TSTP Solution File: LCL520+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL520+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:52:52 EDT 2022
% Result : Theorem 103.90s 104.14s
% Output : CNFRefutation 103.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 83
% Syntax : Number of formulae : 437 ( 220 unt; 0 def)
% Number of atoms : 759 ( 467 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 625 ( 303 ~; 290 |; 13 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 15 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 790 ( 10 sgn 64 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ) ).
fof(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ) ).
fof(kn3,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(rosser_op_or,axiom,
op_or ).
fof(rosser_op_implies_and,axiom,
op_implies_and ).
fof(rosser_op_equiv,axiom,
op_equiv ).
fof(rosser_modus_ponens,axiom,
modus_ponens ).
fof(rosser_kn1,axiom,
kn1 ).
fof(rosser_kn2,axiom,
kn2 ).
fof(rosser_kn3,axiom,
kn3 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_op_and,axiom,
op_and ).
fof(principia_op_equiv,axiom,
op_equiv ).
fof(principia_r3,conjecture,
r3 ).
fof(subgoal_0,plain,
r3,
inference(strip,[],[principia_r3]) ).
fof(negate_0_0,plain,
~ r3,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_1,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_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8)))
| r3 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ r3,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ modus_ponens
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y)
| modus_ponens )
& ( is_a_theorem(implies(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| modus_ponens )
& ( is_a_theorem(skolemFOFtoCNF_X)
| modus_ponens )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
modus_ponens,
inference(canonicalize,[],[rosser_modus_ponens]) ).
fof(normalize_0_8,plain,
( ~ kn3
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(canonicalize,[],[kn3]) ).
fof(normalize_0_9,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_2,skolemFOFtoCNF_Q_1),implies(not(and(skolemFOFtoCNF_Q_1,skolemFOFtoCNF_R)),not(and(skolemFOFtoCNF_R,skolemFOFtoCNF_P_2)))))
| kn3 )
& ( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [P,Q,R] :
( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
kn3,
inference(canonicalize,[],[rosser_kn3]) ).
fof(normalize_0_12,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
op_implies_and,
inference(canonicalize,[],[rosser_op_implies_and]) ).
fof(normalize_0_15,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_18,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_21,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
op_or,
inference(canonicalize,[],[rosser_op_or]) ).
fof(normalize_0_24,plain,
( ~ kn2
<=> ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[kn2]) ).
fof(normalize_0_25,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_P_1,skolemFOFtoCNF_Q),skolemFOFtoCNF_P_1))
| kn2 )
& ( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [P,Q] :
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
kn2,
inference(canonicalize,[],[rosser_kn2]) ).
fof(normalize_0_28,plain,
( ~ kn1
<=> ? [P] : ~ is_a_theorem(implies(P,and(P,P))) ),
inference(canonicalize,[],[kn1]) ).
fof(normalize_0_29,plain,
! [P] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_P,and(skolemFOFtoCNF_P,skolemFOFtoCNF_P)))
| kn1 )
& ( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [P] :
( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
kn1,
inference(canonicalize,[],[rosser_kn1]) ).
fof(normalize_0_32,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_33,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_32]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_36,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_37,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
op_equiv,
inference(canonicalize,[],[principia_op_equiv]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8)))
| r3 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ r3,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8))),
inference(resolve,[$cnf( r3 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(or(X_199,X_200),or(and(X_200,X_201),implies(X_201,X_199))))
| ~ is_a_theorem(or(X_199,X_200))
| is_a_theorem(or(and(X_200,X_201),implies(X_201,X_199))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(or(X_199,X_200))),bind(Y,$fot(or(and(X_200,X_201),implies(X_201,X_199))))]]) ).
cnf(refute_0_7,plain,
( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
kn3,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))),
inference(resolve,[$cnf( kn3 )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
implies(X,or(X_35,not(X_34))) = not(and(X,not(or(X_35,not(X_34))))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(or(X_35,not(X_34))))]]) ).
cnf(refute_0_14,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_15,plain,
op_and,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_18,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_19,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_21,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_24,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_24:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_26,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_27,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_28,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_31,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_16,refute_0_31]) ).
cnf(refute_0_33,plain,
and(not(X_5),Y) = not(implies(not(X_5),not(Y))),
inference(subst,[],[refute_0_32:[bind(X,$fot(not(X_5)))]]) ).
cnf(refute_0_34,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_35,plain,
op_or,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_36,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_38,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_12,refute_0_37]) ).
cnf(refute_0_39,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_38:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_40,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_41,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
or(X_5,not(Y)) = implies(not(X_5),not(Y)),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_5)),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_44,plain,
( or(X_5,not(Y)) != implies(not(X_5),not(Y))
| implies(not(X_5),not(Y)) = or(X_5,not(Y)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(or(X_5,not(Y)))),bind(Y0,$fot(implies(not(X_5),not(Y))))]]) ).
cnf(refute_0_45,plain,
implies(not(X_5),not(Y)) = or(X_5,not(Y)),
inference(resolve,[$cnf( $equal(or(X_5,not(Y)),implies(not(X_5),not(Y))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( and(not(X_5),Y) != not(implies(not(X_5),not(Y)))
| implies(not(X_5),not(Y)) != or(X_5,not(Y))
| and(not(X_5),Y) = not(or(X_5,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X_5),Y),not(implies(not(X_5),not(Y)))) ),[1,0],$fot(or(X_5,not(Y)))]]) ).
cnf(refute_0_47,plain,
( and(not(X_5),Y) != not(implies(not(X_5),not(Y)))
| and(not(X_5),Y) = not(or(X_5,not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X_5),not(Y)),or(X_5,not(Y))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
and(not(X_5),Y) = not(or(X_5,not(Y))),
inference(resolve,[$cnf( $equal(and(not(X_5),Y),not(implies(not(X_5),not(Y)))) )],[refute_0_33,refute_0_47]) ).
cnf(refute_0_49,plain,
and(not(X_35),X_34) = not(or(X_35,not(X_34))),
inference(subst,[],[refute_0_48:[bind(Y,$fot(X_34)),bind(X_5,$fot(X_35))]]) ).
cnf(refute_0_50,plain,
( and(not(X_35),X_34) != not(or(X_35,not(X_34)))
| not(or(X_35,not(X_34))) = and(not(X_35),X_34) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(and(not(X_35),X_34))),bind(Y0,$fot(not(or(X_35,not(X_34)))))]]) ).
cnf(refute_0_51,plain,
not(or(X_35,not(X_34))) = and(not(X_35),X_34),
inference(resolve,[$cnf( $equal(and(not(X_35),X_34),not(or(X_35,not(X_34)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( implies(X,or(X_35,not(X_34))) != not(and(X,not(or(X_35,not(X_34)))))
| not(or(X_35,not(X_34))) != and(not(X_35),X_34)
| implies(X,or(X_35,not(X_34))) = not(and(X,and(not(X_35),X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,or(X_35,not(X_34))),not(and(X,not(or(X_35,not(X_34)))))) ),[1,0,1],$fot(and(not(X_35),X_34))]]) ).
cnf(refute_0_53,plain,
( implies(X,or(X_35,not(X_34))) != not(and(X,not(or(X_35,not(X_34)))))
| implies(X,or(X_35,not(X_34))) = not(and(X,and(not(X_35),X_34))) ),
inference(resolve,[$cnf( $equal(not(or(X_35,not(X_34))),and(not(X_35),X_34)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
implies(X,or(X_35,not(X_34))) = not(and(X,and(not(X_35),X_34))),
inference(resolve,[$cnf( $equal(implies(X,or(X_35,not(X_34))),not(and(X,not(or(X_35,not(X_34)))))) )],[refute_0_13,refute_0_53]) ).
cnf(refute_0_55,plain,
( implies(X,or(X_35,not(X_34))) != not(and(X,and(not(X_35),X_34)))
| not(and(X,and(not(X_35),X_34))) = implies(X,or(X_35,not(X_34))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(implies(X,or(X_35,not(X_34))))),bind(Y0,$fot(not(and(X,and(not(X_35),X_34)))))]]) ).
cnf(refute_0_56,plain,
not(and(X,and(not(X_35),X_34))) = implies(X,or(X_35,not(X_34))),
inference(resolve,[$cnf( $equal(implies(X,or(X_35,not(X_34))),not(and(X,and(not(X_35),X_34)))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))),
inference(subst,[],[refute_0_56:[bind(X,$fot(implies(P,Q))),bind(X_34,$fot(and(R,P))),bind(X_35,$fot(and(Q,R)))]]) ).
cnf(refute_0_58,plain,
implies(X_10,implies(X,not(Y))) = not(and(X_10,not(implies(X,not(Y))))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_10)),bind(Y,$fot(implies(X,not(Y))))]]) ).
cnf(refute_0_59,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_60,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_32,refute_0_59]) ).
cnf(refute_0_61,plain,
( implies(X_10,implies(X,not(Y))) != not(and(X_10,not(implies(X,not(Y)))))
| not(implies(X,not(Y))) != and(X,Y)
| implies(X_10,implies(X,not(Y))) = not(and(X_10,and(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_10,implies(X,not(Y))),not(and(X_10,not(implies(X,not(Y)))))) ),[1,0,1],$fot(and(X,Y))]]) ).
cnf(refute_0_62,plain,
( implies(X_10,implies(X,not(Y))) != not(and(X_10,not(implies(X,not(Y)))))
| implies(X_10,implies(X,not(Y))) = not(and(X_10,and(X,Y))) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(X_10,implies(X,not(Y))) = not(and(X_10,and(X,Y))),
inference(resolve,[$cnf( $equal(implies(X_10,implies(X,not(Y))),not(and(X_10,not(implies(X,not(Y)))))) )],[refute_0_58,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))),
inference(subst,[],[refute_0_63:[bind(X,$fot(not(and(Q,R)))),bind(Y,$fot(and(R,P))),bind(X_10,$fot(implies(P,Q)))]]) ).
cnf(refute_0_65,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_66,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_22,refute_0_65]) ).
cnf(refute_0_67,plain,
( implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) != not(and(implies(P,Q),and(not(and(Q,R)),and(R,P))))
| not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))) != implies(implies(P,Q),or(and(Q,R),not(and(R,P))))
| implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))),bind(Y0,$fot(not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))))),bind(Z,$fot(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))))]]) ).
cnf(refute_0_68,plain,
( not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))) != implies(implies(P,Q),or(and(Q,R),not(and(R,P))))
| implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))) ),
inference(resolve,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),not(and(implies(P,Q),and(not(and(Q,R)),and(R,P))))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))),
inference(resolve,[$cnf( $equal(not(and(implies(P,Q),and(not(and(Q,R)),and(R,P)))),implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) )],[refute_0_57,refute_0_68]) ).
cnf(refute_0_70,plain,
( implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) != implies(implies(P,Q),or(and(Q,R),not(and(R,P))))
| ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),[0],$fot(implies(implies(P,Q),or(and(Q,R),not(and(R,P)))))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) ),
inference(resolve,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )],[refute_0_9,refute_0_71]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),not(and(X_139,not(Y)))))),
inference(subst,[],[refute_0_72:[bind(P,$fot(not(Y))),bind(Q,$fot(X_138)),bind(R,$fot(X_139))]]) ).
cnf(refute_0_74,plain,
implies(X_139,Y) = not(and(X_139,not(Y))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_139))]]) ).
cnf(refute_0_75,plain,
( implies(X_139,Y) != not(and(X_139,not(Y)))
| not(and(X_139,not(Y))) = implies(X_139,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(implies(X_139,Y))),bind(Y0,$fot(not(and(X_139,not(Y)))))]]) ).
cnf(refute_0_76,plain,
not(and(X_139,not(Y))) = implies(X_139,Y),
inference(resolve,[$cnf( $equal(implies(X_139,Y),not(and(X_139,not(Y)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( not(and(X_139,not(Y))) != implies(X_139,Y)
| ~ is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),not(and(X_139,not(Y))))))
| is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),not(and(X_139,not(Y)))))) ),[0,1,1],$fot(implies(X_139,Y))]]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),not(and(X_139,not(Y))))))
| is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y)))) ),
inference(resolve,[$cnf( $equal(not(and(X_139,not(Y))),implies(X_139,Y)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),not(and(X_139,not(Y)))))) )],[refute_0_73,refute_0_78]) ).
cnf(refute_0_80,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_81,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_42,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(not(Y),X_138) = or(Y,X_138),
inference(subst,[],[refute_0_81:[bind(X,$fot(Y)),bind(Y,$fot(X_138))]]) ).
cnf(refute_0_83,plain,
implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))) = implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))))]]) ).
cnf(refute_0_84,plain,
( implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))) != implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y)))
| implies(not(Y),X_138) != or(Y,X_138)
| implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))) = implies(or(Y,X_138),or(and(X_138,X_139),implies(X_139,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))),implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y)))) ),[1,0],$fot(or(Y,X_138))]]) ).
cnf(refute_0_85,plain,
( implies(not(Y),X_138) != or(Y,X_138)
| implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))) = implies(or(Y,X_138),or(and(X_138,X_139),implies(X_139,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))),implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))) = implies(or(Y,X_138),or(and(X_138,X_139),implies(X_139,Y))),
inference(resolve,[$cnf( $equal(implies(not(Y),X_138),or(Y,X_138)) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
( implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))) != implies(or(Y,X_138),or(and(X_138,X_139),implies(X_139,Y)))
| ~ is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))))
| is_a_theorem(implies(or(Y,X_138),or(and(X_138,X_139),implies(X_139,Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y)))) ),[0],$fot(implies(or(Y,X_138),or(and(X_138,X_139),implies(X_139,Y))))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))))
| is_a_theorem(implies(or(Y,X_138),or(and(X_138,X_139),implies(X_139,Y)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y))),implies(or(Y,X_138),or(and(X_138,X_139),implies(X_139,Y)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(or(Y,X_138),or(and(X_138,X_139),implies(X_139,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_138),or(and(X_138,X_139),implies(X_139,Y)))) )],[refute_0_79,refute_0_88]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(or(X_199,X_200),or(and(X_200,X_201),implies(X_201,X_199)))),
inference(subst,[],[refute_0_89:[bind(Y,$fot(X_199)),bind(X_138,$fot(X_200)),bind(X_139,$fot(X_201))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(or(X_199,X_200))
| is_a_theorem(or(and(X_200,X_201),implies(X_201,X_199))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_199,X_200),or(and(X_200,X_201),implies(X_201,X_199)))) )],[refute_0_90,refute_0_6]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(or(X_4400,not(X_4400)))
| is_a_theorem(or(and(not(X_4400),X_201),implies(X_201,X_4400))) ),
inference(subst,[],[refute_0_91:[bind(X_199,$fot(X_4400)),bind(X_200,$fot(not(X_4400)))]]) ).
cnf(refute_0_93,plain,
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_94,plain,
kn2,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(and(P,Q),P)),
inference(resolve,[$cnf( kn2 )],[refute_0_94,refute_0_93]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(and(not(not(X_36)),Q),not(not(X_36)))),
inference(subst,[],[refute_0_95:[bind(P,$fot(not(not(X_36))))]]) ).
cnf(refute_0_97,plain,
and(not(not(X)),X_34) = not(or(not(X),not(X_34))),
inference(subst,[],[refute_0_48:[bind(Y,$fot(X_34)),bind(X_5,$fot(not(X)))]]) ).
cnf(refute_0_98,plain,
implies(X,not(X_34)) = or(not(X),not(X_34)),
inference(subst,[],[refute_0_19:[bind(Y,$fot(not(X_34)))]]) ).
cnf(refute_0_99,plain,
( implies(X,not(X_34)) != or(not(X),not(X_34))
| or(not(X),not(X_34)) = implies(X,not(X_34)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(implies(X,not(X_34)))),bind(Y0,$fot(or(not(X),not(X_34))))]]) ).
cnf(refute_0_100,plain,
or(not(X),not(X_34)) = implies(X,not(X_34)),
inference(resolve,[$cnf( $equal(implies(X,not(X_34)),or(not(X),not(X_34))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( and(not(not(X)),X_34) != not(or(not(X),not(X_34)))
| or(not(X),not(X_34)) != implies(X,not(X_34))
| and(not(not(X)),X_34) = not(implies(X,not(X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X)),X_34),not(or(not(X),not(X_34)))) ),[1,0],$fot(implies(X,not(X_34)))]]) ).
cnf(refute_0_102,plain,
( and(not(not(X)),X_34) != not(or(not(X),not(X_34)))
| and(not(not(X)),X_34) = not(implies(X,not(X_34))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_34)),implies(X,not(X_34))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
and(not(not(X)),X_34) = not(implies(X,not(X_34))),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_34),not(or(not(X),not(X_34)))) )],[refute_0_97,refute_0_102]) ).
cnf(refute_0_104,plain,
not(implies(X,not(X_34))) = and(X,X_34),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_34))]]) ).
cnf(refute_0_105,plain,
( and(not(not(X)),X_34) != not(implies(X,not(X_34)))
| not(implies(X,not(X_34))) != and(X,X_34)
| and(not(not(X)),X_34) = and(X,X_34) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(not(X)),X_34),and(X,X_34)) ),[0],$fot(not(implies(X,not(X_34))))]]) ).
cnf(refute_0_106,plain,
( and(not(not(X)),X_34) != not(implies(X,not(X_34)))
| and(not(not(X)),X_34) = and(X,X_34) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(X_34))),and(X,X_34)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
and(not(not(X)),X_34) = and(X,X_34),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_34),not(implies(X,not(X_34)))) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
and(not(not(X_36)),Q) = and(X_36,Q),
inference(subst,[],[refute_0_107:[bind(X,$fot(X_36)),bind(X_34,$fot(Q))]]) ).
cnf(refute_0_109,plain,
( and(not(not(X_36)),Q) != and(X_36,Q)
| ~ is_a_theorem(implies(and(not(not(X_36)),Q),not(not(X_36))))
| is_a_theorem(implies(and(X_36,Q),not(not(X_36)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(not(X_36)),Q),not(not(X_36)))) ),[0,0],$fot(and(X_36,Q))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(and(not(not(X_36)),Q),not(not(X_36))))
| is_a_theorem(implies(and(X_36,Q),not(not(X_36)))) ),
inference(resolve,[$cnf( $equal(and(not(not(X_36)),Q),and(X_36,Q)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(and(X_36,Q),not(not(X_36)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(not(X_36)),Q),not(not(X_36)))) )],[refute_0_96,refute_0_110]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(and(not(not(X)),X_83),not(not(not(not(X)))))),
inference(subst,[],[refute_0_111:[bind(Q,$fot(X_83)),bind(X_36,$fot(not(not(X))))]]) ).
cnf(refute_0_113,plain,
and(not(not(X)),X_83) = and(X,X_83),
inference(subst,[],[refute_0_107:[bind(X_34,$fot(X_83))]]) ).
cnf(refute_0_114,plain,
( and(not(not(X)),X_83) != and(X,X_83)
| ~ is_a_theorem(implies(and(not(not(X)),X_83),not(not(not(not(X))))))
| is_a_theorem(implies(and(X,X_83),not(not(not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(not(X)),X_83),not(not(not(not(X)))))) ),[0,0],$fot(and(X,X_83))]]) ).
cnf(refute_0_115,plain,
( ~ is_a_theorem(implies(and(not(not(X)),X_83),not(not(not(not(X))))))
| is_a_theorem(implies(and(X,X_83),not(not(not(not(X)))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_83),and(X,X_83)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(and(X,X_83),not(not(not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(not(X)),X_83),not(not(not(not(X)))))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(and(not(not(X)),X_245),not(not(not(not(not(not(X)))))))),
inference(subst,[],[refute_0_116:[bind(X,$fot(not(not(X)))),bind(X_83,$fot(X_245))]]) ).
cnf(refute_0_118,plain,
and(not(not(X)),X_245) = and(X,X_245),
inference(subst,[],[refute_0_107:[bind(X_34,$fot(X_245))]]) ).
cnf(refute_0_119,plain,
( and(not(not(X)),X_245) != and(X,X_245)
| ~ is_a_theorem(implies(and(not(not(X)),X_245),not(not(not(not(not(not(X))))))))
| is_a_theorem(implies(and(X,X_245),not(not(not(not(not(not(X)))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(not(X)),X_245),not(not(not(not(not(not(X)))))))) ),[0,0],$fot(and(X,X_245))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(and(not(not(X)),X_245),not(not(not(not(not(not(X))))))))
| is_a_theorem(implies(and(X,X_245),not(not(not(not(not(not(X)))))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_245),and(X,X_245)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
is_a_theorem(implies(and(X,X_245),not(not(not(not(not(not(X)))))))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(not(X)),X_245),not(not(not(not(not(not(X)))))))) )],[refute_0_117,refute_0_120]) ).
cnf(refute_0_122,plain,
is_a_theorem(implies(and(not(not(X)),X_509),not(not(not(not(not(not(not(not(X)))))))))),
inference(subst,[],[refute_0_121:[bind(X,$fot(not(not(X)))),bind(X_245,$fot(X_509))]]) ).
cnf(refute_0_123,plain,
and(not(not(X)),X_509) = and(X,X_509),
inference(subst,[],[refute_0_107:[bind(X_34,$fot(X_509))]]) ).
cnf(refute_0_124,plain,
( and(not(not(X)),X_509) != and(X,X_509)
| ~ is_a_theorem(implies(and(not(not(X)),X_509),not(not(not(not(not(not(not(not(X))))))))))
| is_a_theorem(implies(and(X,X_509),not(not(not(not(not(not(not(not(X)))))))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(and(not(not(X)),X_509),not(not(not(not(not(not(not(not(X)))))))))) ),[0,0],$fot(and(X,X_509))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(and(not(not(X)),X_509),not(not(not(not(not(not(not(not(X))))))))))
| is_a_theorem(implies(and(X,X_509),not(not(not(not(not(not(not(not(X)))))))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_509),and(X,X_509)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(and(X,X_509),not(not(not(not(not(not(not(not(X)))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(not(X)),X_509),not(not(not(not(not(not(not(not(X)))))))))) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(and(X_4398,X_4398),not(not(not(not(not(not(not(not(X_4398)))))))))),
inference(subst,[],[refute_0_126:[bind(X,$fot(X_4398)),bind(X_509,$fot(X_4398))]]) ).
cnf(refute_0_128,plain,
( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_129,plain,
kn1,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(P,and(P,P))),
inference(resolve,[$cnf( kn1 )],[refute_0_129,refute_0_128]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(X_1997,and(X_1997,X_1997))),
inference(subst,[],[refute_0_130:[bind(P,$fot(X_1997))]]) ).
cnf(refute_0_132,plain,
( ~ is_a_theorem(implies(X_137,X_138))
| ~ is_a_theorem(implies(implies(X_137,X_138),or(and(X_138,X_139),not(and(X_139,X_137)))))
| is_a_theorem(or(and(X_138,X_139),not(and(X_139,X_137)))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X_137,X_138))),bind(Y,$fot(or(and(X_138,X_139),not(and(X_139,X_137)))))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(X_137,X_138),or(and(X_138,X_139),not(and(X_139,X_137))))),
inference(subst,[],[refute_0_72:[bind(P,$fot(X_137)),bind(Q,$fot(X_138)),bind(R,$fot(X_139))]]) ).
cnf(refute_0_134,plain,
( ~ is_a_theorem(implies(X_137,X_138))
| is_a_theorem(or(and(X_138,X_139),not(and(X_139,X_137)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_137,X_138),or(and(X_138,X_139),not(and(X_139,X_137))))) )],[refute_0_133,refute_0_132]) ).
cnf(refute_0_135,plain,
( ~ is_a_theorem(implies(X_1997,and(X_1997,X_1997)))
| is_a_theorem(or(and(and(X_1997,X_1997),X_1999),not(and(X_1999,X_1997)))) ),
inference(subst,[],[refute_0_134:[bind(X_137,$fot(X_1997)),bind(X_138,$fot(and(X_1997,X_1997))),bind(X_139,$fot(X_1999))]]) ).
cnf(refute_0_136,plain,
is_a_theorem(or(and(and(X_1997,X_1997),X_1999),not(and(X_1999,X_1997)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1997,and(X_1997,X_1997))) )],[refute_0_131,refute_0_135]) ).
cnf(refute_0_137,plain,
is_a_theorem(or(and(and(not(not(X)),not(not(X))),X_2001),not(and(X_2001,not(not(X)))))),
inference(subst,[],[refute_0_136:[bind(X_1997,$fot(not(not(X)))),bind(X_1999,$fot(X_2001))]]) ).
cnf(refute_0_138,plain,
and(not(not(X)),not(not(X))) = and(X,not(not(X))),
inference(subst,[],[refute_0_107:[bind(X_34,$fot(not(not(X))))]]) ).
cnf(refute_0_139,plain,
( and(not(not(X)),not(not(X))) != and(X,not(not(X)))
| ~ is_a_theorem(or(and(and(not(not(X)),not(not(X))),X_2001),not(and(X_2001,not(not(X))))))
| is_a_theorem(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(and(not(not(X)),not(not(X))),X_2001),not(and(X_2001,not(not(X)))))) ),[0,0,0],$fot(and(X,not(not(X))))]]) ).
cnf(refute_0_140,plain,
( ~ is_a_theorem(or(and(and(not(not(X)),not(not(X))),X_2001),not(and(X_2001,not(not(X))))))
| is_a_theorem(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X)))))) ),
inference(resolve,[$cnf( $equal(and(not(not(X)),not(not(X))),and(X,not(not(X)))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
is_a_theorem(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(or(and(and(not(not(X)),not(not(X))),X_2001),not(and(X_2001,not(not(X)))))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
not(and(X_2001,not(not(X)))) = implies(X_2001,not(X)),
inference(subst,[],[refute_0_38:[bind(X,$fot(X_2001)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_143,plain,
or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))),
introduced(tautology,[refl,[$fot(or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))))]]) ).
cnf(refute_0_144,plain,
( not(and(X_2001,not(not(X)))) != implies(X_2001,not(X))
| or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))) != or(and(and(X,X),X_2001),not(and(X_2001,not(not(X)))))
| or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),implies(X_2001,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))),or(and(and(X,X),X_2001),not(and(X_2001,not(not(X)))))) ),[1,1],$fot(implies(X_2001,not(X)))]]) ).
cnf(refute_0_145,plain,
( not(and(X_2001,not(not(X)))) != implies(X_2001,not(X))
| or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),implies(X_2001,not(X))) ),
inference(resolve,[$cnf( $equal(or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))),or(and(and(X,X),X_2001),not(and(X_2001,not(not(X)))))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),implies(X_2001,not(X))),
inference(resolve,[$cnf( $equal(not(and(X_2001,not(not(X)))),implies(X_2001,not(X))) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
not(implies(X,not(X))) = and(X,X),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X))]]) ).
cnf(refute_0_148,plain,
and(not(implies(X,not(X))),X_2001) = and(not(implies(X,not(X))),X_2001),
introduced(tautology,[refl,[$fot(and(not(implies(X,not(X))),X_2001))]]) ).
cnf(refute_0_149,plain,
( and(not(implies(X,not(X))),X_2001) != and(not(implies(X,not(X))),X_2001)
| not(implies(X,not(X))) != and(X,X)
| and(not(implies(X,not(X))),X_2001) = and(and(X,X),X_2001) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(implies(X,not(X))),X_2001),and(not(implies(X,not(X))),X_2001)) ),[1,0],$fot(and(X,X))]]) ).
cnf(refute_0_150,plain,
( not(implies(X,not(X))) != and(X,X)
| and(not(implies(X,not(X))),X_2001) = and(and(X,X),X_2001) ),
inference(resolve,[$cnf( $equal(and(not(implies(X,not(X))),X_2001),and(not(implies(X,not(X))),X_2001)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
and(not(implies(X,not(X))),X_2001) = and(and(X,X),X_2001),
inference(resolve,[$cnf( $equal(not(implies(X,not(X))),and(X,X)) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
and(not(not(and(X,not(Y)))),X_37) = and(and(X,not(Y)),X_37),
inference(subst,[],[refute_0_107:[bind(X,$fot(and(X,not(Y)))),bind(X_34,$fot(X_37))]]) ).
cnf(refute_0_153,plain,
( and(not(not(and(X,not(Y)))),X_37) != and(and(X,not(Y)),X_37)
| not(and(X,not(Y))) != implies(X,Y)
| and(not(implies(X,Y)),X_37) = and(and(X,not(Y)),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(and(X,not(Y)))),X_37),and(and(X,not(Y)),X_37)) ),[0,0,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_154,plain,
( and(not(not(and(X,not(Y)))),X_37) != and(and(X,not(Y)),X_37)
| and(not(implies(X,Y)),X_37) = and(and(X,not(Y)),X_37) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_38,refute_0_153]) ).
cnf(refute_0_155,plain,
and(not(implies(X,Y)),X_37) = and(and(X,not(Y)),X_37),
inference(resolve,[$cnf( $equal(and(not(not(and(X,not(Y)))),X_37),and(and(X,not(Y)),X_37)) )],[refute_0_152,refute_0_154]) ).
cnf(refute_0_156,plain,
( and(not(implies(X,Y)),X_37) != and(and(X,not(Y)),X_37)
| and(and(X,not(Y)),X_37) = and(not(implies(X,Y)),X_37) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(and(not(implies(X,Y)),X_37))),bind(Y0,$fot(and(and(X,not(Y)),X_37)))]]) ).
cnf(refute_0_157,plain,
and(and(X,not(Y)),X_37) = and(not(implies(X,Y)),X_37),
inference(resolve,[$cnf( $equal(and(not(implies(X,Y)),X_37),and(and(X,not(Y)),X_37)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
and(and(X,not(not(X))),X_2001) = and(not(implies(X,not(X))),X_2001),
inference(subst,[],[refute_0_157:[bind(Y,$fot(not(X))),bind(X_37,$fot(X_2001))]]) ).
cnf(refute_0_159,plain,
( and(and(X,not(not(X))),X_2001) != and(not(implies(X,not(X))),X_2001)
| and(not(implies(X,not(X))),X_2001) != and(and(X,X),X_2001)
| and(and(X,not(not(X))),X_2001) = and(and(X,X),X_2001) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(and(and(X,not(not(X))),X_2001))),bind(Y0,$fot(and(not(implies(X,not(X))),X_2001))),bind(Z,$fot(and(and(X,X),X_2001)))]]) ).
cnf(refute_0_160,plain,
( and(not(implies(X,not(X))),X_2001) != and(and(X,X),X_2001)
| and(and(X,not(not(X))),X_2001) = and(and(X,X),X_2001) ),
inference(resolve,[$cnf( $equal(and(and(X,not(not(X))),X_2001),and(not(implies(X,not(X))),X_2001)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
and(and(X,not(not(X))),X_2001) = and(and(X,X),X_2001),
inference(resolve,[$cnf( $equal(and(not(implies(X,not(X))),X_2001),and(and(X,X),X_2001)) )],[refute_0_151,refute_0_160]) ).
cnf(refute_0_162,plain,
or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))),
introduced(tautology,[refl,[$fot(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))))]]) ).
cnf(refute_0_163,plain,
( and(and(X,not(not(X))),X_2001) != and(and(X,X),X_2001)
| or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) != or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X)))))
| or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))),or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X)))))) ),[1,0],$fot(and(and(X,X),X_2001))]]) ).
cnf(refute_0_164,plain,
( and(and(X,not(not(X))),X_2001) != and(and(X,X),X_2001)
| or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))) ),
inference(resolve,[$cnf( $equal(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))),or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X)))))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))),
inference(resolve,[$cnf( $equal(and(and(X,not(not(X))),X_2001),and(and(X,X),X_2001)) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
( or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))) != or(and(and(X,X),X_2001),implies(X_2001,not(X)))
| or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) != or(and(and(X,X),X_2001),not(and(X_2001,not(not(X)))))
| or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),implies(X_2001,not(X))) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))))),bind(Y0,$fot(or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))))),bind(Z,$fot(or(and(and(X,X),X_2001),implies(X_2001,not(X)))))]]) ).
cnf(refute_0_167,plain,
( or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))) != or(and(and(X,X),X_2001),implies(X_2001,not(X)))
| or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),implies(X_2001,not(X))) ),
inference(resolve,[$cnf( $equal(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))),or(and(and(X,X),X_2001),not(and(X_2001,not(not(X)))))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) = or(and(and(X,X),X_2001),implies(X_2001,not(X))),
inference(resolve,[$cnf( $equal(or(and(and(X,X),X_2001),not(and(X_2001,not(not(X))))),or(and(and(X,X),X_2001),implies(X_2001,not(X)))) )],[refute_0_146,refute_0_167]) ).
cnf(refute_0_169,plain,
( or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))) != or(and(and(X,X),X_2001),implies(X_2001,not(X)))
| ~ is_a_theorem(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))))
| is_a_theorem(or(and(and(X,X),X_2001),implies(X_2001,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X)))))) ),[0],$fot(or(and(and(X,X),X_2001),implies(X_2001,not(X))))]]) ).
cnf(refute_0_170,plain,
( ~ is_a_theorem(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))))
| is_a_theorem(or(and(and(X,X),X_2001),implies(X_2001,not(X)))) ),
inference(resolve,[$cnf( $equal(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X))))),or(and(and(X,X),X_2001),implies(X_2001,not(X)))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
is_a_theorem(or(and(and(X,X),X_2001),implies(X_2001,not(X)))),
inference(resolve,[$cnf( is_a_theorem(or(and(and(X,not(not(X))),X_2001),not(and(X_2001,not(not(X)))))) )],[refute_0_141,refute_0_170]) ).
cnf(refute_0_172,plain,
is_a_theorem(or(and(and(X,X),X_4395),implies(X_4395,not(X)))),
inference(subst,[],[refute_0_171:[bind(X_2001,$fot(X_4395))]]) ).
cnf(refute_0_173,plain,
( ~ is_a_theorem(implies(X,not(Y)))
| ~ is_a_theorem(implies(implies(X,not(Y)),X_60))
| is_a_theorem(X_60) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_60))]]) ).
cnf(refute_0_174,plain,
implies(implies(X,not(Y)),X_9) = or(not(implies(X,not(Y))),X_9),
inference(subst,[],[refute_0_19:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_175,plain,
( implies(implies(X,not(Y)),X_9) != or(not(implies(X,not(Y))),X_9)
| not(implies(X,not(Y))) != and(X,Y)
| implies(implies(X,not(Y)),X_9) = or(and(X,Y),X_9) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(Y)),X_9),or(not(implies(X,not(Y))),X_9)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_176,plain,
( implies(implies(X,not(Y)),X_9) != or(not(implies(X,not(Y))),X_9)
| implies(implies(X,not(Y)),X_9) = or(and(X,Y),X_9) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_60,refute_0_175]) ).
cnf(refute_0_177,plain,
implies(implies(X,not(Y)),X_9) = or(and(X,Y),X_9),
inference(resolve,[$cnf( $equal(implies(implies(X,not(Y)),X_9),or(not(implies(X,not(Y))),X_9)) )],[refute_0_174,refute_0_176]) ).
cnf(refute_0_178,plain,
implies(implies(X,not(Y)),X_60) = or(and(X,Y),X_60),
inference(subst,[],[refute_0_177:[bind(X_9,$fot(X_60))]]) ).
cnf(refute_0_179,plain,
( implies(implies(X,not(Y)),X_60) != or(and(X,Y),X_60)
| ~ is_a_theorem(or(and(X,Y),X_60))
| is_a_theorem(implies(implies(X,not(Y)),X_60)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(implies(X,not(Y)),X_60)) ),[0],$fot(or(and(X,Y),X_60))]]) ).
cnf(refute_0_180,plain,
( ~ is_a_theorem(or(and(X,Y),X_60))
| is_a_theorem(implies(implies(X,not(Y)),X_60)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(Y)),X_60),or(and(X,Y),X_60)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
( ~ is_a_theorem(implies(X,not(Y)))
| ~ is_a_theorem(or(and(X,Y),X_60))
| is_a_theorem(X_60) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(Y)),X_60)) )],[refute_0_180,refute_0_173]) ).
cnf(refute_0_182,plain,
( ~ is_a_theorem(implies(and(X,X),not(X_4395)))
| ~ is_a_theorem(or(and(and(X,X),X_4395),implies(X_4395,not(X))))
| is_a_theorem(implies(X_4395,not(X))) ),
inference(subst,[],[refute_0_181:[bind(X,$fot(and(X,X))),bind(Y,$fot(X_4395)),bind(X_60,$fot(implies(X_4395,not(X))))]]) ).
cnf(refute_0_183,plain,
( ~ is_a_theorem(implies(and(X,X),not(X_4395)))
| is_a_theorem(implies(X_4395,not(X))) ),
inference(resolve,[$cnf( is_a_theorem(or(and(and(X,X),X_4395),implies(X_4395,not(X)))) )],[refute_0_172,refute_0_182]) ).
cnf(refute_0_184,plain,
( ~ is_a_theorem(implies(and(X_4398,X_4398),not(not(not(not(not(not(not(not(X_4398))))))))))
| is_a_theorem(implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398))) ),
inference(subst,[],[refute_0_183:[bind(X,$fot(X_4398)),bind(X_4395,$fot(not(not(not(not(not(not(not(X_4398)))))))))]]) ).
cnf(refute_0_185,plain,
is_a_theorem(implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_4398,X_4398),not(not(not(not(not(not(not(not(X_4398)))))))))) )],[refute_0_127,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(not(X_4398),not(X_4398)) = or(X_4398,not(X_4398)),
inference(subst,[],[refute_0_81:[bind(X,$fot(X_4398)),bind(Y,$fot(not(X_4398)))]]) ).
cnf(refute_0_187,plain,
or(not(not(X_4398)),not(X_4398)) = implies(not(X_4398),not(X_4398)),
inference(subst,[],[refute_0_24:[bind(X,$fot(not(X_4398))),bind(Y,$fot(not(X_4398)))]]) ).
cnf(refute_0_188,plain,
( implies(not(X_4398),not(X_4398)) != or(X_4398,not(X_4398))
| or(not(not(X_4398)),not(X_4398)) != implies(not(X_4398),not(X_4398))
| or(not(not(X_4398)),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(or(not(not(X_4398)),not(X_4398)))),bind(Y0,$fot(implies(not(X_4398),not(X_4398)))),bind(Z,$fot(or(X_4398,not(X_4398))))]]) ).
cnf(refute_0_189,plain,
( implies(not(X_4398),not(X_4398)) != or(X_4398,not(X_4398))
| or(not(not(X_4398)),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(resolve,[$cnf( $equal(or(not(not(X_4398)),not(X_4398)),implies(not(X_4398),not(X_4398))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
or(not(not(X_4398)),not(X_4398)) = or(X_4398,not(X_4398)),
inference(resolve,[$cnf( $equal(implies(not(X_4398),not(X_4398)),or(X_4398,not(X_4398))) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
implies(not(not(not(X_4398))),not(X_4398)) = or(not(not(X_4398)),not(X_4398)),
inference(subst,[],[refute_0_81:[bind(X,$fot(not(not(X_4398)))),bind(Y,$fot(not(X_4398)))]]) ).
cnf(refute_0_192,plain,
( implies(not(not(not(X_4398))),not(X_4398)) != or(not(not(X_4398)),not(X_4398))
| or(not(not(X_4398)),not(X_4398)) != or(X_4398,not(X_4398))
| implies(not(not(not(X_4398))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(implies(not(not(not(X_4398))),not(X_4398)))),bind(Y0,$fot(or(not(not(X_4398)),not(X_4398)))),bind(Z,$fot(or(X_4398,not(X_4398))))]]) ).
cnf(refute_0_193,plain,
( or(not(not(X_4398)),not(X_4398)) != or(X_4398,not(X_4398))
| implies(not(not(not(X_4398))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_4398))),not(X_4398)),or(not(not(X_4398)),not(X_4398))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
implies(not(not(not(X_4398))),not(X_4398)) = or(X_4398,not(X_4398)),
inference(resolve,[$cnf( $equal(or(not(not(X_4398)),not(X_4398)),or(X_4398,not(X_4398))) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
or(not(not(not(not(X_4398)))),not(X_4398)) = implies(not(not(not(X_4398))),not(X_4398)),
inference(subst,[],[refute_0_24:[bind(X,$fot(not(not(not(X_4398))))),bind(Y,$fot(not(X_4398)))]]) ).
cnf(refute_0_196,plain,
( implies(not(not(not(X_4398))),not(X_4398)) != or(X_4398,not(X_4398))
| or(not(not(not(not(X_4398)))),not(X_4398)) != implies(not(not(not(X_4398))),not(X_4398))
| or(not(not(not(not(X_4398)))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(or(not(not(not(not(X_4398)))),not(X_4398)))),bind(Y0,$fot(implies(not(not(not(X_4398))),not(X_4398)))),bind(Z,$fot(or(X_4398,not(X_4398))))]]) ).
cnf(refute_0_197,plain,
( implies(not(not(not(X_4398))),not(X_4398)) != or(X_4398,not(X_4398))
| or(not(not(not(not(X_4398)))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(X_4398)))),not(X_4398)),implies(not(not(not(X_4398))),not(X_4398))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
or(not(not(not(not(X_4398)))),not(X_4398)) = or(X_4398,not(X_4398)),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_4398))),not(X_4398)),or(X_4398,not(X_4398))) )],[refute_0_194,refute_0_197]) ).
cnf(refute_0_199,plain,
implies(not(not(not(not(not(X_4398))))),not(X_4398)) = or(not(not(not(not(X_4398)))),not(X_4398)),
inference(subst,[],[refute_0_81:[bind(X,$fot(not(not(not(not(X_4398)))))),bind(Y,$fot(not(X_4398)))]]) ).
cnf(refute_0_200,plain,
( implies(not(not(not(not(not(X_4398))))),not(X_4398)) != or(not(not(not(not(X_4398)))),not(X_4398))
| or(not(not(not(not(X_4398)))),not(X_4398)) != or(X_4398,not(X_4398))
| implies(not(not(not(not(not(X_4398))))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(implies(not(not(not(not(not(X_4398))))),not(X_4398)))),bind(Y0,$fot(or(not(not(not(not(X_4398)))),not(X_4398)))),bind(Z,$fot(or(X_4398,not(X_4398))))]]) ).
cnf(refute_0_201,plain,
( or(not(not(not(not(X_4398)))),not(X_4398)) != or(X_4398,not(X_4398))
| implies(not(not(not(not(not(X_4398))))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(X_4398))))),not(X_4398)),or(not(not(not(not(X_4398)))),not(X_4398))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
implies(not(not(not(not(not(X_4398))))),not(X_4398)) = or(X_4398,not(X_4398)),
inference(resolve,[$cnf( $equal(or(not(not(not(not(X_4398)))),not(X_4398)),or(X_4398,not(X_4398))) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
or(not(not(not(not(not(not(X_4398)))))),not(X_4398)) = implies(not(not(not(not(not(X_4398))))),not(X_4398)),
inference(subst,[],[refute_0_24:[bind(X,$fot(not(not(not(not(not(X_4398))))))),bind(Y,$fot(not(X_4398)))]]) ).
cnf(refute_0_204,plain,
( implies(not(not(not(not(not(X_4398))))),not(X_4398)) != or(X_4398,not(X_4398))
| or(not(not(not(not(not(not(X_4398)))))),not(X_4398)) != implies(not(not(not(not(not(X_4398))))),not(X_4398))
| or(not(not(not(not(not(not(X_4398)))))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(or(not(not(not(not(not(not(X_4398)))))),not(X_4398)))),bind(Y0,$fot(implies(not(not(not(not(not(X_4398))))),not(X_4398)))),bind(Z,$fot(or(X_4398,not(X_4398))))]]) ).
cnf(refute_0_205,plain,
( implies(not(not(not(not(not(X_4398))))),not(X_4398)) != or(X_4398,not(X_4398))
| or(not(not(not(not(not(not(X_4398)))))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(X_4398)))))),not(X_4398)),implies(not(not(not(not(not(X_4398))))),not(X_4398))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
or(not(not(not(not(not(not(X_4398)))))),not(X_4398)) = or(X_4398,not(X_4398)),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(X_4398))))),not(X_4398)),or(X_4398,not(X_4398))) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)) = or(not(not(not(not(not(not(X_4398)))))),not(X_4398)),
inference(subst,[],[refute_0_81:[bind(X,$fot(not(not(not(not(not(not(X_4398)))))))),bind(Y,$fot(not(X_4398)))]]) ).
cnf(refute_0_208,plain,
( implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)) != or(not(not(not(not(not(not(X_4398)))))),not(X_4398))
| or(not(not(not(not(not(not(X_4398)))))),not(X_4398)) != or(X_4398,not(X_4398))
| implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)))),bind(Y0,$fot(or(not(not(not(not(not(not(X_4398)))))),not(X_4398)))),bind(Z,$fot(or(X_4398,not(X_4398))))]]) ).
cnf(refute_0_209,plain,
( or(not(not(not(not(not(not(X_4398)))))),not(X_4398)) != or(X_4398,not(X_4398))
| implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)) = or(X_4398,not(X_4398)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)),or(not(not(not(not(not(not(X_4398)))))),not(X_4398))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)) = or(X_4398,not(X_4398)),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(not(X_4398)))))),not(X_4398)),or(X_4398,not(X_4398))) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
( implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)) != or(X_4398,not(X_4398))
| ~ is_a_theorem(implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)))
| is_a_theorem(or(X_4398,not(X_4398))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398))) ),[0],$fot(or(X_4398,not(X_4398)))]]) ).
cnf(refute_0_212,plain,
( ~ is_a_theorem(implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)))
| is_a_theorem(or(X_4398,not(X_4398))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398)),or(X_4398,not(X_4398))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
is_a_theorem(or(X_4398,not(X_4398))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(not(not(not(not(X_4398))))))),not(X_4398))) )],[refute_0_185,refute_0_212]) ).
cnf(refute_0_214,plain,
is_a_theorem(or(X_4400,not(X_4400))),
inference(subst,[],[refute_0_213:[bind(X_4398,$fot(X_4400))]]) ).
cnf(refute_0_215,plain,
is_a_theorem(or(and(not(X_4400),X_201),implies(X_201,X_4400))),
inference(resolve,[$cnf( is_a_theorem(or(X_4400,not(X_4400))) )],[refute_0_214,refute_0_92]) ).
cnf(refute_0_216,plain,
implies(or(X_35,not(X_34)),Y) = or(not(or(X_35,not(X_34))),Y),
inference(subst,[],[refute_0_19:[bind(X,$fot(or(X_35,not(X_34))))]]) ).
cnf(refute_0_217,plain,
( implies(or(X_35,not(X_34)),Y) != or(not(or(X_35,not(X_34))),Y)
| not(or(X_35,not(X_34))) != and(not(X_35),X_34)
| implies(or(X_35,not(X_34)),Y) = or(and(not(X_35),X_34),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_35,not(X_34)),Y),or(not(or(X_35,not(X_34))),Y)) ),[1,0],$fot(and(not(X_35),X_34))]]) ).
cnf(refute_0_218,plain,
( implies(or(X_35,not(X_34)),Y) != or(not(or(X_35,not(X_34))),Y)
| implies(or(X_35,not(X_34)),Y) = or(and(not(X_35),X_34),Y) ),
inference(resolve,[$cnf( $equal(not(or(X_35,not(X_34))),and(not(X_35),X_34)) )],[refute_0_51,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(or(X_35,not(X_34)),Y) = or(and(not(X_35),X_34),Y),
inference(resolve,[$cnf( $equal(implies(or(X_35,not(X_34)),Y),or(not(or(X_35,not(X_34))),Y)) )],[refute_0_216,refute_0_218]) ).
cnf(refute_0_220,plain,
( implies(or(X_35,not(X_34)),Y) != or(and(not(X_35),X_34),Y)
| or(and(not(X_35),X_34),Y) = implies(or(X_35,not(X_34)),Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(implies(or(X_35,not(X_34)),Y))),bind(Y0,$fot(or(and(not(X_35),X_34),Y)))]]) ).
cnf(refute_0_221,plain,
or(and(not(X_35),X_34),Y) = implies(or(X_35,not(X_34)),Y),
inference(resolve,[$cnf( $equal(implies(or(X_35,not(X_34)),Y),or(and(not(X_35),X_34),Y)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
or(and(not(X_4400),X_201),implies(X_201,X_4400)) = implies(or(X_4400,not(X_201)),implies(X_201,X_4400)),
inference(subst,[],[refute_0_221:[bind(Y,$fot(implies(X_201,X_4400))),bind(X_34,$fot(X_201)),bind(X_35,$fot(X_4400))]]) ).
cnf(refute_0_223,plain,
( or(and(not(X_4400),X_201),implies(X_201,X_4400)) != implies(or(X_4400,not(X_201)),implies(X_201,X_4400))
| ~ is_a_theorem(or(and(not(X_4400),X_201),implies(X_201,X_4400)))
| is_a_theorem(implies(or(X_4400,not(X_201)),implies(X_201,X_4400))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X_4400),X_201),implies(X_201,X_4400))) ),[0],$fot(implies(or(X_4400,not(X_201)),implies(X_201,X_4400)))]]) ).
cnf(refute_0_224,plain,
( ~ is_a_theorem(or(and(not(X_4400),X_201),implies(X_201,X_4400)))
| is_a_theorem(implies(or(X_4400,not(X_201)),implies(X_201,X_4400))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_4400),X_201),implies(X_201,X_4400)),implies(or(X_4400,not(X_201)),implies(X_201,X_4400))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
is_a_theorem(implies(or(X_4400,not(X_201)),implies(X_201,X_4400))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X_4400),X_201),implies(X_201,X_4400))) )],[refute_0_215,refute_0_224]) ).
cnf(refute_0_226,plain,
is_a_theorem(implies(or(X_4426,not(not(X))),implies(not(X),X_4426))),
inference(subst,[],[refute_0_225:[bind(X_201,$fot(not(X))),bind(X_4400,$fot(X_4426))]]) ).
cnf(refute_0_227,plain,
or(X,X_4426) = implies(not(X),X_4426),
inference(subst,[],[refute_0_42:[bind(Y,$fot(X_4426))]]) ).
cnf(refute_0_228,plain,
( or(X,X_4426) != implies(not(X),X_4426)
| implies(not(X),X_4426) = or(X,X_4426) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(or(X,X_4426))),bind(Y0,$fot(implies(not(X),X_4426)))]]) ).
cnf(refute_0_229,plain,
implies(not(X),X_4426) = or(X,X_4426),
inference(resolve,[$cnf( $equal(or(X,X_4426),implies(not(X),X_4426)) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
( implies(not(X),X_4426) != or(X,X_4426)
| ~ is_a_theorem(implies(or(X_4426,not(not(X))),implies(not(X),X_4426)))
| is_a_theorem(implies(or(X_4426,not(not(X))),or(X,X_4426))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_4426,not(not(X))),implies(not(X),X_4426))) ),[0,1],$fot(or(X,X_4426))]]) ).
cnf(refute_0_231,plain,
( ~ is_a_theorem(implies(or(X_4426,not(not(X))),implies(not(X),X_4426)))
| is_a_theorem(implies(or(X_4426,not(not(X))),or(X,X_4426))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_4426),or(X,X_4426)) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
is_a_theorem(implies(or(X_4426,not(not(X))),or(X,X_4426))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_4426,not(not(X))),implies(not(X),X_4426))) )],[refute_0_226,refute_0_231]) ).
cnf(refute_0_233,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_234,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_235,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_234,refute_0_233]) ).
cnf(refute_0_236,plain,
( ~ is_a_theorem(equiv(not(not(X_101)),Y))
| not(not(X_101)) = Y ),
inference(subst,[],[refute_0_235:[bind(X,$fot(not(not(X_101))))]]) ).
cnf(refute_0_237,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_238,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_239,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_238,refute_0_237]) ).
cnf(refute_0_240,plain,
equiv(not(X),X_14) = and(implies(not(X),X_14),implies(X_14,not(X))),
inference(subst,[],[refute_0_239:[bind(X,$fot(not(X))),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_241,plain,
or(X,X_14) = implies(not(X),X_14),
inference(subst,[],[refute_0_42:[bind(Y,$fot(X_14))]]) ).
cnf(refute_0_242,plain,
( or(X,X_14) != implies(not(X),X_14)
| implies(not(X),X_14) = or(X,X_14) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(or(X,X_14))),bind(Y0,$fot(implies(not(X),X_14)))]]) ).
cnf(refute_0_243,plain,
implies(not(X),X_14) = or(X,X_14),
inference(resolve,[$cnf( $equal(or(X,X_14),implies(not(X),X_14)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
( equiv(not(X),X_14) != and(implies(not(X),X_14),implies(X_14,not(X)))
| implies(not(X),X_14) != or(X,X_14)
| equiv(not(X),X_14) = and(or(X,X_14),implies(X_14,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X),X_14),and(implies(not(X),X_14),implies(X_14,not(X)))) ),[1,0],$fot(or(X,X_14))]]) ).
cnf(refute_0_245,plain,
( equiv(not(X),X_14) != and(implies(not(X),X_14),implies(X_14,not(X)))
| equiv(not(X),X_14) = and(or(X,X_14),implies(X_14,not(X))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_14),or(X,X_14)) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
equiv(not(X),X_14) = and(or(X,X_14),implies(X_14,not(X))),
inference(resolve,[$cnf( $equal(equiv(not(X),X_14),and(implies(not(X),X_14),implies(X_14,not(X)))) )],[refute_0_240,refute_0_245]) ).
cnf(refute_0_247,plain,
and(X,implies(X_1,not(X_2))) = not(implies(X,not(implies(X_1,not(X_2))))),
inference(subst,[],[refute_0_32:[bind(Y,$fot(implies(X_1,not(X_2))))]]) ).
cnf(refute_0_248,plain,
and(X_1,X_2) = not(implies(X_1,not(X_2))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_1)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_249,plain,
( and(X_1,X_2) != not(implies(X_1,not(X_2)))
| not(implies(X_1,not(X_2))) = and(X_1,X_2) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(and(X_1,X_2))),bind(Y0,$fot(not(implies(X_1,not(X_2)))))]]) ).
cnf(refute_0_250,plain,
not(implies(X_1,not(X_2))) = and(X_1,X_2),
inference(resolve,[$cnf( $equal(and(X_1,X_2),not(implies(X_1,not(X_2)))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
( and(X,implies(X_1,not(X_2))) != not(implies(X,not(implies(X_1,not(X_2)))))
| not(implies(X_1,not(X_2))) != and(X_1,X_2)
| and(X,implies(X_1,not(X_2))) = not(implies(X,and(X_1,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(X_1,not(X_2))),not(implies(X,not(implies(X_1,not(X_2)))))) ),[1,0,1],$fot(and(X_1,X_2))]]) ).
cnf(refute_0_252,plain,
( and(X,implies(X_1,not(X_2))) != not(implies(X,not(implies(X_1,not(X_2)))))
| and(X,implies(X_1,not(X_2))) = not(implies(X,and(X_1,X_2))) ),
inference(resolve,[$cnf( $equal(not(implies(X_1,not(X_2))),and(X_1,X_2)) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
and(X,implies(X_1,not(X_2))) = not(implies(X,and(X_1,X_2))),
inference(resolve,[$cnf( $equal(and(X,implies(X_1,not(X_2))),not(implies(X,not(implies(X_1,not(X_2)))))) )],[refute_0_247,refute_0_252]) ).
cnf(refute_0_254,plain,
and(or(X,X_14),implies(X_14,not(X))) = not(implies(or(X,X_14),and(X_14,X))),
inference(subst,[],[refute_0_253:[bind(X,$fot(or(X,X_14))),bind(X_1,$fot(X_14)),bind(X_2,$fot(X))]]) ).
cnf(refute_0_255,plain,
( and(or(X,X_14),implies(X_14,not(X))) != not(implies(or(X,X_14),and(X_14,X)))
| equiv(not(X),X_14) != and(or(X,X_14),implies(X_14,not(X)))
| equiv(not(X),X_14) = not(implies(or(X,X_14),and(X_14,X))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X),X_14),and(or(X,X_14),implies(X_14,not(X)))) ),[1],$fot(not(implies(or(X,X_14),and(X_14,X))))]]) ).
cnf(refute_0_256,plain,
( equiv(not(X),X_14) != and(or(X,X_14),implies(X_14,not(X)))
| equiv(not(X),X_14) = not(implies(or(X,X_14),and(X_14,X))) ),
inference(resolve,[$cnf( $equal(and(or(X,X_14),implies(X_14,not(X))),not(implies(or(X,X_14),and(X_14,X)))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
equiv(not(X),X_14) = not(implies(or(X,X_14),and(X_14,X))),
inference(resolve,[$cnf( $equal(equiv(not(X),X_14),and(or(X,X_14),implies(X_14,not(X)))) )],[refute_0_246,refute_0_256]) ).
cnf(refute_0_258,plain,
equiv(not(not(X)),X_29) = not(implies(or(not(X),X_29),and(X_29,not(X)))),
inference(subst,[],[refute_0_257:[bind(X,$fot(not(X))),bind(X_14,$fot(X_29))]]) ).
cnf(refute_0_259,plain,
implies(X,X_29) = or(not(X),X_29),
inference(subst,[],[refute_0_19:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_260,plain,
( implies(X,X_29) != or(not(X),X_29)
| or(not(X),X_29) = implies(X,X_29) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(implies(X,X_29))),bind(Y0,$fot(or(not(X),X_29)))]]) ).
cnf(refute_0_261,plain,
or(not(X),X_29) = implies(X,X_29),
inference(resolve,[$cnf( $equal(implies(X,X_29),or(not(X),X_29)) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
( equiv(not(not(X)),X_29) != not(implies(or(not(X),X_29),and(X_29,not(X))))
| or(not(X),X_29) != implies(X,X_29)
| equiv(not(not(X)),X_29) = not(implies(implies(X,X_29),and(X_29,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(not(X)),X_29),not(implies(or(not(X),X_29),and(X_29,not(X))))) ),[1,0,0],$fot(implies(X,X_29))]]) ).
cnf(refute_0_263,plain,
( equiv(not(not(X)),X_29) != not(implies(or(not(X),X_29),and(X_29,not(X))))
| equiv(not(not(X)),X_29) = not(implies(implies(X,X_29),and(X_29,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_29),implies(X,X_29)) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
equiv(not(not(X)),X_29) = not(implies(implies(X,X_29),and(X_29,not(X)))),
inference(resolve,[$cnf( $equal(equiv(not(not(X)),X_29),not(implies(or(not(X),X_29),and(X_29,not(X))))) )],[refute_0_258,refute_0_263]) ).
cnf(refute_0_265,plain,
( equiv(X,Y) != and(implies(X,Y),implies(Y,X))
| and(implies(X,Y),implies(Y,X)) = equiv(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_266,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_239,refute_0_265]) ).
cnf(refute_0_267,plain,
and(implies(X,X_29),implies(X_29,X)) = equiv(X,X_29),
inference(subst,[],[refute_0_266:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_268,plain,
not(and(implies(X,X_29),implies(X_29,X))) = not(and(implies(X,X_29),implies(X_29,X))),
introduced(tautology,[refl,[$fot(not(and(implies(X,X_29),implies(X_29,X))))]]) ).
cnf(refute_0_269,plain,
( and(implies(X,X_29),implies(X_29,X)) != equiv(X,X_29)
| not(and(implies(X,X_29),implies(X_29,X))) != not(and(implies(X,X_29),implies(X_29,X)))
| not(and(implies(X,X_29),implies(X_29,X))) = not(equiv(X,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X,X_29),implies(X_29,X))),not(and(implies(X,X_29),implies(X_29,X)))) ),[1,0],$fot(equiv(X,X_29))]]) ).
cnf(refute_0_270,plain,
( and(implies(X,X_29),implies(X_29,X)) != equiv(X,X_29)
| not(and(implies(X,X_29),implies(X_29,X))) = not(equiv(X,X_29)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,X_29),implies(X_29,X))),not(and(implies(X,X_29),implies(X_29,X)))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
not(and(implies(X,X_29),implies(X_29,X))) = not(equiv(X,X_29)),
inference(resolve,[$cnf( $equal(and(implies(X,X_29),implies(X_29,X)),equiv(X,X_29)) )],[refute_0_267,refute_0_270]) ).
cnf(refute_0_272,plain,
implies(X,and(X_10,not(X_11))) = not(and(X,not(and(X_10,not(X_11))))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(and(X_10,not(X_11))))]]) ).
cnf(refute_0_273,plain,
implies(X_10,X_11) = not(and(X_10,not(X_11))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_274,plain,
( implies(X_10,X_11) != not(and(X_10,not(X_11)))
| not(and(X_10,not(X_11))) = implies(X_10,X_11) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(implies(X_10,X_11))),bind(Y0,$fot(not(and(X_10,not(X_11)))))]]) ).
cnf(refute_0_275,plain,
not(and(X_10,not(X_11))) = implies(X_10,X_11),
inference(resolve,[$cnf( $equal(implies(X_10,X_11),not(and(X_10,not(X_11)))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
( implies(X,and(X_10,not(X_11))) != not(and(X,not(and(X_10,not(X_11)))))
| not(and(X_10,not(X_11))) != implies(X_10,X_11)
| implies(X,and(X_10,not(X_11))) = not(and(X,implies(X_10,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_10,not(X_11))),not(and(X,not(and(X_10,not(X_11)))))) ),[1,0,1],$fot(implies(X_10,X_11))]]) ).
cnf(refute_0_277,plain,
( implies(X,and(X_10,not(X_11))) != not(and(X,not(and(X_10,not(X_11)))))
| implies(X,and(X_10,not(X_11))) = not(and(X,implies(X_10,X_11))) ),
inference(resolve,[$cnf( $equal(not(and(X_10,not(X_11))),implies(X_10,X_11)) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
implies(X,and(X_10,not(X_11))) = not(and(X,implies(X_10,X_11))),
inference(resolve,[$cnf( $equal(implies(X,and(X_10,not(X_11))),not(and(X,not(and(X_10,not(X_11)))))) )],[refute_0_272,refute_0_277]) ).
cnf(refute_0_279,plain,
implies(implies(X,X_29),and(X_29,not(X))) = not(and(implies(X,X_29),implies(X_29,X))),
inference(subst,[],[refute_0_278:[bind(X,$fot(implies(X,X_29))),bind(X_10,$fot(X_29)),bind(X_11,$fot(X))]]) ).
cnf(refute_0_280,plain,
( implies(implies(X,X_29),and(X_29,not(X))) != not(and(implies(X,X_29),implies(X_29,X)))
| not(and(implies(X,X_29),implies(X_29,X))) != not(equiv(X,X_29))
| implies(implies(X,X_29),and(X_29,not(X))) = not(equiv(X,X_29)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(implies(implies(X,X_29),and(X_29,not(X))))),bind(Y0,$fot(not(and(implies(X,X_29),implies(X_29,X))))),bind(Z,$fot(not(equiv(X,X_29))))]]) ).
cnf(refute_0_281,plain,
( not(and(implies(X,X_29),implies(X_29,X))) != not(equiv(X,X_29))
| implies(implies(X,X_29),and(X_29,not(X))) = not(equiv(X,X_29)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_29),and(X_29,not(X))),not(and(implies(X,X_29),implies(X_29,X)))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
implies(implies(X,X_29),and(X_29,not(X))) = not(equiv(X,X_29)),
inference(resolve,[$cnf( $equal(not(and(implies(X,X_29),implies(X_29,X))),not(equiv(X,X_29))) )],[refute_0_271,refute_0_281]) ).
cnf(refute_0_283,plain,
not(implies(implies(X,X_29),and(X_29,not(X)))) = not(implies(implies(X,X_29),and(X_29,not(X)))),
introduced(tautology,[refl,[$fot(not(implies(implies(X,X_29),and(X_29,not(X)))))]]) ).
cnf(refute_0_284,plain,
( implies(implies(X,X_29),and(X_29,not(X))) != not(equiv(X,X_29))
| not(implies(implies(X,X_29),and(X_29,not(X)))) != not(implies(implies(X,X_29),and(X_29,not(X))))
| not(implies(implies(X,X_29),and(X_29,not(X)))) = not(not(equiv(X,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(X,X_29),and(X_29,not(X)))),not(implies(implies(X,X_29),and(X_29,not(X))))) ),[1,0],$fot(not(equiv(X,X_29)))]]) ).
cnf(refute_0_285,plain,
( implies(implies(X,X_29),and(X_29,not(X))) != not(equiv(X,X_29))
| not(implies(implies(X,X_29),and(X_29,not(X)))) = not(not(equiv(X,X_29))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(X,X_29),and(X_29,not(X)))),not(implies(implies(X,X_29),and(X_29,not(X))))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
not(implies(implies(X,X_29),and(X_29,not(X)))) = not(not(equiv(X,X_29))),
inference(resolve,[$cnf( $equal(implies(implies(X,X_29),and(X_29,not(X))),not(equiv(X,X_29))) )],[refute_0_282,refute_0_285]) ).
cnf(refute_0_287,plain,
( equiv(not(not(X)),X_29) != not(implies(implies(X,X_29),and(X_29,not(X))))
| not(implies(implies(X,X_29),and(X_29,not(X)))) != not(not(equiv(X,X_29)))
| equiv(not(not(X)),X_29) = not(not(equiv(X,X_29))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(equiv(not(not(X)),X_29),not(not(equiv(X,X_29)))) ),[0],$fot(not(implies(implies(X,X_29),and(X_29,not(X)))))]]) ).
cnf(refute_0_288,plain,
( equiv(not(not(X)),X_29) != not(implies(implies(X,X_29),and(X_29,not(X))))
| equiv(not(not(X)),X_29) = not(not(equiv(X,X_29))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(X,X_29),and(X_29,not(X)))),not(not(equiv(X,X_29)))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
equiv(not(not(X)),X_29) = not(not(equiv(X,X_29))),
inference(resolve,[$cnf( $equal(equiv(not(not(X)),X_29),not(implies(implies(X,X_29),and(X_29,not(X))))) )],[refute_0_264,refute_0_288]) ).
cnf(refute_0_290,plain,
equiv(not(not(X_101)),Y) = not(not(equiv(X_101,Y))),
inference(subst,[],[refute_0_289:[bind(X,$fot(X_101)),bind(X_29,$fot(Y))]]) ).
cnf(refute_0_291,plain,
( equiv(not(not(X_101)),Y) != not(not(equiv(X_101,Y)))
| ~ is_a_theorem(not(not(equiv(X_101,Y))))
| is_a_theorem(equiv(not(not(X_101)),Y)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(equiv(not(not(X_101)),Y)) ),[0],$fot(not(not(equiv(X_101,Y))))]]) ).
cnf(refute_0_292,plain,
( ~ is_a_theorem(not(not(equiv(X_101,Y))))
| is_a_theorem(equiv(not(not(X_101)),Y)) ),
inference(resolve,[$cnf( $equal(equiv(not(not(X_101)),Y),not(not(equiv(X_101,Y)))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
( ~ is_a_theorem(not(not(equiv(X_101,Y))))
| not(not(X_101)) = Y ),
inference(resolve,[$cnf( is_a_theorem(equiv(not(not(X_101)),Y)) )],[refute_0_292,refute_0_236]) ).
cnf(refute_0_294,plain,
( ~ is_a_theorem(not(not(equiv(X_4402,X_4402))))
| not(not(X_4402)) = X_4402 ),
inference(subst,[],[refute_0_293:[bind(Y,$fot(X_4402)),bind(X_101,$fot(X_4402))]]) ).
cnf(refute_0_295,plain,
is_a_theorem(implies(X_59,and(X_59,X_59))),
inference(subst,[],[refute_0_130:[bind(P,$fot(X_59))]]) ).
cnf(refute_0_296,plain,
( ~ is_a_theorem(X_59)
| ~ is_a_theorem(implies(X_59,and(X_59,X_59)))
| is_a_theorem(and(X_59,X_59)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_59)),bind(Y,$fot(and(X_59,X_59)))]]) ).
cnf(refute_0_297,plain,
( ~ is_a_theorem(X_59)
| is_a_theorem(and(X_59,X_59)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_59,and(X_59,X_59))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
( ~ is_a_theorem(implies(X_4401,not(not(X_4401))))
| is_a_theorem(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401))))) ),
inference(subst,[],[refute_0_297:[bind(X_59,$fot(implies(X_4401,not(not(X_4401)))))]]) ).
cnf(refute_0_299,plain,
is_a_theorem(implies(and(not(X_4399),not(X_4399)),not(X_4399))),
inference(subst,[],[refute_0_95:[bind(P,$fot(not(X_4399))),bind(Q,$fot(not(X_4399)))]]) ).
cnf(refute_0_300,plain,
( ~ is_a_theorem(implies(and(not(X_4399),not(X_4399)),not(X_4399)))
| is_a_theorem(implies(X_4399,not(not(X_4399)))) ),
inference(subst,[],[refute_0_183:[bind(X,$fot(not(X_4399))),bind(X_4395,$fot(X_4399))]]) ).
cnf(refute_0_301,plain,
is_a_theorem(implies(X_4399,not(not(X_4399)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(not(X_4399),not(X_4399)),not(X_4399))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
is_a_theorem(implies(X_4401,not(not(X_4401)))),
inference(subst,[],[refute_0_301:[bind(X_4399,$fot(X_4401))]]) ).
cnf(refute_0_303,plain,
is_a_theorem(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_4401,not(not(X_4401)))) )],[refute_0_302,refute_0_298]) ).
cnf(refute_0_304,plain,
and(implies(X_4401,X_4401),implies(X_4401,X_4401)) = equiv(X_4401,X_4401),
inference(subst,[],[refute_0_266:[bind(X,$fot(X_4401)),bind(Y,$fot(X_4401))]]) ).
cnf(refute_0_305,plain,
not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))),
introduced(tautology,[refl,[$fot(not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))))]]) ).
cnf(refute_0_306,plain,
( and(implies(X_4401,X_4401),implies(X_4401,X_4401)) != equiv(X_4401,X_4401)
| not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) != not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))
| not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) = not(equiv(X_4401,X_4401)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))),not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))) ),[1,0],$fot(equiv(X_4401,X_4401))]]) ).
cnf(refute_0_307,plain,
( and(implies(X_4401,X_4401),implies(X_4401,X_4401)) != equiv(X_4401,X_4401)
| not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) = not(equiv(X_4401,X_4401)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))),not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) = not(equiv(X_4401,X_4401)),
inference(resolve,[$cnf( $equal(and(implies(X_4401,X_4401),implies(X_4401,X_4401)),equiv(X_4401,X_4401)) )],[refute_0_304,refute_0_307]) ).
cnf(refute_0_309,plain,
implies(implies(X_4401,X_4401),and(X_4401,not(X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))),
inference(subst,[],[refute_0_278:[bind(X,$fot(implies(X_4401,X_4401))),bind(X_10,$fot(X_4401)),bind(X_11,$fot(X_4401))]]) ).
cnf(refute_0_310,plain,
or(and(X_10,not(X_11)),Y) = implies(not(and(X_10,not(X_11))),Y),
inference(subst,[],[refute_0_42:[bind(X,$fot(and(X_10,not(X_11))))]]) ).
cnf(refute_0_311,plain,
( not(and(X_10,not(X_11))) != implies(X_10,X_11)
| or(and(X_10,not(X_11)),Y) != implies(not(and(X_10,not(X_11))),Y)
| or(and(X_10,not(X_11)),Y) = implies(implies(X_10,X_11),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_10,not(X_11)),Y),implies(not(and(X_10,not(X_11))),Y)) ),[1,0],$fot(implies(X_10,X_11))]]) ).
cnf(refute_0_312,plain,
( or(and(X_10,not(X_11)),Y) != implies(not(and(X_10,not(X_11))),Y)
| or(and(X_10,not(X_11)),Y) = implies(implies(X_10,X_11),Y) ),
inference(resolve,[$cnf( $equal(not(and(X_10,not(X_11))),implies(X_10,X_11)) )],[refute_0_275,refute_0_311]) ).
cnf(refute_0_313,plain,
or(and(X_10,not(X_11)),Y) = implies(implies(X_10,X_11),Y),
inference(resolve,[$cnf( $equal(or(and(X_10,not(X_11)),Y),implies(not(and(X_10,not(X_11))),Y)) )],[refute_0_310,refute_0_312]) ).
cnf(refute_0_314,plain,
or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))) = implies(implies(X_4401,X_4401),and(X_4401,not(X_4401))),
inference(subst,[],[refute_0_313:[bind(Y,$fot(and(X_4401,not(X_4401)))),bind(X_10,$fot(X_4401)),bind(X_11,$fot(X_4401))]]) ).
cnf(refute_0_315,plain,
( implies(implies(X_4401,X_4401),and(X_4401,not(X_4401))) != not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))
| or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))) != implies(implies(X_4401,X_4401),and(X_4401,not(X_4401)))
| or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))))),bind(Y0,$fot(implies(implies(X_4401,X_4401),and(X_4401,not(X_4401))))),bind(Z,$fot(not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))))]]) ).
cnf(refute_0_316,plain,
( implies(implies(X_4401,X_4401),and(X_4401,not(X_4401))) != not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))
| or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) ),
inference(resolve,[$cnf( $equal(or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))),implies(implies(X_4401,X_4401),and(X_4401,not(X_4401)))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))),
inference(resolve,[$cnf( $equal(implies(implies(X_4401,X_4401),and(X_4401,not(X_4401))),not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))) )],[refute_0_309,refute_0_316]) ).
cnf(refute_0_318,plain,
or(X,and(X_104,not(X_105))) = implies(not(X),and(X_104,not(X_105))),
inference(subst,[],[refute_0_42:[bind(Y,$fot(and(X_104,not(X_105))))]]) ).
cnf(refute_0_319,plain,
implies(not(X),and(X_104,not(X_105))) = not(and(not(X),implies(X_104,X_105))),
inference(subst,[],[refute_0_278:[bind(X,$fot(not(X))),bind(X_10,$fot(X_104)),bind(X_11,$fot(X_105))]]) ).
cnf(refute_0_320,plain,
( implies(not(X),and(X_104,not(X_105))) != not(and(not(X),implies(X_104,X_105)))
| or(X,and(X_104,not(X_105))) != implies(not(X),and(X_104,not(X_105)))
| or(X,and(X_104,not(X_105))) = not(and(not(X),implies(X_104,X_105))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,and(X_104,not(X_105))),implies(not(X),and(X_104,not(X_105)))) ),[1],$fot(not(and(not(X),implies(X_104,X_105))))]]) ).
cnf(refute_0_321,plain,
( or(X,and(X_104,not(X_105))) != implies(not(X),and(X_104,not(X_105)))
| or(X,and(X_104,not(X_105))) = not(and(not(X),implies(X_104,X_105))) ),
inference(resolve,[$cnf( $equal(implies(not(X),and(X_104,not(X_105))),not(and(not(X),implies(X_104,X_105)))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
or(X,and(X_104,not(X_105))) = not(and(not(X),implies(X_104,X_105))),
inference(resolve,[$cnf( $equal(or(X,and(X_104,not(X_105))),implies(not(X),and(X_104,not(X_105)))) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
( or(X,and(X_104,not(X_105))) != not(and(not(X),implies(X_104,X_105)))
| not(and(not(X),implies(X_104,X_105))) = or(X,and(X_104,not(X_105))) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(or(X,and(X_104,not(X_105))))),bind(Y0,$fot(not(and(not(X),implies(X_104,X_105)))))]]) ).
cnf(refute_0_324,plain,
not(and(not(X),implies(X_104,X_105))) = or(X,and(X_104,not(X_105))),
inference(resolve,[$cnf( $equal(or(X,and(X_104,not(X_105))),not(and(not(X),implies(X_104,X_105)))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))) = or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))),
inference(subst,[],[refute_0_324:[bind(X,$fot(and(X_4401,not(X_4401)))),bind(X_104,$fot(X_4401)),bind(X_105,$fot(X_4401))]]) ).
cnf(refute_0_326,plain,
( not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))) != or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401)))
| or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))) != not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))
| not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))))),bind(Y0,$fot(or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))))),bind(Z,$fot(not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))))]]) ).
cnf(refute_0_327,plain,
( or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))) != not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))
| not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) ),
inference(resolve,[$cnf( $equal(not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))),or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401)))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))),
inference(resolve,[$cnf( $equal(or(and(X_4401,not(X_4401)),and(X_4401,not(X_4401))),not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))) )],[refute_0_317,refute_0_327]) ).
cnf(refute_0_329,plain,
implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) = not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))),
inference(subst,[],[refute_0_278:[bind(X,$fot(not(and(X_4401,not(X_4401))))),bind(X_10,$fot(X_4401)),bind(X_11,$fot(X_4401))]]) ).
cnf(refute_0_330,plain,
( implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) != not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401)))
| not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))) != not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))
| implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))),bind(Y0,$fot(not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))))),bind(Z,$fot(not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))))]]) ).
cnf(refute_0_331,plain,
( not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))) != not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))
| implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) ),
inference(resolve,[$cnf( $equal(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))),not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401)))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) = not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))),
inference(resolve,[$cnf( $equal(not(and(not(and(X_4401,not(X_4401))),implies(X_4401,X_4401))),not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
( implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) != not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))
| not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) != not(equiv(X_4401,X_4401))
| implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) = not(equiv(X_4401,X_4401)) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))),bind(Y0,$fot(not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))))),bind(Z,$fot(not(equiv(X_4401,X_4401))))]]) ).
cnf(refute_0_334,plain,
( not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))) != not(equiv(X_4401,X_4401))
| implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) = not(equiv(X_4401,X_4401)) ),
inference(resolve,[$cnf( $equal(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))),not(and(implies(X_4401,X_4401),implies(X_4401,X_4401)))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) = not(equiv(X_4401,X_4401)),
inference(resolve,[$cnf( $equal(not(and(implies(X_4401,X_4401),implies(X_4401,X_4401))),not(equiv(X_4401,X_4401))) )],[refute_0_308,refute_0_334]) ).
cnf(refute_0_336,plain,
not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))) = not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))),
introduced(tautology,[refl,[$fot(not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))))]]) ).
cnf(refute_0_337,plain,
( implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) != not(equiv(X_4401,X_4401))
| not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))) != not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))
| not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))) = not(not(equiv(X_4401,X_4401))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))),not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))) ),[1,0],$fot(not(equiv(X_4401,X_4401)))]]) ).
cnf(refute_0_338,plain,
( implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))) != not(equiv(X_4401,X_4401))
| not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))) = not(not(equiv(X_4401,X_4401))) ),
inference(resolve,[$cnf( $equal(not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))),not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))) = not(not(equiv(X_4401,X_4401))),
inference(resolve,[$cnf( $equal(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))),not(equiv(X_4401,X_4401))) )],[refute_0_335,refute_0_338]) ).
cnf(refute_0_340,plain,
and(not(and(X_4401,not(X_4401))),implies(X_4401,not(not(X_4401)))) = not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))),
inference(subst,[],[refute_0_253:[bind(X,$fot(not(and(X_4401,not(X_4401))))),bind(X_1,$fot(X_4401)),bind(X_2,$fot(not(X_4401)))]]) ).
cnf(refute_0_341,plain,
and(not(not(implies(X,not(Y)))),X_37) = and(implies(X,not(Y)),X_37),
inference(subst,[],[refute_0_107:[bind(X,$fot(implies(X,not(Y)))),bind(X_34,$fot(X_37))]]) ).
cnf(refute_0_342,plain,
( and(not(not(implies(X,not(Y)))),X_37) != and(implies(X,not(Y)),X_37)
| not(implies(X,not(Y))) != and(X,Y)
| and(not(and(X,Y)),X_37) = and(implies(X,not(Y)),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_37),and(implies(X,not(Y)),X_37)) ),[0,0,0],$fot(and(X,Y))]]) ).
cnf(refute_0_343,plain,
( and(not(not(implies(X,not(Y)))),X_37) != and(implies(X,not(Y)),X_37)
| and(not(and(X,Y)),X_37) = and(implies(X,not(Y)),X_37) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_60,refute_0_342]) ).
cnf(refute_0_344,plain,
and(not(and(X,Y)),X_37) = and(implies(X,not(Y)),X_37),
inference(resolve,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_37),and(implies(X,not(Y)),X_37)) )],[refute_0_341,refute_0_343]) ).
cnf(refute_0_345,plain,
( and(not(and(X,Y)),X_37) != and(implies(X,not(Y)),X_37)
| and(implies(X,not(Y)),X_37) = and(not(and(X,Y)),X_37) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(and(not(and(X,Y)),X_37))),bind(Y0,$fot(and(implies(X,not(Y)),X_37)))]]) ).
cnf(refute_0_346,plain,
and(implies(X,not(Y)),X_37) = and(not(and(X,Y)),X_37),
inference(resolve,[$cnf( $equal(and(not(and(X,Y)),X_37),and(implies(X,not(Y)),X_37)) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) = and(not(and(X_4401,not(X_4401))),implies(X_4401,not(not(X_4401)))),
inference(subst,[],[refute_0_346:[bind(X,$fot(X_4401)),bind(Y,$fot(not(X_4401))),bind(X_37,$fot(implies(X_4401,not(not(X_4401)))))]]) ).
cnf(refute_0_348,plain,
( and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) != and(not(and(X_4401,not(X_4401))),implies(X_4401,not(not(X_4401))))
| and(not(and(X_4401,not(X_4401))),implies(X_4401,not(not(X_4401)))) != not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))
| and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) = not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))))),bind(Y0,$fot(and(not(and(X_4401,not(X_4401))),implies(X_4401,not(not(X_4401)))))),bind(Z,$fot(not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))))]]) ).
cnf(refute_0_349,plain,
( and(not(and(X_4401,not(X_4401))),implies(X_4401,not(not(X_4401)))) != not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))
| and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) = not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))),and(not(and(X_4401,not(X_4401))),implies(X_4401,not(not(X_4401))))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) = not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))),
inference(resolve,[$cnf( $equal(and(not(and(X_4401,not(X_4401))),implies(X_4401,not(not(X_4401)))),not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))) )],[refute_0_340,refute_0_349]) ).
cnf(refute_0_351,plain,
( and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) != not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))
| not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))) != not(not(equiv(X_4401,X_4401)))
| and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) = not(not(equiv(X_4401,X_4401))) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))))),bind(Y0,$fot(not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))))),bind(Z,$fot(not(not(equiv(X_4401,X_4401)))))]]) ).
cnf(refute_0_352,plain,
( not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))) != not(not(equiv(X_4401,X_4401)))
| and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) = not(not(equiv(X_4401,X_4401))) ),
inference(resolve,[$cnf( $equal(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))),not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401))))) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) = not(not(equiv(X_4401,X_4401))),
inference(resolve,[$cnf( $equal(not(implies(not(and(X_4401,not(X_4401))),and(X_4401,not(X_4401)))),not(not(equiv(X_4401,X_4401)))) )],[refute_0_339,refute_0_352]) ).
cnf(refute_0_354,plain,
( and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))) != not(not(equiv(X_4401,X_4401)))
| ~ is_a_theorem(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))))
| is_a_theorem(not(not(equiv(X_4401,X_4401)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401))))) ),[0],$fot(not(not(equiv(X_4401,X_4401))))]]) ).
cnf(refute_0_355,plain,
( ~ is_a_theorem(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))))
| is_a_theorem(not(not(equiv(X_4401,X_4401)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401)))),not(not(equiv(X_4401,X_4401)))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
is_a_theorem(not(not(equiv(X_4401,X_4401)))),
inference(resolve,[$cnf( is_a_theorem(and(implies(X_4401,not(not(X_4401))),implies(X_4401,not(not(X_4401))))) )],[refute_0_303,refute_0_355]) ).
cnf(refute_0_357,plain,
is_a_theorem(not(not(equiv(X_4402,X_4402)))),
inference(subst,[],[refute_0_356:[bind(X_4401,$fot(X_4402))]]) ).
cnf(refute_0_358,plain,
not(not(X_4402)) = X_4402,
inference(resolve,[$cnf( is_a_theorem(not(not(equiv(X_4402,X_4402)))) )],[refute_0_357,refute_0_294]) ).
cnf(refute_0_359,plain,
not(not(X)) = X,
inference(subst,[],[refute_0_358:[bind(X_4402,$fot(X))]]) ).
cnf(refute_0_360,plain,
or(X_4426,not(not(X))) = or(X_4426,not(not(X))),
introduced(tautology,[refl,[$fot(or(X_4426,not(not(X))))]]) ).
cnf(refute_0_361,plain,
( not(not(X)) != X
| or(X_4426,not(not(X))) != or(X_4426,not(not(X)))
| or(X_4426,not(not(X))) = or(X_4426,X) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_4426,not(not(X))),or(X_4426,not(not(X)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_362,plain,
( not(not(X)) != X
| or(X_4426,not(not(X))) = or(X_4426,X) ),
inference(resolve,[$cnf( $equal(or(X_4426,not(not(X))),or(X_4426,not(not(X)))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
or(X_4426,not(not(X))) = or(X_4426,X),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[refute_0_359,refute_0_362]) ).
cnf(refute_0_364,plain,
implies(or(X_4426,not(not(X))),or(X,X_4426)) = implies(or(X_4426,not(not(X))),or(X,X_4426)),
introduced(tautology,[refl,[$fot(implies(or(X_4426,not(not(X))),or(X,X_4426)))]]) ).
cnf(refute_0_365,plain,
( implies(or(X_4426,not(not(X))),or(X,X_4426)) != implies(or(X_4426,not(not(X))),or(X,X_4426))
| or(X_4426,not(not(X))) != or(X_4426,X)
| implies(or(X_4426,not(not(X))),or(X,X_4426)) = implies(or(X_4426,X),or(X,X_4426)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_4426,not(not(X))),or(X,X_4426)),implies(or(X_4426,not(not(X))),or(X,X_4426))) ),[1,0],$fot(or(X_4426,X))]]) ).
cnf(refute_0_366,plain,
( or(X_4426,not(not(X))) != or(X_4426,X)
| implies(or(X_4426,not(not(X))),or(X,X_4426)) = implies(or(X_4426,X),or(X,X_4426)) ),
inference(resolve,[$cnf( $equal(implies(or(X_4426,not(not(X))),or(X,X_4426)),implies(or(X_4426,not(not(X))),or(X,X_4426))) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
implies(or(X_4426,not(not(X))),or(X,X_4426)) = implies(or(X_4426,X),or(X,X_4426)),
inference(resolve,[$cnf( $equal(or(X_4426,not(not(X))),or(X_4426,X)) )],[refute_0_363,refute_0_366]) ).
cnf(refute_0_368,plain,
( implies(or(X_4426,not(not(X))),or(X,X_4426)) != implies(or(X_4426,X),or(X,X_4426))
| ~ is_a_theorem(implies(or(X_4426,not(not(X))),or(X,X_4426)))
| is_a_theorem(implies(or(X_4426,X),or(X,X_4426))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_4426,not(not(X))),or(X,X_4426))) ),[0],$fot(implies(or(X_4426,X),or(X,X_4426)))]]) ).
cnf(refute_0_369,plain,
( ~ is_a_theorem(implies(or(X_4426,not(not(X))),or(X,X_4426)))
| is_a_theorem(implies(or(X_4426,X),or(X,X_4426))) ),
inference(resolve,[$cnf( $equal(implies(or(X_4426,not(not(X))),or(X,X_4426)),implies(or(X_4426,X),or(X,X_4426))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
is_a_theorem(implies(or(X_4426,X),or(X,X_4426))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_4426,not(not(X))),or(X,X_4426))) )],[refute_0_232,refute_0_369]) ).
cnf(refute_0_371,plain,
is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8))),
inference(subst,[],[refute_0_370:[bind(X,$fot(skolemFOFtoCNF_Q_5)),bind(X_4426,$fot(skolemFOFtoCNF_P_8))]]) ).
cnf(refute_0_372,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8))) )],[refute_0_371,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL520+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 15:25:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 103.90/104.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.90/104.14
% 103.90/104.14 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 103.96/104.19
%------------------------------------------------------------------------------