),[1,0],$fot(or(Y,Y))]]) ).
cnf(refute_0_417,plain,
( implies(not(Y),Y) != or(Y,Y)
| not(implies(not(Y),Y)) = not(or(Y,Y)) ),
inference(resolve,[$cnf( $equal(not(implies(not(Y),Y)),not(implies(not(Y),Y))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
not(implies(not(Y),Y)) = not(or(Y,Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),or(Y,Y)) )],[refute_0_414,refute_0_417]) ).
cnf(refute_0_419,plain,
( and(not(Y),not(Y)) != not(implies(not(Y),Y))
| not(implies(not(Y),Y)) != not(or(Y,Y))
| and(not(Y),not(Y)) = not(or(Y,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(Y),not(Y)),not(or(Y,Y))) ),[0],$fot(not(implies(not(Y),Y)))]]) ).
cnf(refute_0_420,plain,
( and(not(Y),not(Y)) != not(implies(not(Y),Y))
| and(not(Y),not(Y)) = not(or(Y,Y)) ),
inference(resolve,[$cnf( $equal(not(implies(not(Y),Y)),not(or(Y,Y))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
and(not(Y),not(Y)) = not(or(Y,Y)),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(implies(not(Y),Y))) )],[refute_0_413,refute_0_420]) ).
cnf(refute_0_422,plain,
( and(not(Y),not(Y)) != not(or(Y,Y))
| ~ is_a_theorem(implies(and(X_2488,and(not(Y),not(Y))),not(not(and(not(Y),and(X_2488,not(Y)))))))
| is_a_theorem(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(X_2488,and(not(Y),not(Y))),not(not(and(not(Y),and(X_2488,not(Y))))))) ),[0,0,1],$fot(not(or(Y,Y)))]]) ).
cnf(refute_0_423,plain,
( ~ is_a_theorem(implies(and(X_2488,and(not(Y),not(Y))),not(not(and(not(Y),and(X_2488,not(Y)))))))
| is_a_theorem(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y))))))) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(or(Y,Y))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
is_a_theorem(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y))))))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_2488,and(not(Y),not(Y))),not(not(and(not(Y),and(X_2488,not(Y))))))) )],[refute_0_108,refute_0_423]) ).
cnf(refute_0_425,plain,
or(X,implies(X_246,not(X_247))) = implies(not(X),implies(X_246,not(X_247))),
inference(subst,[],[refute_0_125:[bind(Y,$fot(implies(X_246,not(X_247))))]]) ).
cnf(refute_0_426,plain,
implies(not(X),implies(X_246,not(X_247))) = not(and(not(X),and(X_246,X_247))),
inference(subst,[],[refute_0_89:[bind(X,$fot(X_246)),bind(Y,$fot(X_247)),bind(X_28,$fot(not(X)))]]) ).
cnf(refute_0_427,plain,
( implies(not(X),implies(X_246,not(X_247))) != not(and(not(X),and(X_246,X_247)))
| or(X,implies(X_246,not(X_247))) != implies(not(X),implies(X_246,not(X_247)))
| or(X,implies(X_246,not(X_247))) = not(and(not(X),and(X_246,X_247))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,implies(X_246,not(X_247))),implies(not(X),implies(X_246,not(X_247)))) ),[1],$fot(not(and(not(X),and(X_246,X_247))))]]) ).
cnf(refute_0_428,plain,
( or(X,implies(X_246,not(X_247))) != implies(not(X),implies(X_246,not(X_247)))
| or(X,implies(X_246,not(X_247))) = not(and(not(X),and(X_246,X_247))) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(X_246,not(X_247))),not(and(not(X),and(X_246,X_247)))) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
or(X,implies(X_246,not(X_247))) = not(and(not(X),and(X_246,X_247))),
inference(resolve,[$cnf( $equal(or(X,implies(X_246,not(X_247))),implies(not(X),implies(X_246,not(X_247)))) )],[refute_0_425,refute_0_428]) ).
cnf(refute_0_430,plain,
or(X_298,implies(X_299,not(not(X_29)))) = not(and(not(X_298),and(X_299,not(X_29)))),
inference(subst,[],[refute_0_429:[bind(X,$fot(X_298)),bind(X_246,$fot(X_299)),bind(X_247,$fot(not(X_29)))]]) ).
cnf(refute_0_431,plain,
and(X,and(X_28,not(X_29))) = not(implies(X,not(and(X_28,not(X_29))))),
inference(subst,[],[refute_0_84:[bind(Y,$fot(and(X_28,not(X_29))))]]) ).
cnf(refute_0_432,plain,
( and(X,and(X_28,not(X_29))) != not(implies(X,not(and(X_28,not(X_29)))))
| not(and(X_28,not(X_29))) != implies(X_28,X_29)
| and(X,and(X_28,not(X_29))) = not(implies(X,implies(X_28,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,and(X_28,not(X_29))),not(implies(X,not(and(X_28,not(X_29)))))) ),[1,0,1],$fot(implies(X_28,X_29))]]) ).
cnf(refute_0_433,plain,
( and(X,and(X_28,not(X_29))) != not(implies(X,not(and(X_28,not(X_29)))))
| and(X,and(X_28,not(X_29))) = not(implies(X,implies(X_28,X_29))) ),
inference(resolve,[$cnf( $equal(not(and(X_28,not(X_29))),implies(X_28,X_29)) )],[refute_0_260,refute_0_432]) ).
cnf(refute_0_434,plain,
and(X,and(X_28,not(X_29))) = not(implies(X,implies(X_28,X_29))),
inference(resolve,[$cnf( $equal(and(X,and(X_28,not(X_29))),not(implies(X,not(and(X_28,not(X_29)))))) )],[refute_0_431,refute_0_433]) ).
cnf(refute_0_435,plain,
and(not(X_298),and(X_299,not(X_29))) = not(implies(not(X_298),implies(X_299,X_29))),
inference(subst,[],[refute_0_434:[bind(X,$fot(not(X_298))),bind(X_28,$fot(X_299))]]) ).
cnf(refute_0_436,plain,
( and(not(X_298),and(X_299,not(X_29))) != not(implies(not(X_298),implies(X_299,X_29)))
| or(X_298,implies(X_299,not(not(X_29)))) != not(and(not(X_298),and(X_299,not(X_29))))
| or(X_298,implies(X_299,not(not(X_29)))) = not(not(implies(not(X_298),implies(X_299,X_29)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_298,implies(X_299,not(not(X_29)))),not(and(not(X_298),and(X_299,not(X_29))))) ),[1,0],$fot(not(implies(not(X_298),implies(X_299,X_29))))]]) ).
cnf(refute_0_437,plain,
( or(X_298,implies(X_299,not(not(X_29)))) != not(and(not(X_298),and(X_299,not(X_29))))
| or(X_298,implies(X_299,not(not(X_29)))) = not(not(implies(not(X_298),implies(X_299,X_29)))) ),
inference(resolve,[$cnf( $equal(and(not(X_298),and(X_299,not(X_29))),not(implies(not(X_298),implies(X_299,X_29)))) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
or(X_298,implies(X_299,not(not(X_29)))) = not(not(implies(not(X_298),implies(X_299,X_29)))),
inference(resolve,[$cnf( $equal(or(X_298,implies(X_299,not(not(X_29)))),not(and(not(X_298),and(X_299,not(X_29))))) )],[refute_0_430,refute_0_437]) ).
cnf(refute_0_439,plain,
implies(not(X_298),implies(X_299,X_29)) = or(X_298,implies(X_299,X_29)),
inference(subst,[],[refute_0_303:[bind(X,$fot(X_298)),bind(Y,$fot(implies(X_299,X_29)))]]) ).
cnf(refute_0_440,plain,
not(implies(not(X_298),implies(X_299,X_29))) = not(implies(not(X_298),implies(X_299,X_29))),
introduced(tautology,[refl,[$fot(not(implies(not(X_298),implies(X_299,X_29))))]]) ).
cnf(refute_0_441,plain,
( implies(not(X_298),implies(X_299,X_29)) != or(X_298,implies(X_299,X_29))
| not(implies(not(X_298),implies(X_299,X_29))) != not(implies(not(X_298),implies(X_299,X_29)))
| not(implies(not(X_298),implies(X_299,X_29))) = not(or(X_298,implies(X_299,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_298),implies(X_299,X_29))),not(implies(not(X_298),implies(X_299,X_29)))) ),[1,0],$fot(or(X_298,implies(X_299,X_29)))]]) ).
cnf(refute_0_442,plain,
( implies(not(X_298),implies(X_299,X_29)) != or(X_298,implies(X_299,X_29))
| not(implies(not(X_298),implies(X_299,X_29))) = not(or(X_298,implies(X_299,X_29))) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_298),implies(X_299,X_29))),not(implies(not(X_298),implies(X_299,X_29)))) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
not(implies(not(X_298),implies(X_299,X_29))) = not(or(X_298,implies(X_299,X_29))),
inference(resolve,[$cnf( $equal(implies(not(X_298),implies(X_299,X_29)),or(X_298,implies(X_299,X_29))) )],[refute_0_439,refute_0_442]) ).
cnf(refute_0_444,plain,
not(not(implies(not(X_298),implies(X_299,X_29)))) = not(not(implies(not(X_298),implies(X_299,X_29)))),
introduced(tautology,[refl,[$fot(not(not(implies(not(X_298),implies(X_299,X_29)))))]]) ).
cnf(refute_0_445,plain,
( not(implies(not(X_298),implies(X_299,X_29))) != not(or(X_298,implies(X_299,X_29)))
| not(not(implies(not(X_298),implies(X_299,X_29)))) != not(not(implies(not(X_298),implies(X_299,X_29))))
| not(not(implies(not(X_298),implies(X_299,X_29)))) = not(not(or(X_298,implies(X_299,X_29)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(not(X_298),implies(X_299,X_29)))),not(not(implies(not(X_298),implies(X_299,X_29))))) ),[1,0],$fot(not(or(X_298,implies(X_299,X_29))))]]) ).
cnf(refute_0_446,plain,
( not(implies(not(X_298),implies(X_299,X_29))) != not(or(X_298,implies(X_299,X_29)))
| not(not(implies(not(X_298),implies(X_299,X_29)))) = not(not(or(X_298,implies(X_299,X_29)))) ),
inference(resolve,[$cnf( $equal(not(not(implies(not(X_298),implies(X_299,X_29)))),not(not(implies(not(X_298),implies(X_299,X_29))))) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
not(not(implies(not(X_298),implies(X_299,X_29)))) = not(not(or(X_298,implies(X_299,X_29)))),
inference(resolve,[$cnf( $equal(not(implies(not(X_298),implies(X_299,X_29))),not(or(X_298,implies(X_299,X_29)))) )],[refute_0_443,refute_0_446]) ).
cnf(refute_0_448,plain,
( not(not(implies(not(X_298),implies(X_299,X_29)))) != not(not(or(X_298,implies(X_299,X_29))))
| or(X_298,implies(X_299,not(not(X_29)))) != not(not(implies(not(X_298),implies(X_299,X_29))))
| or(X_298,implies(X_299,not(not(X_29)))) = not(not(or(X_298,implies(X_299,X_29)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_298,implies(X_299,not(not(X_29)))),not(not(implies(not(X_298),implies(X_299,X_29))))) ),[1],$fot(not(not(or(X_298,implies(X_299,X_29)))))]]) ).
cnf(refute_0_449,plain,
( or(X_298,implies(X_299,not(not(X_29)))) != not(not(implies(not(X_298),implies(X_299,X_29))))
| or(X_298,implies(X_299,not(not(X_29)))) = not(not(or(X_298,implies(X_299,X_29)))) ),
inference(resolve,[$cnf( $equal(not(not(implies(not(X_298),implies(X_299,X_29)))),not(not(or(X_298,implies(X_299,X_29))))) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
or(X_298,implies(X_299,not(not(X_29)))) = not(not(or(X_298,implies(X_299,X_29)))),
inference(resolve,[$cnf( $equal(or(X_298,implies(X_299,not(not(X_29)))),not(not(implies(not(X_298),implies(X_299,X_29))))) )],[refute_0_438,refute_0_449]) ).
cnf(refute_0_451,plain,
or(Y,implies(X_2488,not(not(Y)))) = not(not(or(Y,implies(X_2488,Y)))),
inference(subst,[],[refute_0_450:[bind(X_29,$fot(Y)),bind(X_298,$fot(Y)),bind(X_299,$fot(X_2488))]]) ).
cnf(refute_0_452,plain,
( or(X,implies(X_246,not(X_247))) != not(and(not(X),and(X_246,X_247)))
| not(and(not(X),and(X_246,X_247))) = or(X,implies(X_246,not(X_247))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,implies(X_246,not(X_247))))),bind(Y0,$fot(not(and(not(X),and(X_246,X_247)))))]]) ).
cnf(refute_0_453,plain,
not(and(not(X),and(X_246,X_247))) = or(X,implies(X_246,not(X_247))),
inference(resolve,[$cnf( $equal(or(X,implies(X_246,not(X_247))),not(and(not(X),and(X_246,X_247)))) )],[refute_0_429,refute_0_452]) ).
cnf(refute_0_454,plain,
not(and(not(Y),and(X_2488,not(Y)))) = or(Y,implies(X_2488,not(not(Y)))),
inference(subst,[],[refute_0_453:[bind(X,$fot(Y)),bind(X_246,$fot(X_2488)),bind(X_247,$fot(not(Y)))]]) ).
cnf(refute_0_455,plain,
( not(and(not(Y),and(X_2488,not(Y)))) != or(Y,implies(X_2488,not(not(Y))))
| or(Y,implies(X_2488,not(not(Y)))) != not(not(or(Y,implies(X_2488,Y))))
| not(and(not(Y),and(X_2488,not(Y)))) = not(not(or(Y,implies(X_2488,Y)))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(not(and(not(Y),and(X_2488,not(Y)))))),bind(Y0,$fot(or(Y,implies(X_2488,not(not(Y)))))),bind(Z,$fot(not(not(or(Y,implies(X_2488,Y))))))]]) ).
cnf(refute_0_456,plain,
( or(Y,implies(X_2488,not(not(Y)))) != not(not(or(Y,implies(X_2488,Y))))
| not(and(not(Y),and(X_2488,not(Y)))) = not(not(or(Y,implies(X_2488,Y)))) ),
inference(resolve,[$cnf( $equal(not(and(not(Y),and(X_2488,not(Y)))),or(Y,implies(X_2488,not(not(Y))))) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
not(and(not(Y),and(X_2488,not(Y)))) = not(not(or(Y,implies(X_2488,Y)))),
inference(resolve,[$cnf( $equal(or(Y,implies(X_2488,not(not(Y)))),not(not(or(Y,implies(X_2488,Y))))) )],[refute_0_451,refute_0_456]) ).
cnf(refute_0_458,plain,
not(not(and(not(Y),and(X_2488,not(Y))))) = not(not(and(not(Y),and(X_2488,not(Y))))),
introduced(tautology,[refl,[$fot(not(not(and(not(Y),and(X_2488,not(Y))))))]]) ).
cnf(refute_0_459,plain,
( not(and(not(Y),and(X_2488,not(Y)))) != not(not(or(Y,implies(X_2488,Y))))
| not(not(and(not(Y),and(X_2488,not(Y))))) != not(not(and(not(Y),and(X_2488,not(Y)))))
| not(not(and(not(Y),and(X_2488,not(Y))))) = not(not(not(or(Y,implies(X_2488,Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(and(not(Y),and(X_2488,not(Y))))),not(not(and(not(Y),and(X_2488,not(Y)))))) ),[1,0],$fot(not(not(or(Y,implies(X_2488,Y)))))]]) ).
cnf(refute_0_460,plain,
( not(and(not(Y),and(X_2488,not(Y)))) != not(not(or(Y,implies(X_2488,Y))))
| not(not(and(not(Y),and(X_2488,not(Y))))) = not(not(not(or(Y,implies(X_2488,Y))))) ),
inference(resolve,[$cnf( $equal(not(not(and(not(Y),and(X_2488,not(Y))))),not(not(and(not(Y),and(X_2488,not(Y)))))) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
not(not(and(not(Y),and(X_2488,not(Y))))) = not(not(not(or(Y,implies(X_2488,Y))))),
inference(resolve,[$cnf( $equal(not(and(not(Y),and(X_2488,not(Y)))),not(not(or(Y,implies(X_2488,Y))))) )],[refute_0_457,refute_0_460]) ).
cnf(refute_0_462,plain,
or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))) = or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))),
introduced(tautology,[refl,[$fot(or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))))]]) ).
cnf(refute_0_463,plain,
( not(not(and(not(Y),and(X_2488,not(Y))))) != not(not(not(or(Y,implies(X_2488,Y)))))
| or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))) != or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y))))))
| or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))) = or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y)))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))),or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y))))))) ),[1,1],$fot(not(not(not(or(Y,implies(X_2488,Y))))))]]) ).
cnf(refute_0_464,plain,
( not(not(and(not(Y),and(X_2488,not(Y))))) != not(not(not(or(Y,implies(X_2488,Y)))))
| or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))) = or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y)))))) ),
inference(resolve,[$cnf( $equal(or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))),or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y))))))) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))) = or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y)))))),
inference(resolve,[$cnf( $equal(not(not(and(not(Y),and(X_2488,not(Y))))),not(not(not(or(Y,implies(X_2488,Y)))))) )],[refute_0_461,refute_0_464]) ).
cnf(refute_0_466,plain,
implies(and(X_28,not(X_29)),Y) = or(not(and(X_28,not(X_29))),Y),
inference(subst,[],[refute_0_15:[bind(X,$fot(and(X_28,not(X_29))))]]) ).
cnf(refute_0_467,plain,
( implies(and(X_28,not(X_29)),Y) != or(not(and(X_28,not(X_29))),Y)
| not(and(X_28,not(X_29))) != implies(X_28,X_29)
| implies(and(X_28,not(X_29)),Y) = or(implies(X_28,X_29),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(X_28,not(X_29)),Y),or(not(and(X_28,not(X_29))),Y)) ),[1,0],$fot(implies(X_28,X_29))]]) ).
cnf(refute_0_468,plain,
( implies(and(X_28,not(X_29)),Y) != or(not(and(X_28,not(X_29))),Y)
| implies(and(X_28,not(X_29)),Y) = or(implies(X_28,X_29),Y) ),
inference(resolve,[$cnf( $equal(not(and(X_28,not(X_29))),implies(X_28,X_29)) )],[refute_0_260,refute_0_467]) ).
cnf(refute_0_469,plain,
implies(and(X_28,not(X_29)),Y) = or(implies(X_28,X_29),Y),
inference(resolve,[$cnf( $equal(implies(and(X_28,not(X_29)),Y),or(not(and(X_28,not(X_29))),Y)) )],[refute_0_466,refute_0_468]) ).
cnf(refute_0_470,plain,
implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))) = or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))),
inference(subst,[],[refute_0_469:[bind(Y,$fot(not(not(and(not(Y),and(X_2488,not(Y))))))),bind(X_28,$fot(X_2488)),bind(X_29,$fot(or(Y,Y)))]]) ).
cnf(refute_0_471,plain,
( implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))) != or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y))))))
| or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))) != or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y))))))
| implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))) = or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y)))))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))))),bind(Y0,$fot(or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))))),bind(Z,$fot(or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y))))))))]]) ).
cnf(refute_0_472,plain,
( or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))) != or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y))))))
| implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))) = or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y)))))) ),
inference(resolve,[$cnf( $equal(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))),or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y))))))) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))) = or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y)))))),
inference(resolve,[$cnf( $equal(or(implies(X_2488,or(Y,Y)),not(not(and(not(Y),and(X_2488,not(Y)))))),or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y))))))) )],[refute_0_465,refute_0_472]) ).
cnf(refute_0_474,plain,
( implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))) != or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y))))))
| ~ is_a_theorem(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))))
| is_a_theorem(or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y))))))) ),[0],$fot(or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y)))))))]]) ).
cnf(refute_0_475,plain,
( ~ is_a_theorem(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))))
| is_a_theorem(or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y))))))) ),
inference(resolve,[$cnf( $equal(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y)))))),or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y))))))) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
is_a_theorem(or(implies(X_2488,or(Y,Y)),not(not(not(or(Y,implies(X_2488,Y))))))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_2488,not(or(Y,Y))),not(not(and(not(Y),and(X_2488,not(Y))))))) )],[refute_0_424,refute_0_475]) ).
cnf(refute_0_477,plain,
is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,implies(not(X),X_2490))))))),
inference(subst,[],[refute_0_476:[bind(Y,$fot(X_2490)),bind(X_2488,$fot(not(X)))]]) ).
cnf(refute_0_478,plain,
or(X,X_2490) = implies(not(X),X_2490),
inference(subst,[],[refute_0_125:[bind(Y,$fot(X_2490))]]) ).
cnf(refute_0_479,plain,
( or(X,X_2490) != implies(not(X),X_2490)
| implies(not(X),X_2490) = or(X,X_2490) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,X_2490))),bind(Y0,$fot(implies(not(X),X_2490)))]]) ).
cnf(refute_0_480,plain,
implies(not(X),X_2490) = or(X,X_2490),
inference(resolve,[$cnf( $equal(or(X,X_2490),implies(not(X),X_2490)) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
( implies(not(X),X_2490) != or(X,X_2490)
| ~ is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,implies(not(X),X_2490)))))))
| is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,implies(not(X),X_2490))))))) ),[0,1,0,0,0,1],$fot(or(X,X_2490))]]) ).
cnf(refute_0_482,plain,
( ~ is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,implies(not(X),X_2490)))))))
| is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_2490),or(X,X_2490)) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))),
inference(resolve,[$cnf( is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,implies(not(X),X_2490))))))) )],[refute_0_477,refute_0_482]) ).
cnf(refute_0_484,plain,
implies(not(X),or(X_2490,X_2490)) = or(X,or(X_2490,X_2490)),
inference(subst,[],[refute_0_303:[bind(Y,$fot(or(X_2490,X_2490)))]]) ).
cnf(refute_0_485,plain,
or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),
introduced(tautology,[refl,[$fot(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))))]]) ).
cnf(refute_0_486,plain,
( implies(not(X),or(X_2490,X_2490)) != or(X,or(X_2490,X_2490))
| or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) != or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))
| or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) ),[1,0],$fot(or(X,or(X_2490,X_2490)))]]) ).
cnf(refute_0_487,plain,
( implies(not(X),or(X_2490,X_2490)) != or(X,or(X_2490,X_2490))
| or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) ),
inference(resolve,[$cnf( $equal(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),
inference(resolve,[$cnf( $equal(implies(not(X),or(X_2490,X_2490)),or(X,or(X_2490,X_2490))) )],[refute_0_484,refute_0_487]) ).
cnf(refute_0_489,plain,
( or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) != or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))
| ~ is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))))
| is_a_theorem(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) ),[0],$fot(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))))]]) ).
cnf(refute_0_490,plain,
( ~ is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))))
| is_a_theorem(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) ),
inference(resolve,[$cnf( $equal(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
is_a_theorem(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))),
inference(resolve,[$cnf( is_a_theorem(or(implies(not(X),or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) )],[refute_0_483,refute_0_490]) ).
cnf(refute_0_492,plain,
( ~ is_a_theorem(equiv(and(X_3786,X_3786),X_3786))
| and(X_3786,X_3786) = X_3786 ),
inference(subst,[],[refute_0_111:[bind(X,$fot(and(X_3786,X_3786))),bind(Y,$fot(X_3786))]]) ).
cnf(refute_0_493,plain,
( ~ is_a_theorem(and(implies(and(X_3785,X_3785),X_3785),implies(and(X_3785,X_3785),X_3785)))
| ~ is_a_theorem(implies(and(implies(and(X_3785,X_3785),X_3785),implies(and(X_3785,X_3785),X_3785)),equiv(and(X_3785,X_3785),X_3785)))
| is_a_theorem(equiv(and(X_3785,X_3785),X_3785)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(and(implies(and(X_3785,X_3785),X_3785),implies(and(X_3785,X_3785),X_3785)))),bind(Y,$fot(equiv(and(X_3785,X_3785),X_3785)))]]) ).
cnf(refute_0_494,plain,
( ~ is_a_theorem(or(and(X_3728,implies(X_3729,and(X_3729,X_3729))),not(and(X_3728,X_3728))))
| is_a_theorem(or(not(and(X_3728,X_3728)),and(X_3728,implies(X_3729,and(X_3729,X_3729))))) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(and(X_3728,implies(X_3729,and(X_3729,X_3729))))),bind(Q,$fot(not(and(X_3728,X_3728))))]]) ).
cnf(refute_0_495,plain,
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_496,plain,
r2,
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_497,plain,
is_a_theorem(implies(Q,or(P,Q))),
inference(resolve,[$cnf( r2 )],[refute_0_496,refute_0_495]) ).
cnf(refute_0_498,plain,
is_a_theorem(implies(X_357,or(P,X_357))),
inference(subst,[],[refute_0_497:[bind(Q,$fot(X_357))]]) ).
cnf(refute_0_499,plain,
( ~ is_a_theorem(X_357)
| ~ is_a_theorem(implies(X_357,or(P,X_357)))
| is_a_theorem(or(P,X_357)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_357)),bind(Y,$fot(or(P,X_357)))]]) ).
cnf(refute_0_500,plain,
( ~ is_a_theorem(X_357)
| is_a_theorem(or(P,X_357)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_357,or(P,X_357))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
( ~ is_a_theorem(implies(X_468,and(X_468,X_468)))
| is_a_theorem(or(P,implies(X_468,and(X_468,X_468)))) ),
inference(subst,[],[refute_0_500:[bind(X_357,$fot(implies(X_468,and(X_468,X_468))))]]) ).
cnf(refute_0_502,plain,
is_a_theorem(implies(X_468,and(X_468,X_468))),
inference(subst,[],[refute_0_393:[bind(X,$fot(X_468))]]) ).
cnf(refute_0_503,plain,
is_a_theorem(or(P,implies(X_468,and(X_468,X_468)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_468,and(X_468,X_468))) )],[refute_0_502,refute_0_501]) ).
cnf(refute_0_504,plain,
is_a_theorem(or(X_825,implies(X_468,and(X_468,X_468)))),
inference(subst,[],[refute_0_503:[bind(P,$fot(X_825))]]) ).
cnf(refute_0_505,plain,
( ~ is_a_theorem(or(X_825,implies(X_468,and(X_468,X_468))))
| is_a_theorem(or(implies(X_468,and(X_468,X_468)),X_825)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_825)),bind(Q,$fot(implies(X_468,and(X_468,X_468))))]]) ).
cnf(refute_0_506,plain,
is_a_theorem(or(implies(X_468,and(X_468,X_468)),X_825)),
inference(resolve,[$cnf( is_a_theorem(or(X_825,implies(X_468,and(X_468,X_468)))) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
is_a_theorem(or(implies(X_468,and(X_468,X_468)),X_3604)),
inference(subst,[],[refute_0_506:[bind(X_825,$fot(X_3604))]]) ).
cnf(refute_0_508,plain,
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_509,plain,
r5,
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_510,plain,
is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))),
inference(resolve,[$cnf( r5 )],[refute_0_509,refute_0_508]) ).
cnf(refute_0_511,plain,
is_a_theorem(implies(implies(not(X),X_135),implies(or(X_133,not(X)),or(X_133,X_135)))),
inference(subst,[],[refute_0_510:[bind(P,$fot(X_133)),bind(Q,$fot(not(X))),bind(R,$fot(X_135))]]) ).
cnf(refute_0_512,plain,
or(X,X_135) = implies(not(X),X_135),
inference(subst,[],[refute_0_125:[bind(Y,$fot(X_135))]]) ).
cnf(refute_0_513,plain,
( or(X,X_135) != implies(not(X),X_135)
| implies(not(X),X_135) = or(X,X_135) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,X_135))),bind(Y0,$fot(implies(not(X),X_135)))]]) ).
cnf(refute_0_514,plain,
implies(not(X),X_135) = or(X,X_135),
inference(resolve,[$cnf( $equal(or(X,X_135),implies(not(X),X_135)) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
( implies(not(X),X_135) != or(X,X_135)
| ~ is_a_theorem(implies(implies(not(X),X_135),implies(or(X_133,not(X)),or(X_133,X_135))))
| is_a_theorem(implies(or(X,X_135),implies(or(X_133,not(X)),or(X_133,X_135)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),X_135),implies(or(X_133,not(X)),or(X_133,X_135)))) ),[0,0],$fot(or(X,X_135))]]) ).
cnf(refute_0_516,plain,
( ~ is_a_theorem(implies(implies(not(X),X_135),implies(or(X_133,not(X)),or(X_133,X_135))))
| is_a_theorem(implies(or(X,X_135),implies(or(X_133,not(X)),or(X_133,X_135)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_135),or(X,X_135)) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
is_a_theorem(implies(or(X,X_135),implies(or(X_133,not(X)),or(X_133,X_135)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_135),implies(or(X_133,not(X)),or(X_133,X_135)))) )],[refute_0_511,refute_0_516]) ).
cnf(refute_0_518,plain,
is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),or(not(X),X_316)))),
inference(subst,[],[refute_0_517:[bind(X,$fot(X_314)),bind(X_133,$fot(not(X))),bind(X_135,$fot(X_316))]]) ).
cnf(refute_0_519,plain,
implies(X,X_316) = or(not(X),X_316),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_316))]]) ).
cnf(refute_0_520,plain,
( implies(X,X_316) != or(not(X),X_316)
| or(not(X),X_316) = implies(X,X_316) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,X_316))),bind(Y0,$fot(or(not(X),X_316)))]]) ).
cnf(refute_0_521,plain,
or(not(X),X_316) = implies(X,X_316),
inference(resolve,[$cnf( $equal(implies(X,X_316),or(not(X),X_316)) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
( or(not(X),X_316) != implies(X,X_316)
| ~ is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),or(not(X),X_316))))
| is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),or(not(X),X_316)))) ),[0,1,1],$fot(implies(X,X_316))]]) ).
cnf(refute_0_523,plain,
( ~ is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),or(not(X),X_316))))
| is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_316),implies(X,X_316)) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),or(not(X),X_316)))) )],[refute_0_518,refute_0_523]) ).
cnf(refute_0_525,plain,
implies(implies(X,not(X_314)),implies(X,X_316)) = or(and(X,X_314),implies(X,X_316)),
inference(subst,[],[refute_0_157:[bind(Y,$fot(implies(X,X_316))),bind(X_14,$fot(X)),bind(X_15,$fot(X_314))]]) ).
cnf(refute_0_526,plain,
or(not(X),not(X_314)) = implies(X,not(X_314)),
inference(subst,[],[refute_0_39:[bind(Y,$fot(not(X_314)))]]) ).
cnf(refute_0_527,plain,
implies(or(not(X),not(X_314)),implies(X,X_316)) = implies(or(not(X),not(X_314)),implies(X,X_316)),
introduced(tautology,[refl,[$fot(implies(or(not(X),not(X_314)),implies(X,X_316)))]]) ).
cnf(refute_0_528,plain,
( implies(or(not(X),not(X_314)),implies(X,X_316)) != implies(or(not(X),not(X_314)),implies(X,X_316))
| or(not(X),not(X_314)) != implies(X,not(X_314))
| implies(or(not(X),not(X_314)),implies(X,X_316)) = implies(implies(X,not(X_314)),implies(X,X_316)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),not(X_314)),implies(X,X_316)),implies(or(not(X),not(X_314)),implies(X,X_316))) ),[1,0],$fot(implies(X,not(X_314)))]]) ).
cnf(refute_0_529,plain,
( or(not(X),not(X_314)) != implies(X,not(X_314))
| implies(or(not(X),not(X_314)),implies(X,X_316)) = implies(implies(X,not(X_314)),implies(X,X_316)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),not(X_314)),implies(X,X_316)),implies(or(not(X),not(X_314)),implies(X,X_316))) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
implies(or(not(X),not(X_314)),implies(X,X_316)) = implies(implies(X,not(X_314)),implies(X,X_316)),
inference(resolve,[$cnf( $equal(or(not(X),not(X_314)),implies(X,not(X_314))) )],[refute_0_526,refute_0_529]) ).
cnf(refute_0_531,plain,
( implies(implies(X,not(X_314)),implies(X,X_316)) != or(and(X,X_314),implies(X,X_316))
| implies(or(not(X),not(X_314)),implies(X,X_316)) != implies(implies(X,not(X_314)),implies(X,X_316))
| implies(or(not(X),not(X_314)),implies(X,X_316)) = or(and(X,X_314),implies(X,X_316)) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(implies(or(not(X),not(X_314)),implies(X,X_316)))),bind(Y0,$fot(implies(implies(X,not(X_314)),implies(X,X_316)))),bind(Z,$fot(or(and(X,X_314),implies(X,X_316))))]]) ).
cnf(refute_0_532,plain,
( implies(implies(X,not(X_314)),implies(X,X_316)) != or(and(X,X_314),implies(X,X_316))
| implies(or(not(X),not(X_314)),implies(X,X_316)) = or(and(X,X_314),implies(X,X_316)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),not(X_314)),implies(X,X_316)),implies(implies(X,not(X_314)),implies(X,X_316))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
implies(or(not(X),not(X_314)),implies(X,X_316)) = or(and(X,X_314),implies(X,X_316)),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_314)),implies(X,X_316)),or(and(X,X_314),implies(X,X_316))) )],[refute_0_525,refute_0_532]) ).
cnf(refute_0_534,plain,
implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))) = implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))),
introduced(tautology,[refl,[$fot(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))))]]) ).
cnf(refute_0_535,plain,
( implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))) != implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316)))
| implies(or(not(X),not(X_314)),implies(X,X_316)) != or(and(X,X_314),implies(X,X_316))
| implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))) = implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))),implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316)))) ),[1,1],$fot(or(and(X,X_314),implies(X,X_316)))]]) ).
cnf(refute_0_536,plain,
( implies(or(not(X),not(X_314)),implies(X,X_316)) != or(and(X,X_314),implies(X,X_316))
| implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))) = implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316))) ),
inference(resolve,[$cnf( $equal(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))),implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316)))) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))) = implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316))),
inference(resolve,[$cnf( $equal(implies(or(not(X),not(X_314)),implies(X,X_316)),or(and(X,X_314),implies(X,X_316))) )],[refute_0_533,refute_0_536]) ).
cnf(refute_0_538,plain,
( implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))) != implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316)))
| ~ is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))))
| is_a_theorem(implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316)))) ),[0],$fot(implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316))))]]) ).
cnf(refute_0_539,plain,
( ~ is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))))
| is_a_theorem(implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316))),implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316)))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
is_a_theorem(implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_314,X_316),implies(or(not(X),not(X_314)),implies(X,X_316)))) )],[refute_0_524,refute_0_539]) ).
cnf(refute_0_541,plain,
( ~ is_a_theorem(implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316))))
| ~ is_a_theorem(or(X_314,X_316))
| is_a_theorem(or(and(X,X_314),implies(X,X_316))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_314,X_316))),bind(Y,$fot(or(and(X,X_314),implies(X,X_316))))]]) ).
cnf(refute_0_542,plain,
( ~ is_a_theorem(or(X_314,X_316))
| is_a_theorem(or(and(X,X_314),implies(X,X_316))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_314,X_316),or(and(X,X_314),implies(X,X_316)))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
( ~ is_a_theorem(or(implies(X_468,and(X_468,X_468)),X_3604))
| is_a_theorem(or(and(X_3602,implies(X_468,and(X_468,X_468))),implies(X_3602,X_3604))) ),
inference(subst,[],[refute_0_542:[bind(X,$fot(X_3602)),bind(X_314,$fot(implies(X_468,and(X_468,X_468)))),bind(X_316,$fot(X_3604))]]) ).
cnf(refute_0_544,plain,
is_a_theorem(or(and(X_3602,implies(X_468,and(X_468,X_468))),implies(X_3602,X_3604))),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_468,and(X_468,X_468)),X_3604)) )],[refute_0_507,refute_0_543]) ).
cnf(refute_0_545,plain,
is_a_theorem(or(and(X_3725,implies(X_3727,and(X_3727,X_3727))),implies(X_3725,not(not(not(X_3725)))))),
inference(subst,[],[refute_0_544:[bind(X_3602,$fot(X_3725)),bind(X_3604,$fot(not(not(not(X_3725))))),bind(X_468,$fot(X_3727))]]) ).
cnf(refute_0_546,plain,
( ~ is_a_theorem(equiv(or(X_1805,X_1805),or(X_1805,X_1805)))
| or(X_1805,X_1805) = not(not(or(X_1805,X_1805))) ),
inference(subst,[],[refute_0_185:[bind(X,$fot(or(X_1805,X_1805))),bind(X_118,$fot(or(X_1805,X_1805)))]]) ).
cnf(refute_0_547,plain,
is_a_theorem(implies(or(P,P),or(P,P))),
inference(subst,[],[refute_0_5:[bind(Q,$fot(P))]]) ).
cnf(refute_0_548,plain,
( ~ is_a_theorem(implies(or(P,P),or(P,P)))
| is_a_theorem(equiv(or(P,P),or(P,P))) ),
inference(subst,[],[refute_0_402:[bind(X_480,$fot(or(P,P)))]]) ).
cnf(refute_0_549,plain,
is_a_theorem(equiv(or(P,P),or(P,P))),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,P),or(P,P))) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
is_a_theorem(equiv(or(X_1805,X_1805),or(X_1805,X_1805))),
inference(subst,[],[refute_0_549:[bind(P,$fot(X_1805))]]) ).
cnf(refute_0_551,plain,
or(X_1805,X_1805) = not(not(or(X_1805,X_1805))),
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_1805,X_1805),or(X_1805,X_1805))) )],[refute_0_550,refute_0_546]) ).
cnf(refute_0_552,plain,
or(not(X),not(X)) = not(not(or(not(X),not(X)))),
inference(subst,[],[refute_0_551:[bind(X_1805,$fot(not(X)))]]) ).
cnf(refute_0_553,plain,
( or(not(X),not(X)) != implies(X,not(X))
| or(not(X),not(X)) != not(not(or(not(X),not(X))))
| or(not(X),not(X)) = not(not(implies(X,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(X)),not(not(or(not(X),not(X))))) ),[1,0,0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_554,plain,
( or(not(X),not(X)) != not(not(or(not(X),not(X))))
| or(not(X),not(X)) = not(not(implies(X,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_315,refute_0_553]) ).
cnf(refute_0_555,plain,
or(not(X),not(X)) = not(not(implies(X,not(X)))),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(not(or(not(X),not(X))))) )],[refute_0_552,refute_0_554]) ).
cnf(refute_0_556,plain,
( or(not(X),not(X)) != implies(X,not(X))
| or(not(X),not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(not(implies(X,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X),not(X)),not(not(implies(X,not(X))))) ),[0],$fot(implies(X,not(X)))]]) ).
cnf(refute_0_557,plain,
( or(not(X),not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(not(implies(X,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_315,refute_0_556]) ).
cnf(refute_0_558,plain,
not(not(implies(X,not(X)))) = not(not(implies(X,not(X)))),
introduced(tautology,[refl,[$fot(not(not(implies(X,not(X)))))]]) ).
cnf(refute_0_559,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(implies(X,not(X)))) != not(not(implies(X,not(X))))
| not(not(implies(X,not(X)))) = not(and(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X,not(X)))),not(not(implies(X,not(X))))) ),[1,0],$fot(and(X,X))]]) ).
cnf(refute_0_560,plain,
( not(implies(X,not(X))) != and(X,X)
| not(not(implies(X,not(X)))) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X)))),not(not(implies(X,not(X))))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
not(not(implies(X,not(X)))) = not(and(X,X)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X))),and(X,X)) )],[refute_0_382,refute_0_560]) ).
cnf(refute_0_562,plain,
( implies(X,not(X)) != not(not(implies(X,not(X))))
| not(not(implies(X,not(X)))) != not(and(X,X))
| implies(X,not(X)) = not(and(X,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(X)),not(and(X,X))) ),[0],$fot(not(not(implies(X,not(X)))))]]) ).
cnf(refute_0_563,plain,
( implies(X,not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X)))),not(and(X,X))) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
( or(not(X),not(X)) != not(not(implies(X,not(X))))
| implies(X,not(X)) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(implies(X,not(X)),not(not(implies(X,not(X))))) )],[refute_0_557,refute_0_563]) ).
cnf(refute_0_565,plain,
implies(X,not(X)) = not(and(X,X)),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(not(implies(X,not(X))))) )],[refute_0_555,refute_0_564]) ).
cnf(refute_0_566,plain,
implies(not(X),not(not(X))) = not(and(not(X),not(X))),
inference(subst,[],[refute_0_565:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_567,plain,
( implies(not(X),not(not(X))) != not(and(not(X),not(X)))
| or(X,not(not(X))) != implies(not(X),not(not(X)))
| or(X,not(not(X))) = not(and(not(X),not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(not(X))),implies(not(X),not(not(X)))) ),[1],$fot(not(and(not(X),not(X))))]]) ).
cnf(refute_0_568,plain,
( or(X,not(not(X))) != implies(not(X),not(not(X)))
| or(X,not(not(X))) = not(and(not(X),not(X))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(not(X))),not(and(not(X),not(X)))) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
or(X,not(not(X))) = not(and(not(X),not(X))),
inference(resolve,[$cnf( $equal(or(X,not(not(X))),implies(not(X),not(not(X)))) )],[refute_0_239,refute_0_568]) ).
cnf(refute_0_570,plain,
implies(not(X),X) = or(X,X),
inference(subst,[],[refute_0_303:[bind(Y,$fot(X))]]) ).
cnf(refute_0_571,plain,
not(and(not(X),not(X))) = implies(not(X),X),
inference(subst,[],[refute_0_121:[bind(X,$fot(not(X))),bind(Y,$fot(X))]]) ).
cnf(refute_0_572,plain,
( implies(not(X),X) != or(X,X)
| not(and(not(X),not(X))) != implies(not(X),X)
| not(and(not(X),not(X))) = or(X,X) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(not(and(not(X),not(X))))),bind(Y0,$fot(implies(not(X),X))),bind(Z,$fot(or(X,X)))]]) ).
cnf(refute_0_573,plain,
( implies(not(X),X) != or(X,X)
| not(and(not(X),not(X))) = or(X,X) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(X))),implies(not(X),X)) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
not(and(not(X),not(X))) = or(X,X),
inference(resolve,[$cnf( $equal(implies(not(X),X),or(X,X)) )],[refute_0_570,refute_0_573]) ).
cnf(refute_0_575,plain,
( not(and(not(X),not(X))) != or(X,X)
| or(X,not(not(X))) != not(and(not(X),not(X)))
| or(X,not(not(X))) = or(X,X) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(not(X))),not(and(not(X),not(X)))) ),[1],$fot(or(X,X))]]) ).
cnf(refute_0_576,plain,
( or(X,not(not(X))) != not(and(not(X),not(X)))
| or(X,not(not(X))) = or(X,X) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(X))),or(X,X)) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
or(X,not(not(X))) = or(X,X),
inference(resolve,[$cnf( $equal(or(X,not(not(X))),not(and(not(X),not(X)))) )],[refute_0_569,refute_0_576]) ).
cnf(refute_0_578,plain,
or(not(X),not(not(not(X)))) = or(not(X),not(X)),
inference(subst,[],[refute_0_577:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_579,plain,
( implies(X,not(not(not(X)))) != or(not(X),not(not(not(X))))
| or(not(X),not(not(not(X)))) != or(not(X),not(X))
| implies(X,not(not(not(X)))) = or(not(X),not(X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(not(not(X)))),or(not(X),not(X))) ),[0],$fot(or(not(X),not(not(not(X)))))]]) ).
cnf(refute_0_580,plain,
( implies(X,not(not(not(X)))) != or(not(X),not(not(not(X))))
| implies(X,not(not(not(X)))) = or(not(X),not(X)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(not(X)))),or(not(X),not(X))) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
implies(X,not(not(not(X)))) = or(not(X),not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(not(not(X)))),or(not(X),not(not(not(X))))) )],[refute_0_246,refute_0_580]) ).
cnf(refute_0_582,plain,
( implies(X,not(X)) != not(and(X,X))
| or(not(X),not(X)) != implies(X,not(X))
| or(not(X),not(X)) = not(and(X,X)) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(not(X),not(X)))),bind(Y0,$fot(implies(X,not(X)))),bind(Z,$fot(not(and(X,X))))]]) ).
cnf(refute_0_583,plain,
( implies(X,not(X)) != not(and(X,X))
| or(not(X),not(X)) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),implies(X,not(X))) )],[refute_0_315,refute_0_582]) ).
cnf(refute_0_584,plain,
or(not(X),not(X)) = not(and(X,X)),
inference(resolve,[$cnf( $equal(implies(X,not(X)),not(and(X,X))) )],[refute_0_565,refute_0_583]) ).
cnf(refute_0_585,plain,
( implies(X,not(not(not(X)))) != or(not(X),not(X))
| or(not(X),not(X)) != not(and(X,X))
| implies(X,not(not(not(X)))) = not(and(X,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(not(not(X)))),not(and(X,X))) ),[0],$fot(or(not(X),not(X)))]]) ).
cnf(refute_0_586,plain,
( implies(X,not(not(not(X)))) != or(not(X),not(X))
| implies(X,not(not(not(X)))) = not(and(X,X)) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X)),not(and(X,X))) )],[refute_0_584,refute_0_585]) ).
cnf(refute_0_587,plain,
implies(X,not(not(not(X)))) = not(and(X,X)),
inference(resolve,[$cnf( $equal(implies(X,not(not(not(X)))),or(not(X),not(X))) )],[refute_0_581,refute_0_586]) ).
cnf(refute_0_588,plain,
implies(X_3725,not(not(not(X_3725)))) = not(and(X_3725,X_3725)),
inference(subst,[],[refute_0_587:[bind(X,$fot(X_3725))]]) ).
cnf(refute_0_589,plain,
( implies(X_3725,not(not(not(X_3725)))) != not(and(X_3725,X_3725))
| ~ is_a_theorem(or(and(X_3725,implies(X_3727,and(X_3727,X_3727))),implies(X_3725,not(not(not(X_3725))))))
| is_a_theorem(or(and(X_3725,implies(X_3727,and(X_3727,X_3727))),not(and(X_3725,X_3725)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_3725,implies(X_3727,and(X_3727,X_3727))),implies(X_3725,not(not(not(X_3725)))))) ),[0,1],$fot(not(and(X_3725,X_3725)))]]) ).
cnf(refute_0_590,plain,
( ~ is_a_theorem(or(and(X_3725,implies(X_3727,and(X_3727,X_3727))),implies(X_3725,not(not(not(X_3725))))))
| is_a_theorem(or(and(X_3725,implies(X_3727,and(X_3727,X_3727))),not(and(X_3725,X_3725)))) ),
inference(resolve,[$cnf( $equal(implies(X_3725,not(not(not(X_3725)))),not(and(X_3725,X_3725))) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
is_a_theorem(or(and(X_3725,implies(X_3727,and(X_3727,X_3727))),not(and(X_3725,X_3725)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_3725,implies(X_3727,and(X_3727,X_3727))),implies(X_3725,not(not(not(X_3725)))))) )],[refute_0_545,refute_0_590]) ).
cnf(refute_0_592,plain,
is_a_theorem(or(and(X_3728,implies(X_3729,and(X_3729,X_3729))),not(and(X_3728,X_3728)))),
inference(subst,[],[refute_0_591:[bind(X_3725,$fot(X_3728)),bind(X_3727,$fot(X_3729))]]) ).
cnf(refute_0_593,plain,
is_a_theorem(or(not(and(X_3728,X_3728)),and(X_3728,implies(X_3729,and(X_3729,X_3729))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_3728,implies(X_3729,and(X_3729,X_3729))),not(and(X_3728,X_3728)))) )],[refute_0_592,refute_0_494]) ).
cnf(refute_0_594,plain,
or(not(and(X_3728,X_3728)),and(X_3728,implies(X_3729,and(X_3729,X_3729)))) = implies(and(X_3728,X_3728),and(X_3728,implies(X_3729,and(X_3729,X_3729)))),
inference(subst,[],[refute_0_39:[bind(X,$fot(and(X_3728,X_3728))),bind(Y,$fot(and(X_3728,implies(X_3729,and(X_3729,X_3729)))))]]) ).
cnf(refute_0_595,plain,
( or(not(and(X_3728,X_3728)),and(X_3728,implies(X_3729,and(X_3729,X_3729)))) != implies(and(X_3728,X_3728),and(X_3728,implies(X_3729,and(X_3729,X_3729))))
| ~ is_a_theorem(or(not(and(X_3728,X_3728)),and(X_3728,implies(X_3729,and(X_3729,X_3729)))))
| is_a_theorem(implies(and(X_3728,X_3728),and(X_3728,implies(X_3729,and(X_3729,X_3729))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(and(X_3728,X_3728)),and(X_3728,implies(X_3729,and(X_3729,X_3729))))) ),[0],$fot(implies(and(X_3728,X_3728),and(X_3728,implies(X_3729,and(X_3729,X_3729)))))]]) ).
cnf(refute_0_596,plain,
( ~ is_a_theorem(or(not(and(X_3728,X_3728)),and(X_3728,implies(X_3729,and(X_3729,X_3729)))))
| is_a_theorem(implies(and(X_3728,X_3728),and(X_3728,implies(X_3729,and(X_3729,X_3729))))) ),
inference(resolve,[$cnf( $equal(or(not(and(X_3728,X_3728)),and(X_3728,implies(X_3729,and(X_3729,X_3729)))),implies(and(X_3728,X_3728),and(X_3728,implies(X_3729,and(X_3729,X_3729))))) )],[refute_0_594,refute_0_595]) ).
cnf(refute_0_597,plain,
is_a_theorem(implies(and(X_3728,X_3728),and(X_3728,implies(X_3729,and(X_3729,X_3729))))),
inference(resolve,[$cnf( is_a_theorem(or(not(and(X_3728,X_3728)),and(X_3728,implies(X_3729,and(X_3729,X_3729))))) )],[refute_0_593,refute_0_596]) ).
cnf(refute_0_598,plain,
is_a_theorem(implies(and(implies(and(X_3731,X_3731),X_3731),implies(and(X_3731,X_3731),X_3731)),and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731))))),
inference(subst,[],[refute_0_597:[bind(X_3728,$fot(implies(and(X_3731,X_3731),X_3731))),bind(X_3729,$fot(X_3731))]]) ).
cnf(refute_0_599,plain,
equiv(and(X_3731,X_3731),X_3731) = and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731))),
inference(subst,[],[refute_0_115:[bind(X,$fot(and(X_3731,X_3731))),bind(Y,$fot(X_3731))]]) ).
cnf(refute_0_600,plain,
( equiv(and(X_3731,X_3731),X_3731) != and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731)))
| and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731))) = equiv(and(X_3731,X_3731),X_3731) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(equiv(and(X_3731,X_3731),X_3731))),bind(Y0,$fot(and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731)))))]]) ).
cnf(refute_0_601,plain,
and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731))) = equiv(and(X_3731,X_3731),X_3731),
inference(resolve,[$cnf( $equal(equiv(and(X_3731,X_3731),X_3731),and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731)))) )],[refute_0_599,refute_0_600]) ).
cnf(refute_0_602,plain,
( and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731))) != equiv(and(X_3731,X_3731),X_3731)
| ~ is_a_theorem(implies(and(implies(and(X_3731,X_3731),X_3731),implies(and(X_3731,X_3731),X_3731)),and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731)))))
| is_a_theorem(implies(and(implies(and(X_3731,X_3731),X_3731),implies(and(X_3731,X_3731),X_3731)),equiv(and(X_3731,X_3731),X_3731))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(implies(and(X_3731,X_3731),X_3731),implies(and(X_3731,X_3731),X_3731)),and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731))))) ),[0,1],$fot(equiv(and(X_3731,X_3731),X_3731))]]) ).
cnf(refute_0_603,plain,
( ~ is_a_theorem(implies(and(implies(and(X_3731,X_3731),X_3731),implies(and(X_3731,X_3731),X_3731)),and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731)))))
| is_a_theorem(implies(and(implies(and(X_3731,X_3731),X_3731),implies(and(X_3731,X_3731),X_3731)),equiv(and(X_3731,X_3731),X_3731))) ),
inference(resolve,[$cnf( $equal(and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731))),equiv(and(X_3731,X_3731),X_3731)) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
is_a_theorem(implies(and(implies(and(X_3731,X_3731),X_3731),implies(and(X_3731,X_3731),X_3731)),equiv(and(X_3731,X_3731),X_3731))),
inference(resolve,[$cnf( is_a_theorem(implies(and(implies(and(X_3731,X_3731),X_3731),implies(and(X_3731,X_3731),X_3731)),and(implies(and(X_3731,X_3731),X_3731),implies(X_3731,and(X_3731,X_3731))))) )],[refute_0_598,refute_0_603]) ).
cnf(refute_0_605,plain,
is_a_theorem(implies(and(implies(and(X_3785,X_3785),X_3785),implies(and(X_3785,X_3785),X_3785)),equiv(and(X_3785,X_3785),X_3785))),
inference(subst,[],[refute_0_604:[bind(X_3731,$fot(X_3785))]]) ).
cnf(refute_0_606,plain,
( ~ is_a_theorem(and(implies(and(X_3785,X_3785),X_3785),implies(and(X_3785,X_3785),X_3785)))
| is_a_theorem(equiv(and(X_3785,X_3785),X_3785)) ),
inference(resolve,[$cnf( is_a_theorem(implies(and(implies(and(X_3785,X_3785),X_3785),implies(and(X_3785,X_3785),X_3785)),equiv(and(X_3785,X_3785),X_3785))) )],[refute_0_605,refute_0_493]) ).
cnf(refute_0_607,plain,
( ~ is_a_theorem(X_468)
| ~ is_a_theorem(implies(X_468,and(X_468,X_468)))
| is_a_theorem(and(X_468,X_468)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_468)),bind(Y,$fot(and(X_468,X_468)))]]) ).
cnf(refute_0_608,plain,
( ~ is_a_theorem(X_468)
| is_a_theorem(and(X_468,X_468)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_468,and(X_468,X_468))) )],[refute_0_502,refute_0_607]) ).
cnf(refute_0_609,plain,
( ~ is_a_theorem(implies(and(X_829,X_830),X_830))
| is_a_theorem(and(implies(and(X_829,X_830),X_830),implies(and(X_829,X_830),X_830))) ),
inference(subst,[],[refute_0_608:[bind(X_468,$fot(implies(and(X_829,X_830),X_830)))]]) ).
cnf(refute_0_610,plain,
is_a_theorem(implies(Q,or(not(X_7),Q))),
inference(subst,[],[refute_0_497:[bind(P,$fot(not(X_7)))]]) ).
cnf(refute_0_611,plain,
( or(not(X_7),Q) != implies(X_7,Q)
| ~ is_a_theorem(implies(Q,or(not(X_7),Q)))
| is_a_theorem(implies(Q,implies(X_7,Q))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(Q,or(not(X_7),Q))) ),[0,1],$fot(implies(X_7,Q))]]) ).
cnf(refute_0_612,plain,
( ~ is_a_theorem(implies(Q,or(not(X_7),Q)))
| is_a_theorem(implies(Q,implies(X_7,Q))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),Q),implies(X_7,Q)) )],[refute_0_21,refute_0_611]) ).
cnf(refute_0_613,plain,
is_a_theorem(implies(Q,implies(X_7,Q))),
inference(resolve,[$cnf( is_a_theorem(implies(Q,or(not(X_7),Q))) )],[refute_0_610,refute_0_612]) ).
cnf(refute_0_614,plain,
is_a_theorem(implies(not(X),implies(X_20,not(X)))),
inference(subst,[],[refute_0_613:[bind(Q,$fot(not(X))),bind(X_7,$fot(X_20))]]) ).
cnf(refute_0_615,plain,
or(X,implies(X_20,not(X))) = implies(not(X),implies(X_20,not(X))),
inference(subst,[],[refute_0_125:[bind(Y,$fot(implies(X_20,not(X))))]]) ).
cnf(refute_0_616,plain,
( or(X,implies(X_20,not(X))) != implies(not(X),implies(X_20,not(X)))
| implies(not(X),implies(X_20,not(X))) = or(X,implies(X_20,not(X))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,implies(X_20,not(X))))),bind(Y0,$fot(implies(not(X),implies(X_20,not(X)))))]]) ).
cnf(refute_0_617,plain,
implies(not(X),implies(X_20,not(X))) = or(X,implies(X_20,not(X))),
inference(resolve,[$cnf( $equal(or(X,implies(X_20,not(X))),implies(not(X),implies(X_20,not(X)))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
( implies(not(X),implies(X_20,not(X))) != or(X,implies(X_20,not(X)))
| ~ is_a_theorem(implies(not(X),implies(X_20,not(X))))
| is_a_theorem(or(X,implies(X_20,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X),implies(X_20,not(X)))) ),[0],$fot(or(X,implies(X_20,not(X))))]]) ).
cnf(refute_0_619,plain,
( ~ is_a_theorem(implies(not(X),implies(X_20,not(X))))
| is_a_theorem(or(X,implies(X_20,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(X_20,not(X))),or(X,implies(X_20,not(X)))) )],[refute_0_617,refute_0_618]) ).
cnf(refute_0_620,plain,
is_a_theorem(or(X,implies(X_20,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),implies(X_20,not(X)))) )],[refute_0_614,refute_0_619]) ).
cnf(refute_0_621,plain,
is_a_theorem(or(X_825,implies(X_20,not(X_825)))),
inference(subst,[],[refute_0_620:[bind(X,$fot(X_825))]]) ).
cnf(refute_0_622,plain,
( ~ is_a_theorem(or(X_825,implies(X_20,not(X_825))))
| is_a_theorem(or(implies(X_20,not(X_825)),X_825)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_825)),bind(Q,$fot(implies(X_20,not(X_825))))]]) ).
cnf(refute_0_623,plain,
is_a_theorem(or(implies(X_20,not(X_825)),X_825)),
inference(resolve,[$cnf( is_a_theorem(or(X_825,implies(X_20,not(X_825)))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
or(implies(X_14,not(X_15)),Y) = implies(not(implies(X_14,not(X_15))),Y),
inference(subst,[],[refute_0_125:[bind(X,$fot(implies(X_14,not(X_15))))]]) ).
cnf(refute_0_625,plain,
( not(implies(X_14,not(X_15))) != and(X_14,X_15)
| or(implies(X_14,not(X_15)),Y) != implies(not(implies(X_14,not(X_15))),Y)
| or(implies(X_14,not(X_15)),Y) = implies(and(X_14,X_15),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_14,not(X_15)),Y),implies(not(implies(X_14,not(X_15))),Y)) ),[1,0],$fot(and(X_14,X_15))]]) ).
cnf(refute_0_626,plain,
( or(implies(X_14,not(X_15)),Y) != implies(not(implies(X_14,not(X_15))),Y)
| or(implies(X_14,not(X_15)),Y) = implies(and(X_14,X_15),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_14,not(X_15))),and(X_14,X_15)) )],[refute_0_154,refute_0_625]) ).
cnf(refute_0_627,plain,
or(implies(X_14,not(X_15)),Y) = implies(and(X_14,X_15),Y),
inference(resolve,[$cnf( $equal(or(implies(X_14,not(X_15)),Y),implies(not(implies(X_14,not(X_15))),Y)) )],[refute_0_624,refute_0_626]) ).
cnf(refute_0_628,plain,
or(implies(X_20,not(X_825)),X_825) = implies(and(X_20,X_825),X_825),
inference(subst,[],[refute_0_627:[bind(Y,$fot(X_825)),bind(X_14,$fot(X_20)),bind(X_15,$fot(X_825))]]) ).
cnf(refute_0_629,plain,
( or(implies(X_20,not(X_825)),X_825) != implies(and(X_20,X_825),X_825)
| ~ is_a_theorem(or(implies(X_20,not(X_825)),X_825))
| is_a_theorem(implies(and(X_20,X_825),X_825)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_20,not(X_825)),X_825)) ),[0],$fot(implies(and(X_20,X_825),X_825))]]) ).
cnf(refute_0_630,plain,
( ~ is_a_theorem(or(implies(X_20,not(X_825)),X_825))
| is_a_theorem(implies(and(X_20,X_825),X_825)) ),
inference(resolve,[$cnf( $equal(or(implies(X_20,not(X_825)),X_825),implies(and(X_20,X_825),X_825)) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
is_a_theorem(implies(and(X_20,X_825),X_825)),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_20,not(X_825)),X_825)) )],[refute_0_623,refute_0_630]) ).
cnf(refute_0_632,plain,
is_a_theorem(implies(and(X_829,X_830),X_830)),
inference(subst,[],[refute_0_631:[bind(X_20,$fot(X_829)),bind(X_825,$fot(X_830))]]) ).
cnf(refute_0_633,plain,
is_a_theorem(and(implies(and(X_829,X_830),X_830),implies(and(X_829,X_830),X_830))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_829,X_830),X_830)) )],[refute_0_632,refute_0_609]) ).
cnf(refute_0_634,plain,
is_a_theorem(and(implies(and(X_3785,X_3785),X_3785),implies(and(X_3785,X_3785),X_3785))),
inference(subst,[],[refute_0_633:[bind(X_829,$fot(X_3785)),bind(X_830,$fot(X_3785))]]) ).
cnf(refute_0_635,plain,
is_a_theorem(equiv(and(X_3785,X_3785),X_3785)),
inference(resolve,[$cnf( is_a_theorem(and(implies(and(X_3785,X_3785),X_3785),implies(and(X_3785,X_3785),X_3785))) )],[refute_0_634,refute_0_606]) ).
cnf(refute_0_636,plain,
is_a_theorem(equiv(and(X_3786,X_3786),X_3786)),
inference(subst,[],[refute_0_635:[bind(X_3785,$fot(X_3786))]]) ).
cnf(refute_0_637,plain,
and(X_3786,X_3786) = X_3786,
inference(resolve,[$cnf( is_a_theorem(equiv(and(X_3786,X_3786),X_3786)) )],[refute_0_636,refute_0_492]) ).
cnf(refute_0_638,plain,
( ~ is_a_theorem(equiv(and(X_3786,X_3786),X_3786))
| and(X_3786,X_3786) = not(not(X_3786)) ),
inference(subst,[],[refute_0_185:[bind(X,$fot(X_3786)),bind(X_118,$fot(and(X_3786,X_3786)))]]) ).
cnf(refute_0_639,plain,
and(X_3786,X_3786) = not(not(X_3786)),
inference(resolve,[$cnf( is_a_theorem(equiv(and(X_3786,X_3786),X_3786)) )],[refute_0_636,refute_0_638]) ).
cnf(refute_0_640,plain,
( and(X_3786,X_3786) != X_3786
| and(X_3786,X_3786) != not(not(X_3786))
| not(not(X_3786)) = X_3786 ),
introduced(tautology,[equality,[$cnf( $equal(and(X_3786,X_3786),X_3786) ),[0],$fot(not(not(X_3786)))]]) ).
cnf(refute_0_641,plain,
( and(X_3786,X_3786) != X_3786
| not(not(X_3786)) = X_3786 ),
inference(resolve,[$cnf( $equal(and(X_3786,X_3786),not(not(X_3786))) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
not(not(X_3786)) = X_3786,
inference(resolve,[$cnf( $equal(and(X_3786,X_3786),X_3786) )],[refute_0_637,refute_0_641]) ).
cnf(refute_0_643,plain,
not(not(not(or(X_2490,or(X,X_2490))))) = not(or(X_2490,or(X,X_2490))),
inference(subst,[],[refute_0_642:[bind(X_3786,$fot(not(or(X_2490,or(X,X_2490)))))]]) ).
cnf(refute_0_644,plain,
or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))),
introduced(tautology,[refl,[$fot(or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))))]]) ).
cnf(refute_0_645,plain,
( not(not(not(or(X_2490,or(X,X_2490))))) != not(or(X_2490,or(X,X_2490)))
| or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))) != or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490))))))
| or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(or(X_2490,or(X,X_2490)))) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))),or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490))))))) ),[1,1],$fot(not(or(X_2490,or(X,X_2490))))]]) ).
cnf(refute_0_646,plain,
( not(not(not(or(X_2490,or(X,X_2490))))) != not(or(X_2490,or(X,X_2490)))
| or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(or(X_2490,or(X,X_2490)))) ),
inference(resolve,[$cnf( $equal(or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))),or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490))))))) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(or(X_2490,or(X,X_2490)))),
inference(resolve,[$cnf( $equal(not(not(not(or(X_2490,or(X,X_2490))))),not(or(X_2490,or(X,X_2490)))) )],[refute_0_643,refute_0_646]) ).
cnf(refute_0_648,plain,
not(not(or(X_3791,X_3791))) = or(X_3791,X_3791),
inference(subst,[],[refute_0_642:[bind(X_3786,$fot(or(X_3791,X_3791)))]]) ).
cnf(refute_0_649,plain,
and(not(Y),not(Y)) = not(Y),
inference(subst,[],[refute_0_637:[bind(X_3786,$fot(not(Y)))]]) ).
cnf(refute_0_650,plain,
( and(not(Y),not(Y)) != not(Y)
| and(not(Y),not(Y)) != not(or(Y,Y))
| not(Y) = not(or(Y,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(Y),not(Y)),not(or(Y,Y))) ),[0],$fot(not(Y))]]) ).
cnf(refute_0_651,plain,
( and(not(Y),not(Y)) != not(or(Y,Y))
| not(Y) = not(or(Y,Y)) ),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(Y)) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
not(Y) = not(or(Y,Y)),
inference(resolve,[$cnf( $equal(and(not(Y),not(Y)),not(or(Y,Y))) )],[refute_0_421,refute_0_651]) ).
cnf(refute_0_653,plain,
not(X_3791) = not(or(X_3791,X_3791)),
inference(subst,[],[refute_0_652:[bind(Y,$fot(X_3791))]]) ).
cnf(refute_0_654,plain,
( not(X_3791) != not(or(X_3791,X_3791))
| not(or(X_3791,X_3791)) = not(X_3791) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(not(X_3791))),bind(Y0,$fot(not(or(X_3791,X_3791))))]]) ).
cnf(refute_0_655,plain,
not(or(X_3791,X_3791)) = not(X_3791),
inference(resolve,[$cnf( $equal(not(X_3791),not(or(X_3791,X_3791))) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
( not(not(or(X_3791,X_3791))) != or(X_3791,X_3791)
| not(or(X_3791,X_3791)) != not(X_3791)
| not(not(X_3791)) = or(X_3791,X_3791) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(or(X_3791,X_3791))),or(X_3791,X_3791)) ),[0,0],$fot(not(X_3791))]]) ).
cnf(refute_0_657,plain,
( not(not(or(X_3791,X_3791))) != or(X_3791,X_3791)
| not(not(X_3791)) = or(X_3791,X_3791) ),
inference(resolve,[$cnf( $equal(not(or(X_3791,X_3791)),not(X_3791)) )],[refute_0_655,refute_0_656]) ).
cnf(refute_0_658,plain,
not(not(X_3791)) = or(X_3791,X_3791),
inference(resolve,[$cnf( $equal(not(not(or(X_3791,X_3791))),or(X_3791,X_3791)) )],[refute_0_648,refute_0_657]) ).
cnf(refute_0_659,plain,
not(not(X_3791)) = X_3791,
inference(subst,[],[refute_0_642:[bind(X_3786,$fot(X_3791))]]) ).
cnf(refute_0_660,plain,
( not(not(X_3791)) != X_3791
| not(not(X_3791)) != or(X_3791,X_3791)
| X_3791 = or(X_3791,X_3791) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(X_3791)),or(X_3791,X_3791)) ),[0],$fot(X_3791)]]) ).
cnf(refute_0_661,plain,
( not(not(X_3791)) != or(X_3791,X_3791)
| X_3791 = or(X_3791,X_3791) ),
inference(resolve,[$cnf( $equal(not(not(X_3791)),X_3791) )],[refute_0_659,refute_0_660]) ).
cnf(refute_0_662,plain,
X_3791 = or(X_3791,X_3791),
inference(resolve,[$cnf( $equal(not(not(X_3791)),or(X_3791,X_3791)) )],[refute_0_658,refute_0_661]) ).
cnf(refute_0_663,plain,
( X_3791 != or(X_3791,X_3791)
| or(X_3791,X_3791) = X_3791 ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(X_3791)),bind(Y0,$fot(or(X_3791,X_3791)))]]) ).
cnf(refute_0_664,plain,
or(X_3791,X_3791) = X_3791,
inference(resolve,[$cnf( $equal(X_3791,or(X_3791,X_3791)) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
or(X_2490,X_2490) = X_2490,
inference(subst,[],[refute_0_664:[bind(X_3791,$fot(X_2490))]]) ).
cnf(refute_0_666,plain,
or(X,or(X_2490,X_2490)) = or(X,or(X_2490,X_2490)),
introduced(tautology,[refl,[$fot(or(X,or(X_2490,X_2490)))]]) ).
cnf(refute_0_667,plain,
( or(X,or(X_2490,X_2490)) != or(X,or(X_2490,X_2490))
| or(X_2490,X_2490) != X_2490
| or(X,or(X_2490,X_2490)) = or(X,X_2490) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,or(X_2490,X_2490)),or(X,or(X_2490,X_2490))) ),[1,1],$fot(X_2490)]]) ).
cnf(refute_0_668,plain,
( or(X_2490,X_2490) != X_2490
| or(X,or(X_2490,X_2490)) = or(X,X_2490) ),
inference(resolve,[$cnf( $equal(or(X,or(X_2490,X_2490)),or(X,or(X_2490,X_2490))) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
or(X,or(X_2490,X_2490)) = or(X,X_2490),
inference(resolve,[$cnf( $equal(or(X_2490,X_2490),X_2490) )],[refute_0_665,refute_0_668]) ).
cnf(refute_0_670,plain,
or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),
introduced(tautology,[refl,[$fot(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))))]]) ).
cnf(refute_0_671,plain,
( or(X,or(X_2490,X_2490)) != or(X,X_2490)
| or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) != or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))
| or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) ),[1,0],$fot(or(X,X_2490))]]) ).
cnf(refute_0_672,plain,
( or(X,or(X_2490,X_2490)) != or(X,X_2490)
| or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))) ),
inference(resolve,[$cnf( $equal(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) )],[refute_0_670,refute_0_671]) ).
cnf(refute_0_673,plain,
or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))),
inference(resolve,[$cnf( $equal(or(X,or(X_2490,X_2490)),or(X,X_2490)) )],[refute_0_669,refute_0_672]) ).
cnf(refute_0_674,plain,
( or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))) != or(or(X,X_2490),not(or(X_2490,or(X,X_2490))))
| or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) != or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490))))))
| or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(or(X_2490,or(X,X_2490)))) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))))),bind(Y0,$fot(or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))))),bind(Z,$fot(or(or(X,X_2490),not(or(X_2490,or(X,X_2490))))))]]) ).
cnf(refute_0_675,plain,
( or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))) != or(or(X,X_2490),not(or(X_2490,or(X,X_2490))))
| or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(or(X_2490,or(X,X_2490)))) ),
inference(resolve,[$cnf( $equal(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490))))))) )],[refute_0_673,refute_0_674]) ).
cnf(refute_0_676,plain,
or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) = or(or(X,X_2490),not(or(X_2490,or(X,X_2490)))),
inference(resolve,[$cnf( $equal(or(or(X,X_2490),not(not(not(or(X_2490,or(X,X_2490)))))),or(or(X,X_2490),not(or(X_2490,or(X,X_2490))))) )],[refute_0_647,refute_0_675]) ).
cnf(refute_0_677,plain,
( or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))) != or(or(X,X_2490),not(or(X_2490,or(X,X_2490))))
| ~ is_a_theorem(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))))
| is_a_theorem(or(or(X,X_2490),not(or(X_2490,or(X,X_2490))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) ),[0],$fot(or(or(X,X_2490),not(or(X_2490,or(X,X_2490)))))]]) ).
cnf(refute_0_678,plain,
( ~ is_a_theorem(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))))
| is_a_theorem(or(or(X,X_2490),not(or(X_2490,or(X,X_2490))))) ),
inference(resolve,[$cnf( $equal(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490)))))),or(or(X,X_2490),not(or(X_2490,or(X,X_2490))))) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
is_a_theorem(or(or(X,X_2490),not(or(X_2490,or(X,X_2490))))),
inference(resolve,[$cnf( is_a_theorem(or(or(X,or(X_2490,X_2490)),not(not(not(or(X_2490,or(X,X_2490))))))) )],[refute_0_491,refute_0_678]) ).
cnf(refute_0_680,plain,
is_a_theorem(or(or(X_5108,X_5109),not(or(X_5109,or(X_5108,X_5109))))),
inference(subst,[],[refute_0_679:[bind(X,$fot(X_5108)),bind(X_2490,$fot(X_5109))]]) ).
cnf(refute_0_681,plain,
is_a_theorem(or(not(or(X_5109,or(X_5108,X_5109))),or(X_5108,X_5109))),
inference(resolve,[$cnf( is_a_theorem(or(or(X_5108,X_5109),not(or(X_5109,or(X_5108,X_5109))))) )],[refute_0_680,refute_0_11]) ).
cnf(refute_0_682,plain,
or(not(or(X_5109,or(X_5108,X_5109))),or(X_5108,X_5109)) = implies(or(X_5109,or(X_5108,X_5109)),or(X_5108,X_5109)),
inference(subst,[],[refute_0_39:[bind(X,$fot(or(X_5109,or(X_5108,X_5109)))),bind(Y,$fot(or(X_5108,X_5109)))]]) ).
cnf(refute_0_683,plain,
( or(not(or(X_5109,or(X_5108,X_5109))),or(X_5108,X_5109)) != implies(or(X_5109,or(X_5108,X_5109)),or(X_5108,X_5109))
| ~ is_a_theorem(or(not(or(X_5109,or(X_5108,X_5109))),or(X_5108,X_5109)))
| is_a_theorem(implies(or(X_5109,or(X_5108,X_5109)),or(X_5108,X_5109))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(or(X_5109,or(X_5108,X_5109))),or(X_5108,X_5109))) ),[0],$fot(implies(or(X_5109,or(X_5108,X_5109)),or(X_5108,X_5109)))]]) ).
cnf(refute_0_684,plain,
( ~ is_a_theorem(or(not(or(X_5109,or(X_5108,X_5109))),or(X_5108,X_5109)))
| is_a_theorem(implies(or(X_5109,or(X_5108,X_5109)),or(X_5108,X_5109))) ),
inference(resolve,[$cnf( $equal(or(not(or(X_5109,or(X_5108,X_5109))),or(X_5108,X_5109)),implies(or(X_5109,or(X_5108,X_5109)),or(X_5108,X_5109))) )],[refute_0_682,refute_0_683]) ).
cnf(refute_0_685,plain,
is_a_theorem(implies(or(X_5109,or(X_5108,X_5109)),or(X_5108,X_5109))),
inference(resolve,[$cnf( is_a_theorem(or(not(or(X_5109,or(X_5108,X_5109))),or(X_5108,X_5109))) )],[refute_0_681,refute_0_684]) ).
cnf(refute_0_686,plain,
is_a_theorem(implies(or(not(X_20554),or(X_5108,not(X_20554))),or(X_5108,not(X_20554)))),
inference(subst,[],[refute_0_685:[bind(X_5109,$fot(not(X_20554)))]]) ).
cnf(refute_0_687,plain,
( ~ is_a_theorem(equiv(or(X_20548,not(X_20547)),implies(X_20547,X_20548)))
| or(X_20548,not(X_20547)) = implies(X_20547,X_20548) ),
inference(subst,[],[refute_0_111:[bind(X,$fot(or(X_20548,not(X_20547)))),bind(Y,$fot(implies(X_20547,X_20548)))]]) ).
cnf(refute_0_688,plain,
( ~ is_a_theorem(implies(implies(or(X_20541,X_20542),or(X_20542,X_20541)),equiv(or(X_20541,X_20542),or(X_20542,X_20541))))
| ~ is_a_theorem(implies(or(X_20541,X_20542),or(X_20542,X_20541)))
| is_a_theorem(equiv(or(X_20541,X_20542),or(X_20542,X_20541))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(or(X_20541,X_20542),or(X_20542,X_20541)))),bind(Y,$fot(equiv(or(X_20541,X_20542),or(X_20542,X_20541))))]]) ).
cnf(refute_0_689,plain,
( ~ is_a_theorem(not(not(implies(or(X_545,X_544),or(X_544,X_545)))))
| is_a_theorem(or(P,not(not(implies(or(X_545,X_544),or(X_544,X_545)))))) ),
inference(subst,[],[refute_0_500:[bind(X_357,$fot(not(not(implies(or(X_545,X_544),or(X_544,X_545))))))]]) ).
cnf(refute_0_690,plain,
is_a_theorem(implies(or(P,not(X_7)),or(not(X_7),P))),
inference(subst,[],[refute_0_5:[bind(Q,$fot(not(X_7)))]]) ).
cnf(refute_0_691,plain,
implies(X_7,P) = or(not(X_7),P),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_7)),bind(Y,$fot(P))]]) ).
cnf(refute_0_692,plain,
( implies(X_7,P) != or(not(X_7),P)
| or(not(X_7),P) = implies(X_7,P) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X_7,P))),bind(Y0,$fot(or(not(X_7),P)))]]) ).
cnf(refute_0_693,plain,
or(not(X_7),P) = implies(X_7,P),
inference(resolve,[$cnf( $equal(implies(X_7,P),or(not(X_7),P)) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
( or(not(X_7),P) != implies(X_7,P)
| ~ is_a_theorem(implies(or(P,not(X_7)),or(not(X_7),P)))
| is_a_theorem(implies(or(P,not(X_7)),implies(X_7,P))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(P,not(X_7)),or(not(X_7),P))) ),[0,1],$fot(implies(X_7,P))]]) ).
cnf(refute_0_695,plain,
( ~ is_a_theorem(implies(or(P,not(X_7)),or(not(X_7),P)))
| is_a_theorem(implies(or(P,not(X_7)),implies(X_7,P))) ),
inference(resolve,[$cnf( $equal(or(not(X_7),P),implies(X_7,P)) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
is_a_theorem(implies(or(P,not(X_7)),implies(X_7,P))),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,not(X_7)),or(not(X_7),P))) )],[refute_0_690,refute_0_695]) ).
cnf(refute_0_697,plain,
is_a_theorem(implies(or(not(X),not(X_32)),implies(X_32,not(X)))),
inference(subst,[],[refute_0_696:[bind(P,$fot(not(X))),bind(X_7,$fot(X_32))]]) ).
cnf(refute_0_698,plain,
implies(X,not(X_32)) = or(not(X),not(X_32)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(not(X_32)))]]) ).
cnf(refute_0_699,plain,
( implies(X,not(X_32)) != or(not(X),not(X_32))
| or(not(X),not(X_32)) = implies(X,not(X_32)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,not(X_32)))),bind(Y0,$fot(or(not(X),not(X_32))))]]) ).
cnf(refute_0_700,plain,
or(not(X),not(X_32)) = implies(X,not(X_32)),
inference(resolve,[$cnf( $equal(implies(X,not(X_32)),or(not(X),not(X_32))) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
( or(not(X),not(X_32)) != implies(X,not(X_32))
| ~ is_a_theorem(implies(or(not(X),not(X_32)),implies(X_32,not(X))))
| is_a_theorem(implies(implies(X,not(X_32)),implies(X_32,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(X_32)),implies(X_32,not(X)))) ),[0,0],$fot(implies(X,not(X_32)))]]) ).
cnf(refute_0_702,plain,
( ~ is_a_theorem(implies(or(not(X),not(X_32)),implies(X_32,not(X))))
| is_a_theorem(implies(implies(X,not(X_32)),implies(X_32,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_32)),implies(X,not(X_32))) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
is_a_theorem(implies(implies(X,not(X_32)),implies(X_32,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(X_32)),implies(X_32,not(X)))) )],[refute_0_697,refute_0_702]) ).
cnf(refute_0_704,plain,
implies(implies(X,not(X_32)),implies(X_32,not(X))) = not(and(implies(X,not(X_32)),and(X_32,X))),
inference(subst,[],[refute_0_89:[bind(X,$fot(X_32)),bind(Y,$fot(X)),bind(X_28,$fot(implies(X,not(X_32))))]]) ).
cnf(refute_0_705,plain,
( implies(implies(X,not(X_32)),implies(X_32,not(X))) != not(and(implies(X,not(X_32)),and(X_32,X)))
| ~ is_a_theorem(implies(implies(X,not(X_32)),implies(X_32,not(X))))
| is_a_theorem(not(and(implies(X,not(X_32)),and(X_32,X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(X_32)),implies(X_32,not(X)))) ),[0],$fot(not(and(implies(X,not(X_32)),and(X_32,X))))]]) ).
cnf(refute_0_706,plain,
( ~ is_a_theorem(implies(implies(X,not(X_32)),implies(X_32,not(X))))
| is_a_theorem(not(and(implies(X,not(X_32)),and(X_32,X)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_32)),implies(X_32,not(X))),not(and(implies(X,not(X_32)),and(X_32,X)))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
is_a_theorem(not(and(implies(X,not(X_32)),and(X_32,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(X_32)),implies(X_32,not(X)))) )],[refute_0_703,refute_0_706]) ).
cnf(refute_0_708,plain,
is_a_theorem(not(and(implies(not(X),not(X_34)),and(X_34,not(X))))),
inference(subst,[],[refute_0_707:[bind(X,$fot(not(X))),bind(X_32,$fot(X_34))]]) ).
cnf(refute_0_709,plain,
or(X,not(X_34)) = implies(not(X),not(X_34)),
inference(subst,[],[refute_0_125:[bind(Y,$fot(not(X_34)))]]) ).
cnf(refute_0_710,plain,
( or(X,not(X_34)) != implies(not(X),not(X_34))
| implies(not(X),not(X_34)) = or(X,not(X_34)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,not(X_34)))),bind(Y0,$fot(implies(not(X),not(X_34))))]]) ).
cnf(refute_0_711,plain,
implies(not(X),not(X_34)) = or(X,not(X_34)),
inference(resolve,[$cnf( $equal(or(X,not(X_34)),implies(not(X),not(X_34))) )],[refute_0_709,refute_0_710]) ).
cnf(refute_0_712,plain,
( implies(not(X),not(X_34)) != or(X,not(X_34))
| ~ is_a_theorem(not(and(implies(not(X),not(X_34)),and(X_34,not(X)))))
| is_a_theorem(not(and(or(X,not(X_34)),and(X_34,not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(implies(not(X),not(X_34)),and(X_34,not(X))))) ),[0,0,0],$fot(or(X,not(X_34)))]]) ).
cnf(refute_0_713,plain,
( ~ is_a_theorem(not(and(implies(not(X),not(X_34)),and(X_34,not(X)))))
| is_a_theorem(not(and(or(X,not(X_34)),and(X_34,not(X))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_34)),or(X,not(X_34))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
is_a_theorem(not(and(or(X,not(X_34)),and(X_34,not(X))))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(not(X),not(X_34)),and(X_34,not(X))))) )],[refute_0_708,refute_0_713]) ).
cnf(refute_0_715,plain,
and(or(X,not(X_34)),and(X_34,not(X))) = not(implies(or(X,not(X_34)),implies(X_34,X))),
inference(subst,[],[refute_0_434:[bind(X,$fot(or(X,not(X_34)))),bind(X_28,$fot(X_34)),bind(X_29,$fot(X))]]) ).
cnf(refute_0_716,plain,
not(and(or(X,not(X_34)),and(X_34,not(X)))) = not(and(or(X,not(X_34)),and(X_34,not(X)))),
introduced(tautology,[refl,[$fot(not(and(or(X,not(X_34)),and(X_34,not(X)))))]]) ).
cnf(refute_0_717,plain,
( and(or(X,not(X_34)),and(X_34,not(X))) != not(implies(or(X,not(X_34)),implies(X_34,X)))
| not(and(or(X,not(X_34)),and(X_34,not(X)))) != not(and(or(X,not(X_34)),and(X_34,not(X))))
| not(and(or(X,not(X_34)),and(X_34,not(X)))) = not(not(implies(or(X,not(X_34)),implies(X_34,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(or(X,not(X_34)),and(X_34,not(X)))),not(and(or(X,not(X_34)),and(X_34,not(X))))) ),[1,0],$fot(not(implies(or(X,not(X_34)),implies(X_34,X))))]]) ).
cnf(refute_0_718,plain,
( and(or(X,not(X_34)),and(X_34,not(X))) != not(implies(or(X,not(X_34)),implies(X_34,X)))
| not(and(or(X,not(X_34)),and(X_34,not(X)))) = not(not(implies(or(X,not(X_34)),implies(X_34,X)))) ),
inference(resolve,[$cnf( $equal(not(and(or(X,not(X_34)),and(X_34,not(X)))),not(and(or(X,not(X_34)),and(X_34,not(X))))) )],[refute_0_716,refute_0_717]) ).
cnf(refute_0_719,plain,
not(and(or(X,not(X_34)),and(X_34,not(X)))) = not(not(implies(or(X,not(X_34)),implies(X_34,X)))),
inference(resolve,[$cnf( $equal(and(or(X,not(X_34)),and(X_34,not(X))),not(implies(or(X,not(X_34)),implies(X_34,X)))) )],[refute_0_715,refute_0_718]) ).
cnf(refute_0_720,plain,
( not(and(or(X,not(X_34)),and(X_34,not(X)))) != not(not(implies(or(X,not(X_34)),implies(X_34,X))))
| ~ is_a_theorem(not(and(or(X,not(X_34)),and(X_34,not(X)))))
| is_a_theorem(not(not(implies(or(X,not(X_34)),implies(X_34,X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(or(X,not(X_34)),and(X_34,not(X))))) ),[0],$fot(not(not(implies(or(X,not(X_34)),implies(X_34,X)))))]]) ).
cnf(refute_0_721,plain,
( ~ is_a_theorem(not(and(or(X,not(X_34)),and(X_34,not(X)))))
| is_a_theorem(not(not(implies(or(X,not(X_34)),implies(X_34,X))))) ),
inference(resolve,[$cnf( $equal(not(and(or(X,not(X_34)),and(X_34,not(X)))),not(not(implies(or(X,not(X_34)),implies(X_34,X))))) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
is_a_theorem(not(not(implies(or(X,not(X_34)),implies(X_34,X))))),
inference(resolve,[$cnf( is_a_theorem(not(and(or(X,not(X_34)),and(X_34,not(X))))) )],[refute_0_714,refute_0_721]) ).
cnf(refute_0_723,plain,
is_a_theorem(not(not(implies(or(X_39,not(not(X))),implies(not(X),X_39))))),
inference(subst,[],[refute_0_722:[bind(X,$fot(X_39)),bind(X_34,$fot(not(X)))]]) ).
cnf(refute_0_724,plain,
or(X,X_39) = implies(not(X),X_39),
inference(subst,[],[refute_0_125:[bind(Y,$fot(X_39))]]) ).
cnf(refute_0_725,plain,
( or(X,X_39) != implies(not(X),X_39)
| implies(not(X),X_39) = or(X,X_39) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,X_39))),bind(Y0,$fot(implies(not(X),X_39)))]]) ).
cnf(refute_0_726,plain,
implies(not(X),X_39) = or(X,X_39),
inference(resolve,[$cnf( $equal(or(X,X_39),implies(not(X),X_39)) )],[refute_0_724,refute_0_725]) ).
cnf(refute_0_727,plain,
( implies(not(X),X_39) != or(X,X_39)
| ~ is_a_theorem(not(not(implies(or(X_39,not(not(X))),implies(not(X),X_39)))))
| is_a_theorem(not(not(implies(or(X_39,not(not(X))),or(X,X_39))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(not(implies(or(X_39,not(not(X))),implies(not(X),X_39))))) ),[0,0,0,1],$fot(or(X,X_39))]]) ).
cnf(refute_0_728,plain,
( ~ is_a_theorem(not(not(implies(or(X_39,not(not(X))),implies(not(X),X_39)))))
| is_a_theorem(not(not(implies(or(X_39,not(not(X))),or(X,X_39))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_39),or(X,X_39)) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
is_a_theorem(not(not(implies(or(X_39,not(not(X))),or(X,X_39))))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(or(X_39,not(not(X))),implies(not(X),X_39))))) )],[refute_0_723,refute_0_728]) ).
cnf(refute_0_730,plain,
or(and(not(X),not(X_151)),X_149) = implies(implies(not(X),X_151),X_149),
inference(subst,[],[refute_0_263:[bind(Y,$fot(X_149)),bind(X_28,$fot(not(X))),bind(X_29,$fot(X_151))]]) ).
cnf(refute_0_731,plain,
or(X,X_151) = implies(not(X),X_151),
inference(subst,[],[refute_0_125:[bind(Y,$fot(X_151))]]) ).
cnf(refute_0_732,plain,
( or(X,X_151) != implies(not(X),X_151)
| implies(not(X),X_151) = or(X,X_151) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(or(X,X_151))),bind(Y0,$fot(implies(not(X),X_151)))]]) ).
cnf(refute_0_733,plain,
implies(not(X),X_151) = or(X,X_151),
inference(resolve,[$cnf( $equal(or(X,X_151),implies(not(X),X_151)) )],[refute_0_731,refute_0_732]) ).
cnf(refute_0_734,plain,
( implies(not(X),X_151) != or(X,X_151)
| or(and(not(X),not(X_151)),X_149) != implies(implies(not(X),X_151),X_149)
| or(and(not(X),not(X_151)),X_149) = implies(or(X,X_151),X_149) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X),not(X_151)),X_149),implies(implies(not(X),X_151),X_149)) ),[1,0],$fot(or(X,X_151))]]) ).
cnf(refute_0_735,plain,
( or(and(not(X),not(X_151)),X_149) != implies(implies(not(X),X_151),X_149)
| or(and(not(X),not(X_151)),X_149) = implies(or(X,X_151),X_149) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_151),or(X,X_151)) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
or(and(not(X),not(X_151)),X_149) = implies(or(X,X_151),X_149),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_151)),X_149),implies(implies(not(X),X_151),X_149)) )],[refute_0_730,refute_0_735]) ).
cnf(refute_0_737,plain,
implies(or(X_41,not(X_42)),Y) = or(not(or(X_41,not(X_42))),Y),
inference(subst,[],[refute_0_15:[bind(X,$fot(or(X_41,not(X_42))))]]) ).
cnf(refute_0_738,plain,
( implies(or(X_41,not(X_42)),Y) != or(not(or(X_41,not(X_42))),Y)
| not(or(X_41,not(X_42))) != and(not(X_41),X_42)
| implies(or(X_41,not(X_42)),Y) = or(and(not(X_41),X_42),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_41,not(X_42)),Y),or(not(or(X_41,not(X_42))),Y)) ),[1,0],$fot(and(not(X_41),X_42))]]) ).
cnf(refute_0_739,plain,
( implies(or(X_41,not(X_42)),Y) != or(not(or(X_41,not(X_42))),Y)
| implies(or(X_41,not(X_42)),Y) = or(and(not(X_41),X_42),Y) ),
inference(resolve,[$cnf( $equal(not(or(X_41,not(X_42))),and(not(X_41),X_42)) )],[refute_0_192,refute_0_738]) ).
cnf(refute_0_740,plain,
implies(or(X_41,not(X_42)),Y) = or(and(not(X_41),X_42),Y),
inference(resolve,[$cnf( $equal(implies(or(X_41,not(X_42)),Y),or(not(or(X_41,not(X_42))),Y)) )],[refute_0_737,refute_0_739]) ).
cnf(refute_0_741,plain,
( implies(or(X_41,not(X_42)),Y) != or(and(not(X_41),X_42),Y)
| or(and(not(X_41),X_42),Y) = implies(or(X_41,not(X_42)),Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(or(X_41,not(X_42)),Y))),bind(Y0,$fot(or(and(not(X_41),X_42),Y)))]]) ).
cnf(refute_0_742,plain,
or(and(not(X_41),X_42),Y) = implies(or(X_41,not(X_42)),Y),
inference(resolve,[$cnf( $equal(implies(or(X_41,not(X_42)),Y),or(and(not(X_41),X_42),Y)) )],[refute_0_740,refute_0_741]) ).
cnf(refute_0_743,plain,
or(and(not(X),not(X_151)),X_149) = implies(or(X,not(not(X_151))),X_149),
inference(subst,[],[refute_0_742:[bind(Y,$fot(X_149)),bind(X_41,$fot(X)),bind(X_42,$fot(not(X_151)))]]) ).
cnf(refute_0_744,plain,
( or(and(not(X),not(X_151)),X_149) != implies(or(X,X_151),X_149)
| or(and(not(X),not(X_151)),X_149) != implies(or(X,not(not(X_151))),X_149)
| implies(or(X,not(not(X_151))),X_149) = implies(or(X,X_151),X_149) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X),not(X_151)),X_149),implies(or(X,X_151),X_149)) ),[0],$fot(implies(or(X,not(not(X_151))),X_149))]]) ).
cnf(refute_0_745,plain,
( or(and(not(X),not(X_151)),X_149) != implies(or(X,X_151),X_149)
| implies(or(X,not(not(X_151))),X_149) = implies(or(X,X_151),X_149) ),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_151)),X_149),implies(or(X,not(not(X_151))),X_149)) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
implies(or(X,not(not(X_151))),X_149) = implies(or(X,X_151),X_149),
inference(resolve,[$cnf( $equal(or(and(not(X),not(X_151)),X_149),implies(or(X,X_151),X_149)) )],[refute_0_736,refute_0_745]) ).
cnf(refute_0_747,plain,
implies(or(X_39,not(not(X))),or(X,X_39)) = implies(or(X_39,X),or(X,X_39)),
inference(subst,[],[refute_0_746:[bind(X,$fot(X_39)),bind(X_149,$fot(or(X,X_39))),bind(X_151,$fot(X))]]) ).
cnf(refute_0_748,plain,
not(implies(or(X_39,not(not(X))),or(X,X_39))) = not(implies(or(X_39,not(not(X))),or(X,X_39))),
introduced(tautology,[refl,[$fot(not(implies(or(X_39,not(not(X))),or(X,X_39))))]]) ).
cnf(refute_0_749,plain,
( implies(or(X_39,not(not(X))),or(X,X_39)) != implies(or(X_39,X),or(X,X_39))
| not(implies(or(X_39,not(not(X))),or(X,X_39))) != not(implies(or(X_39,not(not(X))),or(X,X_39)))
| not(implies(or(X_39,not(not(X))),or(X,X_39))) = not(implies(or(X_39,X),or(X,X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(or(X_39,not(not(X))),or(X,X_39))),not(implies(or(X_39,not(not(X))),or(X,X_39)))) ),[1,0],$fot(implies(or(X_39,X),or(X,X_39)))]]) ).
cnf(refute_0_750,plain,
( implies(or(X_39,not(not(X))),or(X,X_39)) != implies(or(X_39,X),or(X,X_39))
| not(implies(or(X_39,not(not(X))),or(X,X_39))) = not(implies(or(X_39,X),or(X,X_39))) ),
inference(resolve,[$cnf( $equal(not(implies(or(X_39,not(not(X))),or(X,X_39))),not(implies(or(X_39,not(not(X))),or(X,X_39)))) )],[refute_0_748,refute_0_749]) ).
cnf(refute_0_751,plain,
not(implies(or(X_39,not(not(X))),or(X,X_39))) = not(implies(or(X_39,X),or(X,X_39))),
inference(resolve,[$cnf( $equal(implies(or(X_39,not(not(X))),or(X,X_39)),implies(or(X_39,X),or(X,X_39))) )],[refute_0_747,refute_0_750]) ).
cnf(refute_0_752,plain,
not(not(implies(or(X_39,not(not(X))),or(X,X_39)))) = not(not(implies(or(X_39,not(not(X))),or(X,X_39)))),
introduced(tautology,[refl,[$fot(not(not(implies(or(X_39,not(not(X))),or(X,X_39)))))]]) ).
cnf(refute_0_753,plain,
( not(implies(or(X_39,not(not(X))),or(X,X_39))) != not(implies(or(X_39,X),or(X,X_39)))
| not(not(implies(or(X_39,not(not(X))),or(X,X_39)))) != not(not(implies(or(X_39,not(not(X))),or(X,X_39))))
| not(not(implies(or(X_39,not(not(X))),or(X,X_39)))) = not(not(implies(or(X_39,X),or(X,X_39)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(or(X_39,not(not(X))),or(X,X_39)))),not(not(implies(or(X_39,not(not(X))),or(X,X_39))))) ),[1,0],$fot(not(implies(or(X_39,X),or(X,X_39))))]]) ).
cnf(refute_0_754,plain,
( not(implies(or(X_39,not(not(X))),or(X,X_39))) != not(implies(or(X_39,X),or(X,X_39)))
| not(not(implies(or(X_39,not(not(X))),or(X,X_39)))) = not(not(implies(or(X_39,X),or(X,X_39)))) ),
inference(resolve,[$cnf( $equal(not(not(implies(or(X_39,not(not(X))),or(X,X_39)))),not(not(implies(or(X_39,not(not(X))),or(X,X_39))))) )],[refute_0_752,refute_0_753]) ).
cnf(refute_0_755,plain,
not(not(implies(or(X_39,not(not(X))),or(X,X_39)))) = not(not(implies(or(X_39,X),or(X,X_39)))),
inference(resolve,[$cnf( $equal(not(implies(or(X_39,not(not(X))),or(X,X_39))),not(implies(or(X_39,X),or(X,X_39)))) )],[refute_0_751,refute_0_754]) ).
cnf(refute_0_756,plain,
( not(not(implies(or(X_39,not(not(X))),or(X,X_39)))) != not(not(implies(or(X_39,X),or(X,X_39))))
| ~ is_a_theorem(not(not(implies(or(X_39,not(not(X))),or(X,X_39)))))
| is_a_theorem(not(not(implies(or(X_39,X),or(X,X_39))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(not(implies(or(X_39,not(not(X))),or(X,X_39))))) ),[0],$fot(not(not(implies(or(X_39,X),or(X,X_39)))))]]) ).
cnf(refute_0_757,plain,
( ~ is_a_theorem(not(not(implies(or(X_39,not(not(X))),or(X,X_39)))))
| is_a_theorem(not(not(implies(or(X_39,X),or(X,X_39))))) ),
inference(resolve,[$cnf( $equal(not(not(implies(or(X_39,not(not(X))),or(X,X_39)))),not(not(implies(or(X_39,X),or(X,X_39))))) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
is_a_theorem(not(not(implies(or(X_39,X),or(X,X_39))))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(or(X_39,not(not(X))),or(X,X_39))))) )],[refute_0_729,refute_0_757]) ).
cnf(refute_0_759,plain,
is_a_theorem(not(not(implies(or(X_545,X_544),or(X_544,X_545))))),
inference(subst,[],[refute_0_758:[bind(X,$fot(X_544)),bind(X_39,$fot(X_545))]]) ).
cnf(refute_0_760,plain,
is_a_theorem(or(P,not(not(implies(or(X_545,X_544),or(X_544,X_545)))))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(or(X_545,X_544),or(X_544,X_545))))) )],[refute_0_759,refute_0_689]) ).
cnf(refute_0_761,plain,
is_a_theorem(or(X_825,not(not(implies(or(X_545,X_544),or(X_544,X_545)))))),
inference(subst,[],[refute_0_760:[bind(P,$fot(X_825))]]) ).
cnf(refute_0_762,plain,
( ~ is_a_theorem(or(X_825,not(not(implies(or(X_545,X_544),or(X_544,X_545))))))
| is_a_theorem(or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825)) ),
inference(subst,[],[refute_0_10:[bind(P,$fot(X_825)),bind(Q,$fot(not(not(implies(or(X_545,X_544),or(X_544,X_545))))))]]) ).
cnf(refute_0_763,plain,
is_a_theorem(or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825)),
inference(resolve,[$cnf( is_a_theorem(or(X_825,not(not(implies(or(X_545,X_544),or(X_544,X_545)))))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
implies(not(implies(or(X_545,X_544),or(X_544,X_545))),X_825) = or(implies(or(X_545,X_544),or(X_544,X_545)),X_825),
inference(subst,[],[refute_0_303:[bind(X,$fot(implies(or(X_545,X_544),or(X_544,X_545)))),bind(Y,$fot(X_825))]]) ).
cnf(refute_0_765,plain,
or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825) = implies(not(implies(or(X_545,X_544),or(X_544,X_545))),X_825),
inference(subst,[],[refute_0_39:[bind(X,$fot(not(implies(or(X_545,X_544),or(X_544,X_545))))),bind(Y,$fot(X_825))]]) ).
cnf(refute_0_766,plain,
( implies(not(implies(or(X_545,X_544),or(X_544,X_545))),X_825) != or(implies(or(X_545,X_544),or(X_544,X_545)),X_825)
| or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825) != implies(not(implies(or(X_545,X_544),or(X_544,X_545))),X_825)
| or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825) = or(implies(or(X_545,X_544),or(X_544,X_545)),X_825) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825))),bind(Y0,$fot(implies(not(implies(or(X_545,X_544),or(X_544,X_545))),X_825))),bind(Z,$fot(or(implies(or(X_545,X_544),or(X_544,X_545)),X_825)))]]) ).
cnf(refute_0_767,plain,
( implies(not(implies(or(X_545,X_544),or(X_544,X_545))),X_825) != or(implies(or(X_545,X_544),or(X_544,X_545)),X_825)
| or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825) = or(implies(or(X_545,X_544),or(X_544,X_545)),X_825) ),
inference(resolve,[$cnf( $equal(or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825),implies(not(implies(or(X_545,X_544),or(X_544,X_545))),X_825)) )],[refute_0_765,refute_0_766]) ).
cnf(refute_0_768,plain,
or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825) = or(implies(or(X_545,X_544),or(X_544,X_545)),X_825),
inference(resolve,[$cnf( $equal(implies(not(implies(or(X_545,X_544),or(X_544,X_545))),X_825),or(implies(or(X_545,X_544),or(X_544,X_545)),X_825)) )],[refute_0_764,refute_0_767]) ).
cnf(refute_0_769,plain,
( or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825) != or(implies(or(X_545,X_544),or(X_544,X_545)),X_825)
| ~ is_a_theorem(or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825))
| is_a_theorem(or(implies(or(X_545,X_544),or(X_544,X_545)),X_825)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825)) ),[0],$fot(or(implies(or(X_545,X_544),or(X_544,X_545)),X_825))]]) ).
cnf(refute_0_770,plain,
( ~ is_a_theorem(or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825))
| is_a_theorem(or(implies(or(X_545,X_544),or(X_544,X_545)),X_825)) ),
inference(resolve,[$cnf( $equal(or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825),or(implies(or(X_545,X_544),or(X_544,X_545)),X_825)) )],[refute_0_768,refute_0_769]) ).
cnf(refute_0_771,plain,
is_a_theorem(or(implies(or(X_545,X_544),or(X_544,X_545)),X_825)),
inference(resolve,[$cnf( is_a_theorem(or(not(not(implies(or(X_545,X_544),or(X_544,X_545)))),X_825)) )],[refute_0_763,refute_0_770]) ).
cnf(refute_0_772,plain,
is_a_theorem(or(implies(or(X_545,X_544),or(X_544,X_545)),X_3604)),
inference(subst,[],[refute_0_771:[bind(X_825,$fot(X_3604))]]) ).
cnf(refute_0_773,plain,
( ~ is_a_theorem(or(implies(or(X_545,X_544),or(X_544,X_545)),X_3604))
| is_a_theorem(or(and(X_3602,implies(or(X_545,X_544),or(X_544,X_545))),implies(X_3602,X_3604))) ),
inference(subst,[],[refute_0_542:[bind(X,$fot(X_3602)),bind(X_314,$fot(implies(or(X_545,X_544),or(X_544,X_545)))),bind(X_316,$fot(X_3604))]]) ).
cnf(refute_0_774,plain,
is_a_theorem(or(and(X_3602,implies(or(X_545,X_544),or(X_544,X_545))),implies(X_3602,X_3604))),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(X_545,X_544),or(X_544,X_545)),X_3604)) )],[refute_0_772,refute_0_773]) ).
cnf(refute_0_775,plain,
is_a_theorem(or(and(X_8634,implies(or(X_545,X_544),or(X_544,X_545))),implies(X_8634,X_8636))),
inference(subst,[],[refute_0_774:[bind(X_3602,$fot(X_8634)),bind(X_3604,$fot(X_8636))]]) ).
cnf(refute_0_776,plain,
is_a_theorem(implies(or(X_130,or(not(X),X_132)),or(not(X),or(X_130,X_132)))),
inference(subst,[],[refute_0_30:[bind(P,$fot(X_130)),bind(Q,$fot(not(X))),bind(R,$fot(X_132))]]) ).
cnf(refute_0_777,plain,
implies(X,or(X_130,X_132)) = or(not(X),or(X_130,X_132)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(or(X_130,X_132)))]]) ).
cnf(refute_0_778,plain,
( implies(X,or(X_130,X_132)) != or(not(X),or(X_130,X_132))
| or(not(X),or(X_130,X_132)) = implies(X,or(X_130,X_132)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,or(X_130,X_132)))),bind(Y0,$fot(or(not(X),or(X_130,X_132))))]]) ).
cnf(refute_0_779,plain,
or(not(X),or(X_130,X_132)) = implies(X,or(X_130,X_132)),
inference(resolve,[$cnf( $equal(implies(X,or(X_130,X_132)),or(not(X),or(X_130,X_132))) )],[refute_0_777,refute_0_778]) ).
cnf(refute_0_780,plain,
( or(not(X),or(X_130,X_132)) != implies(X,or(X_130,X_132))
| ~ is_a_theorem(implies(or(X_130,or(not(X),X_132)),or(not(X),or(X_130,X_132))))
| is_a_theorem(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_130,or(not(X),X_132)),or(not(X),or(X_130,X_132)))) ),[0,1],$fot(implies(X,or(X_130,X_132)))]]) ).
cnf(refute_0_781,plain,
( ~ is_a_theorem(implies(or(X_130,or(not(X),X_132)),or(not(X),or(X_130,X_132))))
| is_a_theorem(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_130,X_132)),implies(X,or(X_130,X_132))) )],[refute_0_779,refute_0_780]) ).
cnf(refute_0_782,plain,
is_a_theorem(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_130,or(not(X),X_132)),or(not(X),or(X_130,X_132)))) )],[refute_0_776,refute_0_781]) ).
cnf(refute_0_783,plain,
or(X_130,or(not(X),X_132)) = or(X_130,or(not(X),X_132)),
introduced(tautology,[refl,[$fot(or(X_130,or(not(X),X_132)))]]) ).
cnf(refute_0_784,plain,
( or(X_130,or(not(X),X_132)) != or(X_130,or(not(X),X_132))
| or(not(X),X_132) != implies(X,X_132)
| or(X_130,or(not(X),X_132)) = or(X_130,implies(X,X_132)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_130,or(not(X),X_132)),or(X_130,or(not(X),X_132))) ),[1,1],$fot(implies(X,X_132))]]) ).
cnf(refute_0_785,plain,
( or(not(X),X_132) != implies(X,X_132)
| or(X_130,or(not(X),X_132)) = or(X_130,implies(X,X_132)) ),
inference(resolve,[$cnf( $equal(or(X_130,or(not(X),X_132)),or(X_130,or(not(X),X_132))) )],[refute_0_783,refute_0_784]) ).
cnf(refute_0_786,plain,
or(X_130,or(not(X),X_132)) = or(X_130,implies(X,X_132)),
inference(resolve,[$cnf( $equal(or(not(X),X_132),implies(X,X_132)) )],[refute_0_34,refute_0_785]) ).
cnf(refute_0_787,plain,
implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))) = implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))),
introduced(tautology,[refl,[$fot(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))))]]) ).
cnf(refute_0_788,plain,
( implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))) != implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132)))
| or(X_130,or(not(X),X_132)) != or(X_130,implies(X,X_132))
| implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))) = implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))),implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132)))) ),[1,0],$fot(or(X_130,implies(X,X_132)))]]) ).
cnf(refute_0_789,plain,
( or(X_130,or(not(X),X_132)) != or(X_130,implies(X,X_132))
| implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))) = implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132))) ),
inference(resolve,[$cnf( $equal(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))),implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132)))) )],[refute_0_787,refute_0_788]) ).
cnf(refute_0_790,plain,
implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))) = implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132))),
inference(resolve,[$cnf( $equal(or(X_130,or(not(X),X_132)),or(X_130,implies(X,X_132))) )],[refute_0_786,refute_0_789]) ).
cnf(refute_0_791,plain,
( implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))) != implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132)))
| ~ is_a_theorem(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))))
| is_a_theorem(implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132)))) ),[0],$fot(implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132))))]]) ).
cnf(refute_0_792,plain,
( ~ is_a_theorem(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))))
| is_a_theorem(implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132))),implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132)))) )],[refute_0_790,refute_0_791]) ).
cnf(refute_0_793,plain,
is_a_theorem(implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_130,or(not(X),X_132)),implies(X,or(X_130,X_132)))) )],[refute_0_782,refute_0_792]) ).
cnf(refute_0_794,plain,
( ~ is_a_theorem(implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132))))
| ~ is_a_theorem(or(X_130,implies(X,X_132)))
| is_a_theorem(implies(X,or(X_130,X_132))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_130,implies(X,X_132)))),bind(Y,$fot(implies(X,or(X_130,X_132))))]]) ).
cnf(refute_0_795,plain,
( ~ is_a_theorem(or(X_130,implies(X,X_132)))
| is_a_theorem(implies(X,or(X_130,X_132))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_130,implies(X,X_132)),implies(X,or(X_130,X_132)))) )],[refute_0_793,refute_0_794]) ).
cnf(refute_0_796,plain,
( ~ is_a_theorem(or(and(X_8634,implies(or(X_545,X_544),or(X_544,X_545))),implies(X_8634,X_8636)))
| is_a_theorem(implies(X_8634,or(and(X_8634,implies(or(X_545,X_544),or(X_544,X_545))),X_8636))) ),
inference(subst,[],[refute_0_795:[bind(X,$fot(X_8634)),bind(X_130,$fot(and(X_8634,implies(or(X_545,X_544),or(X_544,X_545))))),bind(X_132,$fot(X_8636))]]) ).
cnf(refute_0_797,plain,
is_a_theorem(implies(X_8634,or(and(X_8634,implies(or(X_545,X_544),or(X_544,X_545))),X_8636))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_8634,implies(or(X_545,X_544),or(X_544,X_545))),implies(X_8634,X_8636))) )],[refute_0_775,refute_0_796]) ).
cnf(refute_0_798,plain,
is_a_theorem(implies(X_8806,or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))))),
inference(subst,[],[refute_0_797:[bind(X_544,$fot(X_8804)),bind(X_545,$fot(X_8805)),bind(X_8634,$fot(X_8806)),bind(X_8636,$fot(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))))]]) ).
cnf(refute_0_799,plain,
and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))) = or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))),
inference(subst,[],[refute_0_662:[bind(X_3791,$fot(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))))]]) ).
cnf(refute_0_800,plain,
( and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))) != or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))
| or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))) = and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))),bind(Y0,$fot(or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))))]]) ).
cnf(refute_0_801,plain,
or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))) = and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),
inference(resolve,[$cnf( $equal(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))) )],[refute_0_799,refute_0_800]) ).
cnf(refute_0_802,plain,
( or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))) != and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))
| ~ is_a_theorem(implies(X_8806,or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))))
| is_a_theorem(implies(X_8806,and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_8806,or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))))) ),[0,1],$fot(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))]]) ).
cnf(refute_0_803,plain,
( ~ is_a_theorem(implies(X_8806,or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))))
| is_a_theorem(implies(X_8806,and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))) ),
inference(resolve,[$cnf( $equal(or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))) )],[refute_0_801,refute_0_802]) ).
cnf(refute_0_804,plain,
is_a_theorem(implies(X_8806,and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_8806,or(and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805))),and(X_8806,implies(or(X_8805,X_8804),or(X_8804,X_8805)))))) )],[refute_0_798,refute_0_803]) ).
cnf(refute_0_805,plain,
is_a_theorem(implies(implies(or(X_9729,X_9730),or(X_9730,X_9729)),and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730))))),
inference(subst,[],[refute_0_804:[bind(X_8804,$fot(X_9729)),bind(X_8805,$fot(X_9730)),bind(X_8806,$fot(implies(or(X_9729,X_9730),or(X_9730,X_9729))))]]) ).
cnf(refute_0_806,plain,
equiv(or(X_9729,X_9730),or(X_9730,X_9729)) = and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730))),
inference(subst,[],[refute_0_115:[bind(X,$fot(or(X_9729,X_9730))),bind(Y,$fot(or(X_9730,X_9729)))]]) ).
cnf(refute_0_807,plain,
( equiv(or(X_9729,X_9730),or(X_9730,X_9729)) != and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730)))
| and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730))) = equiv(or(X_9729,X_9730),or(X_9730,X_9729)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(equiv(or(X_9729,X_9730),or(X_9730,X_9729)))),bind(Y0,$fot(and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730)))))]]) ).
cnf(refute_0_808,plain,
and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730))) = equiv(or(X_9729,X_9730),or(X_9730,X_9729)),
inference(resolve,[$cnf( $equal(equiv(or(X_9729,X_9730),or(X_9730,X_9729)),and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730)))) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
( and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730))) != equiv(or(X_9729,X_9730),or(X_9730,X_9729))
| ~ is_a_theorem(implies(implies(or(X_9729,X_9730),or(X_9730,X_9729)),and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730)))))
| is_a_theorem(implies(implies(or(X_9729,X_9730),or(X_9730,X_9729)),equiv(or(X_9729,X_9730),or(X_9730,X_9729)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(or(X_9729,X_9730),or(X_9730,X_9729)),and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730))))) ),[0,1],$fot(equiv(or(X_9729,X_9730),or(X_9730,X_9729)))]]) ).
cnf(refute_0_810,plain,
( ~ is_a_theorem(implies(implies(or(X_9729,X_9730),or(X_9730,X_9729)),and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730)))))
| is_a_theorem(implies(implies(or(X_9729,X_9730),or(X_9730,X_9729)),equiv(or(X_9729,X_9730),or(X_9730,X_9729)))) ),
inference(resolve,[$cnf( $equal(and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730))),equiv(or(X_9729,X_9730),or(X_9730,X_9729))) )],[refute_0_808,refute_0_809]) ).
cnf(refute_0_811,plain,
is_a_theorem(implies(implies(or(X_9729,X_9730),or(X_9730,X_9729)),equiv(or(X_9729,X_9730),or(X_9730,X_9729)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_9729,X_9730),or(X_9730,X_9729)),and(implies(or(X_9729,X_9730),or(X_9730,X_9729)),implies(or(X_9730,X_9729),or(X_9729,X_9730))))) )],[refute_0_805,refute_0_810]) ).
cnf(refute_0_812,plain,
is_a_theorem(implies(implies(or(X_20541,X_20542),or(X_20542,X_20541)),equiv(or(X_20541,X_20542),or(X_20542,X_20541)))),
inference(subst,[],[refute_0_811:[bind(X_9729,$fot(X_20541)),bind(X_9730,$fot(X_20542))]]) ).
cnf(refute_0_813,plain,
( ~ is_a_theorem(implies(or(X_20541,X_20542),or(X_20542,X_20541)))
| is_a_theorem(equiv(or(X_20541,X_20542),or(X_20542,X_20541))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_20541,X_20542),or(X_20542,X_20541)),equiv(or(X_20541,X_20542),or(X_20542,X_20541)))) )],[refute_0_812,refute_0_688]) ).
cnf(refute_0_814,plain,
is_a_theorem(implies(or(X_20541,X_20542),or(X_20542,X_20541))),
inference(subst,[],[refute_0_5:[bind(P,$fot(X_20541)),bind(Q,$fot(X_20542))]]) ).
cnf(refute_0_815,plain,
is_a_theorem(equiv(or(X_20541,X_20542),or(X_20542,X_20541))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_20541,X_20542),or(X_20542,X_20541))) )],[refute_0_814,refute_0_813]) ).
cnf(refute_0_816,plain,
is_a_theorem(equiv(or(X_20543,not(X)),or(not(X),X_20543))),
inference(subst,[],[refute_0_815:[bind(X_20541,$fot(X_20543)),bind(X_20542,$fot(not(X)))]]) ).
cnf(refute_0_817,plain,
implies(X,X_20543) = or(not(X),X_20543),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_20543))]]) ).
cnf(refute_0_818,plain,
( implies(X,X_20543) != or(not(X),X_20543)
| or(not(X),X_20543) = implies(X,X_20543) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(implies(X,X_20543))),bind(Y0,$fot(or(not(X),X_20543)))]]) ).
cnf(refute_0_819,plain,
or(not(X),X_20543) = implies(X,X_20543),
inference(resolve,[$cnf( $equal(implies(X,X_20543),or(not(X),X_20543)) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
( or(not(X),X_20543) != implies(X,X_20543)
| ~ is_a_theorem(equiv(or(X_20543,not(X)),or(not(X),X_20543)))
| is_a_theorem(equiv(or(X_20543,not(X)),implies(X,X_20543))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(equiv(or(X_20543,not(X)),or(not(X),X_20543))) ),[0,1],$fot(implies(X,X_20543))]]) ).
cnf(refute_0_821,plain,
( ~ is_a_theorem(equiv(or(X_20543,not(X)),or(not(X),X_20543)))
| is_a_theorem(equiv(or(X_20543,not(X)),implies(X,X_20543))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_20543),implies(X,X_20543)) )],[refute_0_819,refute_0_820]) ).
cnf(refute_0_822,plain,
is_a_theorem(equiv(or(X_20543,not(X)),implies(X,X_20543))),
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_20543,not(X)),or(not(X),X_20543))) )],[refute_0_816,refute_0_821]) ).
cnf(refute_0_823,plain,
is_a_theorem(equiv(or(X_20548,not(X_20547)),implies(X_20547,X_20548))),
inference(subst,[],[refute_0_822:[bind(X,$fot(X_20547)),bind(X_20543,$fot(X_20548))]]) ).
cnf(refute_0_824,plain,
or(X_20548,not(X_20547)) = implies(X_20547,X_20548),
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_20548,not(X_20547)),implies(X_20547,X_20548))) )],[refute_0_823,refute_0_687]) ).
cnf(refute_0_825,plain,
or(X_5108,not(X_20554)) = implies(X_20554,X_5108),
inference(subst,[],[refute_0_824:[bind(X_20547,$fot(X_20554)),bind(X_20548,$fot(X_5108))]]) ).
cnf(refute_0_826,plain,
( or(X_5108,not(X_20554)) != implies(X_20554,X_5108)
| ~ is_a_theorem(implies(or(not(X_20554),or(X_5108,not(X_20554))),or(X_5108,not(X_20554))))
| is_a_theorem(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_20554),or(X_5108,not(X_20554))),or(X_5108,not(X_20554)))) ),[0,0,1],$fot(implies(X_20554,X_5108))]]) ).
cnf(refute_0_827,plain,
( ~ is_a_theorem(implies(or(not(X_20554),or(X_5108,not(X_20554))),or(X_5108,not(X_20554))))
| is_a_theorem(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554)))) ),
inference(resolve,[$cnf( $equal(or(X_5108,not(X_20554)),implies(X_20554,X_5108)) )],[refute_0_825,refute_0_826]) ).
cnf(refute_0_828,plain,
is_a_theorem(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_20554),or(X_5108,not(X_20554))),or(X_5108,not(X_20554)))) )],[refute_0_686,refute_0_827]) ).
cnf(refute_0_829,plain,
implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))),
introduced(tautology,[refl,[$fot(implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))))]]) ).
cnf(refute_0_830,plain,
( implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))) != implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554)))
| or(X_5108,not(X_20554)) != implies(X_20554,X_5108)
| implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))),implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554)))) ),[1,1],$fot(implies(X_20554,X_5108))]]) ).
cnf(refute_0_831,plain,
( or(X_5108,not(X_20554)) != implies(X_20554,X_5108)
| implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))),implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554)))) )],[refute_0_829,refute_0_830]) ).
cnf(refute_0_832,plain,
implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108)),
inference(resolve,[$cnf( $equal(or(X_5108,not(X_20554)),implies(X_20554,X_5108)) )],[refute_0_825,refute_0_831]) ).
cnf(refute_0_833,plain,
or(not(X_20554),implies(X_20554,X_5108)) = implies(X_20554,implies(X_20554,X_5108)),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_20554)),bind(Y,$fot(implies(X_20554,X_5108)))]]) ).
cnf(refute_0_834,plain,
implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))),
introduced(tautology,[refl,[$fot(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))))]]) ).
cnf(refute_0_835,plain,
( implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) != implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554)))
| or(not(X_20554),implies(X_20554,X_5108)) != implies(X_20554,implies(X_20554,X_5108))
| implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))),implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554)))) ),[1,0],$fot(implies(X_20554,implies(X_20554,X_5108)))]]) ).
cnf(refute_0_836,plain,
( or(not(X_20554),implies(X_20554,X_5108)) != implies(X_20554,implies(X_20554,X_5108))
| implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))),implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554)))) )],[refute_0_834,refute_0_835]) ).
cnf(refute_0_837,plain,
implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))),
inference(resolve,[$cnf( $equal(or(not(X_20554),implies(X_20554,X_5108)),implies(X_20554,implies(X_20554,X_5108))) )],[refute_0_833,refute_0_836]) ).
cnf(refute_0_838,plain,
( implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))) != implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108))
| implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) != implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554)))
| implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108)) ),
inference(subst,[],[refute_0_101:[bind(X0,$fot(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))))),bind(Y0,$fot(implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))))),bind(Z,$fot(implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108))))]]) ).
cnf(refute_0_839,plain,
( implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))) != implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108))
| implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))),implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554)))) )],[refute_0_837,refute_0_838]) ).
cnf(refute_0_840,plain,
implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) = implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108)),
inference(resolve,[$cnf( $equal(implies(implies(X_20554,implies(X_20554,X_5108)),or(X_5108,not(X_20554))),implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108))) )],[refute_0_832,refute_0_839]) ).
cnf(refute_0_841,plain,
( implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))) != implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108))
| ~ is_a_theorem(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))))
| is_a_theorem(implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554)))) ),[0],$fot(implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108)))]]) ).
cnf(refute_0_842,plain,
( ~ is_a_theorem(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))))
| is_a_theorem(implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554))),implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108))) )],[refute_0_840,refute_0_841]) ).
cnf(refute_0_843,plain,
is_a_theorem(implies(implies(X_20554,implies(X_20554,X_5108)),implies(X_20554,X_5108))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X_20554),implies(X_20554,X_5108)),or(X_5108,not(X_20554)))) )],[refute_0_828,refute_0_842]) ).
cnf(refute_0_844,plain,
is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4))),
inference(subst,[],[refute_0_843:[bind(X_20554,$fot(skolemFOFtoCNF_X_4)),bind(X_5108,$fot(skolemFOFtoCNF_Y_4))]]) ).
cnf(refute_0_845,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4))) )],[refute_0_844,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL485+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 15:53:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 58.93/59.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.93/59.16
% 58.93/59.16 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 59.10/59.29
%------------------------------------------------------------------------------