TSTP Solution File: LCL458+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL458+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 12:52:27 EDT 2022
% Result : Theorem 148.49s 148.67s
% Output : CNFRefutation 148.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 74
% Syntax : Number of formulae : 352 ( 177 unt; 0 def)
% Number of atoms : 614 ( 355 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 506 ( 244 ~; 231 |; 13 &)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 14 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 764 ( 0 sgn 63 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ) ).
fof(equivalence_3,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
fof(hilbert_modus_ponens,axiom,
modus_ponens ).
fof(hilbert_modus_tollens,axiom,
modus_tollens ).
fof(hilbert_implies_3,axiom,
implies_3 ).
fof(hilbert_equivalence_3,axiom,
equivalence_3 ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_op_and,axiom,
op_and ).
fof(principia_r5,conjecture,
r5 ).
fof(subgoal_0,plain,
r5,
inference(strip,[],[principia_r5]) ).
fof(negate_0_0,plain,
~ r5,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ r5
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[r5]) ).
fof(normalize_0_1,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3))))
| r5 )
& ( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3))))
| r5 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ r5,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ modus_tollens
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[modus_tollens]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(implies(not(skolemFOFtoCNF_Y_2),not(skolemFOFtoCNF_X_2)),implies(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y_2)))
| modus_tollens )
& ( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
modus_tollens,
inference(canonicalize,[],[hilbert_modus_tollens]) ).
fof(normalize_0_8,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_11,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_14,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_17,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_20,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_21,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_20]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_24,plain,
( ~ implies_3
<=> ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(canonicalize,[],[implies_3]) ).
fof(normalize_0_25,plain,
! [X,Y,Z] :
( ( ~ implies_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Y_5),implies(implies(skolemFOFtoCNF_Y_5,skolemFOFtoCNF_Z),implies(skolemFOFtoCNF_X_5,skolemFOFtoCNF_Z))))
| implies_3 ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X,Y,Z] :
( ~ implies_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
implies_3,
inference(canonicalize,[],[hilbert_implies_3]) ).
fof(normalize_0_28,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_29,plain,
! [X,Y] :
( ( skolemFOFtoCNF_X_1 != skolemFOFtoCNF_Y_1
| substitution_of_equivalents )
& ( is_a_theorem(equiv(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| substitution_of_equivalents )
& ( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_32,plain,
( ~ equivalence_3
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(canonicalize,[],[equivalence_3]) ).
fof(normalize_0_33,plain,
! [X,Y] :
( ( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14),implies(implies(skolemFOFtoCNF_Y_14,skolemFOFtoCNF_X_14),equiv(skolemFOFtoCNF_X_14,skolemFOFtoCNF_Y_14))))
| equivalence_3 ) ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
equivalence_3,
inference(canonicalize,[],[hilbert_equivalence_3]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3))))
| r5 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ r5,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3)))),
inference(resolve,[$cnf( r5 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
modus_tollens,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))),
inference(resolve,[$cnf( modus_tollens )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
implies(or(X_24,not(X_25)),Y) = or(not(or(X_24,not(X_25))),Y),
inference(subst,[],[refute_0_8:[bind(X,$fot(or(X_24,not(X_25))))]]) ).
cnf(refute_0_10,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
op_and,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_14,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_15,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_17,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_17:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_19,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_20,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_21,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_24,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_12,refute_0_24]) ).
cnf(refute_0_26,plain,
and(not(X),X_9) = not(implies(not(X),not(X_9))),
inference(subst,[],[refute_0_25:[bind(X,$fot(not(X))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_27,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_28,plain,
op_or,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_29,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_31,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_32,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_34,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_34:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_36,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_37,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_29,refute_0_37]) ).
cnf(refute_0_39,plain,
or(X,not(X_9)) = implies(not(X),not(X_9)),
inference(subst,[],[refute_0_38:[bind(Y,$fot(not(X_9)))]]) ).
cnf(refute_0_40,plain,
( or(X,not(X_9)) != implies(not(X),not(X_9))
| implies(not(X),not(X_9)) = or(X,not(X_9)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,not(X_9)))),bind(Y0,$fot(implies(not(X),not(X_9))))]]) ).
cnf(refute_0_41,plain,
implies(not(X),not(X_9)) = or(X,not(X_9)),
inference(resolve,[$cnf( $equal(or(X,not(X_9)),implies(not(X),not(X_9))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( and(not(X),X_9) != not(implies(not(X),not(X_9)))
| implies(not(X),not(X_9)) != or(X,not(X_9))
| and(not(X),X_9) = not(or(X,not(X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X),X_9),not(implies(not(X),not(X_9)))) ),[1,0],$fot(or(X,not(X_9)))]]) ).
cnf(refute_0_43,plain,
( and(not(X),X_9) != not(implies(not(X),not(X_9)))
| and(not(X),X_9) = not(or(X,not(X_9))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_9)),or(X,not(X_9))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
and(not(X),X_9) = not(or(X,not(X_9))),
inference(resolve,[$cnf( $equal(and(not(X),X_9),not(implies(not(X),not(X_9)))) )],[refute_0_26,refute_0_43]) ).
cnf(refute_0_45,plain,
and(not(X_24),X_25) = not(or(X_24,not(X_25))),
inference(subst,[],[refute_0_44:[bind(X,$fot(X_24)),bind(X_9,$fot(X_25))]]) ).
cnf(refute_0_46,plain,
( and(not(X_24),X_25) != not(or(X_24,not(X_25)))
| not(or(X_24,not(X_25))) = and(not(X_24),X_25) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(not(X_24),X_25))),bind(Y0,$fot(not(or(X_24,not(X_25)))))]]) ).
cnf(refute_0_47,plain,
not(or(X_24,not(X_25))) = and(not(X_24),X_25),
inference(resolve,[$cnf( $equal(and(not(X_24),X_25),not(or(X_24,not(X_25)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( implies(or(X_24,not(X_25)),Y) != or(not(or(X_24,not(X_25))),Y)
| not(or(X_24,not(X_25))) != and(not(X_24),X_25)
| implies(or(X_24,not(X_25)),Y) = or(and(not(X_24),X_25),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_24,not(X_25)),Y),or(not(or(X_24,not(X_25))),Y)) ),[1,0],$fot(and(not(X_24),X_25))]]) ).
cnf(refute_0_49,plain,
( implies(or(X_24,not(X_25)),Y) != or(not(or(X_24,not(X_25))),Y)
| implies(or(X_24,not(X_25)),Y) = or(and(not(X_24),X_25),Y) ),
inference(resolve,[$cnf( $equal(not(or(X_24,not(X_25))),and(not(X_24),X_25)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(or(X_24,not(X_25)),Y) = or(and(not(X_24),X_25),Y),
inference(resolve,[$cnf( $equal(implies(or(X_24,not(X_25)),Y),or(not(or(X_24,not(X_25))),Y)) )],[refute_0_9,refute_0_49]) ).
cnf(refute_0_51,plain,
( implies(or(X_24,not(X_25)),Y) != or(and(not(X_24),X_25),Y)
| or(and(not(X_24),X_25),Y) = implies(or(X_24,not(X_25)),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(or(X_24,not(X_25)),Y))),bind(Y0,$fot(or(and(not(X_24),X_25),Y)))]]) ).
cnf(refute_0_52,plain,
or(and(not(X_24),X_25),Y) = implies(or(X_24,not(X_25)),Y),
inference(resolve,[$cnf( $equal(implies(or(X_24,not(X_25)),Y),or(and(not(X_24),X_25),Y)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
or(and(not(Y),X),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)),
inference(subst,[],[refute_0_52:[bind(Y,$fot(implies(X,Y))),bind(X_24,$fot(Y)),bind(X_25,$fot(X))]]) ).
cnf(refute_0_54,plain,
implies(implies(X,not(Y)),X_23) = or(not(implies(X,not(Y))),X_23),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X,not(Y)))),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_55,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_56,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_25,refute_0_55]) ).
cnf(refute_0_57,plain,
( implies(implies(X,not(Y)),X_23) != or(not(implies(X,not(Y))),X_23)
| not(implies(X,not(Y))) != and(X,Y)
| implies(implies(X,not(Y)),X_23) = or(and(X,Y),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(Y)),X_23),or(not(implies(X,not(Y))),X_23)) ),[1,0],$fot(and(X,Y))]]) ).
cnf(refute_0_58,plain,
( implies(implies(X,not(Y)),X_23) != or(not(implies(X,not(Y))),X_23)
| implies(implies(X,not(Y)),X_23) = or(and(X,Y),X_23) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
implies(implies(X,not(Y)),X_23) = or(and(X,Y),X_23),
inference(resolve,[$cnf( $equal(implies(implies(X,not(Y)),X_23),or(not(implies(X,not(Y))),X_23)) )],[refute_0_54,refute_0_58]) ).
cnf(refute_0_60,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = or(and(not(Y),X),implies(X,Y)),
inference(subst,[],[refute_0_59:[bind(X,$fot(not(Y))),bind(Y,$fot(X)),bind(X_23,$fot(implies(X,Y)))]]) ).
cnf(refute_0_61,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_62,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_15,refute_0_61]) ).
cnf(refute_0_63,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != or(and(not(Y),X),implies(X,Y))
| or(and(not(Y),X),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(implies(implies(not(Y),not(X)),implies(X,Y)))),bind(Y0,$fot(or(and(not(Y),X),implies(X,Y)))),bind(Z0,$fot(implies(or(Y,not(X)),implies(X,Y))))]]) ).
cnf(refute_0_64,plain,
( or(and(not(Y),X),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),or(and(not(Y),X),implies(X,Y))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
implies(implies(not(Y),not(X)),implies(X,Y)) = implies(or(Y,not(X)),implies(X,Y)),
inference(resolve,[$cnf( $equal(or(and(not(Y),X),implies(X,Y)),implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_53,refute_0_64]) ).
cnf(refute_0_66,plain,
( implies(implies(not(Y),not(X)),implies(X,Y)) != implies(or(Y,not(X)),implies(X,Y))
| ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),[0],$fot(implies(or(Y,not(X)),implies(X,Y)))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| is_a_theorem(implies(or(Y,not(X)),implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),implies(X,Y)),implies(or(Y,not(X)),implies(X,Y))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(or(Y,not(X)),implies(X,Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )],[refute_0_5,refute_0_67]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(or(not(X),not(X_30)),implies(X_30,not(X)))),
inference(subst,[],[refute_0_68:[bind(X,$fot(X_30)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_70,plain,
implies(X,not(X_30)) = or(not(X),not(X_30)),
inference(subst,[],[refute_0_8:[bind(Y,$fot(not(X_30)))]]) ).
cnf(refute_0_71,plain,
( implies(X,not(X_30)) != or(not(X),not(X_30))
| or(not(X),not(X_30)) = implies(X,not(X_30)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,not(X_30)))),bind(Y0,$fot(or(not(X),not(X_30))))]]) ).
cnf(refute_0_72,plain,
or(not(X),not(X_30)) = implies(X,not(X_30)),
inference(resolve,[$cnf( $equal(implies(X,not(X_30)),or(not(X),not(X_30))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( or(not(X),not(X_30)) != implies(X,not(X_30))
| ~ is_a_theorem(implies(or(not(X),not(X_30)),implies(X_30,not(X))))
| is_a_theorem(implies(implies(X,not(X_30)),implies(X_30,not(X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),not(X_30)),implies(X_30,not(X)))) ),[0,0],$fot(implies(X,not(X_30)))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(or(not(X),not(X_30)),implies(X_30,not(X))))
| is_a_theorem(implies(implies(X,not(X_30)),implies(X_30,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_30)),implies(X,not(X_30))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(X,not(X_30)),implies(X_30,not(X)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),not(X_30)),implies(X_30,not(X)))) )],[refute_0_69,refute_0_74]) ).
cnf(refute_0_76,plain,
implies(X_26,implies(X,not(Y))) = not(and(X_26,not(implies(X,not(Y))))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_26)),bind(Y,$fot(implies(X,not(Y))))]]) ).
cnf(refute_0_77,plain,
( implies(X_26,implies(X,not(Y))) != not(and(X_26,not(implies(X,not(Y)))))
| not(implies(X,not(Y))) != and(X,Y)
| implies(X_26,implies(X,not(Y))) = not(and(X_26,and(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_26,implies(X,not(Y))),not(and(X_26,not(implies(X,not(Y)))))) ),[1,0,1],$fot(and(X,Y))]]) ).
cnf(refute_0_78,plain,
( implies(X_26,implies(X,not(Y))) != not(and(X_26,not(implies(X,not(Y)))))
| implies(X_26,implies(X,not(Y))) = not(and(X_26,and(X,Y))) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_56,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(X_26,implies(X,not(Y))) = not(and(X_26,and(X,Y))),
inference(resolve,[$cnf( $equal(implies(X_26,implies(X,not(Y))),not(and(X_26,not(implies(X,not(Y)))))) )],[refute_0_76,refute_0_78]) ).
cnf(refute_0_80,plain,
implies(implies(X,not(X_30)),implies(X_30,not(X))) = not(and(implies(X,not(X_30)),and(X_30,X))),
inference(subst,[],[refute_0_79:[bind(X,$fot(X_30)),bind(Y,$fot(X)),bind(X_26,$fot(implies(X,not(X_30))))]]) ).
cnf(refute_0_81,plain,
( implies(implies(X,not(X_30)),implies(X_30,not(X))) != not(and(implies(X,not(X_30)),and(X_30,X)))
| ~ is_a_theorem(implies(implies(X,not(X_30)),implies(X_30,not(X))))
| is_a_theorem(not(and(implies(X,not(X_30)),and(X_30,X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X,not(X_30)),implies(X_30,not(X)))) ),[0],$fot(not(and(implies(X,not(X_30)),and(X_30,X))))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(implies(implies(X,not(X_30)),implies(X_30,not(X))))
| is_a_theorem(not(and(implies(X,not(X_30)),and(X_30,X)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_30)),implies(X_30,not(X))),not(and(implies(X,not(X_30)),and(X_30,X)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
is_a_theorem(not(and(implies(X,not(X_30)),and(X_30,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,not(X_30)),implies(X_30,not(X)))) )],[refute_0_75,refute_0_82]) ).
cnf(refute_0_84,plain,
and(implies(X_88,not(X_89)),Y) = not(implies(implies(X_88,not(X_89)),not(Y))),
inference(subst,[],[refute_0_25:[bind(X,$fot(implies(X_88,not(X_89))))]]) ).
cnf(refute_0_85,plain,
implies(implies(X_88,not(X_89)),not(Y)) = or(and(X_88,X_89),not(Y)),
inference(subst,[],[refute_0_59:[bind(X,$fot(X_88)),bind(Y,$fot(X_89)),bind(X_23,$fot(not(Y)))]]) ).
cnf(refute_0_86,plain,
( and(implies(X_88,not(X_89)),Y) != not(implies(implies(X_88,not(X_89)),not(Y)))
| implies(implies(X_88,not(X_89)),not(Y)) != or(and(X_88,X_89),not(Y))
| and(implies(X_88,not(X_89)),Y) = not(or(and(X_88,X_89),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(implies(X_88,not(X_89)),Y),not(implies(implies(X_88,not(X_89)),not(Y)))) ),[1,0],$fot(or(and(X_88,X_89),not(Y)))]]) ).
cnf(refute_0_87,plain,
( and(implies(X_88,not(X_89)),Y) != not(implies(implies(X_88,not(X_89)),not(Y)))
| and(implies(X_88,not(X_89)),Y) = not(or(and(X_88,X_89),not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_88,not(X_89)),not(Y)),or(and(X_88,X_89),not(Y))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
and(implies(X_88,not(X_89)),Y) = not(or(and(X_88,X_89),not(Y))),
inference(resolve,[$cnf( $equal(and(implies(X_88,not(X_89)),Y),not(implies(implies(X_88,not(X_89)),not(Y)))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( and(not(X),X_9) != not(or(X,not(X_9)))
| not(or(X,not(X_9))) = and(not(X),X_9) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(not(X),X_9))),bind(Y0,$fot(not(or(X,not(X_9)))))]]) ).
cnf(refute_0_90,plain,
not(or(X,not(X_9))) = and(not(X),X_9),
inference(resolve,[$cnf( $equal(and(not(X),X_9),not(or(X,not(X_9)))) )],[refute_0_44,refute_0_89]) ).
cnf(refute_0_91,plain,
not(or(and(X_88,X_89),not(Y))) = and(not(and(X_88,X_89)),Y),
inference(subst,[],[refute_0_90:[bind(X,$fot(and(X_88,X_89))),bind(X_9,$fot(Y))]]) ).
cnf(refute_0_92,plain,
( and(implies(X_88,not(X_89)),Y) != not(or(and(X_88,X_89),not(Y)))
| not(or(and(X_88,X_89),not(Y))) != and(not(and(X_88,X_89)),Y)
| and(implies(X_88,not(X_89)),Y) = and(not(and(X_88,X_89)),Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(implies(X_88,not(X_89)),Y),and(not(and(X_88,X_89)),Y)) ),[0],$fot(not(or(and(X_88,X_89),not(Y))))]]) ).
cnf(refute_0_93,plain,
( and(implies(X_88,not(X_89)),Y) != not(or(and(X_88,X_89),not(Y)))
| and(implies(X_88,not(X_89)),Y) = and(not(and(X_88,X_89)),Y) ),
inference(resolve,[$cnf( $equal(not(or(and(X_88,X_89),not(Y))),and(not(and(X_88,X_89)),Y)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
and(implies(X_88,not(X_89)),Y) = and(not(and(X_88,X_89)),Y),
inference(resolve,[$cnf( $equal(and(implies(X_88,not(X_89)),Y),not(or(and(X_88,X_89),not(Y)))) )],[refute_0_88,refute_0_93]) ).
cnf(refute_0_95,plain,
and(implies(X,not(X_30)),and(X_30,X)) = and(not(and(X,X_30)),and(X_30,X)),
inference(subst,[],[refute_0_94:[bind(Y,$fot(and(X_30,X))),bind(X_88,$fot(X)),bind(X_89,$fot(X_30))]]) ).
cnf(refute_0_96,plain,
not(and(implies(X,not(X_30)),and(X_30,X))) = not(and(implies(X,not(X_30)),and(X_30,X))),
introduced(tautology,[refl,[$fot(not(and(implies(X,not(X_30)),and(X_30,X))))]]) ).
cnf(refute_0_97,plain,
( and(implies(X,not(X_30)),and(X_30,X)) != and(not(and(X,X_30)),and(X_30,X))
| not(and(implies(X,not(X_30)),and(X_30,X))) != not(and(implies(X,not(X_30)),and(X_30,X)))
| not(and(implies(X,not(X_30)),and(X_30,X))) = not(and(not(and(X,X_30)),and(X_30,X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X,not(X_30)),and(X_30,X))),not(and(implies(X,not(X_30)),and(X_30,X)))) ),[1,0],$fot(and(not(and(X,X_30)),and(X_30,X)))]]) ).
cnf(refute_0_98,plain,
( and(implies(X,not(X_30)),and(X_30,X)) != and(not(and(X,X_30)),and(X_30,X))
| not(and(implies(X,not(X_30)),and(X_30,X))) = not(and(not(and(X,X_30)),and(X_30,X))) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,not(X_30)),and(X_30,X))),not(and(implies(X,not(X_30)),and(X_30,X)))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
not(and(implies(X,not(X_30)),and(X_30,X))) = not(and(not(and(X,X_30)),and(X_30,X))),
inference(resolve,[$cnf( $equal(and(implies(X,not(X_30)),and(X_30,X)),and(not(and(X,X_30)),and(X_30,X))) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
( not(and(implies(X,not(X_30)),and(X_30,X))) != not(and(not(and(X,X_30)),and(X_30,X)))
| ~ is_a_theorem(not(and(implies(X,not(X_30)),and(X_30,X))))
| is_a_theorem(not(and(not(and(X,X_30)),and(X_30,X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(implies(X,not(X_30)),and(X_30,X)))) ),[0],$fot(not(and(not(and(X,X_30)),and(X_30,X))))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(not(and(implies(X,not(X_30)),and(X_30,X))))
| is_a_theorem(not(and(not(and(X,X_30)),and(X_30,X)))) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,not(X_30)),and(X_30,X))),not(and(not(and(X,X_30)),and(X_30,X)))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
is_a_theorem(not(and(not(and(X,X_30)),and(X_30,X)))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(X,not(X_30)),and(X_30,X)))) )],[refute_0_83,refute_0_101]) ).
cnf(refute_0_103,plain,
is_a_theorem(not(and(not(and(X_93,not(Y))),and(not(Y),X_93)))),
inference(subst,[],[refute_0_102:[bind(X,$fot(X_93)),bind(X_30,$fot(not(Y)))]]) ).
cnf(refute_0_104,plain,
implies(X_93,Y) = not(and(X_93,not(Y))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_93))]]) ).
cnf(refute_0_105,plain,
( implies(X_93,Y) != not(and(X_93,not(Y)))
| not(and(X_93,not(Y))) = implies(X_93,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_93,Y))),bind(Y0,$fot(not(and(X_93,not(Y)))))]]) ).
cnf(refute_0_106,plain,
not(and(X_93,not(Y))) = implies(X_93,Y),
inference(resolve,[$cnf( $equal(implies(X_93,Y),not(and(X_93,not(Y)))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( not(and(X_93,not(Y))) != implies(X_93,Y)
| ~ is_a_theorem(not(and(not(and(X_93,not(Y))),and(not(Y),X_93))))
| is_a_theorem(not(and(implies(X_93,Y),and(not(Y),X_93)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(not(and(X_93,not(Y))),and(not(Y),X_93)))) ),[0,0,0],$fot(implies(X_93,Y))]]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(not(and(not(and(X_93,not(Y))),and(not(Y),X_93))))
| is_a_theorem(not(and(implies(X_93,Y),and(not(Y),X_93)))) ),
inference(resolve,[$cnf( $equal(not(and(X_93,not(Y))),implies(X_93,Y)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
is_a_theorem(not(and(implies(X_93,Y),and(not(Y),X_93)))),
inference(resolve,[$cnf( is_a_theorem(not(and(not(and(X_93,not(Y))),and(not(Y),X_93)))) )],[refute_0_103,refute_0_108]) ).
cnf(refute_0_110,plain,
implies(X_26,or(X,not(X_9))) = not(and(X_26,not(or(X,not(X_9))))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_26)),bind(Y,$fot(or(X,not(X_9))))]]) ).
cnf(refute_0_111,plain,
( implies(X_26,or(X,not(X_9))) != not(and(X_26,not(or(X,not(X_9)))))
| not(or(X,not(X_9))) != and(not(X),X_9)
| implies(X_26,or(X,not(X_9))) = not(and(X_26,and(not(X),X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_26,or(X,not(X_9))),not(and(X_26,not(or(X,not(X_9)))))) ),[1,0,1],$fot(and(not(X),X_9))]]) ).
cnf(refute_0_112,plain,
( implies(X_26,or(X,not(X_9))) != not(and(X_26,not(or(X,not(X_9)))))
| implies(X_26,or(X,not(X_9))) = not(and(X_26,and(not(X),X_9))) ),
inference(resolve,[$cnf( $equal(not(or(X,not(X_9))),and(not(X),X_9)) )],[refute_0_90,refute_0_111]) ).
cnf(refute_0_113,plain,
implies(X_26,or(X,not(X_9))) = not(and(X_26,and(not(X),X_9))),
inference(resolve,[$cnf( $equal(implies(X_26,or(X,not(X_9))),not(and(X_26,not(or(X,not(X_9)))))) )],[refute_0_110,refute_0_112]) ).
cnf(refute_0_114,plain,
( implies(X_26,or(X,not(X_9))) != not(and(X_26,and(not(X),X_9)))
| not(and(X_26,and(not(X),X_9))) = implies(X_26,or(X,not(X_9))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_26,or(X,not(X_9))))),bind(Y0,$fot(not(and(X_26,and(not(X),X_9)))))]]) ).
cnf(refute_0_115,plain,
not(and(X_26,and(not(X),X_9))) = implies(X_26,or(X,not(X_9))),
inference(resolve,[$cnf( $equal(implies(X_26,or(X,not(X_9))),not(and(X_26,and(not(X),X_9)))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
not(and(implies(X_93,Y),and(not(Y),X_93))) = implies(implies(X_93,Y),or(Y,not(X_93))),
inference(subst,[],[refute_0_115:[bind(X,$fot(Y)),bind(X_26,$fot(implies(X_93,Y))),bind(X_9,$fot(X_93))]]) ).
cnf(refute_0_117,plain,
( not(and(implies(X_93,Y),and(not(Y),X_93))) != implies(implies(X_93,Y),or(Y,not(X_93)))
| ~ is_a_theorem(not(and(implies(X_93,Y),and(not(Y),X_93))))
| is_a_theorem(implies(implies(X_93,Y),or(Y,not(X_93)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(and(implies(X_93,Y),and(not(Y),X_93)))) ),[0],$fot(implies(implies(X_93,Y),or(Y,not(X_93))))]]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(not(and(implies(X_93,Y),and(not(Y),X_93))))
| is_a_theorem(implies(implies(X_93,Y),or(Y,not(X_93)))) ),
inference(resolve,[$cnf( $equal(not(and(implies(X_93,Y),and(not(Y),X_93))),implies(implies(X_93,Y),or(Y,not(X_93)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(X_93,Y),or(Y,not(X_93)))),
inference(resolve,[$cnf( is_a_theorem(not(and(implies(X_93,Y),and(not(Y),X_93)))) )],[refute_0_109,refute_0_118]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_121,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_121,refute_0_120]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(implies(X_93,Y))
| ~ is_a_theorem(implies(implies(X_93,Y),or(Y,not(X_93))))
| is_a_theorem(or(Y,not(X_93))) ),
inference(subst,[],[refute_0_122:[bind(X,$fot(implies(X_93,Y))),bind(Y,$fot(or(Y,not(X_93))))]]) ).
cnf(refute_0_124,plain,
( ~ is_a_theorem(implies(X_93,Y))
| is_a_theorem(or(Y,not(X_93))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_93,Y),or(Y,not(X_93)))) )],[refute_0_119,refute_0_123]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(or(X_1116,not(X_1117)),implies(or(X_1117,X_1118),or(X_1116,X_1118))))
| is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117))))) ),
inference(subst,[],[refute_0_124:[bind(Y,$fot(implies(or(X_1117,X_1118),or(X_1116,X_1118)))),bind(X_93,$fot(or(X_1116,not(X_1117))))]]) ).
cnf(refute_0_126,plain,
( ~ implies_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_127,plain,
implies_3,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(resolve,[$cnf( implies_3 )],[refute_0_127,refute_0_126]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(X_198,not(X)),implies(implies(not(X),X_200),implies(X_198,X_200)))),
inference(subst,[],[refute_0_128:[bind(X,$fot(X_198)),bind(Y,$fot(not(X))),bind(Z,$fot(X_200))]]) ).
cnf(refute_0_130,plain,
or(X,X_200) = implies(not(X),X_200),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_200))]]) ).
cnf(refute_0_131,plain,
( or(X,X_200) != implies(not(X),X_200)
| implies(not(X),X_200) = or(X,X_200) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_200))),bind(Y0,$fot(implies(not(X),X_200)))]]) ).
cnf(refute_0_132,plain,
implies(not(X),X_200) = or(X,X_200),
inference(resolve,[$cnf( $equal(or(X,X_200),implies(not(X),X_200)) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( implies(not(X),X_200) != or(X,X_200)
| ~ is_a_theorem(implies(implies(X_198,not(X)),implies(implies(not(X),X_200),implies(X_198,X_200))))
| is_a_theorem(implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_198,not(X)),implies(implies(not(X),X_200),implies(X_198,X_200)))) ),[0,1,0],$fot(or(X,X_200))]]) ).
cnf(refute_0_134,plain,
( ~ is_a_theorem(implies(implies(X_198,not(X)),implies(implies(not(X),X_200),implies(X_198,X_200))))
| is_a_theorem(implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_200),or(X,X_200)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_198,not(X)),implies(implies(not(X),X_200),implies(X_198,X_200)))) )],[refute_0_129,refute_0_134]) ).
cnf(refute_0_136,plain,
implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200))) = or(and(X_198,X),implies(or(X,X_200),implies(X_198,X_200))),
inference(subst,[],[refute_0_59:[bind(X,$fot(X_198)),bind(Y,$fot(X)),bind(X_23,$fot(implies(or(X,X_200),implies(X_198,X_200))))]]) ).
cnf(refute_0_137,plain,
( implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200))) != or(and(X_198,X),implies(or(X,X_200),implies(X_198,X_200)))
| ~ is_a_theorem(implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200))))
| is_a_theorem(or(and(X_198,X),implies(or(X,X_200),implies(X_198,X_200)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200)))) ),[0],$fot(or(and(X_198,X),implies(or(X,X_200),implies(X_198,X_200))))]]) ).
cnf(refute_0_138,plain,
( ~ is_a_theorem(implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200))))
| is_a_theorem(or(and(X_198,X),implies(or(X,X_200),implies(X_198,X_200)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200))),or(and(X_198,X),implies(or(X,X_200),implies(X_198,X_200)))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
is_a_theorem(or(and(X_198,X),implies(or(X,X_200),implies(X_198,X_200)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_198,not(X)),implies(or(X,X_200),implies(X_198,X_200)))) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),implies(not(X),X_266)))),
inference(subst,[],[refute_0_139:[bind(X,$fot(X_264)),bind(X_198,$fot(not(X))),bind(X_200,$fot(X_266))]]) ).
cnf(refute_0_141,plain,
or(X,X_266) = implies(not(X),X_266),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_266))]]) ).
cnf(refute_0_142,plain,
( or(X,X_266) != implies(not(X),X_266)
| implies(not(X),X_266) = or(X,X_266) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_266))),bind(Y0,$fot(implies(not(X),X_266)))]]) ).
cnf(refute_0_143,plain,
implies(not(X),X_266) = or(X,X_266),
inference(resolve,[$cnf( $equal(or(X,X_266),implies(not(X),X_266)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( implies(not(X),X_266) != or(X,X_266)
| ~ is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),implies(not(X),X_266))))
| is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),implies(not(X),X_266)))) ),[0,1,1],$fot(or(X,X_266))]]) ).
cnf(refute_0_145,plain,
( ~ is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),implies(not(X),X_266))))
| is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_266),or(X,X_266)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266)))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),implies(not(X),X_266)))) )],[refute_0_140,refute_0_145]) ).
cnf(refute_0_147,plain,
or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266))) = implies(or(X,not(X_264)),implies(or(X_264,X_266),or(X,X_266))),
inference(subst,[],[refute_0_52:[bind(Y,$fot(implies(or(X_264,X_266),or(X,X_266)))),bind(X_24,$fot(X)),bind(X_25,$fot(X_264))]]) ).
cnf(refute_0_148,plain,
( or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266))) != implies(or(X,not(X_264)),implies(or(X_264,X_266),or(X,X_266)))
| ~ is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266))))
| is_a_theorem(implies(or(X,not(X_264)),implies(or(X_264,X_266),or(X,X_266)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266)))) ),[0],$fot(implies(or(X,not(X_264)),implies(or(X_264,X_266),or(X,X_266))))]]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266))))
| is_a_theorem(implies(or(X,not(X_264)),implies(or(X_264,X_266),or(X,X_266)))) ),
inference(resolve,[$cnf( $equal(or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266))),implies(or(X,not(X_264)),implies(or(X_264,X_266),or(X,X_266)))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(or(X,not(X_264)),implies(or(X_264,X_266),or(X,X_266)))),
inference(resolve,[$cnf( is_a_theorem(or(and(not(X),X_264),implies(or(X_264,X_266),or(X,X_266)))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
is_a_theorem(implies(or(X_1116,not(X_1117)),implies(or(X_1117,X_1118),or(X_1116,X_1118)))),
inference(subst,[],[refute_0_150:[bind(X,$fot(X_1116)),bind(X_264,$fot(X_1117)),bind(X_266,$fot(X_1118))]]) ).
cnf(refute_0_152,plain,
is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117))))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_1116,not(X_1117)),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) )],[refute_0_151,refute_0_125]) ).
cnf(refute_0_153,plain,
not(or(X_1116,not(X_1117))) = and(not(X_1116),X_1117),
inference(subst,[],[refute_0_90:[bind(X,$fot(X_1116)),bind(X_9,$fot(X_1117))]]) ).
cnf(refute_0_154,plain,
or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))) = or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))),
introduced(tautology,[refl,[$fot(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))))]]) ).
cnf(refute_0_155,plain,
( not(or(X_1116,not(X_1117))) != and(not(X_1116),X_1117)
| or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))) != or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117))))
| or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))) = or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))),or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117))))) ),[1,1],$fot(and(not(X_1116),X_1117))]]) ).
cnf(refute_0_156,plain,
( not(or(X_1116,not(X_1117))) != and(not(X_1116),X_1117)
| or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))) = or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))),or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117))))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))) = or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)),
inference(resolve,[$cnf( $equal(not(or(X_1116,not(X_1117))),and(not(X_1116),X_1117)) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))) != or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117))
| ~ is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))))
| is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117))))) ),[0],$fot(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)))]]) ).
cnf(refute_0_159,plain,
( ~ is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))))
| is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117))) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117)))),or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117))),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),not(or(X_1116,not(X_1117))))) )],[refute_0_152,refute_0_159]) ).
cnf(refute_0_161,plain,
or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118))) = implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118))),
inference(subst,[],[refute_0_17:[bind(X,$fot(implies(X_1117,X_1116))),bind(Y,$fot(implies(or(X_1117,X_1118),or(X_1116,X_1118))))]]) ).
cnf(refute_0_162,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_163,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_164,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_163,refute_0_162]) ).
cnf(refute_0_165,plain,
( ~ is_a_theorem(equiv(or(X_1643,X_1642),or(X_1642,X_1643)))
| or(X_1643,X_1642) = or(X_1642,X_1643) ),
inference(subst,[],[refute_0_164:[bind(X,$fot(or(X_1643,X_1642))),bind(Y,$fot(or(X_1642,X_1643)))]]) ).
cnf(refute_0_166,plain,
( ~ is_a_theorem(implies(implies(or(X_1640,X_1641),or(X_1641,X_1640)),equiv(or(X_1641,X_1640),or(X_1640,X_1641))))
| ~ is_a_theorem(implies(or(X_1640,X_1641),or(X_1641,X_1640)))
| is_a_theorem(equiv(or(X_1641,X_1640),or(X_1640,X_1641))) ),
inference(subst,[],[refute_0_122:[bind(X,$fot(implies(or(X_1640,X_1641),or(X_1641,X_1640)))),bind(Y,$fot(equiv(or(X_1641,X_1640),or(X_1640,X_1641))))]]) ).
cnf(refute_0_167,plain,
is_a_theorem(implies(or(X_31,not(not(X))),implies(not(X),X_31))),
inference(subst,[],[refute_0_68:[bind(X,$fot(not(X))),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_168,plain,
or(X,X_31) = implies(not(X),X_31),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_31))]]) ).
cnf(refute_0_169,plain,
( or(X,X_31) != implies(not(X),X_31)
| implies(not(X),X_31) = or(X,X_31) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,X_31))),bind(Y0,$fot(implies(not(X),X_31)))]]) ).
cnf(refute_0_170,plain,
implies(not(X),X_31) = or(X,X_31),
inference(resolve,[$cnf( $equal(or(X,X_31),implies(not(X),X_31)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
( implies(not(X),X_31) != or(X,X_31)
| ~ is_a_theorem(implies(or(X_31,not(not(X))),implies(not(X),X_31)))
| is_a_theorem(implies(or(X_31,not(not(X))),or(X,X_31))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_31,not(not(X))),implies(not(X),X_31))) ),[0,1],$fot(or(X,X_31))]]) ).
cnf(refute_0_172,plain,
( ~ is_a_theorem(implies(or(X_31,not(not(X))),implies(not(X),X_31)))
| is_a_theorem(implies(or(X_31,not(not(X))),or(X,X_31))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_31),or(X,X_31)) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
is_a_theorem(implies(or(X_31,not(not(X))),or(X,X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_31,not(not(X))),implies(not(X),X_31))) )],[refute_0_167,refute_0_172]) ).
cnf(refute_0_174,plain,
or(and(X_26,not(X_27)),Y) = implies(not(and(X_26,not(X_27))),Y),
inference(subst,[],[refute_0_38:[bind(X,$fot(and(X_26,not(X_27))))]]) ).
cnf(refute_0_175,plain,
implies(X_26,X_27) = not(and(X_26,not(X_27))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_26)),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_176,plain,
( implies(X_26,X_27) != not(and(X_26,not(X_27)))
| not(and(X_26,not(X_27))) = implies(X_26,X_27) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_26,X_27))),bind(Y0,$fot(not(and(X_26,not(X_27)))))]]) ).
cnf(refute_0_177,plain,
not(and(X_26,not(X_27))) = implies(X_26,X_27),
inference(resolve,[$cnf( $equal(implies(X_26,X_27),not(and(X_26,not(X_27)))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
( not(and(X_26,not(X_27))) != implies(X_26,X_27)
| or(and(X_26,not(X_27)),Y) != implies(not(and(X_26,not(X_27))),Y)
| or(and(X_26,not(X_27)),Y) = implies(implies(X_26,X_27),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X_26,not(X_27)),Y),implies(not(and(X_26,not(X_27))),Y)) ),[1,0],$fot(implies(X_26,X_27))]]) ).
cnf(refute_0_179,plain,
( or(and(X_26,not(X_27)),Y) != implies(not(and(X_26,not(X_27))),Y)
| or(and(X_26,not(X_27)),Y) = implies(implies(X_26,X_27),Y) ),
inference(resolve,[$cnf( $equal(not(and(X_26,not(X_27))),implies(X_26,X_27)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
or(and(X_26,not(X_27)),Y) = implies(implies(X_26,X_27),Y),
inference(resolve,[$cnf( $equal(or(and(X_26,not(X_27)),Y),implies(not(and(X_26,not(X_27))),Y)) )],[refute_0_174,refute_0_179]) ).
cnf(refute_0_181,plain,
or(and(not(X_164),not(X_27)),Y) = implies(implies(not(X_164),X_27),Y),
inference(subst,[],[refute_0_180:[bind(X_26,$fot(not(X_164)))]]) ).
cnf(refute_0_182,plain,
implies(or(X_164,not(not(X_27))),Y) = or(and(not(X_164),not(X_27)),Y),
inference(subst,[],[refute_0_50:[bind(X_24,$fot(X_164)),bind(X_25,$fot(not(X_27)))]]) ).
cnf(refute_0_183,plain,
( implies(or(X_164,not(not(X_27))),Y) != or(and(not(X_164),not(X_27)),Y)
| or(and(not(X_164),not(X_27)),Y) = implies(or(X_164,not(not(X_27))),Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(or(X_164,not(not(X_27))),Y))),bind(Y0,$fot(or(and(not(X_164),not(X_27)),Y)))]]) ).
cnf(refute_0_184,plain,
or(and(not(X_164),not(X_27)),Y) = implies(or(X_164,not(not(X_27))),Y),
inference(resolve,[$cnf( $equal(implies(or(X_164,not(not(X_27))),Y),or(and(not(X_164),not(X_27)),Y)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
( or(and(not(X_164),not(X_27)),Y) != implies(implies(not(X_164),X_27),Y)
| or(and(not(X_164),not(X_27)),Y) != implies(or(X_164,not(not(X_27))),Y)
| implies(or(X_164,not(not(X_27))),Y) = implies(implies(not(X_164),X_27),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_164),not(X_27)),Y),implies(implies(not(X_164),X_27),Y)) ),[0],$fot(implies(or(X_164,not(not(X_27))),Y))]]) ).
cnf(refute_0_186,plain,
( or(and(not(X_164),not(X_27)),Y) != implies(implies(not(X_164),X_27),Y)
| implies(or(X_164,not(not(X_27))),Y) = implies(implies(not(X_164),X_27),Y) ),
inference(resolve,[$cnf( $equal(or(and(not(X_164),not(X_27)),Y),implies(or(X_164,not(not(X_27))),Y)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
implies(or(X_164,not(not(X_27))),Y) = implies(implies(not(X_164),X_27),Y),
inference(resolve,[$cnf( $equal(or(and(not(X_164),not(X_27)),Y),implies(implies(not(X_164),X_27),Y)) )],[refute_0_181,refute_0_186]) ).
cnf(refute_0_188,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_189,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[refute_0_38,refute_0_188]) ).
cnf(refute_0_190,plain,
implies(not(X_164),X_27) = or(X_164,X_27),
inference(subst,[],[refute_0_189:[bind(X,$fot(X_164)),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_191,plain,
implies(implies(not(X_164),X_27),Y) = implies(implies(not(X_164),X_27),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(X_164),X_27),Y))]]) ).
cnf(refute_0_192,plain,
( implies(implies(not(X_164),X_27),Y) != implies(implies(not(X_164),X_27),Y)
| implies(not(X_164),X_27) != or(X_164,X_27)
| implies(implies(not(X_164),X_27),Y) = implies(or(X_164,X_27),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_164),X_27),Y),implies(implies(not(X_164),X_27),Y)) ),[1,0],$fot(or(X_164,X_27))]]) ).
cnf(refute_0_193,plain,
( implies(not(X_164),X_27) != or(X_164,X_27)
| implies(implies(not(X_164),X_27),Y) = implies(or(X_164,X_27),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_164),X_27),Y),implies(implies(not(X_164),X_27),Y)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
implies(implies(not(X_164),X_27),Y) = implies(or(X_164,X_27),Y),
inference(resolve,[$cnf( $equal(implies(not(X_164),X_27),or(X_164,X_27)) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
( implies(implies(not(X_164),X_27),Y) != implies(or(X_164,X_27),Y)
| implies(or(X_164,not(not(X_27))),Y) != implies(implies(not(X_164),X_27),Y)
| implies(or(X_164,not(not(X_27))),Y) = implies(or(X_164,X_27),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_164,not(not(X_27))),Y),implies(implies(not(X_164),X_27),Y)) ),[1],$fot(implies(or(X_164,X_27),Y))]]) ).
cnf(refute_0_196,plain,
( implies(or(X_164,not(not(X_27))),Y) != implies(implies(not(X_164),X_27),Y)
| implies(or(X_164,not(not(X_27))),Y) = implies(or(X_164,X_27),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_164),X_27),Y),implies(or(X_164,X_27),Y)) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(or(X_164,not(not(X_27))),Y) = implies(or(X_164,X_27),Y),
inference(resolve,[$cnf( $equal(implies(or(X_164,not(not(X_27))),Y),implies(implies(not(X_164),X_27),Y)) )],[refute_0_187,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(or(X_31,not(not(X))),or(X,X_31)) = implies(or(X_31,X),or(X,X_31)),
inference(subst,[],[refute_0_197:[bind(Y,$fot(or(X,X_31))),bind(X_164,$fot(X_31)),bind(X_27,$fot(X))]]) ).
cnf(refute_0_199,plain,
( implies(or(X_31,not(not(X))),or(X,X_31)) != implies(or(X_31,X),or(X,X_31))
| ~ is_a_theorem(implies(or(X_31,not(not(X))),or(X,X_31)))
| is_a_theorem(implies(or(X_31,X),or(X,X_31))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(X_31,not(not(X))),or(X,X_31))) ),[0],$fot(implies(or(X_31,X),or(X,X_31)))]]) ).
cnf(refute_0_200,plain,
( ~ is_a_theorem(implies(or(X_31,not(not(X))),or(X,X_31)))
| is_a_theorem(implies(or(X_31,X),or(X,X_31))) ),
inference(resolve,[$cnf( $equal(implies(or(X_31,not(not(X))),or(X,X_31)),implies(or(X_31,X),or(X,X_31))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
is_a_theorem(implies(or(X_31,X),or(X,X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_31,not(not(X))),or(X,X_31))) )],[refute_0_173,refute_0_200]) ).
cnf(refute_0_202,plain,
( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_203,plain,
equivalence_3,
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_204,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))),
inference(resolve,[$cnf( equivalence_3 )],[refute_0_203,refute_0_202]) ).
cnf(refute_0_205,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| is_a_theorem(implies(implies(Y,X),equiv(X,Y))) ),
inference(subst,[],[refute_0_122:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,X),equiv(X,Y))))]]) ).
cnf(refute_0_206,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,X),equiv(X,Y))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
( ~ is_a_theorem(implies(or(X_31,X),or(X,X_31)))
| is_a_theorem(implies(implies(or(X,X_31),or(X_31,X)),equiv(or(X_31,X),or(X,X_31)))) ),
inference(subst,[],[refute_0_206:[bind(X,$fot(or(X_31,X))),bind(Y,$fot(or(X,X_31)))]]) ).
cnf(refute_0_208,plain,
is_a_theorem(implies(implies(or(X,X_31),or(X_31,X)),equiv(or(X_31,X),or(X,X_31)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_31,X),or(X,X_31))) )],[refute_0_201,refute_0_207]) ).
cnf(refute_0_209,plain,
is_a_theorem(implies(implies(or(X_1640,X_1641),or(X_1641,X_1640)),equiv(or(X_1641,X_1640),or(X_1640,X_1641)))),
inference(subst,[],[refute_0_208:[bind(X,$fot(X_1640)),bind(X_31,$fot(X_1641))]]) ).
cnf(refute_0_210,plain,
( ~ is_a_theorem(implies(or(X_1640,X_1641),or(X_1641,X_1640)))
| is_a_theorem(equiv(or(X_1641,X_1640),or(X_1640,X_1641))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(or(X_1640,X_1641),or(X_1641,X_1640)),equiv(or(X_1641,X_1640),or(X_1640,X_1641)))) )],[refute_0_209,refute_0_166]) ).
cnf(refute_0_211,plain,
is_a_theorem(implies(or(X_1640,X_1641),or(X_1641,X_1640))),
inference(subst,[],[refute_0_201:[bind(X,$fot(X_1641)),bind(X_31,$fot(X_1640))]]) ).
cnf(refute_0_212,plain,
is_a_theorem(equiv(or(X_1641,X_1640),or(X_1640,X_1641))),
inference(resolve,[$cnf( is_a_theorem(implies(or(X_1640,X_1641),or(X_1641,X_1640))) )],[refute_0_211,refute_0_210]) ).
cnf(refute_0_213,plain,
is_a_theorem(equiv(or(X_1643,X_1642),or(X_1642,X_1643))),
inference(subst,[],[refute_0_212:[bind(X_1640,$fot(X_1642)),bind(X_1641,$fot(X_1643))]]) ).
cnf(refute_0_214,plain,
or(X_1643,X_1642) = or(X_1642,X_1643),
inference(resolve,[$cnf( is_a_theorem(equiv(or(X_1643,X_1642),or(X_1642,X_1643))) )],[refute_0_213,refute_0_165]) ).
cnf(refute_0_215,plain,
or(X,not(X_9)) = or(not(X_9),X),
inference(subst,[],[refute_0_214:[bind(X_1642,$fot(not(X_9))),bind(X_1643,$fot(X))]]) ).
cnf(refute_0_216,plain,
( and(not(X),X_9) != not(or(X,not(X_9)))
| or(X,not(X_9)) != or(not(X_9),X)
| and(not(X),X_9) = not(or(not(X_9),X)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X),X_9),not(or(X,not(X_9)))) ),[1,0],$fot(or(not(X_9),X))]]) ).
cnf(refute_0_217,plain,
( and(not(X),X_9) != not(or(X,not(X_9)))
| and(not(X),X_9) = not(or(not(X_9),X)) ),
inference(resolve,[$cnf( $equal(or(X,not(X_9)),or(not(X_9),X)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
and(not(X),X_9) = not(or(not(X_9),X)),
inference(resolve,[$cnf( $equal(and(not(X),X_9),not(or(X,not(X_9)))) )],[refute_0_44,refute_0_217]) ).
cnf(refute_0_219,plain,
or(not(X_9),X) = implies(X_9,X),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_9)),bind(Y,$fot(X))]]) ).
cnf(refute_0_220,plain,
not(or(not(X_9),X)) = not(or(not(X_9),X)),
introduced(tautology,[refl,[$fot(not(or(not(X_9),X)))]]) ).
cnf(refute_0_221,plain,
( not(or(not(X_9),X)) != not(or(not(X_9),X))
| or(not(X_9),X) != implies(X_9,X)
| not(or(not(X_9),X)) = not(implies(X_9,X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_9),X)),not(or(not(X_9),X))) ),[1,0],$fot(implies(X_9,X))]]) ).
cnf(refute_0_222,plain,
( or(not(X_9),X) != implies(X_9,X)
| not(or(not(X_9),X)) = not(implies(X_9,X)) ),
inference(resolve,[$cnf( $equal(not(or(not(X_9),X)),not(or(not(X_9),X))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
not(or(not(X_9),X)) = not(implies(X_9,X)),
inference(resolve,[$cnf( $equal(or(not(X_9),X),implies(X_9,X)) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
( and(not(X),X_9) != not(or(not(X_9),X))
| not(or(not(X_9),X)) != not(implies(X_9,X))
| and(not(X),X_9) = not(implies(X_9,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(X),X_9),not(implies(X_9,X))) ),[0],$fot(not(or(not(X_9),X)))]]) ).
cnf(refute_0_225,plain,
( and(not(X),X_9) != not(or(not(X_9),X))
| and(not(X),X_9) = not(implies(X_9,X)) ),
inference(resolve,[$cnf( $equal(not(or(not(X_9),X)),not(implies(X_9,X))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
and(not(X),X_9) = not(implies(X_9,X)),
inference(resolve,[$cnf( $equal(and(not(X),X_9),not(or(not(X_9),X))) )],[refute_0_218,refute_0_225]) ).
cnf(refute_0_227,plain,
and(not(X_1116),X_1117) = not(implies(X_1117,X_1116)),
inference(subst,[],[refute_0_226:[bind(X,$fot(X_1116)),bind(X_9,$fot(X_1117))]]) ).
cnf(refute_0_228,plain,
or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) = or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))),
introduced(tautology,[refl,[$fot(or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))))]]) ).
cnf(refute_0_229,plain,
( and(not(X_1116),X_1117) != not(implies(X_1117,X_1116))
| or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) != or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118)))
| or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) = or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118))) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))),or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) ),[1,0],$fot(not(implies(X_1117,X_1116)))]]) ).
cnf(refute_0_230,plain,
( and(not(X_1116),X_1117) != not(implies(X_1117,X_1116))
| or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) = or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))),or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) = or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118))),
inference(resolve,[$cnf( $equal(and(not(X_1116),X_1117),not(implies(X_1117,X_1116))) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
( or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) != or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118)))
| or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118))) != implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))
| or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) = implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118))) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))))),bind(Y0,$fot(or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118))))),bind(Z0,$fot(implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))))]]) ).
cnf(refute_0_233,plain,
( or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118))) != implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))
| or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) = implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118))) ),
inference(resolve,[$cnf( $equal(or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))),or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) = implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118))),
inference(resolve,[$cnf( $equal(or(not(implies(X_1117,X_1116)),implies(or(X_1117,X_1118),or(X_1116,X_1118))),implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) )],[refute_0_161,refute_0_233]) ).
cnf(refute_0_235,plain,
or(or(X_24,not(X_25)),Y) = implies(not(or(X_24,not(X_25))),Y),
inference(subst,[],[refute_0_38:[bind(X,$fot(or(X_24,not(X_25))))]]) ).
cnf(refute_0_236,plain,
( not(or(X_24,not(X_25))) != and(not(X_24),X_25)
| or(or(X_24,not(X_25)),Y) != implies(not(or(X_24,not(X_25))),Y)
| or(or(X_24,not(X_25)),Y) = implies(and(not(X_24),X_25),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X_24,not(X_25)),Y),implies(not(or(X_24,not(X_25))),Y)) ),[1,0],$fot(and(not(X_24),X_25))]]) ).
cnf(refute_0_237,plain,
( or(or(X_24,not(X_25)),Y) != implies(not(or(X_24,not(X_25))),Y)
| or(or(X_24,not(X_25)),Y) = implies(and(not(X_24),X_25),Y) ),
inference(resolve,[$cnf( $equal(not(or(X_24,not(X_25))),and(not(X_24),X_25)) )],[refute_0_47,refute_0_236]) ).
cnf(refute_0_238,plain,
or(or(X_24,not(X_25)),Y) = implies(and(not(X_24),X_25),Y),
inference(resolve,[$cnf( $equal(or(or(X_24,not(X_25)),Y),implies(not(or(X_24,not(X_25))),Y)) )],[refute_0_235,refute_0_237]) ).
cnf(refute_0_239,plain,
or(or(X_24,not(X_25)),Y) = or(Y,or(X_24,not(X_25))),
inference(subst,[],[refute_0_214:[bind(X_1642,$fot(Y)),bind(X_1643,$fot(or(X_24,not(X_25))))]]) ).
cnf(refute_0_240,plain,
( or(or(X_24,not(X_25)),Y) != implies(and(not(X_24),X_25),Y)
| or(or(X_24,not(X_25)),Y) != or(Y,or(X_24,not(X_25)))
| or(Y,or(X_24,not(X_25))) = implies(and(not(X_24),X_25),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X_24,not(X_25)),Y),implies(and(not(X_24),X_25),Y)) ),[0],$fot(or(Y,or(X_24,not(X_25))))]]) ).
cnf(refute_0_241,plain,
( or(or(X_24,not(X_25)),Y) != implies(and(not(X_24),X_25),Y)
| or(Y,or(X_24,not(X_25))) = implies(and(not(X_24),X_25),Y) ),
inference(resolve,[$cnf( $equal(or(or(X_24,not(X_25)),Y),or(Y,or(X_24,not(X_25)))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
or(Y,or(X_24,not(X_25))) = implies(and(not(X_24),X_25),Y),
inference(resolve,[$cnf( $equal(or(or(X_24,not(X_25)),Y),implies(and(not(X_24),X_25),Y)) )],[refute_0_238,refute_0_241]) ).
cnf(refute_0_243,plain,
or(not(X),Y) = or(Y,not(X)),
inference(subst,[],[refute_0_214:[bind(X_1642,$fot(Y)),bind(X_1643,$fot(not(X)))]]) ).
cnf(refute_0_244,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) != or(Y,not(X))
| implies(X,Y) = or(Y,not(X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,Y),or(Y,not(X))) ),[0],$fot(or(not(X),Y))]]) ).
cnf(refute_0_245,plain,
( implies(X,Y) != or(not(X),Y)
| implies(X,Y) = or(Y,not(X)) ),
inference(resolve,[$cnf( $equal(or(not(X),Y),or(Y,not(X))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
implies(X,Y) = or(Y,not(X)),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_8,refute_0_245]) ).
cnf(refute_0_247,plain,
( implies(X,Y) != or(Y,not(X))
| or(Y,not(X)) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(Y,not(X))))]]) ).
cnf(refute_0_248,plain,
or(Y,not(X)) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(Y,not(X))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
or(X_24,not(X_25)) = implies(X_25,X_24),
inference(subst,[],[refute_0_248:[bind(X,$fot(X_25)),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_250,plain,
or(Y,or(X_24,not(X_25))) = or(Y,or(X_24,not(X_25))),
introduced(tautology,[refl,[$fot(or(Y,or(X_24,not(X_25))))]]) ).
cnf(refute_0_251,plain,
( or(Y,or(X_24,not(X_25))) != or(Y,or(X_24,not(X_25)))
| or(X_24,not(X_25)) != implies(X_25,X_24)
| or(Y,or(X_24,not(X_25))) = or(Y,implies(X_25,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,or(X_24,not(X_25))),or(Y,or(X_24,not(X_25)))) ),[1,1],$fot(implies(X_25,X_24))]]) ).
cnf(refute_0_252,plain,
( or(X_24,not(X_25)) != implies(X_25,X_24)
| or(Y,or(X_24,not(X_25))) = or(Y,implies(X_25,X_24)) ),
inference(resolve,[$cnf( $equal(or(Y,or(X_24,not(X_25))),or(Y,or(X_24,not(X_25)))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
or(Y,or(X_24,not(X_25))) = or(Y,implies(X_25,X_24)),
inference(resolve,[$cnf( $equal(or(X_24,not(X_25)),implies(X_25,X_24)) )],[refute_0_249,refute_0_252]) ).
cnf(refute_0_254,plain,
( or(Y,or(X_24,not(X_25))) != implies(and(not(X_24),X_25),Y)
| or(Y,or(X_24,not(X_25))) != or(Y,implies(X_25,X_24))
| or(Y,implies(X_25,X_24)) = implies(and(not(X_24),X_25),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,or(X_24,not(X_25))),implies(and(not(X_24),X_25),Y)) ),[0],$fot(or(Y,implies(X_25,X_24)))]]) ).
cnf(refute_0_255,plain,
( or(Y,or(X_24,not(X_25))) != implies(and(not(X_24),X_25),Y)
| or(Y,implies(X_25,X_24)) = implies(and(not(X_24),X_25),Y) ),
inference(resolve,[$cnf( $equal(or(Y,or(X_24,not(X_25))),or(Y,implies(X_25,X_24))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
or(Y,implies(X_25,X_24)) = implies(and(not(X_24),X_25),Y),
inference(resolve,[$cnf( $equal(or(Y,or(X_24,not(X_25))),implies(and(not(X_24),X_25),Y)) )],[refute_0_242,refute_0_255]) ).
cnf(refute_0_257,plain,
implies(not(implies(X_25,X_24)),Y) = or(implies(X_25,X_24),Y),
inference(subst,[],[refute_0_189:[bind(X,$fot(implies(X_25,X_24)))]]) ).
cnf(refute_0_258,plain,
and(not(X_24),X_25) = not(implies(X_25,X_24)),
inference(subst,[],[refute_0_226:[bind(X,$fot(X_24)),bind(X_9,$fot(X_25))]]) ).
cnf(refute_0_259,plain,
implies(and(not(X_24),X_25),Y) = implies(and(not(X_24),X_25),Y),
introduced(tautology,[refl,[$fot(implies(and(not(X_24),X_25),Y))]]) ).
cnf(refute_0_260,plain,
( and(not(X_24),X_25) != not(implies(X_25,X_24))
| implies(and(not(X_24),X_25),Y) != implies(and(not(X_24),X_25),Y)
| implies(and(not(X_24),X_25),Y) = implies(not(implies(X_25,X_24)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(not(X_24),X_25),Y),implies(and(not(X_24),X_25),Y)) ),[1,0],$fot(not(implies(X_25,X_24)))]]) ).
cnf(refute_0_261,plain,
( and(not(X_24),X_25) != not(implies(X_25,X_24))
| implies(and(not(X_24),X_25),Y) = implies(not(implies(X_25,X_24)),Y) ),
inference(resolve,[$cnf( $equal(implies(and(not(X_24),X_25),Y),implies(and(not(X_24),X_25),Y)) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
implies(and(not(X_24),X_25),Y) = implies(not(implies(X_25,X_24)),Y),
inference(resolve,[$cnf( $equal(and(not(X_24),X_25),not(implies(X_25,X_24))) )],[refute_0_258,refute_0_261]) ).
cnf(refute_0_263,plain,
( implies(and(not(X_24),X_25),Y) != implies(not(implies(X_25,X_24)),Y)
| implies(not(implies(X_25,X_24)),Y) != or(implies(X_25,X_24),Y)
| implies(and(not(X_24),X_25),Y) = or(implies(X_25,X_24),Y) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(implies(and(not(X_24),X_25),Y))),bind(Y0,$fot(implies(not(implies(X_25,X_24)),Y))),bind(Z0,$fot(or(implies(X_25,X_24),Y)))]]) ).
cnf(refute_0_264,plain,
( implies(not(implies(X_25,X_24)),Y) != or(implies(X_25,X_24),Y)
| implies(and(not(X_24),X_25),Y) = or(implies(X_25,X_24),Y) ),
inference(resolve,[$cnf( $equal(implies(and(not(X_24),X_25),Y),implies(not(implies(X_25,X_24)),Y)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
implies(and(not(X_24),X_25),Y) = or(implies(X_25,X_24),Y),
inference(resolve,[$cnf( $equal(implies(not(implies(X_25,X_24)),Y),or(implies(X_25,X_24),Y)) )],[refute_0_257,refute_0_264]) ).
cnf(refute_0_266,plain,
( implies(and(not(X_24),X_25),Y) != or(implies(X_25,X_24),Y)
| or(Y,implies(X_25,X_24)) != implies(and(not(X_24),X_25),Y)
| or(Y,implies(X_25,X_24)) = or(implies(X_25,X_24),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(Y,implies(X_25,X_24)),implies(and(not(X_24),X_25),Y)) ),[1],$fot(or(implies(X_25,X_24),Y))]]) ).
cnf(refute_0_267,plain,
( or(Y,implies(X_25,X_24)) != implies(and(not(X_24),X_25),Y)
| or(Y,implies(X_25,X_24)) = or(implies(X_25,X_24),Y) ),
inference(resolve,[$cnf( $equal(implies(and(not(X_24),X_25),Y),or(implies(X_25,X_24),Y)) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
or(Y,implies(X_25,X_24)) = or(implies(X_25,X_24),Y),
inference(resolve,[$cnf( $equal(or(Y,implies(X_25,X_24)),implies(and(not(X_24),X_25),Y)) )],[refute_0_256,refute_0_267]) ).
cnf(refute_0_269,plain,
( or(Y,implies(X_25,X_24)) != or(implies(X_25,X_24),Y)
| or(implies(X_25,X_24),Y) = or(Y,implies(X_25,X_24)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(Y,implies(X_25,X_24)))),bind(Y0,$fot(or(implies(X_25,X_24),Y)))]]) ).
cnf(refute_0_270,plain,
or(implies(X_25,X_24),Y) = or(Y,implies(X_25,X_24)),
inference(resolve,[$cnf( $equal(or(Y,implies(X_25,X_24)),or(implies(X_25,X_24),Y)) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)) = or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))),
inference(subst,[],[refute_0_270:[bind(Y,$fot(and(not(X_1116),X_1117))),bind(X_24,$fot(or(X_1116,X_1118))),bind(X_25,$fot(or(X_1117,X_1118)))]]) ).
cnf(refute_0_272,plain,
( or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) != implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))
| or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)) != or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118)))
| or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)) = implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118))) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)))),bind(Y0,$fot(or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))))),bind(Z0,$fot(implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))))]]) ).
cnf(refute_0_273,plain,
( or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))) != implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))
| or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)) = implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118))) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)),or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)) = implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118))),
inference(resolve,[$cnf( $equal(or(and(not(X_1116),X_1117),implies(or(X_1117,X_1118),or(X_1116,X_1118))),implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) )],[refute_0_234,refute_0_273]) ).
cnf(refute_0_275,plain,
( or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)) != implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))
| ~ is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)))
| is_a_theorem(implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117))) ),[0],$fot(implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118))))]]) ).
cnf(refute_0_276,plain,
( ~ is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)))
| is_a_theorem(implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) ),
inference(resolve,[$cnf( $equal(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117)),implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
is_a_theorem(implies(implies(X_1117,X_1116),implies(or(X_1117,X_1118),or(X_1116,X_1118)))),
inference(resolve,[$cnf( is_a_theorem(or(implies(or(X_1117,X_1118),or(X_1116,X_1118)),and(not(X_1116),X_1117))) )],[refute_0_160,refute_0_276]) ).
cnf(refute_0_278,plain,
is_a_theorem(implies(implies(X_2473,X_2472),implies(or(X_2473,X_2474),or(X_2472,X_2474)))),
inference(subst,[],[refute_0_277:[bind(X_1116,$fot(X_2472)),bind(X_1117,$fot(X_2473)),bind(X_1118,$fot(X_2474))]]) ).
cnf(refute_0_279,plain,
or(X_2474,X_2473) = or(X_2473,X_2474),
inference(subst,[],[refute_0_214:[bind(X_1642,$fot(X_2473)),bind(X_1643,$fot(X_2474))]]) ).
cnf(refute_0_280,plain,
( or(X_2474,X_2473) != or(X_2473,X_2474)
| or(X_2473,X_2474) = or(X_2474,X_2473) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_2474,X_2473))),bind(Y0,$fot(or(X_2473,X_2474)))]]) ).
cnf(refute_0_281,plain,
or(X_2473,X_2474) = or(X_2474,X_2473),
inference(resolve,[$cnf( $equal(or(X_2474,X_2473),or(X_2473,X_2474)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
( or(X_2473,X_2474) != or(X_2474,X_2473)
| ~ is_a_theorem(implies(implies(X_2473,X_2472),implies(or(X_2473,X_2474),or(X_2472,X_2474))))
| is_a_theorem(implies(implies(X_2473,X_2472),implies(or(X_2474,X_2473),or(X_2472,X_2474)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_2473,X_2472),implies(or(X_2473,X_2474),or(X_2472,X_2474)))) ),[0,1,0],$fot(or(X_2474,X_2473))]]) ).
cnf(refute_0_283,plain,
( ~ is_a_theorem(implies(implies(X_2473,X_2472),implies(or(X_2473,X_2474),or(X_2472,X_2474))))
| is_a_theorem(implies(implies(X_2473,X_2472),implies(or(X_2474,X_2473),or(X_2472,X_2474)))) ),
inference(resolve,[$cnf( $equal(or(X_2473,X_2474),or(X_2474,X_2473)) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
is_a_theorem(implies(implies(X_2473,X_2472),implies(or(X_2474,X_2473),or(X_2472,X_2474)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2473,X_2472),implies(or(X_2473,X_2474),or(X_2472,X_2474)))) )],[refute_0_278,refute_0_283]) ).
cnf(refute_0_285,plain,
is_a_theorem(implies(implies(X_2489,X_2488),implies(or(X_2490,X_2489),or(X_2488,X_2490)))),
inference(subst,[],[refute_0_284:[bind(X_2472,$fot(X_2488)),bind(X_2473,$fot(X_2489)),bind(X_2474,$fot(X_2490))]]) ).
cnf(refute_0_286,plain,
or(X_2490,X_2488) = or(X_2488,X_2490),
inference(subst,[],[refute_0_214:[bind(X_1642,$fot(X_2488)),bind(X_1643,$fot(X_2490))]]) ).
cnf(refute_0_287,plain,
( or(X_2490,X_2488) != or(X_2488,X_2490)
| or(X_2488,X_2490) = or(X_2490,X_2488) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_2490,X_2488))),bind(Y0,$fot(or(X_2488,X_2490)))]]) ).
cnf(refute_0_288,plain,
or(X_2488,X_2490) = or(X_2490,X_2488),
inference(resolve,[$cnf( $equal(or(X_2490,X_2488),or(X_2488,X_2490)) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
( or(X_2488,X_2490) != or(X_2490,X_2488)
| ~ is_a_theorem(implies(implies(X_2489,X_2488),implies(or(X_2490,X_2489),or(X_2488,X_2490))))
| is_a_theorem(implies(implies(X_2489,X_2488),implies(or(X_2490,X_2489),or(X_2490,X_2488)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_2489,X_2488),implies(or(X_2490,X_2489),or(X_2488,X_2490)))) ),[0,1,1],$fot(or(X_2490,X_2488))]]) ).
cnf(refute_0_290,plain,
( ~ is_a_theorem(implies(implies(X_2489,X_2488),implies(or(X_2490,X_2489),or(X_2488,X_2490))))
| is_a_theorem(implies(implies(X_2489,X_2488),implies(or(X_2490,X_2489),or(X_2490,X_2488)))) ),
inference(resolve,[$cnf( $equal(or(X_2488,X_2490),or(X_2490,X_2488)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
is_a_theorem(implies(implies(X_2489,X_2488),implies(or(X_2490,X_2489),or(X_2490,X_2488)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2489,X_2488),implies(or(X_2490,X_2489),or(X_2488,X_2490)))) )],[refute_0_285,refute_0_290]) ).
cnf(refute_0_292,plain,
is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3)))),
inference(subst,[],[refute_0_291:[bind(X_2488,$fot(skolemFOFtoCNF_R_3)),bind(X_2489,$fot(skolemFOFtoCNF_Q_7)),bind(X_2490,$fot(skolemFOFtoCNF_P_10))]]) ).
cnf(refute_0_293,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3)))) )],[refute_0_292,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15 % Problem : LCL458+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.15 % Command : metis --show proof --show saturation %s
% 0.16/0.36 % Computer : n004.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Sat Jul 2 19:08:08 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.16/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 148.49/148.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 148.49/148.67
% 148.49/148.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 148.49/148.71
%------------------------------------------------------------------------------