TSTP Solution File: LCL454+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL454+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:52:25 EDT 2022
% Result : Theorem 1.74s 1.95s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 86
% Syntax : Number of formulae : 413 ( 210 unt; 0 def)
% Number of atoms : 710 ( 411 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 574 ( 277 ~; 259 |; 15 &)
% ( 16 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 17 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 15 con; 0-2 aty)
% Number of variables : 665 ( 4 sgn 74 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ) ).
fof(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ) ).
fof(equivalence_3,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ).
fof(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
fof(hilbert_op_equiv,axiom,
op_equiv ).
fof(hilbert_modus_ponens,axiom,
modus_ponens ).
fof(hilbert_implies_1,axiom,
implies_1 ).
fof(hilbert_implies_2,axiom,
implies_2 ).
fof(hilbert_and_2,axiom,
and_2 ).
fof(hilbert_and_3,axiom,
and_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_op_equiv,axiom,
op_equiv ).
fof(principia_r1,conjecture,
r1 ).
fof(subgoal_0,plain,
r1,
inference(strip,[],[principia_r1]) ).
fof(negate_0_0,plain,
~ r1,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ r1
<=> ? [P] : ~ is_a_theorem(implies(or(P,P),P)) ),
inference(canonicalize,[],[r1]) ).
fof(normalize_0_1,plain,
! [P] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6))
| r1 )
& ( ~ r1
| is_a_theorem(implies(or(P,P),P)) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6))
| r1 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ r1,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ op_equiv
| ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[op_equiv]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
op_equiv,
inference(canonicalize,[],[principia_op_equiv]) ).
fof(normalize_0_7,plain,
( ~ substitution_of_equivalents
<=> ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) ),
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
substitution_of_equivalents,
inference(canonicalize,[],[substitution_of_equivalents]) ).
fof(normalize_0_11,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_12,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_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
modus_ponens,
inference(canonicalize,[],[hilbert_modus_ponens]) ).
fof(normalize_0_15,plain,
( ~ and_3
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[and_3]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) )
& ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_8,implies(skolemFOFtoCNF_Y_8,and(skolemFOFtoCNF_X_8,skolemFOFtoCNF_Y_8))))
| and_3 ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
and_3,
inference(canonicalize,[],[hilbert_and_3]) ).
fof(normalize_0_19,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_22,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_25,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_28,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_29,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
fof(normalize_0_31,plain,
( ~ implies_2
<=> ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[implies_2]) ).
fof(normalize_0_32,plain,
! [X,Y] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_X_4,implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)),implies(skolemFOFtoCNF_X_4,skolemFOFtoCNF_Y_4)))
| implies_2 ) ),
inference(clausify,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [X,Y] :
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(conjunct,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
implies_2,
inference(canonicalize,[],[hilbert_implies_2]) ).
fof(normalize_0_35,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_36,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_35]) ).
fof(normalize_0_37,plain,
! [X,Y] :
( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(conjunct,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
equivalence_3,
inference(canonicalize,[],[hilbert_equivalence_3]) ).
fof(normalize_0_39,plain,
( ~ implies_1
<=> ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X))) ),
inference(canonicalize,[],[implies_1]) ).
fof(normalize_0_40,plain,
! [X,Y] :
( ( ~ implies_1
| is_a_theorem(implies(X,implies(Y,X))) )
& ( ~ is_a_theorem(implies(skolemFOFtoCNF_X_3,implies(skolemFOFtoCNF_Y_3,skolemFOFtoCNF_X_3)))
| implies_1 ) ),
inference(clausify,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [X,Y] :
( ~ implies_1
| is_a_theorem(implies(X,implies(Y,X))) ),
inference(conjunct,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
implies_1,
inference(canonicalize,[],[hilbert_implies_1]) ).
fof(normalize_0_43,plain,
( ~ and_2
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[and_2]) ).
fof(normalize_0_44,plain,
! [X,Y] :
( ( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) )
& ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_7,skolemFOFtoCNF_Y_7),skolemFOFtoCNF_Y_7))
| and_2 ) ),
inference(clausify,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [X,Y] :
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(conjunct,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
and_2,
inference(canonicalize,[],[hilbert_and_2]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6))
| r1 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ r1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6)),
inference(resolve,[$cnf( r1 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ op_equiv
| equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
op_equiv,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
equiv(X,Y) = and(implies(X,Y),implies(Y,X)),
inference(resolve,[$cnf( op_equiv )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
equiv(Y,Y) = and(implies(Y,Y),implies(Y,Y)),
inference(subst,[],[refute_0_5:[bind(X,$fot(Y))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(equiv(X,Y))
| ~ substitution_of_equivalents
| X = Y ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
substitution_of_equivalents,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(equiv(X,Y))
| X = Y ),
inference(resolve,[$cnf( substitution_of_equivalents )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equiv(X_993,and(X_993,X_993)))
| X_993 = and(X_993,X_993) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_993)),bind(Y,$fot(and(X_993,X_993)))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(and(X_992,X_992),X_992))
| ~ is_a_theorem(implies(implies(and(X_992,X_992),X_992),equiv(X_992,and(X_992,X_992))))
| is_a_theorem(equiv(X_992,and(X_992,X_992))) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(implies(and(X_992,X_992),X_992))),bind(Y,$fot(equiv(X_992,and(X_992,X_992))))]]) ).
cnf(refute_0_15,plain,
( ~ and_3
| is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
and_3,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(X,implies(Y,and(X,Y)))),
inference(resolve,[$cnf( and_3 )],[refute_0_16,refute_0_15]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(not(X),implies(X_17,and(not(X),X_17)))),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(X))),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_19,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_20,plain,
op_or,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_21,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_23,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_24,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_26,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_27,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_29,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_29:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_31,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_32,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_21,refute_0_32]) ).
cnf(refute_0_34,plain,
or(X,implies(X_17,and(not(X),X_17))) = implies(not(X),implies(X_17,and(not(X),X_17))),
inference(subst,[],[refute_0_33:[bind(Y,$fot(implies(X_17,and(not(X),X_17))))]]) ).
cnf(refute_0_35,plain,
( or(X,implies(X_17,and(not(X),X_17))) != implies(not(X),implies(X_17,and(not(X),X_17)))
| implies(not(X),implies(X_17,and(not(X),X_17))) = or(X,implies(X_17,and(not(X),X_17))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(or(X,implies(X_17,and(not(X),X_17))))),bind(Y0,$fot(implies(not(X),implies(X_17,and(not(X),X_17)))))]]) ).
cnf(refute_0_36,plain,
implies(not(X),implies(X_17,and(not(X),X_17))) = or(X,implies(X_17,and(not(X),X_17))),
inference(resolve,[$cnf( $equal(or(X,implies(X_17,and(not(X),X_17))),implies(not(X),implies(X_17,and(not(X),X_17)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( implies(not(X),implies(X_17,and(not(X),X_17))) != or(X,implies(X_17,and(not(X),X_17)))
| ~ is_a_theorem(implies(not(X),implies(X_17,and(not(X),X_17))))
| is_a_theorem(or(X,implies(X_17,and(not(X),X_17)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X),implies(X_17,and(not(X),X_17)))) ),[0],$fot(or(X,implies(X_17,and(not(X),X_17))))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(not(X),implies(X_17,and(not(X),X_17))))
| is_a_theorem(or(X,implies(X_17,and(not(X),X_17)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(X_17,and(not(X),X_17))),or(X,implies(X_17,and(not(X),X_17)))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
is_a_theorem(or(X,implies(X_17,and(not(X),X_17)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),implies(X_17,and(not(X),X_17)))) )],[refute_0_18,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(or(X_18,implies(not(X),and(not(X_18),not(X))))),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_18)),bind(X_17,$fot(not(X)))]]) ).
cnf(refute_0_41,plain,
or(X,and(not(X_18),not(X))) = implies(not(X),and(not(X_18),not(X))),
inference(subst,[],[refute_0_33:[bind(Y,$fot(and(not(X_18),not(X))))]]) ).
cnf(refute_0_42,plain,
( or(X,and(not(X_18),not(X))) != implies(not(X),and(not(X_18),not(X)))
| implies(not(X),and(not(X_18),not(X))) = or(X,and(not(X_18),not(X))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(or(X,and(not(X_18),not(X))))),bind(Y0,$fot(implies(not(X),and(not(X_18),not(X)))))]]) ).
cnf(refute_0_43,plain,
implies(not(X),and(not(X_18),not(X))) = or(X,and(not(X_18),not(X))),
inference(resolve,[$cnf( $equal(or(X,and(not(X_18),not(X))),implies(not(X),and(not(X_18),not(X)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( implies(not(X),and(not(X_18),not(X))) != or(X,and(not(X_18),not(X)))
| ~ is_a_theorem(or(X_18,implies(not(X),and(not(X_18),not(X)))))
| is_a_theorem(or(X_18,or(X,and(not(X_18),not(X))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_18,implies(not(X),and(not(X_18),not(X))))) ),[0,1],$fot(or(X,and(not(X_18),not(X))))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(or(X_18,implies(not(X),and(not(X_18),not(X)))))
| is_a_theorem(or(X_18,or(X,and(not(X_18),not(X))))) ),
inference(resolve,[$cnf( $equal(implies(not(X),and(not(X_18),not(X))),or(X,and(not(X_18),not(X)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
is_a_theorem(or(X_18,or(X,and(not(X_18),not(X))))),
inference(resolve,[$cnf( is_a_theorem(or(X_18,implies(not(X),and(not(X_18),not(X))))) )],[refute_0_40,refute_0_45]) ).
cnf(refute_0_47,plain,
is_a_theorem(or(not(X),or(X_62,and(not(not(X)),not(X_62))))),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_62)),bind(X_18,$fot(not(X)))]]) ).
cnf(refute_0_48,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_49,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_50,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_49,refute_0_48]) ).
cnf(refute_0_51,plain,
implies(X,or(X_62,and(not(not(X)),not(X_62)))) = or(not(X),or(X_62,and(not(not(X)),not(X_62)))),
inference(subst,[],[refute_0_50:[bind(Y,$fot(or(X_62,and(not(not(X)),not(X_62)))))]]) ).
cnf(refute_0_52,plain,
( implies(X,or(X_62,and(not(not(X)),not(X_62)))) != or(not(X),or(X_62,and(not(not(X)),not(X_62))))
| or(not(X),or(X_62,and(not(not(X)),not(X_62)))) = implies(X,or(X_62,and(not(not(X)),not(X_62)))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(implies(X,or(X_62,and(not(not(X)),not(X_62)))))),bind(Y0,$fot(or(not(X),or(X_62,and(not(not(X)),not(X_62))))))]]) ).
cnf(refute_0_53,plain,
or(not(X),or(X_62,and(not(not(X)),not(X_62)))) = implies(X,or(X_62,and(not(not(X)),not(X_62)))),
inference(resolve,[$cnf( $equal(implies(X,or(X_62,and(not(not(X)),not(X_62)))),or(not(X),or(X_62,and(not(not(X)),not(X_62))))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( or(not(X),or(X_62,and(not(not(X)),not(X_62)))) != implies(X,or(X_62,and(not(not(X)),not(X_62))))
| ~ is_a_theorem(or(not(X),or(X_62,and(not(not(X)),not(X_62)))))
| is_a_theorem(implies(X,or(X_62,and(not(not(X)),not(X_62))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(not(X),or(X_62,and(not(not(X)),not(X_62))))) ),[0],$fot(implies(X,or(X_62,and(not(not(X)),not(X_62)))))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(or(not(X),or(X_62,and(not(not(X)),not(X_62)))))
| is_a_theorem(implies(X,or(X_62,and(not(not(X)),not(X_62))))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_62,and(not(not(X)),not(X_62)))),implies(X,or(X_62,and(not(not(X)),not(X_62))))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(X,or(X_62,and(not(not(X)),not(X_62))))),
inference(resolve,[$cnf( is_a_theorem(or(not(X),or(X_62,and(not(not(X)),not(X_62))))) )],[refute_0_47,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_58,plain,
op_and,
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_59,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_58,refute_0_57]) ).
cnf(refute_0_60,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_61,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_50,refute_0_60]) ).
cnf(refute_0_62,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_61:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_63,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_64,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_65,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_68,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_59,refute_0_68]) ).
cnf(refute_0_70,plain,
and(not(X),X_37) = not(implies(not(X),not(X_37))),
inference(subst,[],[refute_0_69:[bind(X,$fot(not(X))),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_71,plain,
or(X,not(X_37)) = implies(not(X),not(X_37)),
inference(subst,[],[refute_0_33:[bind(Y,$fot(not(X_37)))]]) ).
cnf(refute_0_72,plain,
( or(X,not(X_37)) != implies(not(X),not(X_37))
| implies(not(X),not(X_37)) = or(X,not(X_37)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(or(X,not(X_37)))),bind(Y0,$fot(implies(not(X),not(X_37))))]]) ).
cnf(refute_0_73,plain,
implies(not(X),not(X_37)) = or(X,not(X_37)),
inference(resolve,[$cnf( $equal(or(X,not(X_37)),implies(not(X),not(X_37))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( and(not(X),X_37) != not(implies(not(X),not(X_37)))
| implies(not(X),not(X_37)) != or(X,not(X_37))
| and(not(X),X_37) = not(or(X,not(X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(X),X_37),not(implies(not(X),not(X_37)))) ),[1,0],$fot(or(X,not(X_37)))]]) ).
cnf(refute_0_75,plain,
( and(not(X),X_37) != not(implies(not(X),not(X_37)))
| and(not(X),X_37) = not(or(X,not(X_37))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X_37)),or(X,not(X_37))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
and(not(X),X_37) = not(or(X,not(X_37))),
inference(resolve,[$cnf( $equal(and(not(X),X_37),not(implies(not(X),not(X_37)))) )],[refute_0_70,refute_0_75]) ).
cnf(refute_0_77,plain,
and(not(not(X)),X_39) = not(or(not(X),not(X_39))),
inference(subst,[],[refute_0_76:[bind(X,$fot(not(X))),bind(X_37,$fot(X_39))]]) ).
cnf(refute_0_78,plain,
implies(X,not(X_39)) = or(not(X),not(X_39)),
inference(subst,[],[refute_0_50:[bind(Y,$fot(not(X_39)))]]) ).
cnf(refute_0_79,plain,
( implies(X,not(X_39)) != or(not(X),not(X_39))
| or(not(X),not(X_39)) = implies(X,not(X_39)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(implies(X,not(X_39)))),bind(Y0,$fot(or(not(X),not(X_39))))]]) ).
cnf(refute_0_80,plain,
or(not(X),not(X_39)) = implies(X,not(X_39)),
inference(resolve,[$cnf( $equal(implies(X,not(X_39)),or(not(X),not(X_39))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( and(not(not(X)),X_39) != not(or(not(X),not(X_39)))
| or(not(X),not(X_39)) != implies(X,not(X_39))
| and(not(not(X)),X_39) = not(implies(X,not(X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(X)),X_39),not(or(not(X),not(X_39)))) ),[1,0],$fot(implies(X,not(X_39)))]]) ).
cnf(refute_0_82,plain,
( and(not(not(X)),X_39) != not(or(not(X),not(X_39)))
| and(not(not(X)),X_39) = not(implies(X,not(X_39))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_39)),implies(X,not(X_39))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
and(not(not(X)),X_39) = not(implies(X,not(X_39))),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_39),not(or(not(X),not(X_39)))) )],[refute_0_77,refute_0_82]) ).
cnf(refute_0_84,plain,
( and(X,Y) != not(implies(X,not(Y)))
| not(implies(X,not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(implies(X,not(Y)))))]]) ).
cnf(refute_0_85,plain,
not(implies(X,not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(implies(X,not(Y)))) )],[refute_0_69,refute_0_84]) ).
cnf(refute_0_86,plain,
not(implies(X,not(X_39))) = and(X,X_39),
inference(subst,[],[refute_0_85:[bind(Y,$fot(X_39))]]) ).
cnf(refute_0_87,plain,
( and(not(not(X)),X_39) != not(implies(X,not(X_39)))
| not(implies(X,not(X_39))) != and(X,X_39)
| and(not(not(X)),X_39) = and(X,X_39) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(not(not(X)),X_39),and(X,X_39)) ),[0],$fot(not(implies(X,not(X_39))))]]) ).
cnf(refute_0_88,plain,
( and(not(not(X)),X_39) != not(implies(X,not(X_39)))
| and(not(not(X)),X_39) = and(X,X_39) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(X_39))),and(X,X_39)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
and(not(not(X)),X_39) = and(X,X_39),
inference(resolve,[$cnf( $equal(and(not(not(X)),X_39),not(implies(X,not(X_39)))) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
and(not(not(X)),not(X_62)) = and(X,not(X_62)),
inference(subst,[],[refute_0_89:[bind(X_39,$fot(not(X_62)))]]) ).
cnf(refute_0_91,plain,
or(X_62,and(not(not(X)),not(X_62))) = or(X_62,and(not(not(X)),not(X_62))),
introduced(tautology,[refl,[$fot(or(X_62,and(not(not(X)),not(X_62))))]]) ).
cnf(refute_0_92,plain,
( and(not(not(X)),not(X_62)) != and(X,not(X_62))
| or(X_62,and(not(not(X)),not(X_62))) != or(X_62,and(not(not(X)),not(X_62)))
| or(X_62,and(not(not(X)),not(X_62))) = or(X_62,and(X,not(X_62))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_62,and(not(not(X)),not(X_62))),or(X_62,and(not(not(X)),not(X_62)))) ),[1,1],$fot(and(X,not(X_62)))]]) ).
cnf(refute_0_93,plain,
( and(not(not(X)),not(X_62)) != and(X,not(X_62))
| or(X_62,and(not(not(X)),not(X_62))) = or(X_62,and(X,not(X_62))) ),
inference(resolve,[$cnf( $equal(or(X_62,and(not(not(X)),not(X_62))),or(X_62,and(not(not(X)),not(X_62)))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
or(X_62,and(not(not(X)),not(X_62))) = or(X_62,and(X,not(X_62))),
inference(resolve,[$cnf( $equal(and(not(not(X)),not(X_62)),and(X,not(X_62))) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
implies(X,or(X_62,and(not(not(X)),not(X_62)))) = implies(X,or(X_62,and(not(not(X)),not(X_62)))),
introduced(tautology,[refl,[$fot(implies(X,or(X_62,and(not(not(X)),not(X_62)))))]]) ).
cnf(refute_0_96,plain,
( implies(X,or(X_62,and(not(not(X)),not(X_62)))) != implies(X,or(X_62,and(not(not(X)),not(X_62))))
| or(X_62,and(not(not(X)),not(X_62))) != or(X_62,and(X,not(X_62)))
| implies(X,or(X_62,and(not(not(X)),not(X_62)))) = implies(X,or(X_62,and(X,not(X_62)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,or(X_62,and(not(not(X)),not(X_62)))),implies(X,or(X_62,and(not(not(X)),not(X_62))))) ),[1,1],$fot(or(X_62,and(X,not(X_62))))]]) ).
cnf(refute_0_97,plain,
( or(X_62,and(not(not(X)),not(X_62))) != or(X_62,and(X,not(X_62)))
| implies(X,or(X_62,and(not(not(X)),not(X_62)))) = implies(X,or(X_62,and(X,not(X_62)))) ),
inference(resolve,[$cnf( $equal(implies(X,or(X_62,and(not(not(X)),not(X_62)))),implies(X,or(X_62,and(not(not(X)),not(X_62))))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
implies(X,or(X_62,and(not(not(X)),not(X_62)))) = implies(X,or(X_62,and(X,not(X_62)))),
inference(resolve,[$cnf( $equal(or(X_62,and(not(not(X)),not(X_62))),or(X_62,and(X,not(X_62)))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( implies(X,or(X_62,and(not(not(X)),not(X_62)))) != implies(X,or(X_62,and(X,not(X_62))))
| ~ is_a_theorem(implies(X,or(X_62,and(not(not(X)),not(X_62)))))
| is_a_theorem(implies(X,or(X_62,and(X,not(X_62))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X,or(X_62,and(not(not(X)),not(X_62))))) ),[0],$fot(implies(X,or(X_62,and(X,not(X_62)))))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(X,or(X_62,and(not(not(X)),not(X_62)))))
| is_a_theorem(implies(X,or(X_62,and(X,not(X_62))))) ),
inference(resolve,[$cnf( $equal(implies(X,or(X_62,and(not(not(X)),not(X_62)))),implies(X,or(X_62,and(X,not(X_62))))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(X,or(X_62,and(X,not(X_62))))),
inference(resolve,[$cnf( is_a_theorem(implies(X,or(X_62,and(not(not(X)),not(X_62))))) )],[refute_0_56,refute_0_100]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(X_64,or(not(X),and(X_64,not(not(X)))))),
inference(subst,[],[refute_0_101:[bind(X,$fot(X_64)),bind(X_62,$fot(not(X)))]]) ).
cnf(refute_0_103,plain,
implies(X,and(X_64,not(not(X)))) = or(not(X),and(X_64,not(not(X)))),
inference(subst,[],[refute_0_50:[bind(Y,$fot(and(X_64,not(not(X)))))]]) ).
cnf(refute_0_104,plain,
( implies(X,and(X_64,not(not(X)))) != or(not(X),and(X_64,not(not(X))))
| or(not(X),and(X_64,not(not(X)))) = implies(X,and(X_64,not(not(X)))) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(implies(X,and(X_64,not(not(X)))))),bind(Y0,$fot(or(not(X),and(X_64,not(not(X))))))]]) ).
cnf(refute_0_105,plain,
or(not(X),and(X_64,not(not(X)))) = implies(X,and(X_64,not(not(X)))),
inference(resolve,[$cnf( $equal(implies(X,and(X_64,not(not(X)))),or(not(X),and(X_64,not(not(X))))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( or(not(X),and(X_64,not(not(X)))) != implies(X,and(X_64,not(not(X))))
| ~ is_a_theorem(implies(X_64,or(not(X),and(X_64,not(not(X))))))
| is_a_theorem(implies(X_64,implies(X,and(X_64,not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_64,or(not(X),and(X_64,not(not(X)))))) ),[0,1],$fot(implies(X,and(X_64,not(not(X)))))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(X_64,or(not(X),and(X_64,not(not(X))))))
| is_a_theorem(implies(X_64,implies(X,and(X_64,not(not(X)))))) ),
inference(resolve,[$cnf( $equal(or(not(X),and(X_64,not(not(X)))),implies(X,and(X_64,not(not(X))))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(X_64,implies(X,and(X_64,not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_64,or(not(X),and(X_64,not(not(X)))))) )],[refute_0_102,refute_0_107]) ).
cnf(refute_0_109,plain,
and(X,implies(X_36,not(X_37))) = not(implies(X,not(implies(X_36,not(X_37))))),
inference(subst,[],[refute_0_69:[bind(Y,$fot(implies(X_36,not(X_37))))]]) ).
cnf(refute_0_110,plain,
and(X_36,X_37) = not(implies(X_36,not(X_37))),
inference(subst,[],[refute_0_69:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_111,plain,
( and(X_36,X_37) != not(implies(X_36,not(X_37)))
| not(implies(X_36,not(X_37))) = and(X_36,X_37) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(and(X_36,X_37))),bind(Y0,$fot(not(implies(X_36,not(X_37)))))]]) ).
cnf(refute_0_112,plain,
not(implies(X_36,not(X_37))) = and(X_36,X_37),
inference(resolve,[$cnf( $equal(and(X_36,X_37),not(implies(X_36,not(X_37)))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( and(X,implies(X_36,not(X_37))) != not(implies(X,not(implies(X_36,not(X_37)))))
| not(implies(X_36,not(X_37))) != and(X_36,X_37)
| and(X,implies(X_36,not(X_37))) = not(implies(X,and(X_36,X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,implies(X_36,not(X_37))),not(implies(X,not(implies(X_36,not(X_37)))))) ),[1,0,1],$fot(and(X_36,X_37))]]) ).
cnf(refute_0_114,plain,
( and(X,implies(X_36,not(X_37))) != not(implies(X,not(implies(X_36,not(X_37)))))
| and(X,implies(X_36,not(X_37))) = not(implies(X,and(X_36,X_37))) ),
inference(resolve,[$cnf( $equal(not(implies(X_36,not(X_37))),and(X_36,X_37)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
and(X,implies(X_36,not(X_37))) = not(implies(X,and(X_36,X_37))),
inference(resolve,[$cnf( $equal(and(X,implies(X_36,not(X_37))),not(implies(X,not(implies(X_36,not(X_37)))))) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
and(X,implies(X_64,not(X))) = not(implies(X,and(X_64,X))),
inference(subst,[],[refute_0_115:[bind(X_36,$fot(X_64)),bind(X_37,$fot(X))]]) ).
cnf(refute_0_117,plain,
not(and(X,implies(X_64,not(X)))) = not(and(X,implies(X_64,not(X)))),
introduced(tautology,[refl,[$fot(not(and(X,implies(X_64,not(X)))))]]) ).
cnf(refute_0_118,plain,
( and(X,implies(X_64,not(X))) != not(implies(X,and(X_64,X)))
| not(and(X,implies(X_64,not(X)))) != not(and(X,implies(X_64,not(X))))
| not(and(X,implies(X_64,not(X)))) = not(not(implies(X,and(X_64,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(X,implies(X_64,not(X)))),not(and(X,implies(X_64,not(X))))) ),[1,0],$fot(not(implies(X,and(X_64,X))))]]) ).
cnf(refute_0_119,plain,
( and(X,implies(X_64,not(X))) != not(implies(X,and(X_64,X)))
| not(and(X,implies(X_64,not(X)))) = not(not(implies(X,and(X_64,X)))) ),
inference(resolve,[$cnf( $equal(not(and(X,implies(X_64,not(X)))),not(and(X,implies(X_64,not(X))))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
not(and(X,implies(X_64,not(X)))) = not(not(implies(X,and(X_64,X)))),
inference(resolve,[$cnf( $equal(and(X,implies(X_64,not(X))),not(implies(X,and(X_64,X)))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
implies(X,and(X_30,not(X_31))) = not(and(X,not(and(X_30,not(X_31))))),
inference(subst,[],[refute_0_24:[bind(Y,$fot(and(X_30,not(X_31))))]]) ).
cnf(refute_0_122,plain,
implies(X_30,X_31) = not(and(X_30,not(X_31))),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_30)),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_123,plain,
( implies(X_30,X_31) != not(and(X_30,not(X_31)))
| not(and(X_30,not(X_31))) = implies(X_30,X_31) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(implies(X_30,X_31))),bind(Y0,$fot(not(and(X_30,not(X_31)))))]]) ).
cnf(refute_0_124,plain,
not(and(X_30,not(X_31))) = implies(X_30,X_31),
inference(resolve,[$cnf( $equal(implies(X_30,X_31),not(and(X_30,not(X_31)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
( implies(X,and(X_30,not(X_31))) != not(and(X,not(and(X_30,not(X_31)))))
| not(and(X_30,not(X_31))) != implies(X_30,X_31)
| implies(X,and(X_30,not(X_31))) = not(and(X,implies(X_30,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and(X_30,not(X_31))),not(and(X,not(and(X_30,not(X_31)))))) ),[1,0,1],$fot(implies(X_30,X_31))]]) ).
cnf(refute_0_126,plain,
( implies(X,and(X_30,not(X_31))) != not(and(X,not(and(X_30,not(X_31)))))
| implies(X,and(X_30,not(X_31))) = not(and(X,implies(X_30,X_31))) ),
inference(resolve,[$cnf( $equal(not(and(X_30,not(X_31))),implies(X_30,X_31)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
implies(X,and(X_30,not(X_31))) = not(and(X,implies(X_30,X_31))),
inference(resolve,[$cnf( $equal(implies(X,and(X_30,not(X_31))),not(and(X,not(and(X_30,not(X_31)))))) )],[refute_0_121,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(X,and(X_64,not(not(X)))) = not(and(X,implies(X_64,not(X)))),
inference(subst,[],[refute_0_127:[bind(X_30,$fot(X_64)),bind(X_31,$fot(not(X)))]]) ).
cnf(refute_0_129,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_130,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_27,refute_0_129]) ).
cnf(refute_0_131,plain,
( implies(X,and(X_64,not(not(X)))) != not(and(X,implies(X_64,not(X))))
| not(and(X,implies(X_64,not(X)))) != not(not(implies(X,and(X_64,X))))
| implies(X,and(X_64,not(not(X)))) = not(not(implies(X,and(X_64,X)))) ),
inference(subst,[],[refute_0_130:[bind(X0,$fot(implies(X,and(X_64,not(not(X)))))),bind(Y0,$fot(not(and(X,implies(X_64,not(X)))))),bind(Z,$fot(not(not(implies(X,and(X_64,X))))))]]) ).
cnf(refute_0_132,plain,
( not(and(X,implies(X_64,not(X)))) != not(not(implies(X,and(X_64,X))))
| implies(X,and(X_64,not(not(X)))) = not(not(implies(X,and(X_64,X)))) ),
inference(resolve,[$cnf( $equal(implies(X,and(X_64,not(not(X)))),not(and(X,implies(X_64,not(X))))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(X,and(X_64,not(not(X)))) = not(not(implies(X,and(X_64,X)))),
inference(resolve,[$cnf( $equal(not(and(X,implies(X_64,not(X)))),not(not(implies(X,and(X_64,X))))) )],[refute_0_120,refute_0_132]) ).
cnf(refute_0_134,plain,
implies(X_64,implies(X,and(X_64,not(not(X))))) = implies(X_64,implies(X,and(X_64,not(not(X))))),
introduced(tautology,[refl,[$fot(implies(X_64,implies(X,and(X_64,not(not(X))))))]]) ).
cnf(refute_0_135,plain,
( implies(X,and(X_64,not(not(X)))) != not(not(implies(X,and(X_64,X))))
| implies(X_64,implies(X,and(X_64,not(not(X))))) != implies(X_64,implies(X,and(X_64,not(not(X)))))
| implies(X_64,implies(X,and(X_64,not(not(X))))) = implies(X_64,not(not(implies(X,and(X_64,X))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_64,implies(X,and(X_64,not(not(X))))),implies(X_64,implies(X,and(X_64,not(not(X)))))) ),[1,1],$fot(not(not(implies(X,and(X_64,X)))))]]) ).
cnf(refute_0_136,plain,
( implies(X,and(X_64,not(not(X)))) != not(not(implies(X,and(X_64,X))))
| implies(X_64,implies(X,and(X_64,not(not(X))))) = implies(X_64,not(not(implies(X,and(X_64,X))))) ),
inference(resolve,[$cnf( $equal(implies(X_64,implies(X,and(X_64,not(not(X))))),implies(X_64,implies(X,and(X_64,not(not(X)))))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(X_64,implies(X,and(X_64,not(not(X))))) = implies(X_64,not(not(implies(X,and(X_64,X))))),
inference(resolve,[$cnf( $equal(implies(X,and(X_64,not(not(X)))),not(not(implies(X,and(X_64,X))))) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
( implies(X_64,implies(X,and(X_64,not(not(X))))) != implies(X_64,not(not(implies(X,and(X_64,X)))))
| ~ is_a_theorem(implies(X_64,implies(X,and(X_64,not(not(X))))))
| is_a_theorem(implies(X_64,not(not(implies(X,and(X_64,X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(X_64,implies(X,and(X_64,not(not(X)))))) ),[0],$fot(implies(X_64,not(not(implies(X,and(X_64,X))))))]]) ).
cnf(refute_0_139,plain,
( ~ is_a_theorem(implies(X_64,implies(X,and(X_64,not(not(X))))))
| is_a_theorem(implies(X_64,not(not(implies(X,and(X_64,X)))))) ),
inference(resolve,[$cnf( $equal(implies(X_64,implies(X,and(X_64,not(not(X))))),implies(X_64,not(not(implies(X,and(X_64,X)))))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(X_64,not(not(implies(X,and(X_64,X)))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_64,implies(X,and(X_64,not(not(X)))))) )],[refute_0_108,refute_0_139]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(X_208,not(not(implies(X,and(X_208,X)))))),
inference(subst,[],[refute_0_140:[bind(X_64,$fot(X_208))]]) ).
cnf(refute_0_142,plain,
( ~ is_a_theorem(X_208)
| ~ is_a_theorem(implies(X_208,not(not(implies(X,and(X_208,X))))))
| is_a_theorem(not(not(implies(X,and(X_208,X))))) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_208)),bind(Y,$fot(not(not(implies(X,and(X_208,X))))))]]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(X_208)
| is_a_theorem(not(not(implies(X,and(X_208,X))))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_208,not(not(implies(X,and(X_208,X)))))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( ~ is_a_theorem(implies(X_912,and(X_912,X_912)))
| is_a_theorem(not(not(implies(X,and(implies(X_912,and(X_912,X_912)),X))))) ),
inference(subst,[],[refute_0_143:[bind(X_208,$fot(implies(X_912,and(X_912,X_912))))]]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(X_909,implies(X_909,and(X_909,X_909)))),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_909)),bind(Y,$fot(X_909))]]) ).
cnf(refute_0_146,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_147,plain,
implies_2,
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))),
inference(resolve,[$cnf( implies_2 )],[refute_0_147,refute_0_146]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(implies(X,implies(X,Y)))),bind(Y,$fot(implies(X,Y)))]]) ).
cnf(refute_0_150,plain,
( ~ is_a_theorem(implies(X,implies(X,Y)))
| is_a_theorem(implies(X,Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( ~ is_a_theorem(implies(X_909,implies(X_909,and(X_909,X_909))))
| is_a_theorem(implies(X_909,and(X_909,X_909))) ),
inference(subst,[],[refute_0_150:[bind(X,$fot(X_909)),bind(Y,$fot(and(X_909,X_909)))]]) ).
cnf(refute_0_152,plain,
is_a_theorem(implies(X_909,and(X_909,X_909))),
inference(resolve,[$cnf( is_a_theorem(implies(X_909,implies(X_909,and(X_909,X_909)))) )],[refute_0_145,refute_0_151]) ).
cnf(refute_0_153,plain,
is_a_theorem(implies(X_912,and(X_912,X_912))),
inference(subst,[],[refute_0_152:[bind(X_909,$fot(X_912))]]) ).
cnf(refute_0_154,plain,
is_a_theorem(not(not(implies(X,and(implies(X_912,and(X_912,X_912)),X))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_912,and(X_912,X_912))) )],[refute_0_153,refute_0_144]) ).
cnf(refute_0_155,plain,
( ~ is_a_theorem(equiv(not(not(X)),X_121))
| not(not(X)) = X_121 ),
inference(subst,[],[refute_0_9:[bind(X,$fot(not(not(X)))),bind(Y,$fot(X_121))]]) ).
cnf(refute_0_156,plain,
equiv(not(X),X_43) = and(implies(not(X),X_43),implies(X_43,not(X))),
inference(subst,[],[refute_0_5:[bind(X,$fot(not(X))),bind(Y,$fot(X_43))]]) ).
cnf(refute_0_157,plain,
or(X,X_43) = implies(not(X),X_43),
inference(subst,[],[refute_0_33:[bind(Y,$fot(X_43))]]) ).
cnf(refute_0_158,plain,
( or(X,X_43) != implies(not(X),X_43)
| implies(not(X),X_43) = or(X,X_43) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(or(X,X_43))),bind(Y0,$fot(implies(not(X),X_43)))]]) ).
cnf(refute_0_159,plain,
implies(not(X),X_43) = or(X,X_43),
inference(resolve,[$cnf( $equal(or(X,X_43),implies(not(X),X_43)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( equiv(not(X),X_43) != and(implies(not(X),X_43),implies(X_43,not(X)))
| implies(not(X),X_43) != or(X,X_43)
| equiv(not(X),X_43) = and(or(X,X_43),implies(X_43,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X),X_43),and(implies(not(X),X_43),implies(X_43,not(X)))) ),[1,0],$fot(or(X,X_43))]]) ).
cnf(refute_0_161,plain,
( equiv(not(X),X_43) != and(implies(not(X),X_43),implies(X_43,not(X)))
| equiv(not(X),X_43) = and(or(X,X_43),implies(X_43,not(X))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_43),or(X,X_43)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
equiv(not(X),X_43) = and(or(X,X_43),implies(X_43,not(X))),
inference(resolve,[$cnf( $equal(equiv(not(X),X_43),and(implies(not(X),X_43),implies(X_43,not(X)))) )],[refute_0_156,refute_0_161]) ).
cnf(refute_0_163,plain,
and(or(X,X_43),implies(X_43,not(X))) = not(implies(or(X,X_43),and(X_43,X))),
inference(subst,[],[refute_0_115:[bind(X,$fot(or(X,X_43))),bind(X_36,$fot(X_43)),bind(X_37,$fot(X))]]) ).
cnf(refute_0_164,plain,
( and(or(X,X_43),implies(X_43,not(X))) != not(implies(or(X,X_43),and(X_43,X)))
| equiv(not(X),X_43) != and(or(X,X_43),implies(X_43,not(X)))
| equiv(not(X),X_43) = not(implies(or(X,X_43),and(X_43,X))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(X),X_43),and(or(X,X_43),implies(X_43,not(X)))) ),[1],$fot(not(implies(or(X,X_43),and(X_43,X))))]]) ).
cnf(refute_0_165,plain,
( equiv(not(X),X_43) != and(or(X,X_43),implies(X_43,not(X)))
| equiv(not(X),X_43) = not(implies(or(X,X_43),and(X_43,X))) ),
inference(resolve,[$cnf( $equal(and(or(X,X_43),implies(X_43,not(X))),not(implies(or(X,X_43),and(X_43,X)))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
equiv(not(X),X_43) = not(implies(or(X,X_43),and(X_43,X))),
inference(resolve,[$cnf( $equal(equiv(not(X),X_43),and(or(X,X_43),implies(X_43,not(X)))) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
equiv(not(not(X)),X_45) = not(implies(or(not(X),X_45),and(X_45,not(X)))),
inference(subst,[],[refute_0_166:[bind(X,$fot(not(X))),bind(X_43,$fot(X_45))]]) ).
cnf(refute_0_168,plain,
implies(X,X_45) = or(not(X),X_45),
inference(subst,[],[refute_0_50:[bind(Y,$fot(X_45))]]) ).
cnf(refute_0_169,plain,
( implies(X,X_45) != or(not(X),X_45)
| or(not(X),X_45) = implies(X,X_45) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(implies(X,X_45))),bind(Y0,$fot(or(not(X),X_45)))]]) ).
cnf(refute_0_170,plain,
or(not(X),X_45) = implies(X,X_45),
inference(resolve,[$cnf( $equal(implies(X,X_45),or(not(X),X_45)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
( equiv(not(not(X)),X_45) != not(implies(or(not(X),X_45),and(X_45,not(X))))
| or(not(X),X_45) != implies(X,X_45)
| equiv(not(not(X)),X_45) = not(implies(implies(X,X_45),and(X_45,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(not(not(X)),X_45),not(implies(or(not(X),X_45),and(X_45,not(X))))) ),[1,0,0],$fot(implies(X,X_45))]]) ).
cnf(refute_0_172,plain,
( equiv(not(not(X)),X_45) != not(implies(or(not(X),X_45),and(X_45,not(X))))
| equiv(not(not(X)),X_45) = not(implies(implies(X,X_45),and(X_45,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_45),implies(X,X_45)) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
equiv(not(not(X)),X_45) = not(implies(implies(X,X_45),and(X_45,not(X)))),
inference(resolve,[$cnf( $equal(equiv(not(not(X)),X_45),not(implies(or(not(X),X_45),and(X_45,not(X))))) )],[refute_0_167,refute_0_172]) ).
cnf(refute_0_174,plain,
( equiv(X,Y) != and(implies(X,Y),implies(Y,X))
| and(implies(X,Y),implies(Y,X)) = equiv(X,Y) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(equiv(X,Y))),bind(Y0,$fot(and(implies(X,Y),implies(Y,X))))]]) ).
cnf(refute_0_175,plain,
and(implies(X,Y),implies(Y,X)) = equiv(X,Y),
inference(resolve,[$cnf( $equal(equiv(X,Y),and(implies(X,Y),implies(Y,X))) )],[refute_0_5,refute_0_174]) ).
cnf(refute_0_176,plain,
and(implies(X,X_45),implies(X_45,X)) = equiv(X,X_45),
inference(subst,[],[refute_0_175:[bind(Y,$fot(X_45))]]) ).
cnf(refute_0_177,plain,
not(and(implies(X,X_45),implies(X_45,X))) = not(and(implies(X,X_45),implies(X_45,X))),
introduced(tautology,[refl,[$fot(not(and(implies(X,X_45),implies(X_45,X))))]]) ).
cnf(refute_0_178,plain,
( and(implies(X,X_45),implies(X_45,X)) != equiv(X,X_45)
| not(and(implies(X,X_45),implies(X_45,X))) != not(and(implies(X,X_45),implies(X_45,X)))
| not(and(implies(X,X_45),implies(X_45,X))) = not(equiv(X,X_45)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and(implies(X,X_45),implies(X_45,X))),not(and(implies(X,X_45),implies(X_45,X)))) ),[1,0],$fot(equiv(X,X_45))]]) ).
cnf(refute_0_179,plain,
( and(implies(X,X_45),implies(X_45,X)) != equiv(X,X_45)
| not(and(implies(X,X_45),implies(X_45,X))) = not(equiv(X,X_45)) ),
inference(resolve,[$cnf( $equal(not(and(implies(X,X_45),implies(X_45,X))),not(and(implies(X,X_45),implies(X_45,X)))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
not(and(implies(X,X_45),implies(X_45,X))) = not(equiv(X,X_45)),
inference(resolve,[$cnf( $equal(and(implies(X,X_45),implies(X_45,X)),equiv(X,X_45)) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(implies(X,X_45),and(X_45,not(X))) = not(and(implies(X,X_45),implies(X_45,X))),
inference(subst,[],[refute_0_127:[bind(X,$fot(implies(X,X_45))),bind(X_30,$fot(X_45)),bind(X_31,$fot(X))]]) ).
cnf(refute_0_182,plain,
( implies(implies(X,X_45),and(X_45,not(X))) != not(and(implies(X,X_45),implies(X_45,X)))
| not(and(implies(X,X_45),implies(X_45,X))) != not(equiv(X,X_45))
| implies(implies(X,X_45),and(X_45,not(X))) = not(equiv(X,X_45)) ),
inference(subst,[],[refute_0_130:[bind(X0,$fot(implies(implies(X,X_45),and(X_45,not(X))))),bind(Y0,$fot(not(and(implies(X,X_45),implies(X_45,X))))),bind(Z,$fot(not(equiv(X,X_45))))]]) ).
cnf(refute_0_183,plain,
( not(and(implies(X,X_45),implies(X_45,X))) != not(equiv(X,X_45))
| implies(implies(X,X_45),and(X_45,not(X))) = not(equiv(X,X_45)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_45),and(X_45,not(X))),not(and(implies(X,X_45),implies(X_45,X)))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
implies(implies(X,X_45),and(X_45,not(X))) = not(equiv(X,X_45)),
inference(resolve,[$cnf( $equal(not(and(implies(X,X_45),implies(X_45,X))),not(equiv(X,X_45))) )],[refute_0_180,refute_0_183]) ).
cnf(refute_0_185,plain,
not(implies(implies(X,X_45),and(X_45,not(X)))) = not(implies(implies(X,X_45),and(X_45,not(X)))),
introduced(tautology,[refl,[$fot(not(implies(implies(X,X_45),and(X_45,not(X)))))]]) ).
cnf(refute_0_186,plain,
( implies(implies(X,X_45),and(X_45,not(X))) != not(equiv(X,X_45))
| not(implies(implies(X,X_45),and(X_45,not(X)))) != not(implies(implies(X,X_45),and(X_45,not(X))))
| not(implies(implies(X,X_45),and(X_45,not(X)))) = not(not(equiv(X,X_45))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(X,X_45),and(X_45,not(X)))),not(implies(implies(X,X_45),and(X_45,not(X))))) ),[1,0],$fot(not(equiv(X,X_45)))]]) ).
cnf(refute_0_187,plain,
( implies(implies(X,X_45),and(X_45,not(X))) != not(equiv(X,X_45))
| not(implies(implies(X,X_45),and(X_45,not(X)))) = not(not(equiv(X,X_45))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(X,X_45),and(X_45,not(X)))),not(implies(implies(X,X_45),and(X_45,not(X))))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
not(implies(implies(X,X_45),and(X_45,not(X)))) = not(not(equiv(X,X_45))),
inference(resolve,[$cnf( $equal(implies(implies(X,X_45),and(X_45,not(X))),not(equiv(X,X_45))) )],[refute_0_184,refute_0_187]) ).
cnf(refute_0_189,plain,
( equiv(not(not(X)),X_45) != not(implies(implies(X,X_45),and(X_45,not(X))))
| not(implies(implies(X,X_45),and(X_45,not(X)))) != not(not(equiv(X,X_45)))
| equiv(not(not(X)),X_45) = not(not(equiv(X,X_45))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(equiv(not(not(X)),X_45),not(not(equiv(X,X_45)))) ),[0],$fot(not(implies(implies(X,X_45),and(X_45,not(X)))))]]) ).
cnf(refute_0_190,plain,
( equiv(not(not(X)),X_45) != not(implies(implies(X,X_45),and(X_45,not(X))))
| equiv(not(not(X)),X_45) = not(not(equiv(X,X_45))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(X,X_45),and(X_45,not(X)))),not(not(equiv(X,X_45)))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
equiv(not(not(X)),X_45) = not(not(equiv(X,X_45))),
inference(resolve,[$cnf( $equal(equiv(not(not(X)),X_45),not(implies(implies(X,X_45),and(X_45,not(X))))) )],[refute_0_173,refute_0_190]) ).
cnf(refute_0_192,plain,
equiv(not(not(X)),X_121) = not(not(equiv(X,X_121))),
inference(subst,[],[refute_0_191:[bind(X_45,$fot(X_121))]]) ).
cnf(refute_0_193,plain,
( equiv(not(not(X)),X_121) != not(not(equiv(X,X_121)))
| ~ is_a_theorem(not(not(equiv(X,X_121))))
| is_a_theorem(equiv(not(not(X)),X_121)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(equiv(not(not(X)),X_121)) ),[0],$fot(not(not(equiv(X,X_121))))]]) ).
cnf(refute_0_194,plain,
( ~ is_a_theorem(not(not(equiv(X,X_121))))
| is_a_theorem(equiv(not(not(X)),X_121)) ),
inference(resolve,[$cnf( $equal(equiv(not(not(X)),X_121),not(not(equiv(X,X_121)))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
( ~ is_a_theorem(not(not(equiv(X,X_121))))
| not(not(X)) = X_121 ),
inference(resolve,[$cnf( is_a_theorem(equiv(not(not(X)),X_121)) )],[refute_0_194,refute_0_155]) ).
cnf(refute_0_196,plain,
( ~ is_a_theorem(not(not(equiv(X_921,X_921))))
| not(not(X_921)) = X_921 ),
inference(subst,[],[refute_0_195:[bind(X,$fot(X_921)),bind(X_121,$fot(X_921))]]) ).
cnf(refute_0_197,plain,
( ~ is_a_theorem(implies(X_915,X_915))
| ~ is_a_theorem(implies(implies(X_915,X_915),equiv(X_915,X_915)))
| is_a_theorem(equiv(X_915,X_915)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(implies(X_915,X_915))),bind(Y,$fot(equiv(X_915,X_915)))]]) ).
cnf(refute_0_198,plain,
( ~ equivalence_3
| is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_199,plain,
equivalence_3,
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_200,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))),
inference(resolve,[$cnf( equivalence_3 )],[refute_0_199,refute_0_198]) ).
cnf(refute_0_201,plain,
is_a_theorem(implies(implies(X,X),implies(implies(X,X),equiv(X,X)))),
inference(subst,[],[refute_0_200:[bind(Y,$fot(X))]]) ).
cnf(refute_0_202,plain,
( ~ is_a_theorem(implies(implies(X,X),implies(implies(X,X),equiv(X,X))))
| is_a_theorem(implies(implies(X,X),equiv(X,X))) ),
inference(subst,[],[refute_0_150:[bind(X,$fot(implies(X,X))),bind(Y,$fot(equiv(X,X)))]]) ).
cnf(refute_0_203,plain,
is_a_theorem(implies(implies(X,X),equiv(X,X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,X),implies(implies(X,X),equiv(X,X)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
is_a_theorem(implies(implies(X_915,X_915),equiv(X_915,X_915))),
inference(subst,[],[refute_0_203:[bind(X,$fot(X_915))]]) ).
cnf(refute_0_205,plain,
( ~ is_a_theorem(implies(X_915,X_915))
| is_a_theorem(equiv(X_915,X_915)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_915,X_915),equiv(X_915,X_915))) )],[refute_0_204,refute_0_197]) ).
cnf(refute_0_206,plain,
( ~ implies_1
| is_a_theorem(implies(X,implies(Y,X))) ),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_207,plain,
implies_1,
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_208,plain,
is_a_theorem(implies(X,implies(Y,X))),
inference(resolve,[$cnf( implies_1 )],[refute_0_207,refute_0_206]) ).
cnf(refute_0_209,plain,
is_a_theorem(implies(X_910,implies(X_910,X_910))),
inference(subst,[],[refute_0_208:[bind(X,$fot(X_910)),bind(Y,$fot(X_910))]]) ).
cnf(refute_0_210,plain,
( ~ is_a_theorem(implies(X_910,implies(X_910,X_910)))
| is_a_theorem(implies(X_910,X_910)) ),
inference(subst,[],[refute_0_150:[bind(X,$fot(X_910)),bind(Y,$fot(X_910))]]) ).
cnf(refute_0_211,plain,
is_a_theorem(implies(X_910,X_910)),
inference(resolve,[$cnf( is_a_theorem(implies(X_910,implies(X_910,X_910))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
is_a_theorem(implies(X_915,X_915)),
inference(subst,[],[refute_0_211:[bind(X_910,$fot(X_915))]]) ).
cnf(refute_0_213,plain,
is_a_theorem(equiv(X_915,X_915)),
inference(resolve,[$cnf( is_a_theorem(implies(X_915,X_915)) )],[refute_0_212,refute_0_205]) ).
cnf(refute_0_214,plain,
is_a_theorem(equiv(not(not(X)),not(not(X)))),
inference(subst,[],[refute_0_213:[bind(X_915,$fot(not(not(X))))]]) ).
cnf(refute_0_215,plain,
equiv(not(not(X)),not(not(X))) = not(not(equiv(X,not(not(X))))),
inference(subst,[],[refute_0_191:[bind(X_45,$fot(not(not(X))))]]) ).
cnf(refute_0_216,plain,
( equiv(not(not(X)),not(not(X))) != not(not(equiv(X,not(not(X)))))
| ~ is_a_theorem(equiv(not(not(X)),not(not(X))))
| is_a_theorem(not(not(equiv(X,not(not(X)))))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(equiv(not(not(X)),not(not(X)))) ),[0],$fot(not(not(equiv(X,not(not(X))))))]]) ).
cnf(refute_0_217,plain,
( ~ is_a_theorem(equiv(not(not(X)),not(not(X))))
| is_a_theorem(not(not(equiv(X,not(not(X)))))) ),
inference(resolve,[$cnf( $equal(equiv(not(not(X)),not(not(X))),not(not(equiv(X,not(not(X)))))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
is_a_theorem(not(not(equiv(X,not(not(X)))))),
inference(resolve,[$cnf( is_a_theorem(equiv(not(not(X)),not(not(X)))) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
equiv(X_42,not(X)) = and(implies(X_42,not(X)),implies(not(X),X_42)),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_42)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_220,plain,
or(X,X_42) = implies(not(X),X_42),
inference(subst,[],[refute_0_33:[bind(Y,$fot(X_42))]]) ).
cnf(refute_0_221,plain,
( or(X,X_42) != implies(not(X),X_42)
| implies(not(X),X_42) = or(X,X_42) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(or(X,X_42))),bind(Y0,$fot(implies(not(X),X_42)))]]) ).
cnf(refute_0_222,plain,
implies(not(X),X_42) = or(X,X_42),
inference(resolve,[$cnf( $equal(or(X,X_42),implies(not(X),X_42)) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
( equiv(X_42,not(X)) != and(implies(X_42,not(X)),implies(not(X),X_42))
| implies(not(X),X_42) != or(X,X_42)
| equiv(X_42,not(X)) = and(implies(X_42,not(X)),or(X,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_42,not(X)),and(implies(X_42,not(X)),implies(not(X),X_42))) ),[1,1],$fot(or(X,X_42))]]) ).
cnf(refute_0_224,plain,
( equiv(X_42,not(X)) != and(implies(X_42,not(X)),implies(not(X),X_42))
| equiv(X_42,not(X)) = and(implies(X_42,not(X)),or(X,X_42)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_42),or(X,X_42)) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
equiv(X_42,not(X)) = and(implies(X_42,not(X)),or(X,X_42)),
inference(resolve,[$cnf( $equal(equiv(X_42,not(X)),and(implies(X_42,not(X)),implies(not(X),X_42))) )],[refute_0_219,refute_0_224]) ).
cnf(refute_0_226,plain,
equiv(X_91,not(not(X))) = and(implies(X_91,not(not(X))),or(not(X),X_91)),
inference(subst,[],[refute_0_225:[bind(X,$fot(not(X))),bind(X_42,$fot(X_91))]]) ).
cnf(refute_0_227,plain,
implies(X,X_91) = or(not(X),X_91),
inference(subst,[],[refute_0_50:[bind(Y,$fot(X_91))]]) ).
cnf(refute_0_228,plain,
( implies(X,X_91) != or(not(X),X_91)
| or(not(X),X_91) = implies(X,X_91) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(implies(X,X_91))),bind(Y0,$fot(or(not(X),X_91)))]]) ).
cnf(refute_0_229,plain,
or(not(X),X_91) = implies(X,X_91),
inference(resolve,[$cnf( $equal(implies(X,X_91),or(not(X),X_91)) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
( equiv(X_91,not(not(X))) != and(implies(X_91,not(not(X))),or(not(X),X_91))
| or(not(X),X_91) != implies(X,X_91)
| equiv(X_91,not(not(X))) = and(implies(X_91,not(not(X))),implies(X,X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_91,not(not(X))),and(implies(X_91,not(not(X))),or(not(X),X_91))) ),[1,1],$fot(implies(X,X_91))]]) ).
cnf(refute_0_231,plain,
( equiv(X_91,not(not(X))) != and(implies(X_91,not(not(X))),or(not(X),X_91))
| equiv(X_91,not(not(X))) = and(implies(X_91,not(not(X))),implies(X,X_91)) ),
inference(resolve,[$cnf( $equal(or(not(X),X_91),implies(X,X_91)) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
equiv(X_91,not(not(X))) = and(implies(X_91,not(not(X))),implies(X,X_91)),
inference(resolve,[$cnf( $equal(equiv(X_91,not(not(X))),and(implies(X_91,not(not(X))),or(not(X),X_91))) )],[refute_0_226,refute_0_231]) ).
cnf(refute_0_233,plain,
and(implies(X_91,X),implies(X,X_91)) = equiv(X_91,X),
inference(subst,[],[refute_0_175:[bind(X,$fot(X_91)),bind(Y,$fot(X))]]) ).
cnf(refute_0_234,plain,
not(and(X_91,not(X))) = implies(X_91,X),
inference(subst,[],[refute_0_29:[bind(X,$fot(X_91)),bind(Y,$fot(X))]]) ).
cnf(refute_0_235,plain,
and(not(and(X_91,not(X))),implies(X,X_91)) = and(not(and(X_91,not(X))),implies(X,X_91)),
introduced(tautology,[refl,[$fot(and(not(and(X_91,not(X))),implies(X,X_91)))]]) ).
cnf(refute_0_236,plain,
( and(not(and(X_91,not(X))),implies(X,X_91)) != and(not(and(X_91,not(X))),implies(X,X_91))
| not(and(X_91,not(X))) != implies(X_91,X)
| and(not(and(X_91,not(X))),implies(X,X_91)) = and(implies(X_91,X),implies(X,X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(and(X_91,not(X))),implies(X,X_91)),and(not(and(X_91,not(X))),implies(X,X_91))) ),[1,0],$fot(implies(X_91,X))]]) ).
cnf(refute_0_237,plain,
( not(and(X_91,not(X))) != implies(X_91,X)
| and(not(and(X_91,not(X))),implies(X,X_91)) = and(implies(X_91,X),implies(X,X_91)) ),
inference(resolve,[$cnf( $equal(and(not(and(X_91,not(X))),implies(X,X_91)),and(not(and(X_91,not(X))),implies(X,X_91))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
and(not(and(X_91,not(X))),implies(X,X_91)) = and(implies(X_91,X),implies(X,X_91)),
inference(resolve,[$cnf( $equal(not(and(X_91,not(X))),implies(X_91,X)) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
( and(implies(X_91,X),implies(X,X_91)) != equiv(X_91,X)
| and(not(and(X_91,not(X))),implies(X,X_91)) != and(implies(X_91,X),implies(X,X_91))
| and(not(and(X_91,not(X))),implies(X,X_91)) = equiv(X_91,X) ),
inference(subst,[],[refute_0_130:[bind(X0,$fot(and(not(and(X_91,not(X))),implies(X,X_91)))),bind(Y0,$fot(and(implies(X_91,X),implies(X,X_91)))),bind(Z,$fot(equiv(X_91,X)))]]) ).
cnf(refute_0_240,plain,
( and(implies(X_91,X),implies(X,X_91)) != equiv(X_91,X)
| and(not(and(X_91,not(X))),implies(X,X_91)) = equiv(X_91,X) ),
inference(resolve,[$cnf( $equal(and(not(and(X_91,not(X))),implies(X,X_91)),and(implies(X_91,X),implies(X,X_91))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
and(not(and(X_91,not(X))),implies(X,X_91)) = equiv(X_91,X),
inference(resolve,[$cnf( $equal(and(implies(X_91,X),implies(X,X_91)),equiv(X_91,X)) )],[refute_0_233,refute_0_240]) ).
cnf(refute_0_242,plain,
and(not(not(implies(X,not(Y)))),X_104) = and(implies(X,not(Y)),X_104),
inference(subst,[],[refute_0_89:[bind(X,$fot(implies(X,not(Y)))),bind(X_39,$fot(X_104))]]) ).
cnf(refute_0_243,plain,
( and(not(not(implies(X,not(Y)))),X_104) != and(implies(X,not(Y)),X_104)
| not(implies(X,not(Y))) != and(X,Y)
| and(not(and(X,Y)),X_104) = and(implies(X,not(Y)),X_104) ),
introduced(tautology,[equality,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_104),and(implies(X,not(Y)),X_104)) ),[0,0,0],$fot(and(X,Y))]]) ).
cnf(refute_0_244,plain,
( and(not(not(implies(X,not(Y)))),X_104) != and(implies(X,not(Y)),X_104)
| and(not(and(X,Y)),X_104) = and(implies(X,not(Y)),X_104) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(Y))),and(X,Y)) )],[refute_0_85,refute_0_243]) ).
cnf(refute_0_245,plain,
and(not(and(X,Y)),X_104) = and(implies(X,not(Y)),X_104),
inference(resolve,[$cnf( $equal(and(not(not(implies(X,not(Y)))),X_104),and(implies(X,not(Y)),X_104)) )],[refute_0_242,refute_0_244]) ).
cnf(refute_0_246,plain,
( and(not(and(X,Y)),X_104) != and(implies(X,not(Y)),X_104)
| and(implies(X,not(Y)),X_104) = and(not(and(X,Y)),X_104) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(and(not(and(X,Y)),X_104))),bind(Y0,$fot(and(implies(X,not(Y)),X_104)))]]) ).
cnf(refute_0_247,plain,
and(implies(X,not(Y)),X_104) = and(not(and(X,Y)),X_104),
inference(resolve,[$cnf( $equal(and(not(and(X,Y)),X_104),and(implies(X,not(Y)),X_104)) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
and(implies(X_91,not(not(X))),implies(X,X_91)) = and(not(and(X_91,not(X))),implies(X,X_91)),
inference(subst,[],[refute_0_247:[bind(X,$fot(X_91)),bind(Y,$fot(not(X))),bind(X_104,$fot(implies(X,X_91)))]]) ).
cnf(refute_0_249,plain,
( and(implies(X_91,not(not(X))),implies(X,X_91)) != and(not(and(X_91,not(X))),implies(X,X_91))
| and(not(and(X_91,not(X))),implies(X,X_91)) != equiv(X_91,X)
| and(implies(X_91,not(not(X))),implies(X,X_91)) = equiv(X_91,X) ),
inference(subst,[],[refute_0_130:[bind(X0,$fot(and(implies(X_91,not(not(X))),implies(X,X_91)))),bind(Y0,$fot(and(not(and(X_91,not(X))),implies(X,X_91)))),bind(Z,$fot(equiv(X_91,X)))]]) ).
cnf(refute_0_250,plain,
( and(not(and(X_91,not(X))),implies(X,X_91)) != equiv(X_91,X)
| and(implies(X_91,not(not(X))),implies(X,X_91)) = equiv(X_91,X) ),
inference(resolve,[$cnf( $equal(and(implies(X_91,not(not(X))),implies(X,X_91)),and(not(and(X_91,not(X))),implies(X,X_91))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
and(implies(X_91,not(not(X))),implies(X,X_91)) = equiv(X_91,X),
inference(resolve,[$cnf( $equal(and(not(and(X_91,not(X))),implies(X,X_91)),equiv(X_91,X)) )],[refute_0_241,refute_0_250]) ).
cnf(refute_0_252,plain,
( and(implies(X_91,not(not(X))),implies(X,X_91)) != equiv(X_91,X)
| equiv(X_91,not(not(X))) != and(implies(X_91,not(not(X))),implies(X,X_91))
| equiv(X_91,not(not(X))) = equiv(X_91,X) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(X_91,not(not(X))),and(implies(X_91,not(not(X))),implies(X,X_91))) ),[1],$fot(equiv(X_91,X))]]) ).
cnf(refute_0_253,plain,
( equiv(X_91,not(not(X))) != and(implies(X_91,not(not(X))),implies(X,X_91))
| equiv(X_91,not(not(X))) = equiv(X_91,X) ),
inference(resolve,[$cnf( $equal(and(implies(X_91,not(not(X))),implies(X,X_91)),equiv(X_91,X)) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
equiv(X_91,not(not(X))) = equiv(X_91,X),
inference(resolve,[$cnf( $equal(equiv(X_91,not(not(X))),and(implies(X_91,not(not(X))),implies(X,X_91))) )],[refute_0_232,refute_0_253]) ).
cnf(refute_0_255,plain,
equiv(X,not(not(X))) = equiv(X,X),
inference(subst,[],[refute_0_254:[bind(X_91,$fot(X))]]) ).
cnf(refute_0_256,plain,
not(equiv(X,not(not(X)))) = not(equiv(X,not(not(X)))),
introduced(tautology,[refl,[$fot(not(equiv(X,not(not(X)))))]]) ).
cnf(refute_0_257,plain,
( equiv(X,not(not(X))) != equiv(X,X)
| not(equiv(X,not(not(X)))) != not(equiv(X,not(not(X))))
| not(equiv(X,not(not(X)))) = not(equiv(X,X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(equiv(X,not(not(X)))),not(equiv(X,not(not(X))))) ),[1,0],$fot(equiv(X,X))]]) ).
cnf(refute_0_258,plain,
( equiv(X,not(not(X))) != equiv(X,X)
| not(equiv(X,not(not(X)))) = not(equiv(X,X)) ),
inference(resolve,[$cnf( $equal(not(equiv(X,not(not(X)))),not(equiv(X,not(not(X))))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
not(equiv(X,not(not(X)))) = not(equiv(X,X)),
inference(resolve,[$cnf( $equal(equiv(X,not(not(X))),equiv(X,X)) )],[refute_0_255,refute_0_258]) ).
cnf(refute_0_260,plain,
not(not(equiv(X,not(not(X))))) = not(not(equiv(X,not(not(X))))),
introduced(tautology,[refl,[$fot(not(not(equiv(X,not(not(X))))))]]) ).
cnf(refute_0_261,plain,
( not(equiv(X,not(not(X)))) != not(equiv(X,X))
| not(not(equiv(X,not(not(X))))) != not(not(equiv(X,not(not(X)))))
| not(not(equiv(X,not(not(X))))) = not(not(equiv(X,X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(equiv(X,not(not(X))))),not(not(equiv(X,not(not(X)))))) ),[1,0],$fot(not(equiv(X,X)))]]) ).
cnf(refute_0_262,plain,
( not(equiv(X,not(not(X)))) != not(equiv(X,X))
| not(not(equiv(X,not(not(X))))) = not(not(equiv(X,X))) ),
inference(resolve,[$cnf( $equal(not(not(equiv(X,not(not(X))))),not(not(equiv(X,not(not(X)))))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
not(not(equiv(X,not(not(X))))) = not(not(equiv(X,X))),
inference(resolve,[$cnf( $equal(not(equiv(X,not(not(X)))),not(equiv(X,X))) )],[refute_0_259,refute_0_262]) ).
cnf(refute_0_264,plain,
( not(not(equiv(X,not(not(X))))) != not(not(equiv(X,X)))
| ~ is_a_theorem(not(not(equiv(X,not(not(X))))))
| is_a_theorem(not(not(equiv(X,X)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(not(equiv(X,not(not(X)))))) ),[0],$fot(not(not(equiv(X,X))))]]) ).
cnf(refute_0_265,plain,
( ~ is_a_theorem(not(not(equiv(X,not(not(X))))))
| is_a_theorem(not(not(equiv(X,X)))) ),
inference(resolve,[$cnf( $equal(not(not(equiv(X,not(not(X))))),not(not(equiv(X,X)))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
is_a_theorem(not(not(equiv(X,X)))),
inference(resolve,[$cnf( is_a_theorem(not(not(equiv(X,not(not(X)))))) )],[refute_0_218,refute_0_265]) ).
cnf(refute_0_267,plain,
is_a_theorem(not(not(equiv(X_921,X_921)))),
inference(subst,[],[refute_0_266:[bind(X,$fot(X_921))]]) ).
cnf(refute_0_268,plain,
not(not(X_921)) = X_921,
inference(resolve,[$cnf( is_a_theorem(not(not(equiv(X_921,X_921)))) )],[refute_0_267,refute_0_196]) ).
cnf(refute_0_269,plain,
not(not(implies(X,and(implies(X_912,and(X_912,X_912)),X)))) = implies(X,and(implies(X_912,and(X_912,X_912)),X)),
inference(subst,[],[refute_0_268:[bind(X_921,$fot(implies(X,and(implies(X_912,and(X_912,X_912)),X))))]]) ).
cnf(refute_0_270,plain,
( not(not(implies(X,and(implies(X_912,and(X_912,X_912)),X)))) != implies(X,and(implies(X_912,and(X_912,X_912)),X))
| ~ is_a_theorem(not(not(implies(X,and(implies(X_912,and(X_912,X_912)),X)))))
| is_a_theorem(implies(X,and(implies(X_912,and(X_912,X_912)),X))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(not(not(implies(X,and(implies(X_912,and(X_912,X_912)),X))))) ),[0],$fot(implies(X,and(implies(X_912,and(X_912,X_912)),X)))]]) ).
cnf(refute_0_271,plain,
( ~ is_a_theorem(not(not(implies(X,and(implies(X_912,and(X_912,X_912)),X)))))
| is_a_theorem(implies(X,and(implies(X_912,and(X_912,X_912)),X))) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,and(implies(X_912,and(X_912,X_912)),X)))),implies(X,and(implies(X_912,and(X_912,X_912)),X))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
is_a_theorem(implies(X,and(implies(X_912,and(X_912,X_912)),X))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(X,and(implies(X_912,and(X_912,X_912)),X))))) )],[refute_0_154,refute_0_271]) ).
cnf(refute_0_273,plain,
is_a_theorem(implies(implies(and(X_989,X_989),X_989),and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989)))),
inference(subst,[],[refute_0_272:[bind(X,$fot(implies(and(X_989,X_989),X_989))),bind(X_912,$fot(X_989))]]) ).
cnf(refute_0_274,plain,
equiv(X_989,and(X_989,X_989)) = and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989)),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_989)),bind(Y,$fot(and(X_989,X_989)))]]) ).
cnf(refute_0_275,plain,
( equiv(X_989,and(X_989,X_989)) != and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989))
| and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989)) = equiv(X_989,and(X_989,X_989)) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(equiv(X_989,and(X_989,X_989)))),bind(Y0,$fot(and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989))))]]) ).
cnf(refute_0_276,plain,
and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989)) = equiv(X_989,and(X_989,X_989)),
inference(resolve,[$cnf( $equal(equiv(X_989,and(X_989,X_989)),and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
( and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989)) != equiv(X_989,and(X_989,X_989))
| ~ is_a_theorem(implies(implies(and(X_989,X_989),X_989),and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989))))
| is_a_theorem(implies(implies(and(X_989,X_989),X_989),equiv(X_989,and(X_989,X_989)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(and(X_989,X_989),X_989),and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989)))) ),[0,1],$fot(equiv(X_989,and(X_989,X_989)))]]) ).
cnf(refute_0_278,plain,
( ~ is_a_theorem(implies(implies(and(X_989,X_989),X_989),and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989))))
| is_a_theorem(implies(implies(and(X_989,X_989),X_989),equiv(X_989,and(X_989,X_989)))) ),
inference(resolve,[$cnf( $equal(and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989)),equiv(X_989,and(X_989,X_989))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
is_a_theorem(implies(implies(and(X_989,X_989),X_989),equiv(X_989,and(X_989,X_989)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_989,X_989),X_989),and(implies(X_989,and(X_989,X_989)),implies(and(X_989,X_989),X_989)))) )],[refute_0_273,refute_0_278]) ).
cnf(refute_0_280,plain,
is_a_theorem(implies(implies(and(X_992,X_992),X_992),equiv(X_992,and(X_992,X_992)))),
inference(subst,[],[refute_0_279:[bind(X_989,$fot(X_992))]]) ).
cnf(refute_0_281,plain,
( ~ is_a_theorem(implies(and(X_992,X_992),X_992))
| is_a_theorem(equiv(X_992,and(X_992,X_992))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(and(X_992,X_992),X_992),equiv(X_992,and(X_992,X_992)))) )],[refute_0_280,refute_0_14]) ).
cnf(refute_0_282,plain,
( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_283,plain,
and_2,
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_284,plain,
is_a_theorem(implies(and(X,Y),Y)),
inference(resolve,[$cnf( and_2 )],[refute_0_283,refute_0_282]) ).
cnf(refute_0_285,plain,
is_a_theorem(implies(and(X_992,X_992),X_992)),
inference(subst,[],[refute_0_284:[bind(X,$fot(X_992)),bind(Y,$fot(X_992))]]) ).
cnf(refute_0_286,plain,
is_a_theorem(equiv(X_992,and(X_992,X_992))),
inference(resolve,[$cnf( is_a_theorem(implies(and(X_992,X_992),X_992)) )],[refute_0_285,refute_0_281]) ).
cnf(refute_0_287,plain,
is_a_theorem(equiv(X_993,and(X_993,X_993))),
inference(subst,[],[refute_0_286:[bind(X_992,$fot(X_993))]]) ).
cnf(refute_0_288,plain,
X_993 = and(X_993,X_993),
inference(resolve,[$cnf( is_a_theorem(equiv(X_993,and(X_993,X_993))) )],[refute_0_287,refute_0_10]) ).
cnf(refute_0_289,plain,
implies(Y,Y) = and(implies(Y,Y),implies(Y,Y)),
inference(subst,[],[refute_0_288:[bind(X_993,$fot(implies(Y,Y)))]]) ).
cnf(refute_0_290,plain,
( implies(Y,Y) != and(implies(Y,Y),implies(Y,Y))
| and(implies(Y,Y),implies(Y,Y)) = implies(Y,Y) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(implies(Y,Y))),bind(Y0,$fot(and(implies(Y,Y),implies(Y,Y))))]]) ).
cnf(refute_0_291,plain,
and(implies(Y,Y),implies(Y,Y)) = implies(Y,Y),
inference(resolve,[$cnf( $equal(implies(Y,Y),and(implies(Y,Y),implies(Y,Y))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
( and(implies(Y,Y),implies(Y,Y)) != implies(Y,Y)
| equiv(Y,Y) != and(implies(Y,Y),implies(Y,Y))
| equiv(Y,Y) = implies(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(equiv(Y,Y),and(implies(Y,Y),implies(Y,Y))) ),[1],$fot(implies(Y,Y))]]) ).
cnf(refute_0_293,plain,
( equiv(Y,Y) != and(implies(Y,Y),implies(Y,Y))
| equiv(Y,Y) = implies(Y,Y) ),
inference(resolve,[$cnf( $equal(and(implies(Y,Y),implies(Y,Y)),implies(Y,Y)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
equiv(Y,Y) = implies(Y,Y),
inference(resolve,[$cnf( $equal(equiv(Y,Y),and(implies(Y,Y),implies(Y,Y))) )],[refute_0_6,refute_0_293]) ).
cnf(refute_0_295,plain,
( equiv(Y,Y) != implies(Y,Y)
| implies(Y,Y) = equiv(Y,Y) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(equiv(Y,Y))),bind(Y0,$fot(implies(Y,Y)))]]) ).
cnf(refute_0_296,plain,
implies(Y,Y) = equiv(Y,Y),
inference(resolve,[$cnf( $equal(equiv(Y,Y),implies(Y,Y)) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
implies(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6) = equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),
inference(subst,[],[refute_0_296:[bind(Y,$fot(skolemFOFtoCNF_P_6))]]) ).
cnf(refute_0_298,plain,
implies(or(X_38,not(X_39)),Y) = or(not(or(X_38,not(X_39))),Y),
inference(subst,[],[refute_0_50:[bind(X,$fot(or(X_38,not(X_39))))]]) ).
cnf(refute_0_299,plain,
and(not(X_38),X_39) = not(or(X_38,not(X_39))),
inference(subst,[],[refute_0_76:[bind(X,$fot(X_38)),bind(X_37,$fot(X_39))]]) ).
cnf(refute_0_300,plain,
( and(not(X_38),X_39) != not(or(X_38,not(X_39)))
| not(or(X_38,not(X_39))) = and(not(X_38),X_39) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(and(not(X_38),X_39))),bind(Y0,$fot(not(or(X_38,not(X_39)))))]]) ).
cnf(refute_0_301,plain,
not(or(X_38,not(X_39))) = and(not(X_38),X_39),
inference(resolve,[$cnf( $equal(and(not(X_38),X_39),not(or(X_38,not(X_39)))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
( implies(or(X_38,not(X_39)),Y) != or(not(or(X_38,not(X_39))),Y)
| not(or(X_38,not(X_39))) != and(not(X_38),X_39)
| implies(or(X_38,not(X_39)),Y) = or(and(not(X_38),X_39),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_38,not(X_39)),Y),or(not(or(X_38,not(X_39))),Y)) ),[1,0],$fot(and(not(X_38),X_39))]]) ).
cnf(refute_0_303,plain,
( implies(or(X_38,not(X_39)),Y) != or(not(or(X_38,not(X_39))),Y)
| implies(or(X_38,not(X_39)),Y) = or(and(not(X_38),X_39),Y) ),
inference(resolve,[$cnf( $equal(not(or(X_38,not(X_39))),and(not(X_38),X_39)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
implies(or(X_38,not(X_39)),Y) = or(and(not(X_38),X_39),Y),
inference(resolve,[$cnf( $equal(implies(or(X_38,not(X_39)),Y),or(not(or(X_38,not(X_39))),Y)) )],[refute_0_298,refute_0_303]) ).
cnf(refute_0_305,plain,
implies(or(X_38,not(not(X_38))),Y) = or(and(not(X_38),not(X_38)),Y),
inference(subst,[],[refute_0_304:[bind(X_39,$fot(not(X_38)))]]) ).
cnf(refute_0_306,plain,
not(X_38) = and(not(X_38),not(X_38)),
inference(subst,[],[refute_0_288:[bind(X_993,$fot(not(X_38)))]]) ).
cnf(refute_0_307,plain,
( not(X_38) != and(not(X_38),not(X_38))
| and(not(X_38),not(X_38)) = not(X_38) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(not(X_38))),bind(Y0,$fot(and(not(X_38),not(X_38))))]]) ).
cnf(refute_0_308,plain,
and(not(X_38),not(X_38)) = not(X_38),
inference(resolve,[$cnf( $equal(not(X_38),and(not(X_38),not(X_38))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
( and(not(X_38),not(X_38)) != not(X_38)
| implies(or(X_38,not(not(X_38))),Y) != or(and(not(X_38),not(X_38)),Y)
| implies(or(X_38,not(not(X_38))),Y) = or(not(X_38),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_38,not(not(X_38))),Y),or(and(not(X_38),not(X_38)),Y)) ),[1,0],$fot(not(X_38))]]) ).
cnf(refute_0_310,plain,
( implies(or(X_38,not(not(X_38))),Y) != or(and(not(X_38),not(X_38)),Y)
| implies(or(X_38,not(not(X_38))),Y) = or(not(X_38),Y) ),
inference(resolve,[$cnf( $equal(and(not(X_38),not(X_38)),not(X_38)) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
implies(or(X_38,not(not(X_38))),Y) = or(not(X_38),Y),
inference(resolve,[$cnf( $equal(implies(or(X_38,not(not(X_38))),Y),or(and(not(X_38),not(X_38)),Y)) )],[refute_0_305,refute_0_310]) ).
cnf(refute_0_312,plain,
not(not(X_38)) = X_38,
inference(subst,[],[refute_0_268:[bind(X_921,$fot(X_38))]]) ).
cnf(refute_0_313,plain,
or(X_38,not(not(X_38))) = or(X_38,not(not(X_38))),
introduced(tautology,[refl,[$fot(or(X_38,not(not(X_38))))]]) ).
cnf(refute_0_314,plain,
( not(not(X_38)) != X_38
| or(X_38,not(not(X_38))) != or(X_38,not(not(X_38)))
| or(X_38,not(not(X_38))) = or(X_38,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_38,not(not(X_38))),or(X_38,not(not(X_38)))) ),[1,1],$fot(X_38)]]) ).
cnf(refute_0_315,plain,
( not(not(X_38)) != X_38
| or(X_38,not(not(X_38))) = or(X_38,X_38) ),
inference(resolve,[$cnf( $equal(or(X_38,not(not(X_38))),or(X_38,not(not(X_38)))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
or(X_38,not(not(X_38))) = or(X_38,X_38),
inference(resolve,[$cnf( $equal(not(not(X_38)),X_38) )],[refute_0_312,refute_0_315]) ).
cnf(refute_0_317,plain,
implies(or(X_38,not(not(X_38))),Y) = implies(or(X_38,not(not(X_38))),Y),
introduced(tautology,[refl,[$fot(implies(or(X_38,not(not(X_38))),Y))]]) ).
cnf(refute_0_318,plain,
( implies(or(X_38,not(not(X_38))),Y) != implies(or(X_38,not(not(X_38))),Y)
| or(X_38,not(not(X_38))) != or(X_38,X_38)
| implies(or(X_38,not(not(X_38))),Y) = implies(or(X_38,X_38),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_38,not(not(X_38))),Y),implies(or(X_38,not(not(X_38))),Y)) ),[1,0],$fot(or(X_38,X_38))]]) ).
cnf(refute_0_319,plain,
( or(X_38,not(not(X_38))) != or(X_38,X_38)
| implies(or(X_38,not(not(X_38))),Y) = implies(or(X_38,X_38),Y) ),
inference(resolve,[$cnf( $equal(implies(or(X_38,not(not(X_38))),Y),implies(or(X_38,not(not(X_38))),Y)) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
implies(or(X_38,not(not(X_38))),Y) = implies(or(X_38,X_38),Y),
inference(resolve,[$cnf( $equal(or(X_38,not(not(X_38))),or(X_38,X_38)) )],[refute_0_316,refute_0_319]) ).
cnf(refute_0_321,plain,
( implies(or(X_38,not(not(X_38))),Y) != implies(or(X_38,X_38),Y)
| implies(or(X_38,not(not(X_38))),Y) != or(not(X_38),Y)
| implies(or(X_38,X_38),Y) = or(not(X_38),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_38,not(not(X_38))),Y),or(not(X_38),Y)) ),[0],$fot(implies(or(X_38,X_38),Y))]]) ).
cnf(refute_0_322,plain,
( implies(or(X_38,not(not(X_38))),Y) != or(not(X_38),Y)
| implies(or(X_38,X_38),Y) = or(not(X_38),Y) ),
inference(resolve,[$cnf( $equal(implies(or(X_38,not(not(X_38))),Y),implies(or(X_38,X_38),Y)) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
or(not(X_38),Y) = implies(X_38,Y),
inference(subst,[],[refute_0_61:[bind(X,$fot(X_38))]]) ).
cnf(refute_0_324,plain,
( implies(or(X_38,X_38),Y) != or(not(X_38),Y)
| or(not(X_38),Y) != implies(X_38,Y)
| implies(or(X_38,X_38),Y) = implies(X_38,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(or(X_38,X_38),Y),implies(X_38,Y)) ),[0],$fot(or(not(X_38),Y))]]) ).
cnf(refute_0_325,plain,
( implies(or(X_38,X_38),Y) != or(not(X_38),Y)
| implies(or(X_38,X_38),Y) = implies(X_38,Y) ),
inference(resolve,[$cnf( $equal(or(not(X_38),Y),implies(X_38,Y)) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
( implies(or(X_38,not(not(X_38))),Y) != or(not(X_38),Y)
| implies(or(X_38,X_38),Y) = implies(X_38,Y) ),
inference(resolve,[$cnf( $equal(implies(or(X_38,X_38),Y),or(not(X_38),Y)) )],[refute_0_322,refute_0_325]) ).
cnf(refute_0_327,plain,
implies(or(X_38,X_38),Y) = implies(X_38,Y),
inference(resolve,[$cnf( $equal(implies(or(X_38,not(not(X_38))),Y),or(not(X_38),Y)) )],[refute_0_311,refute_0_326]) ).
cnf(refute_0_328,plain,
implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6) = implies(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),
inference(subst,[],[refute_0_327:[bind(Y,$fot(skolemFOFtoCNF_P_6)),bind(X_38,$fot(skolemFOFtoCNF_P_6))]]) ).
cnf(refute_0_329,plain,
( implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6) != implies(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)
| implies(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6) != equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)
| implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6) = equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6) ),
inference(subst,[],[refute_0_130:[bind(X0,$fot(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6))),bind(Y0,$fot(implies(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6))),bind(Z,$fot(equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)))]]) ).
cnf(refute_0_330,plain,
( implies(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6) != equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)
| implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6) = equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6) ),
inference(resolve,[$cnf( $equal(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6),implies(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6) = equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),
inference(resolve,[$cnf( $equal(implies(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)) )],[refute_0_297,refute_0_330]) ).
cnf(refute_0_332,plain,
( implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6) != equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)
| ~ is_a_theorem(equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6))
| is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6)) ),
introduced(tautology,[equality,[$cnf( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6)) ),[0],$fot(equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6))]]) ).
cnf(refute_0_333,plain,
( ~ is_a_theorem(equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6))
| is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6)) ),
inference(resolve,[$cnf( $equal(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6),equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
~ is_a_theorem(equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)),
inference(resolve,[$cnf( is_a_theorem(implies(or(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6),skolemFOFtoCNF_P_6)) )],[refute_0_333,refute_0_2]) ).
cnf(refute_0_335,plain,
is_a_theorem(equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)),
inference(subst,[],[refute_0_213:[bind(X_915,$fot(skolemFOFtoCNF_P_6))]]) ).
cnf(refute_0_336,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equiv(skolemFOFtoCNF_P_6,skolemFOFtoCNF_P_6)) )],[refute_0_335,refute_0_334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL454+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 06:10:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.74/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.74/1.95
% 1.74/1.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.82/1.99
%------------------------------------------------------------------------------