TSTP Solution File: LCL517+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL517+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 12:52:51 EDT 2022
% Result : Timeout 286.53s 286.68s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 72
% Syntax : Number of formulae : 412 ( 209 unt; 0 def)
% Number of atoms : 703 ( 259 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 570 ( 279 ~; 267 |; 10 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 12 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 738 ( 19 sgn 44 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(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(cn3,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(rosser_op_or,axiom,
op_or ).
fof(rosser_op_implies_and,axiom,
op_implies_and ).
fof(rosser_op_equiv,axiom,
op_equiv ).
fof(rosser_modus_ponens,axiom,
modus_ponens ).
fof(rosser_kn1,axiom,
kn1 ).
fof(rosser_kn2,axiom,
kn2 ).
fof(rosser_kn3,axiom,
kn3 ).
fof(luka_op_or,axiom,
op_or ).
fof(luka_op_equiv,axiom,
op_equiv ).
fof(luka_cn3,conjecture,
cn3 ).
fof(subgoal_0,plain,
cn3,
inference(strip,[],[luka_cn3]) ).
fof(negate_0_0,plain,
~ cn3,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ cn3
<=> ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P)) ),
inference(canonicalize,[],[cn3]) ).
fof(normalize_0_1,plain,
! [P] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(P),P),P)) )
& ( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
op_or,
inference(canonicalize,[],[luka_op_or]) ).
fof(normalize_0_6,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
op_implies_and,
inference(canonicalize,[],[rosser_op_implies_and]) ).
fof(normalize_0_9,plain,
~ cn3,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,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_11,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_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
modus_ponens,
inference(canonicalize,[],[rosser_modus_ponens]) ).
fof(normalize_0_14,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_15,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_14]) ).
fof(normalize_0_16,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_15]) ).
fof(normalize_0_17,plain,
kn3,
inference(canonicalize,[],[rosser_kn3]) ).
fof(normalize_0_18,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
op_equiv,
inference(canonicalize,[],[luka_op_equiv]) ).
fof(normalize_0_21,plain,
( ~ kn2
<=> ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[kn2]) ).
fof(normalize_0_22,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_21]) ).
fof(normalize_0_23,plain,
! [P,Q] :
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
kn2,
inference(canonicalize,[],[rosser_kn2]) ).
fof(normalize_0_25,plain,
( ~ kn1
<=> ? [P] : ~ is_a_theorem(implies(P,and(P,P))) ),
inference(canonicalize,[],[kn1]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,plain,
! [P] :
( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
kn1,
inference(canonicalize,[],[rosser_kn1]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
op_or,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_11,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_11:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_13,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_14,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_3,refute_0_14]) ).
cnf(refute_0_16,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_17,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_P_5)),bind(Y,$fot(skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_19,plain,
implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),
introduced(tautology,[refl,[$fot(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_20,plain,
( implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)
| implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5)
| implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),[1,0],$fot(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_21,plain,
( implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5)
| implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) ),
inference(resolve,[$cnf( $equal(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) = implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),
inference(resolve,[$cnf( $equal(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5) != implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)
| ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),[0],$fot(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5))
| cn3 ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_24,refute_0_0]) ).
cnf(refute_0_26,plain,
~ cn3,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_27,plain,
~ is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)),
inference(resolve,[$cnf( cn3 )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_29,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(not(X),X_99))
| ~ is_a_theorem(not(X))
| is_a_theorem(X_99) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(not(X))),bind(Y,$fot(X_99))]]) ).
cnf(refute_0_32,plain,
or(X,X_99) = implies(not(X),X_99),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_99))]]) ).
cnf(refute_0_33,plain,
( or(X,X_99) != implies(not(X),X_99)
| implies(not(X),X_99) = or(X,X_99) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,X_99))),bind(Y0,$fot(implies(not(X),X_99)))]]) ).
cnf(refute_0_34,plain,
implies(not(X),X_99) = or(X,X_99),
inference(resolve,[$cnf( $equal(or(X,X_99),implies(not(X),X_99)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( implies(not(X),X_99) != or(X,X_99)
| ~ is_a_theorem(or(X,X_99))
| is_a_theorem(implies(not(X),X_99)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(not(X),X_99)) ),[0],$fot(or(X,X_99))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(or(X,X_99))
| is_a_theorem(implies(not(X),X_99)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_99),or(X,X_99)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(not(X))
| ~ is_a_theorem(or(X,X_99))
| is_a_theorem(X_99) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),X_99)) )],[refute_0_36,refute_0_31]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(not(equiv(X_3282,X_3281)))
| ~ is_a_theorem(or(equiv(X_3282,X_3281),implies(implies(X_3281,X_3282),X_3282)))
| is_a_theorem(implies(implies(X_3281,X_3282),X_3282)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(equiv(X_3282,X_3281))),bind(X_99,$fot(implies(implies(X_3281,X_3282),X_3282)))]]) ).
cnf(refute_0_39,plain,
( ~ kn3
| is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_40,plain,
kn3,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))),
inference(resolve,[$cnf( kn3 )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
implies(not(and(Q,R)),not(and(R,P))) = or(and(Q,R),not(and(R,P))),
inference(subst,[],[refute_0_17:[bind(X,$fot(and(Q,R))),bind(Y,$fot(not(and(R,P))))]]) ).
cnf(refute_0_43,plain,
implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),
introduced(tautology,[refl,[$fot(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))]]) ).
cnf(refute_0_44,plain,
( implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) != implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))
| implies(not(and(Q,R)),not(and(R,P))) != or(and(Q,R),not(and(R,P)))
| implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),[1,1],$fot(or(and(Q,R),not(and(R,P))))]]) ).
cnf(refute_0_45,plain,
( implies(not(and(Q,R)),not(and(R,P))) != or(and(Q,R),not(and(R,P)))
| implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))) ),
inference(resolve,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) = implies(implies(P,Q),or(and(Q,R),not(and(R,P)))),
inference(resolve,[$cnf( $equal(implies(not(and(Q,R)),not(and(R,P))),or(and(Q,R),not(and(R,P)))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))) != implies(implies(P,Q),or(and(Q,R),not(and(R,P))))
| ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),[0],$fot(implies(implies(P,Q),or(and(Q,R),not(and(R,P)))))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) ),
inference(resolve,[$cnf( $equal(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))),implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )],[refute_0_41,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(X_48,implies(X,Y)),or(and(implies(X,Y),implies(Y,X)),not(and(implies(Y,X),X_48))))),
inference(subst,[],[refute_0_49:[bind(P,$fot(X_48)),bind(Q,$fot(implies(X,Y))),bind(R,$fot(implies(Y,X)))]]) ).
cnf(refute_0_51,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_52,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_53,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,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_9:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_55,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( and(implies(X,Y),implies(Y,X)) != equiv(X,Y)
| ~ is_a_theorem(implies(implies(X_48,implies(X,Y)),or(and(implies(X,Y),implies(Y,X)),not(and(implies(Y,X),X_48)))))
| is_a_theorem(implies(implies(X_48,implies(X,Y)),or(equiv(X,Y),not(and(implies(Y,X),X_48))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_48,implies(X,Y)),or(and(implies(X,Y),implies(Y,X)),not(and(implies(Y,X),X_48))))) ),[0,1,0],$fot(equiv(X,Y))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(implies(implies(X_48,implies(X,Y)),or(and(implies(X,Y),implies(Y,X)),not(and(implies(Y,X),X_48)))))
| is_a_theorem(implies(implies(X_48,implies(X,Y)),or(equiv(X,Y),not(and(implies(Y,X),X_48))))) ),
inference(resolve,[$cnf( $equal(and(implies(X,Y),implies(Y,X)),equiv(X,Y)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(X_48,implies(X,Y)),or(equiv(X,Y),not(and(implies(Y,X),X_48))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_48,implies(X,Y)),or(and(implies(X,Y),implies(Y,X)),not(and(implies(Y,X),X_48))))) )],[refute_0_50,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(X_48,implies(X,Y)))
| ~ is_a_theorem(implies(implies(X_48,implies(X,Y)),or(equiv(X,Y),not(and(implies(Y,X),X_48)))))
| is_a_theorem(or(equiv(X,Y),not(and(implies(Y,X),X_48)))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(implies(X_48,implies(X,Y)))),bind(Y,$fot(or(equiv(X,Y),not(and(implies(Y,X),X_48)))))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(X_48,implies(X,Y)))
| is_a_theorem(or(equiv(X,Y),not(and(implies(Y,X),X_48)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_48,implies(X,Y)),or(equiv(X,Y),not(and(implies(Y,X),X_48))))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(not(X),implies(X_657,X_658)))
| is_a_theorem(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X))))) ),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_657)),bind(Y,$fot(X_658)),bind(X_48,$fot(not(X)))]]) ).
cnf(refute_0_62,plain,
or(X,implies(X_657,X_658)) = implies(not(X),implies(X_657,X_658)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(implies(X_657,X_658)))]]) ).
cnf(refute_0_63,plain,
( or(X,implies(X_657,X_658)) != implies(not(X),implies(X_657,X_658))
| implies(not(X),implies(X_657,X_658)) = or(X,implies(X_657,X_658)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,implies(X_657,X_658)))),bind(Y0,$fot(implies(not(X),implies(X_657,X_658))))]]) ).
cnf(refute_0_64,plain,
implies(not(X),implies(X_657,X_658)) = or(X,implies(X_657,X_658)),
inference(resolve,[$cnf( $equal(or(X,implies(X_657,X_658)),implies(not(X),implies(X_657,X_658))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( implies(not(X),implies(X_657,X_658)) != or(X,implies(X_657,X_658))
| ~ is_a_theorem(or(X,implies(X_657,X_658)))
| is_a_theorem(implies(not(X),implies(X_657,X_658))) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(not(X),implies(X_657,X_658))) ),[0],$fot(or(X,implies(X_657,X_658)))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(or(X,implies(X_657,X_658)))
| is_a_theorem(implies(not(X),implies(X_657,X_658))) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(X_657,X_658)),or(X,implies(X_657,X_658))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(or(X,implies(X_657,X_658)))
| is_a_theorem(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X))))) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),implies(X_657,X_658))) )],[refute_0_66,refute_0_61]) ).
cnf(refute_0_68,plain,
not(and(implies(X_658,X_657),not(X))) = implies(implies(X_658,X_657),X),
inference(subst,[],[refute_0_11:[bind(X,$fot(implies(X_658,X_657))),bind(Y,$fot(X))]]) ).
cnf(refute_0_69,plain,
or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))) = or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))),
introduced(tautology,[refl,[$fot(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))))]]) ).
cnf(refute_0_70,plain,
( not(and(implies(X_658,X_657),not(X))) != implies(implies(X_658,X_657),X)
| or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))) != or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X))))
| or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))) = or(equiv(X_657,X_658),implies(implies(X_658,X_657),X)) ),
introduced(tautology,[equality,[$cnf( $equal(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))),or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X))))) ),[1,1],$fot(implies(implies(X_658,X_657),X))]]) ).
cnf(refute_0_71,plain,
( not(and(implies(X_658,X_657),not(X))) != implies(implies(X_658,X_657),X)
| or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))) = or(equiv(X_657,X_658),implies(implies(X_658,X_657),X)) ),
inference(resolve,[$cnf( $equal(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))),or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X))))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))) = or(equiv(X_657,X_658),implies(implies(X_658,X_657),X)),
inference(resolve,[$cnf( $equal(not(and(implies(X_658,X_657),not(X))),implies(implies(X_658,X_657),X)) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
( or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))) != or(equiv(X_657,X_658),implies(implies(X_658,X_657),X))
| ~ is_a_theorem(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))))
| is_a_theorem(or(equiv(X_657,X_658),implies(implies(X_658,X_657),X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X))))) ),[0],$fot(or(equiv(X_657,X_658),implies(implies(X_658,X_657),X)))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))))
| is_a_theorem(or(equiv(X_657,X_658),implies(implies(X_658,X_657),X))) ),
inference(resolve,[$cnf( $equal(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X)))),or(equiv(X_657,X_658),implies(implies(X_658,X_657),X))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(or(X,implies(X_657,X_658)))
| is_a_theorem(or(equiv(X_657,X_658),implies(implies(X_658,X_657),X))) ),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_657,X_658),not(and(implies(X_658,X_657),not(X))))) )],[refute_0_67,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(or(X_3276,implies(X_3276,X_3275)))
| is_a_theorem(or(equiv(X_3276,X_3275),implies(implies(X_3275,X_3276),X_3276))) ),
inference(subst,[],[refute_0_75:[bind(X,$fot(X_3276)),bind(X_657,$fot(X_3276)),bind(X_658,$fot(X_3275))]]) ).
cnf(refute_0_77,plain,
( ~ kn2
| is_a_theorem(implies(and(P,Q),P)) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_78,plain,
kn2,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(and(P,Q),P)),
inference(resolve,[$cnf( kn2 )],[refute_0_78,refute_0_77]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(and(X_3263,Q),X_3263)),
inference(subst,[],[refute_0_79:[bind(P,$fot(X_3263))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(X_1138,X_1137))
| ~ is_a_theorem(implies(implies(X_1138,X_1137),or(X_1137,not(X_1138))))
| is_a_theorem(or(X_1137,not(X_1138))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(implies(X_1138,X_1137))),bind(Y,$fot(or(X_1137,not(X_1138))))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),not(and(X_50,not(Y)))))),
inference(subst,[],[refute_0_49:[bind(P,$fot(not(Y))),bind(Q,$fot(X_49)),bind(R,$fot(X_50))]]) ).
cnf(refute_0_83,plain,
implies(X_50,Y) = not(and(X_50,not(Y))),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_84,plain,
( implies(X_50,Y) != not(and(X_50,not(Y)))
| not(and(X_50,not(Y))) = implies(X_50,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(implies(X_50,Y))),bind(Y0,$fot(not(and(X_50,not(Y)))))]]) ).
cnf(refute_0_85,plain,
not(and(X_50,not(Y))) = implies(X_50,Y),
inference(resolve,[$cnf( $equal(implies(X_50,Y),not(and(X_50,not(Y)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( not(and(X_50,not(Y))) != implies(X_50,Y)
| ~ is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),not(and(X_50,not(Y))))))
| is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),not(and(X_50,not(Y)))))) ),[0,1,1],$fot(implies(X_50,Y))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),not(and(X_50,not(Y))))))
| is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y)))) ),
inference(resolve,[$cnf( $equal(not(and(X_50,not(Y))),implies(X_50,Y)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),not(and(X_50,not(Y)))))) )],[refute_0_82,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(not(Y),X_49) = or(Y,X_49),
inference(subst,[],[refute_0_17:[bind(X,$fot(Y)),bind(Y,$fot(X_49))]]) ).
cnf(refute_0_90,plain,
implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))) = implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))))]]) ).
cnf(refute_0_91,plain,
( implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))) != implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y)))
| implies(not(Y),X_49) != or(Y,X_49)
| implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))) = implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))),implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y)))) ),[1,0],$fot(or(Y,X_49))]]) ).
cnf(refute_0_92,plain,
( implies(not(Y),X_49) != or(Y,X_49)
| implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))) = implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))),implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y)))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))) = implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y))),
inference(resolve,[$cnf( $equal(implies(not(Y),X_49),or(Y,X_49)) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
( implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))) != implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y)))
| ~ is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))))
| is_a_theorem(implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y)))) ),[0],$fot(implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y))))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))))
| is_a_theorem(implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y))),implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y)))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),X_49),or(and(X_49,X_50),implies(X_50,Y)))) )],[refute_0_88,refute_0_95]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y))))
| ~ is_a_theorem(or(Y,X_49))
| is_a_theorem(or(and(X_49,X_50),implies(X_50,Y))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(or(Y,X_49))),bind(Y,$fot(or(and(X_49,X_50),implies(X_50,Y))))]]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(or(Y,X_49))
| is_a_theorem(or(and(X_49,X_50),implies(X_50,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(Y,X_49),or(and(X_49,X_50),implies(X_50,Y)))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(or(not(X_1120),X_1120))
| is_a_theorem(or(and(X_1120,X_50),implies(X_50,not(X_1120)))) ),
inference(subst,[],[refute_0_98:[bind(Y,$fot(not(X_1120))),bind(X_49,$fot(X_1120))]]) ).
cnf(refute_0_100,plain,
is_a_theorem(implies(and(X_1117,X_1117),X_1117)),
inference(subst,[],[refute_0_79:[bind(P,$fot(X_1117)),bind(Q,$fot(X_1117))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(and(X_354,X_354),X_353))
| ~ is_a_theorem(implies(implies(and(X_354,X_354),X_353),not(and(not(X_353),X_354))))
| is_a_theorem(not(and(not(X_353),X_354))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(implies(and(X_354,X_354),X_353))),bind(Y,$fot(not(and(not(X_353),X_354))))]]) ).
cnf(refute_0_102,plain,
( ~ kn1
| is_a_theorem(implies(P,and(P,P))) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_103,plain,
kn1,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(P,and(P,P))),
inference(resolve,[$cnf( kn1 )],[refute_0_103,refute_0_102]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(X_293,and(X_293,X_293))),
inference(subst,[],[refute_0_104:[bind(P,$fot(X_293))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(P,Q))
| ~ is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P)))))
| is_a_theorem(or(and(Q,R),not(and(R,P)))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(implies(P,Q))),bind(Y,$fot(or(and(Q,R),not(and(R,P)))))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(P,Q))
| is_a_theorem(or(and(Q,R),not(and(R,P)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),or(and(Q,R),not(and(R,P))))) )],[refute_0_49,refute_0_106]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(X_293,and(X_293,X_293)))
| is_a_theorem(or(and(and(X_293,X_293),X_295),not(and(X_295,X_293)))) ),
inference(subst,[],[refute_0_107:[bind(P,$fot(X_293)),bind(Q,$fot(and(X_293,X_293))),bind(R,$fot(X_295))]]) ).
cnf(refute_0_109,plain,
is_a_theorem(or(and(and(X_293,X_293),X_295),not(and(X_295,X_293)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_293,and(X_293,X_293))) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
is_a_theorem(or(and(and(X_307,X_307),not(Y)),not(and(not(Y),X_307)))),
inference(subst,[],[refute_0_109:[bind(X_293,$fot(X_307)),bind(X_295,$fot(not(Y)))]]) ).
cnf(refute_0_111,plain,
or(and(X,not(Y)),X_4) = implies(not(and(X,not(Y))),X_4),
inference(subst,[],[refute_0_15:[bind(X,$fot(and(X,not(Y)))),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_112,plain,
( not(and(X,not(Y))) != implies(X,Y)
| or(and(X,not(Y)),X_4) != implies(not(and(X,not(Y))),X_4)
| or(and(X,not(Y)),X_4) = implies(implies(X,Y),X_4) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),X_4),implies(not(and(X,not(Y))),X_4)) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_113,plain,
( or(and(X,not(Y)),X_4) != implies(not(and(X,not(Y))),X_4)
| or(and(X,not(Y)),X_4) = implies(implies(X,Y),X_4) ),
inference(resolve,[$cnf( $equal(not(and(X,not(Y))),implies(X,Y)) )],[refute_0_11,refute_0_112]) ).
cnf(refute_0_114,plain,
or(and(X,not(Y)),X_4) = implies(implies(X,Y),X_4),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),X_4),implies(not(and(X,not(Y))),X_4)) )],[refute_0_111,refute_0_113]) ).
cnf(refute_0_115,plain,
or(and(and(X_307,X_307),not(Y)),not(and(not(Y),X_307))) = implies(implies(and(X_307,X_307),Y),not(and(not(Y),X_307))),
inference(subst,[],[refute_0_114:[bind(X,$fot(and(X_307,X_307))),bind(X_4,$fot(not(and(not(Y),X_307))))]]) ).
cnf(refute_0_116,plain,
( or(and(and(X_307,X_307),not(Y)),not(and(not(Y),X_307))) != implies(implies(and(X_307,X_307),Y),not(and(not(Y),X_307)))
| ~ is_a_theorem(or(and(and(X_307,X_307),not(Y)),not(and(not(Y),X_307))))
| is_a_theorem(implies(implies(and(X_307,X_307),Y),not(and(not(Y),X_307)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(and(X_307,X_307),not(Y)),not(and(not(Y),X_307)))) ),[0],$fot(implies(implies(and(X_307,X_307),Y),not(and(not(Y),X_307))))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(or(and(and(X_307,X_307),not(Y)),not(and(not(Y),X_307))))
| is_a_theorem(implies(implies(and(X_307,X_307),Y),not(and(not(Y),X_307)))) ),
inference(resolve,[$cnf( $equal(or(and(and(X_307,X_307),not(Y)),not(and(not(Y),X_307))),implies(implies(and(X_307,X_307),Y),not(and(not(Y),X_307)))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(and(X_307,X_307),Y),not(and(not(Y),X_307)))),
inference(resolve,[$cnf( is_a_theorem(or(and(and(X_307,X_307),not(Y)),not(and(not(Y),X_307)))) )],[refute_0_110,refute_0_117]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(and(X_354,X_354),X_353),not(and(not(X_353),X_354)))),
inference(subst,[],[refute_0_118:[bind(Y,$fot(X_353)),bind(X_307,$fot(X_354))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(and(X_354,X_354),X_353))
| is_a_theorem(not(and(not(X_353),X_354))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_354,X_354),X_353),not(and(not(X_353),X_354)))) )],[refute_0_119,refute_0_101]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(and(X_1117,X_1117),X_1117))
| is_a_theorem(not(and(not(X_1117),X_1117))) ),
inference(subst,[],[refute_0_120:[bind(X_353,$fot(X_1117)),bind(X_354,$fot(X_1117))]]) ).
cnf(refute_0_122,plain,
is_a_theorem(not(and(not(X_1117),X_1117))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_1117,X_1117),X_1117)) )],[refute_0_100,refute_0_121]) ).
cnf(refute_0_123,plain,
is_a_theorem(not(and(not(not(Y)),not(Y)))),
inference(subst,[],[refute_0_122:[bind(X_1117,$fot(not(Y)))]]) ).
cnf(refute_0_124,plain,
implies(not(not(Y)),Y) = not(and(not(not(Y)),not(Y))),
inference(subst,[],[refute_0_6:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_125,plain,
( implies(not(not(Y)),Y) != not(and(not(not(Y)),not(Y)))
| not(and(not(not(Y)),not(Y))) = implies(not(not(Y)),Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(implies(not(not(Y)),Y))),bind(Y0,$fot(not(and(not(not(Y)),not(Y)))))]]) ).
cnf(refute_0_126,plain,
not(and(not(not(Y)),not(Y))) = implies(not(not(Y)),Y),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),not(and(not(not(Y)),not(Y)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( not(and(not(not(Y)),not(Y))) != implies(not(not(Y)),Y)
| ~ is_a_theorem(not(and(not(not(Y)),not(Y))))
| is_a_theorem(implies(not(not(Y)),Y)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(not(not(Y)),not(Y)))) ),[0],$fot(implies(not(not(Y)),Y))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(not(and(not(not(Y)),not(Y))))
| is_a_theorem(implies(not(not(Y)),Y)) ),
inference(resolve,[$cnf( $equal(not(and(not(not(Y)),not(Y))),implies(not(not(Y)),Y)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(not(not(Y)),Y)),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(Y)),not(Y)))) )],[refute_0_123,refute_0_128]) ).
cnf(refute_0_130,plain,
implies(not(not(Y)),Y) = or(not(Y),Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_131,plain,
( implies(not(not(Y)),Y) != or(not(Y),Y)
| ~ is_a_theorem(implies(not(not(Y)),Y))
| is_a_theorem(or(not(Y),Y)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(not(Y)),Y)) ),[0],$fot(or(not(Y),Y))]]) ).
cnf(refute_0_132,plain,
( ~ is_a_theorem(implies(not(not(Y)),Y))
| is_a_theorem(or(not(Y),Y)) ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),or(not(Y),Y)) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
is_a_theorem(or(not(Y),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(Y)),Y)) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
is_a_theorem(or(not(X_1120),X_1120)),
inference(subst,[],[refute_0_133:[bind(Y,$fot(X_1120))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(or(and(X_1120,X_50),implies(X_50,not(X_1120)))),
inference(resolve,[$cnf( is_a_theorem(or(not(X_1120),X_1120)) )],[refute_0_134,refute_0_99]) ).
cnf(refute_0_136,plain,
is_a_theorem(or(and(X_1130,not(X)),implies(not(X),not(X_1130)))),
inference(subst,[],[refute_0_135:[bind(X_1120,$fot(X_1130)),bind(X_50,$fot(not(X)))]]) ).
cnf(refute_0_137,plain,
or(X,not(X_1130)) = implies(not(X),not(X_1130)),
inference(subst,[],[refute_0_15:[bind(Y,$fot(not(X_1130)))]]) ).
cnf(refute_0_138,plain,
( or(X,not(X_1130)) != implies(not(X),not(X_1130))
| implies(not(X),not(X_1130)) = or(X,not(X_1130)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,not(X_1130)))),bind(Y0,$fot(implies(not(X),not(X_1130))))]]) ).
cnf(refute_0_139,plain,
implies(not(X),not(X_1130)) = or(X,not(X_1130)),
inference(resolve,[$cnf( $equal(or(X,not(X_1130)),implies(not(X),not(X_1130))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
( implies(not(X),not(X_1130)) != or(X,not(X_1130))
| ~ is_a_theorem(or(and(X_1130,not(X)),implies(not(X),not(X_1130))))
| is_a_theorem(or(and(X_1130,not(X)),or(X,not(X_1130)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_1130,not(X)),implies(not(X),not(X_1130)))) ),[0,1],$fot(or(X,not(X_1130)))]]) ).
cnf(refute_0_141,plain,
( ~ is_a_theorem(or(and(X_1130,not(X)),implies(not(X),not(X_1130))))
| is_a_theorem(or(and(X_1130,not(X)),or(X,not(X_1130)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_1130)),or(X,not(X_1130))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
is_a_theorem(or(and(X_1130,not(X)),or(X,not(X_1130)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_1130,not(X)),implies(not(X),not(X_1130)))) )],[refute_0_136,refute_0_141]) ).
cnf(refute_0_143,plain,
or(and(X_1130,not(X)),or(X,not(X_1130))) = implies(implies(X_1130,X),or(X,not(X_1130))),
inference(subst,[],[refute_0_114:[bind(X,$fot(X_1130)),bind(Y,$fot(X)),bind(X_4,$fot(or(X,not(X_1130))))]]) ).
cnf(refute_0_144,plain,
( or(and(X_1130,not(X)),or(X,not(X_1130))) != implies(implies(X_1130,X),or(X,not(X_1130)))
| ~ is_a_theorem(or(and(X_1130,not(X)),or(X,not(X_1130))))
| is_a_theorem(implies(implies(X_1130,X),or(X,not(X_1130)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_1130,not(X)),or(X,not(X_1130)))) ),[0],$fot(implies(implies(X_1130,X),or(X,not(X_1130))))]]) ).
cnf(refute_0_145,plain,
( ~ is_a_theorem(or(and(X_1130,not(X)),or(X,not(X_1130))))
| is_a_theorem(implies(implies(X_1130,X),or(X,not(X_1130)))) ),
inference(resolve,[$cnf( $equal(or(and(X_1130,not(X)),or(X,not(X_1130))),implies(implies(X_1130,X),or(X,not(X_1130)))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(implies(X_1130,X),or(X,not(X_1130)))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_1130,not(X)),or(X,not(X_1130)))) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(implies(X_1138,X_1137),or(X_1137,not(X_1138)))),
inference(subst,[],[refute_0_146:[bind(X,$fot(X_1137)),bind(X_1130,$fot(X_1138))]]) ).
cnf(refute_0_148,plain,
( ~ is_a_theorem(implies(X_1138,X_1137))
| is_a_theorem(or(X_1137,not(X_1138))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1138,X_1137),or(X_1137,not(X_1138)))) )],[refute_0_147,refute_0_81]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(implies(and(X_3263,Q),X_3263))
| is_a_theorem(or(X_3263,not(and(X_3263,Q)))) ),
inference(subst,[],[refute_0_148:[bind(X_1137,$fot(X_3263)),bind(X_1138,$fot(and(X_3263,Q)))]]) ).
cnf(refute_0_150,plain,
is_a_theorem(or(X_3263,not(and(X_3263,Q)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_3263,Q),X_3263)) )],[refute_0_80,refute_0_149]) ).
cnf(refute_0_151,plain,
is_a_theorem(or(X_3266,not(and(X_3266,not(Y))))),
inference(subst,[],[refute_0_150:[bind(Q,$fot(not(Y))),bind(X_3263,$fot(X_3266))]]) ).
cnf(refute_0_152,plain,
implies(X_3266,Y) = not(and(X_3266,not(Y))),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_3266))]]) ).
cnf(refute_0_153,plain,
( implies(X_3266,Y) != not(and(X_3266,not(Y)))
| not(and(X_3266,not(Y))) = implies(X_3266,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(implies(X_3266,Y))),bind(Y0,$fot(not(and(X_3266,not(Y)))))]]) ).
cnf(refute_0_154,plain,
not(and(X_3266,not(Y))) = implies(X_3266,Y),
inference(resolve,[$cnf( $equal(implies(X_3266,Y),not(and(X_3266,not(Y)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( not(and(X_3266,not(Y))) != implies(X_3266,Y)
| ~ is_a_theorem(or(X_3266,not(and(X_3266,not(Y)))))
| is_a_theorem(or(X_3266,implies(X_3266,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_3266,not(and(X_3266,not(Y))))) ),[0,1],$fot(implies(X_3266,Y))]]) ).
cnf(refute_0_156,plain,
( ~ is_a_theorem(or(X_3266,not(and(X_3266,not(Y)))))
| is_a_theorem(or(X_3266,implies(X_3266,Y))) ),
inference(resolve,[$cnf( $equal(not(and(X_3266,not(Y))),implies(X_3266,Y)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
is_a_theorem(or(X_3266,implies(X_3266,Y))),
inference(resolve,[$cnf( is_a_theorem(or(X_3266,not(and(X_3266,not(Y))))) )],[refute_0_151,refute_0_156]) ).
cnf(refute_0_158,plain,
is_a_theorem(or(X_3276,implies(X_3276,X_3275))),
inference(subst,[],[refute_0_157:[bind(Y,$fot(X_3275)),bind(X_3266,$fot(X_3276))]]) ).
cnf(refute_0_159,plain,
is_a_theorem(or(equiv(X_3276,X_3275),implies(implies(X_3275,X_3276),X_3276))),
inference(resolve,[$cnf( is_a_theorem(or(X_3276,implies(X_3276,X_3275))) )],[refute_0_158,refute_0_76]) ).
cnf(refute_0_160,plain,
is_a_theorem(or(equiv(X_3282,X_3281),implies(implies(X_3281,X_3282),X_3282))),
inference(subst,[],[refute_0_159:[bind(X_3275,$fot(X_3281)),bind(X_3276,$fot(X_3282))]]) ).
cnf(refute_0_161,plain,
( ~ is_a_theorem(not(equiv(X_3282,X_3281)))
| is_a_theorem(implies(implies(X_3281,X_3282),X_3282)) ),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_3282,X_3281),implies(implies(X_3281,X_3282),X_3282))) )],[refute_0_160,refute_0_38]) ).
cnf(refute_0_162,plain,
( ~ is_a_theorem(not(equiv(X_47910,not(X_47910))))
| is_a_theorem(implies(implies(not(X_47910),X_47910),X_47910)) ),
inference(subst,[],[refute_0_161:[bind(X_3281,$fot(not(X_47910))),bind(X_3282,$fot(X_47910))]]) ).
cnf(refute_0_163,plain,
( ~ is_a_theorem(implies(or(not(not(or(not(X_47909),not(X_47909)))),and(X_47909,not(not(X_47909)))),not(equiv(X_47909,not(X_47909)))))
| ~ is_a_theorem(or(not(not(or(not(X_47909),not(X_47909)))),and(X_47909,not(not(X_47909)))))
| is_a_theorem(not(equiv(X_47909,not(X_47909)))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(or(not(not(or(not(X_47909),not(X_47909)))),and(X_47909,not(not(X_47909)))))),bind(Y,$fot(not(equiv(X_47909,not(X_47909)))))]]) ).
cnf(refute_0_164,plain,
( ~ is_a_theorem(implies(implies(or(X_171,X_172),X_170),or(and(X_170,implies(X_172,not(X_171))),not(equiv(X_172,not(X_171))))))
| ~ is_a_theorem(implies(or(X_171,X_172),X_170))
| is_a_theorem(or(and(X_170,implies(X_172,not(X_171))),not(equiv(X_172,not(X_171))))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(implies(or(X_171,X_172),X_170))),bind(Y,$fot(or(and(X_170,implies(X_172,not(X_171))),not(equiv(X_172,not(X_171))))))]]) ).
cnf(refute_0_165,plain,
is_a_theorem(implies(implies(or(X_54,X_55),Q),or(and(Q,implies(X_55,not(X_54))),not(and(implies(X_55,not(X_54)),or(X_54,X_55)))))),
inference(subst,[],[refute_0_49:[bind(P,$fot(or(X_54,X_55))),bind(R,$fot(implies(X_55,not(X_54))))]]) ).
cnf(refute_0_166,plain,
equiv(X_6,not(X)) = and(implies(X_6,not(X)),implies(not(X),X_6)),
inference(subst,[],[refute_0_53:[bind(X,$fot(X_6)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_167,plain,
or(X,X_6) = implies(not(X),X_6),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_6))]]) ).
cnf(refute_0_168,plain,
( or(X,X_6) != implies(not(X),X_6)
| implies(not(X),X_6) = or(X,X_6) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,X_6))),bind(Y0,$fot(implies(not(X),X_6)))]]) ).
cnf(refute_0_169,plain,
implies(not(X),X_6) = or(X,X_6),
inference(resolve,[$cnf( $equal(or(X,X_6),implies(not(X),X_6)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
( equiv(X_6,not(X)) != and(implies(X_6,not(X)),implies(not(X),X_6))
| implies(not(X),X_6) != or(X,X_6)
| equiv(X_6,not(X)) = and(implies(X_6,not(X)),or(X,X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_6,not(X)),and(implies(X_6,not(X)),implies(not(X),X_6))) ),[1,1],$fot(or(X,X_6))]]) ).
cnf(refute_0_171,plain,
( equiv(X_6,not(X)) != and(implies(X_6,not(X)),implies(not(X),X_6))
| equiv(X_6,not(X)) = and(implies(X_6,not(X)),or(X,X_6)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_6),or(X,X_6)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
equiv(X_6,not(X)) = and(implies(X_6,not(X)),or(X,X_6)),
inference(resolve,[$cnf( $equal(equiv(X_6,not(X)),and(implies(X_6,not(X)),implies(not(X),X_6))) )],[refute_0_166,refute_0_171]) ).
cnf(refute_0_173,plain,
equiv(X_55,not(X_54)) = and(implies(X_55,not(X_54)),or(X_54,X_55)),
inference(subst,[],[refute_0_172:[bind(X,$fot(X_54)),bind(X_6,$fot(X_55))]]) ).
cnf(refute_0_174,plain,
( equiv(X_55,not(X_54)) != and(implies(X_55,not(X_54)),or(X_54,X_55))
| and(implies(X_55,not(X_54)),or(X_54,X_55)) = equiv(X_55,not(X_54)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(equiv(X_55,not(X_54)))),bind(Y0,$fot(and(implies(X_55,not(X_54)),or(X_54,X_55))))]]) ).
cnf(refute_0_175,plain,
and(implies(X_55,not(X_54)),or(X_54,X_55)) = equiv(X_55,not(X_54)),
inference(resolve,[$cnf( $equal(equiv(X_55,not(X_54)),and(implies(X_55,not(X_54)),or(X_54,X_55))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
( and(implies(X_55,not(X_54)),or(X_54,X_55)) != equiv(X_55,not(X_54))
| ~ is_a_theorem(implies(implies(or(X_54,X_55),Q),or(and(Q,implies(X_55,not(X_54))),not(and(implies(X_55,not(X_54)),or(X_54,X_55))))))
| is_a_theorem(implies(implies(or(X_54,X_55),Q),or(and(Q,implies(X_55,not(X_54))),not(equiv(X_55,not(X_54)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(or(X_54,X_55),Q),or(and(Q,implies(X_55,not(X_54))),not(and(implies(X_55,not(X_54)),or(X_54,X_55)))))) ),[0,1,1,0],$fot(equiv(X_55,not(X_54)))]]) ).
cnf(refute_0_177,plain,
( ~ is_a_theorem(implies(implies(or(X_54,X_55),Q),or(and(Q,implies(X_55,not(X_54))),not(and(implies(X_55,not(X_54)),or(X_54,X_55))))))
| is_a_theorem(implies(implies(or(X_54,X_55),Q),or(and(Q,implies(X_55,not(X_54))),not(equiv(X_55,not(X_54)))))) ),
inference(resolve,[$cnf( $equal(and(implies(X_55,not(X_54)),or(X_54,X_55)),equiv(X_55,not(X_54))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
is_a_theorem(implies(implies(or(X_54,X_55),Q),or(and(Q,implies(X_55,not(X_54))),not(equiv(X_55,not(X_54)))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_54,X_55),Q),or(and(Q,implies(X_55,not(X_54))),not(and(implies(X_55,not(X_54)),or(X_54,X_55)))))) )],[refute_0_165,refute_0_177]) ).
cnf(refute_0_179,plain,
is_a_theorem(implies(implies(or(X_171,X_172),X_170),or(and(X_170,implies(X_172,not(X_171))),not(equiv(X_172,not(X_171)))))),
inference(subst,[],[refute_0_178:[bind(Q,$fot(X_170)),bind(X_54,$fot(X_171)),bind(X_55,$fot(X_172))]]) ).
cnf(refute_0_180,plain,
( ~ is_a_theorem(implies(or(X_171,X_172),X_170))
| is_a_theorem(or(and(X_170,implies(X_172,not(X_171))),not(equiv(X_172,not(X_171))))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_171,X_172),X_170),or(and(X_170,implies(X_172,not(X_171))),not(equiv(X_172,not(X_171)))))) )],[refute_0_179,refute_0_164]) ).
cnf(refute_0_181,plain,
( ~ is_a_theorem(implies(or(X_40664,X_40664),not(not(not(or(not(X_40664),not(X_40664)))))))
| is_a_theorem(or(and(not(not(not(or(not(X_40664),not(X_40664))))),implies(X_40664,not(X_40664))),not(equiv(X_40664,not(X_40664))))) ),
inference(subst,[],[refute_0_180:[bind(X_170,$fot(not(not(not(or(not(X_40664),not(X_40664))))))),bind(X_171,$fot(X_40664)),bind(X_172,$fot(X_40664))]]) ).
cnf(refute_0_182,plain,
( ~ is_a_theorem(not(and(X_1130,X_1131)))
| ~ is_a_theorem(or(and(X_1130,X_1131),implies(X_1131,not(X_1130))))
| is_a_theorem(implies(X_1131,not(X_1130))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(X_1130,X_1131))),bind(X_99,$fot(implies(X_1131,not(X_1130))))]]) ).
cnf(refute_0_183,plain,
is_a_theorem(or(and(X_1130,X_1131),implies(X_1131,not(X_1130)))),
inference(subst,[],[refute_0_135:[bind(X_1120,$fot(X_1130)),bind(X_50,$fot(X_1131))]]) ).
cnf(refute_0_184,plain,
( ~ is_a_theorem(not(and(X_1130,X_1131)))
| is_a_theorem(implies(X_1131,not(X_1130))) ),
inference(resolve,[$cnf( is_a_theorem(or(and(X_1130,X_1131),implies(X_1131,not(X_1130)))) )],[refute_0_183,refute_0_182]) ).
cnf(refute_0_185,plain,
( ~ is_a_theorem(not(and(not(not(or(not(X_40663),not(X_40663)))),or(X_40663,X_40663))))
| is_a_theorem(implies(or(X_40663,X_40663),not(not(not(or(not(X_40663),not(X_40663))))))) ),
inference(subst,[],[refute_0_184:[bind(X_1130,$fot(not(not(or(not(X_40663),not(X_40663)))))),bind(X_1131,$fot(or(X_40663,X_40663)))]]) ).
cnf(refute_0_186,plain,
( ~ is_a_theorem(implies(implies(or(X_1565,not(not(X_1564))),X_1566),not(and(not(X_1566),or(X_1564,X_1565)))))
| ~ is_a_theorem(implies(or(X_1565,not(not(X_1564))),X_1566))
| is_a_theorem(not(and(not(X_1566),or(X_1564,X_1565)))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(implies(or(X_1565,not(not(X_1564))),X_1566))),bind(Y,$fot(not(and(not(X_1566),or(X_1564,X_1565)))))]]) ).
cnf(refute_0_187,plain,
is_a_theorem(implies(implies(not(X),X_1137),or(X_1137,not(not(X))))),
inference(subst,[],[refute_0_146:[bind(X,$fot(X_1137)),bind(X_1130,$fot(not(X)))]]) ).
cnf(refute_0_188,plain,
or(X,X_1137) = implies(not(X),X_1137),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_1137))]]) ).
cnf(refute_0_189,plain,
( or(X,X_1137) != implies(not(X),X_1137)
| implies(not(X),X_1137) = or(X,X_1137) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,X_1137))),bind(Y0,$fot(implies(not(X),X_1137)))]]) ).
cnf(refute_0_190,plain,
implies(not(X),X_1137) = or(X,X_1137),
inference(resolve,[$cnf( $equal(or(X,X_1137),implies(not(X),X_1137)) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( implies(not(X),X_1137) != or(X,X_1137)
| ~ is_a_theorem(implies(implies(not(X),X_1137),or(X_1137,not(not(X)))))
| is_a_theorem(implies(or(X,X_1137),or(X_1137,not(not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X),X_1137),or(X_1137,not(not(X))))) ),[0,0],$fot(or(X,X_1137))]]) ).
cnf(refute_0_192,plain,
( ~ is_a_theorem(implies(implies(not(X),X_1137),or(X_1137,not(not(X)))))
| is_a_theorem(implies(or(X,X_1137),or(X_1137,not(not(X))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_1137),or(X,X_1137)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
is_a_theorem(implies(or(X,X_1137),or(X_1137,not(not(X))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_1137),or(X_1137,not(not(X))))) )],[refute_0_187,refute_0_192]) ).
cnf(refute_0_194,plain,
( ~ is_a_theorem(implies(X_115,X_116))
| ~ is_a_theorem(implies(implies(X_115,X_116),implies(implies(X_116,X_114),not(and(not(X_114),X_115)))))
| is_a_theorem(implies(implies(X_116,X_114),not(and(not(X_114),X_115)))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(implies(X_115,X_116))),bind(Y,$fot(implies(implies(X_116,X_114),not(and(not(X_114),X_115)))))]]) ).
cnf(refute_0_195,plain,
is_a_theorem(implies(implies(X_48,X_49),or(and(X_49,not(Y)),not(and(not(Y),X_48))))),
inference(subst,[],[refute_0_49:[bind(P,$fot(X_48)),bind(Q,$fot(X_49)),bind(R,$fot(not(Y)))]]) ).
cnf(refute_0_196,plain,
or(and(X_49,not(Y)),not(and(not(Y),X_48))) = implies(implies(X_49,Y),not(and(not(Y),X_48))),
inference(subst,[],[refute_0_114:[bind(X,$fot(X_49)),bind(X_4,$fot(not(and(not(Y),X_48))))]]) ).
cnf(refute_0_197,plain,
( or(and(X_49,not(Y)),not(and(not(Y),X_48))) != implies(implies(X_49,Y),not(and(not(Y),X_48)))
| ~ is_a_theorem(implies(implies(X_48,X_49),or(and(X_49,not(Y)),not(and(not(Y),X_48)))))
| is_a_theorem(implies(implies(X_48,X_49),implies(implies(X_49,Y),not(and(not(Y),X_48))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_48,X_49),or(and(X_49,not(Y)),not(and(not(Y),X_48))))) ),[0,1],$fot(implies(implies(X_49,Y),not(and(not(Y),X_48))))]]) ).
cnf(refute_0_198,plain,
( ~ is_a_theorem(implies(implies(X_48,X_49),or(and(X_49,not(Y)),not(and(not(Y),X_48)))))
| is_a_theorem(implies(implies(X_48,X_49),implies(implies(X_49,Y),not(and(not(Y),X_48))))) ),
inference(resolve,[$cnf( $equal(or(and(X_49,not(Y)),not(and(not(Y),X_48))),implies(implies(X_49,Y),not(and(not(Y),X_48)))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
is_a_theorem(implies(implies(X_48,X_49),implies(implies(X_49,Y),not(and(not(Y),X_48))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_48,X_49),or(and(X_49,not(Y)),not(and(not(Y),X_48))))) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
is_a_theorem(implies(implies(X_115,X_116),implies(implies(X_116,X_114),not(and(not(X_114),X_115))))),
inference(subst,[],[refute_0_199:[bind(Y,$fot(X_114)),bind(X_48,$fot(X_115)),bind(X_49,$fot(X_116))]]) ).
cnf(refute_0_201,plain,
( ~ is_a_theorem(implies(X_115,X_116))
| is_a_theorem(implies(implies(X_116,X_114),not(and(not(X_114),X_115)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_115,X_116),implies(implies(X_116,X_114),not(and(not(X_114),X_115))))) )],[refute_0_200,refute_0_194]) ).
cnf(refute_0_202,plain,
( ~ is_a_theorem(implies(or(X,X_1137),or(X_1137,not(not(X)))))
| is_a_theorem(implies(implies(or(X_1137,not(not(X))),X_1541),not(and(not(X_1541),or(X,X_1137))))) ),
inference(subst,[],[refute_0_201:[bind(X_114,$fot(X_1541)),bind(X_115,$fot(or(X,X_1137))),bind(X_116,$fot(or(X_1137,not(not(X)))))]]) ).
cnf(refute_0_203,plain,
is_a_theorem(implies(implies(or(X_1137,not(not(X))),X_1541),not(and(not(X_1541),or(X,X_1137))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X,X_1137),or(X_1137,not(not(X))))) )],[refute_0_193,refute_0_202]) ).
cnf(refute_0_204,plain,
is_a_theorem(implies(implies(or(X_1565,not(not(X_1564))),X_1566),not(and(not(X_1566),or(X_1564,X_1565))))),
inference(subst,[],[refute_0_203:[bind(X,$fot(X_1564)),bind(X_1137,$fot(X_1565)),bind(X_1541,$fot(X_1566))]]) ).
cnf(refute_0_205,plain,
( ~ is_a_theorem(implies(or(X_1565,not(not(X_1564))),X_1566))
| is_a_theorem(not(and(not(X_1566),or(X_1564,X_1565)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_1565,not(not(X_1564))),X_1566),not(and(not(X_1566),or(X_1564,X_1565))))) )],[refute_0_204,refute_0_186]) ).
cnf(refute_0_206,plain,
( ~ is_a_theorem(implies(or(X_40662,not(not(X_40662))),not(or(not(X_40662),not(X_40662)))))
| is_a_theorem(not(and(not(not(or(not(X_40662),not(X_40662)))),or(X_40662,X_40662)))) ),
inference(subst,[],[refute_0_205:[bind(X_1564,$fot(X_40662)),bind(X_1565,$fot(X_40662)),bind(X_1566,$fot(not(or(not(X_40662),not(X_40662)))))]]) ).
cnf(refute_0_207,plain,
( ~ is_a_theorem(not(equiv(X_1162,not(X_1161))))
| ~ is_a_theorem(or(equiv(X_1162,not(X_1161)),implies(or(X_1161,X_1162),not(implies(X_1162,not(X_1161))))))
| is_a_theorem(implies(or(X_1161,X_1162),not(implies(X_1162,not(X_1161))))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(equiv(X_1162,not(X_1161)))),bind(X_99,$fot(implies(or(X_1161,X_1162),not(implies(X_1162,not(X_1161))))))]]) ).
cnf(refute_0_208,plain,
is_a_theorem(or(and(implies(X_6,not(X)),or(X,X_6)),implies(or(X,X_6),not(implies(X_6,not(X)))))),
inference(subst,[],[refute_0_135:[bind(X_1120,$fot(implies(X_6,not(X)))),bind(X_50,$fot(or(X,X_6)))]]) ).
cnf(refute_0_209,plain,
( equiv(X_6,not(X)) != and(implies(X_6,not(X)),or(X,X_6))
| and(implies(X_6,not(X)),or(X,X_6)) = equiv(X_6,not(X)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(equiv(X_6,not(X)))),bind(Y0,$fot(and(implies(X_6,not(X)),or(X,X_6))))]]) ).
cnf(refute_0_210,plain,
and(implies(X_6,not(X)),or(X,X_6)) = equiv(X_6,not(X)),
inference(resolve,[$cnf( $equal(equiv(X_6,not(X)),and(implies(X_6,not(X)),or(X,X_6))) )],[refute_0_172,refute_0_209]) ).
cnf(refute_0_211,plain,
( and(implies(X_6,not(X)),or(X,X_6)) != equiv(X_6,not(X))
| ~ is_a_theorem(or(and(implies(X_6,not(X)),or(X,X_6)),implies(or(X,X_6),not(implies(X_6,not(X))))))
| is_a_theorem(or(equiv(X_6,not(X)),implies(or(X,X_6),not(implies(X_6,not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(implies(X_6,not(X)),or(X,X_6)),implies(or(X,X_6),not(implies(X_6,not(X)))))) ),[0,0],$fot(equiv(X_6,not(X)))]]) ).
cnf(refute_0_212,plain,
( ~ is_a_theorem(or(and(implies(X_6,not(X)),or(X,X_6)),implies(or(X,X_6),not(implies(X_6,not(X))))))
| is_a_theorem(or(equiv(X_6,not(X)),implies(or(X,X_6),not(implies(X_6,not(X)))))) ),
inference(resolve,[$cnf( $equal(and(implies(X_6,not(X)),or(X,X_6)),equiv(X_6,not(X))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
is_a_theorem(or(equiv(X_6,not(X)),implies(or(X,X_6),not(implies(X_6,not(X)))))),
inference(resolve,[$cnf( is_a_theorem(or(and(implies(X_6,not(X)),or(X,X_6)),implies(or(X,X_6),not(implies(X_6,not(X)))))) )],[refute_0_208,refute_0_212]) ).
cnf(refute_0_214,plain,
is_a_theorem(or(equiv(X_1162,not(X_1161)),implies(or(X_1161,X_1162),not(implies(X_1162,not(X_1161)))))),
inference(subst,[],[refute_0_213:[bind(X,$fot(X_1161)),bind(X_6,$fot(X_1162))]]) ).
cnf(refute_0_215,plain,
( ~ is_a_theorem(not(equiv(X_1162,not(X_1161))))
| is_a_theorem(implies(or(X_1161,X_1162),not(implies(X_1162,not(X_1161))))) ),
inference(resolve,[$cnf( is_a_theorem(or(equiv(X_1162,not(X_1161)),implies(or(X_1161,X_1162),not(implies(X_1162,not(X_1161)))))) )],[refute_0_214,refute_0_207]) ).
cnf(refute_0_216,plain,
( ~ is_a_theorem(not(equiv(not(not(X_40648)),not(X_40648))))
| is_a_theorem(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648))))) ),
inference(subst,[],[refute_0_215:[bind(X_1161,$fot(X_40648)),bind(X_1162,$fot(not(not(X_40648))))]]) ).
cnf(refute_0_217,plain,
( ~ is_a_theorem(not(and(not(not(not(not(not(not(X_40647)))))),or(not(X_40647),not(X_40647)))))
| ~ is_a_theorem(or(and(not(not(not(not(not(not(X_40647)))))),or(not(X_40647),not(X_40647))),not(equiv(not(not(X_40647)),not(X_40647)))))
| is_a_theorem(not(equiv(not(not(X_40647)),not(X_40647)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(not(not(not(not(not(not(X_40647)))))),or(not(X_40647),not(X_40647))))),bind(X_99,$fot(not(equiv(not(not(X_40647)),not(X_40647)))))]]) ).
cnf(refute_0_218,plain,
( ~ is_a_theorem(implies(or(X_39980,not(not(X_39980))),not(not(not(not(not(not(X_39980))))))))
| is_a_theorem(or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))) ),
inference(subst,[],[refute_0_180:[bind(X_170,$fot(not(not(not(not(not(not(X_39980)))))))),bind(X_171,$fot(X_39980)),bind(X_172,$fot(not(not(X_39980))))]]) ).
cnf(refute_0_219,plain,
( ~ is_a_theorem(not(and(not(not(not(not(not(X_39979))))),or(X_39979,not(not(X_39979))))))
| is_a_theorem(implies(or(X_39979,not(not(X_39979))),not(not(not(not(not(not(X_39979)))))))) ),
inference(subst,[],[refute_0_184:[bind(X_1130,$fot(not(not(not(not(not(X_39979))))))),bind(X_1131,$fot(or(X_39979,not(not(X_39979)))))]]) ).
cnf(refute_0_220,plain,
is_a_theorem(implies(X_3264,and(X_3264,X_3264))),
inference(subst,[],[refute_0_104:[bind(P,$fot(X_3264))]]) ).
cnf(refute_0_221,plain,
( ~ is_a_theorem(implies(X_3264,and(X_3264,X_3264)))
| is_a_theorem(or(and(X_3264,X_3264),not(X_3264))) ),
inference(subst,[],[refute_0_148:[bind(X_1137,$fot(and(X_3264,X_3264))),bind(X_1138,$fot(X_3264))]]) ).
cnf(refute_0_222,plain,
is_a_theorem(or(and(X_3264,X_3264),not(X_3264))),
inference(resolve,[$cnf( is_a_theorem(implies(X_3264,and(X_3264,X_3264))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
is_a_theorem(or(and(not(Y),not(Y)),not(not(Y)))),
inference(subst,[],[refute_0_222:[bind(X_3264,$fot(not(Y)))]]) ).
cnf(refute_0_224,plain,
or(and(not(Y),not(Y)),not(not(Y))) = implies(implies(not(Y),Y),not(not(Y))),
inference(subst,[],[refute_0_114:[bind(X,$fot(not(Y))),bind(X_4,$fot(not(not(Y))))]]) ).
cnf(refute_0_225,plain,
( or(and(not(Y),not(Y)),not(not(Y))) != implies(implies(not(Y),Y),not(not(Y)))
| ~ is_a_theorem(or(and(not(Y),not(Y)),not(not(Y))))
| is_a_theorem(implies(implies(not(Y),Y),not(not(Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(Y),not(Y)),not(not(Y)))) ),[0],$fot(implies(implies(not(Y),Y),not(not(Y))))]]) ).
cnf(refute_0_226,plain,
( ~ is_a_theorem(or(and(not(Y),not(Y)),not(not(Y))))
| is_a_theorem(implies(implies(not(Y),Y),not(not(Y)))) ),
inference(resolve,[$cnf( $equal(or(and(not(Y),not(Y)),not(not(Y))),implies(implies(not(Y),Y),not(not(Y)))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
is_a_theorem(implies(implies(not(Y),Y),not(not(Y)))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(Y),not(Y)),not(not(Y)))) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
implies(not(Y),Y) = or(Y,Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(Y))]]) ).
cnf(refute_0_229,plain,
implies(implies(not(Y),Y),not(not(Y))) = implies(implies(not(Y),Y),not(not(Y))),
introduced(tautology,[refl,[$fot(implies(implies(not(Y),Y),not(not(Y))))]]) ).
cnf(refute_0_230,plain,
( implies(implies(not(Y),Y),not(not(Y))) != implies(implies(not(Y),Y),not(not(Y)))
| implies(not(Y),Y) != or(Y,Y)
| implies(implies(not(Y),Y),not(not(Y))) = implies(or(Y,Y),not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),Y),not(not(Y))),implies(implies(not(Y),Y),not(not(Y)))) ),[1,0],$fot(or(Y,Y))]]) ).
cnf(refute_0_231,plain,
( implies(not(Y),Y) != or(Y,Y)
| implies(implies(not(Y),Y),not(not(Y))) = implies(or(Y,Y),not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),Y),not(not(Y))),implies(implies(not(Y),Y),not(not(Y)))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
implies(implies(not(Y),Y),not(not(Y))) = implies(or(Y,Y),not(not(Y))),
inference(resolve,[$cnf( $equal(implies(not(Y),Y),or(Y,Y)) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
( implies(implies(not(Y),Y),not(not(Y))) != implies(or(Y,Y),not(not(Y)))
| ~ is_a_theorem(implies(implies(not(Y),Y),not(not(Y))))
| is_a_theorem(implies(or(Y,Y),not(not(Y)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),Y),not(not(Y)))) ),[0],$fot(implies(or(Y,Y),not(not(Y))))]]) ).
cnf(refute_0_234,plain,
( ~ is_a_theorem(implies(implies(not(Y),Y),not(not(Y))))
| is_a_theorem(implies(or(Y,Y),not(not(Y)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),Y),not(not(Y))),implies(or(Y,Y),not(not(Y)))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
is_a_theorem(implies(or(Y,Y),not(not(Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),Y),not(not(Y)))) )],[refute_0_227,refute_0_234]) ).
cnf(refute_0_236,plain,
is_a_theorem(implies(or(not(not(X_39968)),not(not(X_39968))),not(not(not(not(X_39968)))))),
inference(subst,[],[refute_0_235:[bind(Y,$fot(not(not(X_39968))))]]) ).
cnf(refute_0_237,plain,
( ~ is_a_theorem(implies(or(not(not(X_39968)),not(not(X_39968))),not(not(not(not(X_39968))))))
| is_a_theorem(not(and(not(not(not(not(not(X_39968))))),or(X_39968,not(not(X_39968)))))) ),
inference(subst,[],[refute_0_205:[bind(X_1564,$fot(X_39968)),bind(X_1565,$fot(not(not(X_39968)))),bind(X_1566,$fot(not(not(not(not(X_39968))))))]]) ).
cnf(refute_0_238,plain,
is_a_theorem(not(and(not(not(not(not(not(X_39968))))),or(X_39968,not(not(X_39968)))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(not(X_39968)),not(not(X_39968))),not(not(not(not(X_39968)))))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
is_a_theorem(not(and(not(not(not(not(not(X_39979))))),or(X_39979,not(not(X_39979)))))),
inference(subst,[],[refute_0_238:[bind(X_39968,$fot(X_39979))]]) ).
cnf(refute_0_240,plain,
is_a_theorem(implies(or(X_39979,not(not(X_39979))),not(not(not(not(not(not(X_39979)))))))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(not(not(not(X_39979))))),or(X_39979,not(not(X_39979)))))) )],[refute_0_239,refute_0_219]) ).
cnf(refute_0_241,plain,
is_a_theorem(implies(or(X_39980,not(not(X_39980))),not(not(not(not(not(not(X_39980)))))))),
inference(subst,[],[refute_0_240:[bind(X_39979,$fot(X_39980))]]) ).
cnf(refute_0_242,plain,
is_a_theorem(or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_39980,not(not(X_39980))),not(not(not(not(not(not(X_39980)))))))) )],[refute_0_241,refute_0_218]) ).
cnf(refute_0_243,plain,
implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) = or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))),
inference(subst,[],[refute_0_17:[bind(X,$fot(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))))),bind(Y,$fot(not(equiv(not(not(X_39980)),not(X_39980)))))]]) ).
cnf(refute_0_244,plain,
or(X,and(X_25,not(X_26))) = implies(not(X),and(X_25,not(X_26))),
inference(subst,[],[refute_0_15:[bind(Y,$fot(and(X_25,not(X_26))))]]) ).
cnf(refute_0_245,plain,
implies(X,and(X_1,not(X_2))) = not(and(X,not(and(X_1,not(X_2))))),
inference(subst,[],[refute_0_6:[bind(Y,$fot(and(X_1,not(X_2))))]]) ).
cnf(refute_0_246,plain,
implies(X_1,X_2) = not(and(X_1,not(X_2))),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_1)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_247,plain,
( implies(X_1,X_2) != not(and(X_1,not(X_2)))
| not(and(X_1,not(X_2))) = implies(X_1,X_2) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(implies(X_1,X_2))),bind(Y0,$fot(not(and(X_1,not(X_2)))))]]) ).
cnf(refute_0_248,plain,
not(and(X_1,not(X_2))) = implies(X_1,X_2),
inference(resolve,[$cnf( $equal(implies(X_1,X_2),not(and(X_1,not(X_2)))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
( implies(X,and(X_1,not(X_2))) != not(and(X,not(and(X_1,not(X_2)))))
| not(and(X_1,not(X_2))) != implies(X_1,X_2)
| implies(X,and(X_1,not(X_2))) = not(and(X,implies(X_1,X_2))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_1,not(X_2))),not(and(X,not(and(X_1,not(X_2)))))) ),[1,0,1],$fot(implies(X_1,X_2))]]) ).
cnf(refute_0_250,plain,
( implies(X,and(X_1,not(X_2))) != not(and(X,not(and(X_1,not(X_2)))))
| implies(X,and(X_1,not(X_2))) = not(and(X,implies(X_1,X_2))) ),
inference(resolve,[$cnf( $equal(not(and(X_1,not(X_2))),implies(X_1,X_2)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(X,and(X_1,not(X_2))) = not(and(X,implies(X_1,X_2))),
inference(resolve,[$cnf( $equal(implies(X,and(X_1,not(X_2))),not(and(X,not(and(X_1,not(X_2)))))) )],[refute_0_245,refute_0_250]) ).
cnf(refute_0_252,plain,
implies(not(X),and(X_25,not(X_26))) = not(and(not(X),implies(X_25,X_26))),
inference(subst,[],[refute_0_251:[bind(X,$fot(not(X))),bind(X_1,$fot(X_25)),bind(X_2,$fot(X_26))]]) ).
cnf(refute_0_253,plain,
( implies(not(X),and(X_25,not(X_26))) != not(and(not(X),implies(X_25,X_26)))
| or(X,and(X_25,not(X_26))) != implies(not(X),and(X_25,not(X_26)))
| or(X,and(X_25,not(X_26))) = not(and(not(X),implies(X_25,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,and(X_25,not(X_26))),implies(not(X),and(X_25,not(X_26)))) ),[1],$fot(not(and(not(X),implies(X_25,X_26))))]]) ).
cnf(refute_0_254,plain,
( or(X,and(X_25,not(X_26))) != implies(not(X),and(X_25,not(X_26)))
| or(X,and(X_25,not(X_26))) = not(and(not(X),implies(X_25,X_26))) ),
inference(resolve,[$cnf( $equal(implies(not(X),and(X_25,not(X_26))),not(and(not(X),implies(X_25,X_26)))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
or(X,and(X_25,not(X_26))) = not(and(not(X),implies(X_25,X_26))),
inference(resolve,[$cnf( $equal(or(X,and(X_25,not(X_26))),implies(not(X),and(X_25,not(X_26)))) )],[refute_0_244,refute_0_254]) ).
cnf(refute_0_256,plain,
or(X_27,and(not(X),not(X_29))) = not(and(not(X_27),implies(not(X),X_29))),
inference(subst,[],[refute_0_255:[bind(X,$fot(X_27)),bind(X_25,$fot(not(X))),bind(X_26,$fot(X_29))]]) ).
cnf(refute_0_257,plain,
or(X,X_29) = implies(not(X),X_29),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_258,plain,
( or(X,X_29) != implies(not(X),X_29)
| implies(not(X),X_29) = or(X,X_29) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,X_29))),bind(Y0,$fot(implies(not(X),X_29)))]]) ).
cnf(refute_0_259,plain,
implies(not(X),X_29) = or(X,X_29),
inference(resolve,[$cnf( $equal(or(X,X_29),implies(not(X),X_29)) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
( implies(not(X),X_29) != or(X,X_29)
| or(X_27,and(not(X),not(X_29))) != not(and(not(X_27),implies(not(X),X_29)))
| or(X_27,and(not(X),not(X_29))) = not(and(not(X_27),or(X,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_27,and(not(X),not(X_29))),not(and(not(X_27),implies(not(X),X_29)))) ),[1,0,1],$fot(or(X,X_29))]]) ).
cnf(refute_0_261,plain,
( or(X_27,and(not(X),not(X_29))) != not(and(not(X_27),implies(not(X),X_29)))
| or(X_27,and(not(X),not(X_29))) = not(and(not(X_27),or(X,X_29))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_29),or(X,X_29)) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
or(X_27,and(not(X),not(X_29))) = not(and(not(X_27),or(X,X_29))),
inference(resolve,[$cnf( $equal(or(X_27,and(not(X),not(X_29))),not(and(not(X_27),implies(not(X),X_29)))) )],[refute_0_256,refute_0_261]) ).
cnf(refute_0_263,plain,
or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))) = not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),
inference(subst,[],[refute_0_262:[bind(X,$fot(not(X_39980))),bind(X_27,$fot(not(not(not(not(not(X_39980))))))),bind(X_29,$fot(not(X_39980)))]]) ).
cnf(refute_0_264,plain,
implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) = implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))),
introduced(tautology,[refl,[$fot(implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))))]]) ).
cnf(refute_0_265,plain,
( implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) != implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980))))
| or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))) != not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))))
| implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) = implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))),implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980))))) ),[1,0],$fot(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))))]]) ).
cnf(refute_0_266,plain,
( or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))) != not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))))
| implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) = implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))),implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980))))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) = implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))),
inference(resolve,[$cnf( $equal(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))))) )],[refute_0_263,refute_0_266]) ).
cnf(refute_0_268,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_269,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_9,refute_0_268]) ).
cnf(refute_0_270,plain,
( implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) != or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))
| implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) != implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980))))
| implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) = or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) ),
inference(subst,[],[refute_0_269:[bind(X0,$fot(implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))))),bind(Y0,$fot(implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))))),bind(Z,$fot(or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))))]]) ).
cnf(refute_0_271,plain,
( implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) != or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))
| implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) = or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))),implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980))))) )],[refute_0_267,refute_0_270]) ).
cnf(refute_0_272,plain,
implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) = or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))),
inference(resolve,[$cnf( $equal(implies(not(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))),or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))) )],[refute_0_243,refute_0_271]) ).
cnf(refute_0_273,plain,
or(and(not(X_27),implies(X_28,X_29)),Y) = implies(not(and(not(X_27),implies(X_28,X_29))),Y),
inference(subst,[],[refute_0_15:[bind(X,$fot(and(not(X_27),implies(X_28,X_29))))]]) ).
cnf(refute_0_274,plain,
or(X_27,and(X_28,not(X_29))) = not(and(not(X_27),implies(X_28,X_29))),
inference(subst,[],[refute_0_255:[bind(X,$fot(X_27)),bind(X_25,$fot(X_28)),bind(X_26,$fot(X_29))]]) ).
cnf(refute_0_275,plain,
( or(X_27,and(X_28,not(X_29))) != not(and(not(X_27),implies(X_28,X_29)))
| not(and(not(X_27),implies(X_28,X_29))) = or(X_27,and(X_28,not(X_29))) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X_27,and(X_28,not(X_29))))),bind(Y0,$fot(not(and(not(X_27),implies(X_28,X_29)))))]]) ).
cnf(refute_0_276,plain,
not(and(not(X_27),implies(X_28,X_29))) = or(X_27,and(X_28,not(X_29))),
inference(resolve,[$cnf( $equal(or(X_27,and(X_28,not(X_29))),not(and(not(X_27),implies(X_28,X_29)))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
( not(and(not(X_27),implies(X_28,X_29))) != or(X_27,and(X_28,not(X_29)))
| or(and(not(X_27),implies(X_28,X_29)),Y) != implies(not(and(not(X_27),implies(X_28,X_29))),Y)
| or(and(not(X_27),implies(X_28,X_29)),Y) = implies(or(X_27,and(X_28,not(X_29))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_27),implies(X_28,X_29)),Y),implies(not(and(not(X_27),implies(X_28,X_29))),Y)) ),[1,0],$fot(or(X_27,and(X_28,not(X_29))))]]) ).
cnf(refute_0_278,plain,
( or(and(not(X_27),implies(X_28,X_29)),Y) != implies(not(and(not(X_27),implies(X_28,X_29))),Y)
| or(and(not(X_27),implies(X_28,X_29)),Y) = implies(or(X_27,and(X_28,not(X_29))),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X_27),implies(X_28,X_29))),or(X_27,and(X_28,not(X_29)))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
or(and(not(X_27),implies(X_28,X_29)),Y) = implies(or(X_27,and(X_28,not(X_29))),Y),
inference(resolve,[$cnf( $equal(or(and(not(X_27),implies(X_28,X_29)),Y),implies(not(and(not(X_27),implies(X_28,X_29))),Y)) )],[refute_0_273,refute_0_278]) ).
cnf(refute_0_280,plain,
or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) = implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))),
inference(subst,[],[refute_0_279:[bind(Y,$fot(not(equiv(not(not(X_39980)),not(X_39980))))),bind(X_27,$fot(not(not(not(not(not(X_39980))))))),bind(X_28,$fot(not(not(X_39980)))),bind(X_29,$fot(not(X_39980)))]]) ).
cnf(refute_0_281,plain,
( implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) != or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))
| or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) != implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980))))
| or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) = or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) ),
inference(subst,[],[refute_0_269:[bind(X0,$fot(or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))))),bind(Y0,$fot(implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))))),bind(Z,$fot(or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))))]]) ).
cnf(refute_0_282,plain,
( implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))) != or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))
| or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) = or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) ),
inference(resolve,[$cnf( $equal(or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))),implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980))))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) = or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))),
inference(resolve,[$cnf( $equal(implies(or(not(not(not(not(not(X_39980))))),and(not(not(X_39980)),not(not(X_39980)))),not(equiv(not(not(X_39980)),not(X_39980)))),or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))) )],[refute_0_272,refute_0_282]) ).
cnf(refute_0_284,plain,
( or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))) != or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))
| ~ is_a_theorem(or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))))
| is_a_theorem(or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))) ),[0],$fot(or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))))]]) ).
cnf(refute_0_285,plain,
( ~ is_a_theorem(or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))))
| is_a_theorem(or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))) ),
inference(resolve,[$cnf( $equal(or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980)))),or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
is_a_theorem(or(and(not(not(not(not(not(not(X_39980)))))),or(not(X_39980),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(not(not(not(not(X_39980)))))),implies(not(not(X_39980)),not(X_39980))),not(equiv(not(not(X_39980)),not(X_39980))))) )],[refute_0_242,refute_0_285]) ).
cnf(refute_0_287,plain,
is_a_theorem(or(and(not(not(not(not(not(not(X_40647)))))),or(not(X_40647),not(X_40647))),not(equiv(not(not(X_40647)),not(X_40647))))),
inference(subst,[],[refute_0_286:[bind(X_39980,$fot(X_40647))]]) ).
cnf(refute_0_288,plain,
( ~ is_a_theorem(not(and(not(not(not(not(not(not(X_40647)))))),or(not(X_40647),not(X_40647)))))
| is_a_theorem(not(equiv(not(not(X_40647)),not(X_40647)))) ),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(not(not(not(not(X_40647)))))),or(not(X_40647),not(X_40647))),not(equiv(not(not(X_40647)),not(X_40647))))) )],[refute_0_287,refute_0_217]) ).
cnf(refute_0_289,plain,
( ~ is_a_theorem(implies(and(or(X_13693,X_13693),or(X_13693,X_13693)),not(not(not(not(X_13693))))))
| is_a_theorem(not(and(not(not(not(not(not(X_13693))))),or(X_13693,X_13693)))) ),
inference(subst,[],[refute_0_120:[bind(X_353,$fot(not(not(not(not(X_13693)))))),bind(X_354,$fot(or(X_13693,X_13693)))]]) ).
cnf(refute_0_290,plain,
( ~ is_a_theorem(implies(X_332,X_330))
| ~ is_a_theorem(implies(implies(X_332,X_330),not(and(not(X_330),and(X_332,X_331)))))
| is_a_theorem(not(and(not(X_330),and(X_332,X_331)))) ),
inference(subst,[],[refute_0_30:[bind(X,$fot(implies(X_332,X_330))),bind(Y,$fot(not(and(not(X_330),and(X_332,X_331)))))]]) ).
cnf(refute_0_291,plain,
is_a_theorem(implies(and(X_294,Q),X_294)),
inference(subst,[],[refute_0_79:[bind(P,$fot(X_294))]]) ).
cnf(refute_0_292,plain,
( ~ is_a_theorem(implies(and(X_294,Q),X_294))
| is_a_theorem(or(and(X_294,X_295),not(and(X_295,and(X_294,Q))))) ),
inference(subst,[],[refute_0_107:[bind(P,$fot(and(X_294,Q))),bind(Q,$fot(X_294)),bind(R,$fot(X_295))]]) ).
cnf(refute_0_293,plain,
is_a_theorem(or(and(X_294,X_295),not(and(X_295,and(X_294,Q))))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_294,Q),X_294)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
is_a_theorem(or(and(X_300,not(Y)),not(and(not(Y),and(X_300,X_299))))),
inference(subst,[],[refute_0_293:[bind(Q,$fot(X_299)),bind(X_294,$fot(X_300)),bind(X_295,$fot(not(Y)))]]) ).
cnf(refute_0_295,plain,
or(and(X_300,not(Y)),not(and(not(Y),and(X_300,X_299)))) = implies(implies(X_300,Y),not(and(not(Y),and(X_300,X_299)))),
inference(subst,[],[refute_0_114:[bind(X,$fot(X_300)),bind(X_4,$fot(not(and(not(Y),and(X_300,X_299)))))]]) ).
cnf(refute_0_296,plain,
( or(and(X_300,not(Y)),not(and(not(Y),and(X_300,X_299)))) != implies(implies(X_300,Y),not(and(not(Y),and(X_300,X_299))))
| ~ is_a_theorem(or(and(X_300,not(Y)),not(and(not(Y),and(X_300,X_299)))))
| is_a_theorem(implies(implies(X_300,Y),not(and(not(Y),and(X_300,X_299))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(X_300,not(Y)),not(and(not(Y),and(X_300,X_299))))) ),[0],$fot(implies(implies(X_300,Y),not(and(not(Y),and(X_300,X_299)))))]]) ).
cnf(refute_0_297,plain,
( ~ is_a_theorem(or(and(X_300,not(Y)),not(and(not(Y),and(X_300,X_299)))))
| is_a_theorem(implies(implies(X_300,Y),not(and(not(Y),and(X_300,X_299))))) ),
inference(resolve,[$cnf( $equal(or(and(X_300,not(Y)),not(and(not(Y),and(X_300,X_299)))),implies(implies(X_300,Y),not(and(not(Y),and(X_300,X_299))))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
is_a_theorem(implies(implies(X_300,Y),not(and(not(Y),and(X_300,X_299))))),
inference(resolve,[$cnf( is_a_theorem(or(and(X_300,not(Y)),not(and(not(Y),and(X_300,X_299))))) )],[refute_0_294,refute_0_297]) ).
cnf(refute_0_299,plain,
is_a_theorem(implies(implies(X_332,X_330),not(and(not(X_330),and(X_332,X_331))))),
inference(subst,[],[refute_0_298:[bind(Y,$fot(X_330)),bind(X_299,$fot(X_331)),bind(X_300,$fot(X_332))]]) ).
cnf(refute_0_300,plain,
( ~ is_a_theorem(implies(X_332,X_330))
| is_a_theorem(not(and(not(X_330),and(X_332,X_331)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_332,X_330),not(and(not(X_330),and(X_332,X_331))))) )],[refute_0_299,refute_0_290]) ).
cnf(refute_0_301,plain,
( ~ is_a_theorem(implies(or(X_3269,X_3269),not(not(X_3269))))
| is_a_theorem(not(and(not(not(not(X_3269))),and(or(X_3269,X_3269),X_331)))) ),
inference(subst,[],[refute_0_300:[bind(X_330,$fot(not(not(X_3269)))),bind(X_332,$fot(or(X_3269,X_3269)))]]) ).
cnf(refute_0_302,plain,
is_a_theorem(implies(or(X_3269,X_3269),not(not(X_3269)))),
inference(subst,[],[refute_0_235:[bind(Y,$fot(X_3269))]]) ).
cnf(refute_0_303,plain,
is_a_theorem(not(and(not(not(not(X_3269))),and(or(X_3269,X_3269),X_331)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_3269,X_3269),not(not(X_3269)))) )],[refute_0_302,refute_0_301]) ).
cnf(refute_0_304,plain,
( ~ is_a_theorem(not(and(not(not(not(X_3269))),and(or(X_3269,X_3269),X_331))))
| is_a_theorem(implies(and(or(X_3269,X_3269),X_331),not(not(not(not(X_3269)))))) ),
inference(subst,[],[refute_0_184:[bind(X_1130,$fot(not(not(not(X_3269))))),bind(X_1131,$fot(and(or(X_3269,X_3269),X_331)))]]) ).
cnf(refute_0_305,plain,
is_a_theorem(implies(and(or(X_3269,X_3269),X_331),not(not(not(not(X_3269)))))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(not(X_3269))),and(or(X_3269,X_3269),X_331)))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
is_a_theorem(implies(and(or(X_13693,X_13693),or(X_13693,X_13693)),not(not(not(not(X_13693)))))),
inference(subst,[],[refute_0_305:[bind(X_3269,$fot(X_13693)),bind(X_331,$fot(or(X_13693,X_13693)))]]) ).
cnf(refute_0_307,plain,
is_a_theorem(not(and(not(not(not(not(not(X_13693))))),or(X_13693,X_13693)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(or(X_13693,X_13693),or(X_13693,X_13693)),not(not(not(not(X_13693)))))) )],[refute_0_306,refute_0_289]) ).
cnf(refute_0_308,plain,
is_a_theorem(not(and(not(not(not(not(not(not(X_40647)))))),or(not(X_40647),not(X_40647))))),
inference(subst,[],[refute_0_307:[bind(X_13693,$fot(not(X_40647)))]]) ).
cnf(refute_0_309,plain,
is_a_theorem(not(equiv(not(not(X_40647)),not(X_40647)))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(not(not(not(not(X_40647)))))),or(not(X_40647),not(X_40647))))) )],[refute_0_308,refute_0_288]) ).
cnf(refute_0_310,plain,
is_a_theorem(not(equiv(not(not(X_40648)),not(X_40648)))),
inference(subst,[],[refute_0_309:[bind(X_40647,$fot(X_40648))]]) ).
cnf(refute_0_311,plain,
is_a_theorem(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648))))),
inference(resolve,[$cnf( is_a_theorem(not(equiv(not(not(X_40648)),not(X_40648)))) )],[refute_0_310,refute_0_216]) ).
cnf(refute_0_312,plain,
implies(not(not(X_40648)),not(X_40648)) = or(not(X_40648),not(X_40648)),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(X_40648))),bind(Y,$fot(not(X_40648)))]]) ).
cnf(refute_0_313,plain,
not(implies(not(not(X_40648)),not(X_40648))) = not(implies(not(not(X_40648)),not(X_40648))),
introduced(tautology,[refl,[$fot(not(implies(not(not(X_40648)),not(X_40648))))]]) ).
cnf(refute_0_314,plain,
( implies(not(not(X_40648)),not(X_40648)) != or(not(X_40648),not(X_40648))
| not(implies(not(not(X_40648)),not(X_40648))) != not(implies(not(not(X_40648)),not(X_40648)))
| not(implies(not(not(X_40648)),not(X_40648))) = not(or(not(X_40648),not(X_40648))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(X_40648)),not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))) ),[1,0],$fot(or(not(X_40648),not(X_40648)))]]) ).
cnf(refute_0_315,plain,
( implies(not(not(X_40648)),not(X_40648)) != or(not(X_40648),not(X_40648))
| not(implies(not(not(X_40648)),not(X_40648))) = not(or(not(X_40648),not(X_40648))) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(X_40648)),not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
not(implies(not(not(X_40648)),not(X_40648))) = not(or(not(X_40648),not(X_40648))),
inference(resolve,[$cnf( $equal(implies(not(not(X_40648)),not(X_40648)),or(not(X_40648),not(X_40648))) )],[refute_0_312,refute_0_315]) ).
cnf(refute_0_317,plain,
implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))) = implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))),
introduced(tautology,[refl,[$fot(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))))]]) ).
cnf(refute_0_318,plain,
( implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))) != implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648))))
| not(implies(not(not(X_40648)),not(X_40648))) != not(or(not(X_40648),not(X_40648)))
| implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))) = implies(or(X_40648,not(not(X_40648))),not(or(not(X_40648),not(X_40648)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))),implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648))))) ),[1,1],$fot(not(or(not(X_40648),not(X_40648))))]]) ).
cnf(refute_0_319,plain,
( not(implies(not(not(X_40648)),not(X_40648))) != not(or(not(X_40648),not(X_40648)))
| implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))) = implies(or(X_40648,not(not(X_40648))),not(or(not(X_40648),not(X_40648)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))),implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648))))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))) = implies(or(X_40648,not(not(X_40648))),not(or(not(X_40648),not(X_40648)))),
inference(resolve,[$cnf( $equal(not(implies(not(not(X_40648)),not(X_40648))),not(or(not(X_40648),not(X_40648)))) )],[refute_0_316,refute_0_319]) ).
cnf(refute_0_321,plain,
( implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))) != implies(or(X_40648,not(not(X_40648))),not(or(not(X_40648),not(X_40648))))
| ~ is_a_theorem(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))))
| is_a_theorem(implies(or(X_40648,not(not(X_40648))),not(or(not(X_40648),not(X_40648))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648))))) ),[0],$fot(implies(or(X_40648,not(not(X_40648))),not(or(not(X_40648),not(X_40648)))))]]) ).
cnf(refute_0_322,plain,
( ~ is_a_theorem(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))))
| is_a_theorem(implies(or(X_40648,not(not(X_40648))),not(or(not(X_40648),not(X_40648))))) ),
inference(resolve,[$cnf( $equal(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648)))),implies(or(X_40648,not(not(X_40648))),not(or(not(X_40648),not(X_40648))))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
is_a_theorem(implies(or(X_40648,not(not(X_40648))),not(or(not(X_40648),not(X_40648))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_40648,not(not(X_40648))),not(implies(not(not(X_40648)),not(X_40648))))) )],[refute_0_311,refute_0_322]) ).
cnf(refute_0_324,plain,
is_a_theorem(implies(or(X_40662,not(not(X_40662))),not(or(not(X_40662),not(X_40662))))),
inference(subst,[],[refute_0_323:[bind(X_40648,$fot(X_40662))]]) ).
cnf(refute_0_325,plain,
is_a_theorem(not(and(not(not(or(not(X_40662),not(X_40662)))),or(X_40662,X_40662)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_40662,not(not(X_40662))),not(or(not(X_40662),not(X_40662))))) )],[refute_0_324,refute_0_206]) ).
cnf(refute_0_326,plain,
is_a_theorem(not(and(not(not(or(not(X_40663),not(X_40663)))),or(X_40663,X_40663)))),
inference(subst,[],[refute_0_325:[bind(X_40662,$fot(X_40663))]]) ).
cnf(refute_0_327,plain,
is_a_theorem(implies(or(X_40663,X_40663),not(not(not(or(not(X_40663),not(X_40663))))))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(or(not(X_40663),not(X_40663)))),or(X_40663,X_40663)))) )],[refute_0_326,refute_0_185]) ).
cnf(refute_0_328,plain,
is_a_theorem(implies(or(X_40664,X_40664),not(not(not(or(not(X_40664),not(X_40664))))))),
inference(subst,[],[refute_0_327:[bind(X_40663,$fot(X_40664))]]) ).
cnf(refute_0_329,plain,
is_a_theorem(or(and(not(not(not(or(not(X_40664),not(X_40664))))),implies(X_40664,not(X_40664))),not(equiv(X_40664,not(X_40664))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_40664,X_40664),not(not(not(or(not(X_40664),not(X_40664))))))) )],[refute_0_328,refute_0_181]) ).
cnf(refute_0_330,plain,
or(and(not(not(not(or(not(X_40664),not(X_40664))))),implies(X_40664,not(X_40664))),not(equiv(X_40664,not(X_40664)))) = implies(or(not(not(or(not(X_40664),not(X_40664)))),and(X_40664,not(not(X_40664)))),not(equiv(X_40664,not(X_40664)))),
inference(subst,[],[refute_0_279:[bind(Y,$fot(not(equiv(X_40664,not(X_40664))))),bind(X_27,$fot(not(not(or(not(X_40664),not(X_40664)))))),bind(X_28,$fot(X_40664)),bind(X_29,$fot(not(X_40664)))]]) ).
cnf(refute_0_331,plain,
( or(and(not(not(not(or(not(X_40664),not(X_40664))))),implies(X_40664,not(X_40664))),not(equiv(X_40664,not(X_40664)))) != implies(or(not(not(or(not(X_40664),not(X_40664)))),and(X_40664,not(not(X_40664)))),not(equiv(X_40664,not(X_40664))))
| ~ is_a_theorem(or(and(not(not(not(or(not(X_40664),not(X_40664))))),implies(X_40664,not(X_40664))),not(equiv(X_40664,not(X_40664)))))
| is_a_theorem(implies(or(not(not(or(not(X_40664),not(X_40664)))),and(X_40664,not(not(X_40664)))),not(equiv(X_40664,not(X_40664))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(not(not(or(not(X_40664),not(X_40664))))),implies(X_40664,not(X_40664))),not(equiv(X_40664,not(X_40664))))) ),[0],$fot(implies(or(not(not(or(not(X_40664),not(X_40664)))),and(X_40664,not(not(X_40664)))),not(equiv(X_40664,not(X_40664)))))]]) ).
cnf(refute_0_332,plain,
( ~ is_a_theorem(or(and(not(not(not(or(not(X_40664),not(X_40664))))),implies(X_40664,not(X_40664))),not(equiv(X_40664,not(X_40664)))))
| is_a_theorem(implies(or(not(not(or(not(X_40664),not(X_40664)))),and(X_40664,not(not(X_40664)))),not(equiv(X_40664,not(X_40664))))) ),
inference(resolve,[$cnf( $equal(or(and(not(not(not(or(not(X_40664),not(X_40664))))),implies(X_40664,not(X_40664))),not(equiv(X_40664,not(X_40664)))),implies(or(not(not(or(not(X_40664),not(X_40664)))),and(X_40664,not(not(X_40664)))),not(equiv(X_40664,not(X_40664))))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
is_a_theorem(implies(or(not(not(or(not(X_40664),not(X_40664)))),and(X_40664,not(not(X_40664)))),not(equiv(X_40664,not(X_40664))))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(not(not(or(not(X_40664),not(X_40664))))),implies(X_40664,not(X_40664))),not(equiv(X_40664,not(X_40664))))) )],[refute_0_329,refute_0_332]) ).
cnf(refute_0_334,plain,
is_a_theorem(implies(or(not(not(or(not(X_47909),not(X_47909)))),and(X_47909,not(not(X_47909)))),not(equiv(X_47909,not(X_47909))))),
inference(subst,[],[refute_0_333:[bind(X_40664,$fot(X_47909))]]) ).
cnf(refute_0_335,plain,
( ~ is_a_theorem(or(not(not(or(not(X_47909),not(X_47909)))),and(X_47909,not(not(X_47909)))))
| is_a_theorem(not(equiv(X_47909,not(X_47909)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(not(or(not(X_47909),not(X_47909)))),and(X_47909,not(not(X_47909)))),not(equiv(X_47909,not(X_47909))))) )],[refute_0_334,refute_0_163]) ).
cnf(refute_0_336,plain,
( ~ is_a_theorem(implies(and(implies(X_13256,X_13255),implies(X_13256,X_13255)),not(not(or(X_13255,not(X_13256))))))
| is_a_theorem(not(and(not(not(not(or(X_13255,not(X_13256))))),implies(X_13256,X_13255)))) ),
inference(subst,[],[refute_0_120:[bind(X_353,$fot(not(not(or(X_13255,not(X_13256)))))),bind(X_354,$fot(implies(X_13256,X_13255)))]]) ).
cnf(refute_0_337,plain,
( ~ is_a_theorem(implies(implies(X_1130,X),or(X,not(X_1130))))
| is_a_theorem(not(and(not(or(X,not(X_1130))),and(implies(X_1130,X),X_2281)))) ),
inference(subst,[],[refute_0_300:[bind(X_330,$fot(or(X,not(X_1130)))),bind(X_331,$fot(X_2281)),bind(X_332,$fot(implies(X_1130,X)))]]) ).
cnf(refute_0_338,plain,
is_a_theorem(not(and(not(or(X,not(X_1130))),and(implies(X_1130,X),X_2281)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1130,X),or(X,not(X_1130)))) )],[refute_0_146,refute_0_337]) ).
cnf(refute_0_339,plain,
( ~ is_a_theorem(not(and(not(or(X,not(X_1130))),and(implies(X_1130,X),X_2281))))
| is_a_theorem(implies(and(implies(X_1130,X),X_2281),not(not(or(X,not(X_1130)))))) ),
inference(subst,[],[refute_0_184:[bind(X_1130,$fot(not(or(X,not(X_1130))))),bind(X_1131,$fot(and(implies(X_1130,X),X_2281)))]]) ).
cnf(refute_0_340,plain,
is_a_theorem(implies(and(implies(X_1130,X),X_2281),not(not(or(X,not(X_1130)))))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(or(X,not(X_1130))),and(implies(X_1130,X),X_2281)))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
is_a_theorem(implies(and(implies(X_13256,X_13255),implies(X_13256,X_13255)),not(not(or(X_13255,not(X_13256)))))),
inference(subst,[],[refute_0_340:[bind(X,$fot(X_13255)),bind(X_1130,$fot(X_13256)),bind(X_2281,$fot(implies(X_13256,X_13255)))]]) ).
cnf(refute_0_342,plain,
is_a_theorem(not(and(not(not(not(or(X_13255,not(X_13256))))),implies(X_13256,X_13255)))),
inference(resolve,[$cnf( is_a_theorem(implies(and(implies(X_13256,X_13255),implies(X_13256,X_13255)),not(not(or(X_13255,not(X_13256)))))) )],[refute_0_341,refute_0_336]) ).
cnf(refute_0_343,plain,
( or(X,and(X_25,not(X_26))) != not(and(not(X),implies(X_25,X_26)))
| not(and(not(X),implies(X_25,X_26))) = or(X,and(X_25,not(X_26))) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(or(X,and(X_25,not(X_26))))),bind(Y0,$fot(not(and(not(X),implies(X_25,X_26)))))]]) ).
cnf(refute_0_344,plain,
not(and(not(X),implies(X_25,X_26))) = or(X,and(X_25,not(X_26))),
inference(resolve,[$cnf( $equal(or(X,and(X_25,not(X_26))),not(and(not(X),implies(X_25,X_26)))) )],[refute_0_255,refute_0_343]) ).
cnf(refute_0_345,plain,
not(and(not(not(not(or(X_13255,not(X_13256))))),implies(X_13256,X_13255))) = or(not(not(or(X_13255,not(X_13256)))),and(X_13256,not(X_13255))),
inference(subst,[],[refute_0_344:[bind(X,$fot(not(not(or(X_13255,not(X_13256)))))),bind(X_25,$fot(X_13256)),bind(X_26,$fot(X_13255))]]) ).
cnf(refute_0_346,plain,
( not(and(not(not(not(or(X_13255,not(X_13256))))),implies(X_13256,X_13255))) != or(not(not(or(X_13255,not(X_13256)))),and(X_13256,not(X_13255)))
| ~ is_a_theorem(not(and(not(not(not(or(X_13255,not(X_13256))))),implies(X_13256,X_13255))))
| is_a_theorem(or(not(not(or(X_13255,not(X_13256)))),and(X_13256,not(X_13255)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(not(not(not(or(X_13255,not(X_13256))))),implies(X_13256,X_13255)))) ),[0],$fot(or(not(not(or(X_13255,not(X_13256)))),and(X_13256,not(X_13255))))]]) ).
cnf(refute_0_347,plain,
( ~ is_a_theorem(not(and(not(not(not(or(X_13255,not(X_13256))))),implies(X_13256,X_13255))))
| is_a_theorem(or(not(not(or(X_13255,not(X_13256)))),and(X_13256,not(X_13255)))) ),
inference(resolve,[$cnf( $equal(not(and(not(not(not(or(X_13255,not(X_13256))))),implies(X_13256,X_13255))),or(not(not(or(X_13255,not(X_13256)))),and(X_13256,not(X_13255)))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
is_a_theorem(or(not(not(or(X_13255,not(X_13256)))),and(X_13256,not(X_13255)))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(not(not(or(X_13255,not(X_13256))))),implies(X_13256,X_13255)))) )],[refute_0_342,refute_0_347]) ).
cnf(refute_0_349,plain,
is_a_theorem(or(not(not(or(not(X_47909),not(X_47909)))),and(X_47909,not(not(X_47909))))),
inference(subst,[],[refute_0_348:[bind(X_13255,$fot(not(X_47909))),bind(X_13256,$fot(X_47909))]]) ).
cnf(refute_0_350,plain,
is_a_theorem(not(equiv(X_47909,not(X_47909)))),
inference(resolve,[$cnf( is_a_theorem(or(not(not(or(not(X_47909),not(X_47909)))),and(X_47909,not(not(X_47909))))) )],[refute_0_349,refute_0_335]) ).
cnf(refute_0_351,plain,
is_a_theorem(not(equiv(X_47910,not(X_47910)))),
inference(subst,[],[refute_0_350:[bind(X_47909,$fot(X_47910))]]) ).
cnf(refute_0_352,plain,
is_a_theorem(implies(implies(not(X_47910),X_47910),X_47910)),
inference(resolve,[$cnf( is_a_theorem(not(equiv(X_47910,not(X_47910)))) )],[refute_0_351,refute_0_162]) ).
cnf(refute_0_353,plain,
implies(not(X_47910),X_47910) = or(X_47910,X_47910),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_47910)),bind(Y,$fot(X_47910))]]) ).
cnf(refute_0_354,plain,
implies(implies(not(X_47910),X_47910),X_47910) = implies(implies(not(X_47910),X_47910),X_47910),
introduced(tautology,[refl,[$fot(implies(implies(not(X_47910),X_47910),X_47910))]]) ).
cnf(refute_0_355,plain,
( implies(implies(not(X_47910),X_47910),X_47910) != implies(implies(not(X_47910),X_47910),X_47910)
| implies(not(X_47910),X_47910) != or(X_47910,X_47910)
| implies(implies(not(X_47910),X_47910),X_47910) = implies(or(X_47910,X_47910),X_47910) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_47910),X_47910),X_47910),implies(implies(not(X_47910),X_47910),X_47910)) ),[1,0],$fot(or(X_47910,X_47910))]]) ).
cnf(refute_0_356,plain,
( implies(not(X_47910),X_47910) != or(X_47910,X_47910)
| implies(implies(not(X_47910),X_47910),X_47910) = implies(or(X_47910,X_47910),X_47910) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_47910),X_47910),X_47910),implies(implies(not(X_47910),X_47910),X_47910)) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
implies(implies(not(X_47910),X_47910),X_47910) = implies(or(X_47910,X_47910),X_47910),
inference(resolve,[$cnf( $equal(implies(not(X_47910),X_47910),or(X_47910,X_47910)) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
( implies(implies(not(X_47910),X_47910),X_47910) != implies(or(X_47910,X_47910),X_47910)
| ~ is_a_theorem(implies(implies(not(X_47910),X_47910),X_47910))
| is_a_theorem(implies(or(X_47910,X_47910),X_47910)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(X_47910),X_47910),X_47910)) ),[0],$fot(implies(or(X_47910,X_47910),X_47910))]]) ).
cnf(refute_0_359,plain,
( ~ is_a_theorem(implies(implies(not(X_47910),X_47910),X_47910))
| is_a_theorem(implies(or(X_47910,X_47910),X_47910)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_47910),X_47910),X_47910),implies(or(X_47910,X_47910),X_47910)) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
is_a_theorem(implies(or(X_47910,X_47910),X_47910)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_47910),X_47910),X_47910)) )],[refute_0_352,refute_0_359]) ).
cnf(refute_0_361,plain,
is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)),
inference(subst,[],[refute_0_360:[bind(X_47910,$fot(skolemFOFtoCNF_P_5))]]) ).
cnf(refute_0_362,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(or(skolemFOFtoCNF_P_5,skolemFOFtoCNF_P_5),skolemFOFtoCNF_P_5)) )],[refute_0_361,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL517+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sat Jul 2 16:11:22 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 286.53/286.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 286.53/286.68
% 286.53/286.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 286.57/286.73
%------------------------------------------------------------------------------