%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 16:44:58 EDT 2022

% Result   : Unsatisfiable 0.52s 0.72s
% Output   : CNFRefutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   42
%            Number of leaves      :  132
% Syntax   : Number of clauses     :  524 ( 233 unt;   0 nHn; 464 RR)
%            Number of literals    :  939 ( 938 equ; 416 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;  11 con; 0-2 aty)
%            Number of variables   :  132 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(a1,axiom,
    f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ).

cnf(clause_2,axiom,
    n2 = f(n1,n1) ).

cnf(clause_3,axiom,
    n3 = f(n2,n1) ).

cnf(clause_4,axiom,
    u = f(n2,n2) ).

cnf(clause_5,axiom,
    u1 = f(u,n1) ).

cnf(clause_6,axiom,
    u2 = f(u,n2) ).

cnf(clause_7,axiom,
    u3 = f(u,n3) ).

cnf(clause_8,axiom,
    uu = f(u,u) ).

cnf(clause_9,axiom,
    a = f(f(n3,n2),u2) ).

cnf(clause_10,axiom,
    b = f(u1,u3) ).

cnf(clause_11,axiom,
    v = f(uu,uu) ).

cnf(prove_equation,negated_conjecture,
    f(a,v) != f(b,v) ).

cnf(refute_0_0,plain,
    f(a,f(a,Z)) = f(f(a,a),f(a,Z)),
    inference(subst,[],[a1:[bind(X,$fot(a)),bind(Y,$fot(a))]]) ).

cnf(refute_0_1,plain,
    f(f(n3,n2),f(X_1,u2)) = f(f(f(n3,n2),X_1),f(f(n3,n2),u2)),
    inference(subst,[],[a1:[bind(X,$fot(f(n3,n2))),bind(Y,$fot(X_1)),bind(Z,$fot(u2))]]) ).

cnf(refute_0_2,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_3,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_4,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( a != f(f(n3,n2),u2)
    | f(f(n3,n2),u2) = a ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(a)),bind(Y0,$fot(f(f(n3,n2),u2)))]]) ).

cnf(refute_0_6,plain,
    f(f(n3,n2),u2) = a,
    inference(resolve,[$cnf( $equal(a,f(f(n3,n2),u2)) )],[clause_9,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( f(f(n3,n2),f(X_1,u2)) != f(f(f(n3,n2),X_1),f(f(n3,n2),u2))
    | f(f(n3,n2),u2) != a
    | f(f(n3,n2),f(X_1,u2)) = f(f(f(n3,n2),X_1),a) ),
    introduced(tautology,[equality,[$cnf( $equal(f(f(n3,n2),f(X_1,u2)),f(f(f(n3,n2),X_1),f(f(n3,n2),u2))) ),[1,1],$fot(a)]]) ).

cnf(refute_0_8,plain,
    ( f(f(n3,n2),f(X_1,u2)) != f(f(f(n3,n2),X_1),f(f(n3,n2),u2))
    | f(f(n3,n2),f(X_1,u2)) = f(f(f(n3,n2),X_1),a) ),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),u2),a) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    f(f(n3,n2),f(X_1,u2)) = f(f(f(n3,n2),X_1),a),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),f(X_1,u2)),f(f(f(n3,n2),X_1),f(f(n3,n2),u2))) )],[refute_0_1,refute_0_8]) ).

cnf(refute_0_10,plain,
    f(f(n3,n2),f(u2,u2)) = f(f(f(n3,n2),u2),a),
    inference(subst,[],[refute_0_9:[bind(X_1,$fot(u2))]]) ).

cnf(refute_0_11,plain,
    f(u,f(X_1,n2)) = f(f(u,X_1),f(u,n2)),
    inference(subst,[],[a1:[bind(X,$fot(u)),bind(Y,$fot(X_1)),bind(Z,$fot(n2))]]) ).

cnf(refute_0_12,plain,
    ( u2 != f(u,n2)
    | f(u,n2) = u2 ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(u2)),bind(Y0,$fot(f(u,n2)))]]) ).

cnf(refute_0_13,plain,
    f(u,n2) = u2,
    inference(resolve,[$cnf( $equal(u2,f(u,n2)) )],[clause_6,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( f(u,f(X_1,n2)) != f(f(u,X_1),f(u,n2))
    | f(u,n2) != u2
    | f(u,f(X_1,n2)) = f(f(u,X_1),u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(X_1,n2)),f(f(u,X_1),f(u,n2))) ),[1,1],$fot(u2)]]) ).

cnf(refute_0_15,plain,
    ( f(u,f(X_1,n2)) != f(f(u,X_1),f(u,n2))
    | f(u,f(X_1,n2)) = f(f(u,X_1),u2) ),
    inference(resolve,[$cnf( $equal(f(u,n2),u2) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    f(u,f(X_1,n2)) = f(f(u,X_1),u2),
    inference(resolve,[$cnf( $equal(f(u,f(X_1,n2)),f(f(u,X_1),f(u,n2))) )],[refute_0_11,refute_0_15]) ).

cnf(refute_0_17,plain,
    f(u,f(n2,n2)) = f(f(u,n2),u2),
    inference(subst,[],[refute_0_16:[bind(X_1,$fot(n2))]]) ).

cnf(refute_0_18,plain,
    ( f(u,f(n2,n2)) != f(f(u,n2),u2)
    | f(u,n2) != u2
    | f(u,f(n2,n2)) = f(u2,u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n2,n2)),f(f(u,n2),u2)) ),[1,0],$fot(u2)]]) ).

cnf(refute_0_19,plain,
    ( f(u,f(n2,n2)) != f(f(u,n2),u2)
    | f(u,f(n2,n2)) = f(u2,u2) ),
    inference(resolve,[$cnf( $equal(f(u,n2),u2) )],[refute_0_13,refute_0_18]) ).

cnf(refute_0_20,plain,
    f(u,f(n2,n2)) = f(u2,u2),
    inference(resolve,[$cnf( $equal(f(u,f(n2,n2)),f(f(u,n2),u2)) )],[refute_0_17,refute_0_19]) ).

cnf(refute_0_21,plain,
    f(n2,f(X_1,n2)) = f(f(n2,X_1),f(n2,n2)),
    inference(subst,[],[a1:[bind(X,$fot(n2)),bind(Y,$fot(X_1)),bind(Z,$fot(n2))]]) ).

cnf(refute_0_22,plain,
    ( u != f(n2,n2)
    | f(n2,n2) = u ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(u)),bind(Y0,$fot(f(n2,n2)))]]) ).

cnf(refute_0_23,plain,
    f(n2,n2) = u,
    inference(resolve,[$cnf( $equal(u,f(n2,n2)) )],[clause_4,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( f(n2,f(X_1,n2)) != f(f(n2,X_1),f(n2,n2))
    | f(n2,n2) != u
    | f(n2,f(X_1,n2)) = f(f(n2,X_1),u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(X_1,n2)),f(f(n2,X_1),f(n2,n2))) ),[1,1],$fot(u)]]) ).

cnf(refute_0_25,plain,
    ( f(n2,f(X_1,n2)) != f(f(n2,X_1),f(n2,n2))
    | f(n2,f(X_1,n2)) = f(f(n2,X_1),u) ),
    inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    f(n2,f(X_1,n2)) = f(f(n2,X_1),u),
    inference(resolve,[$cnf( $equal(f(n2,f(X_1,n2)),f(f(n2,X_1),f(n2,n2))) )],[refute_0_21,refute_0_25]) ).

cnf(refute_0_27,plain,
    f(n2,f(n2,n2)) = f(f(n2,n2),u),
    inference(subst,[],[refute_0_26:[bind(X_1,$fot(n2))]]) ).

cnf(refute_0_28,plain,
    ( f(n2,f(n2,n2)) != f(f(n2,n2),u)
    | f(n2,n2) != u
    | f(n2,f(n2,n2)) = f(u,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n2,n2)),f(f(n2,n2),u)) ),[1,0],$fot(u)]]) ).

cnf(refute_0_29,plain,
    ( f(n2,f(n2,n2)) != f(f(n2,n2),u)
    | f(n2,f(n2,n2)) = f(u,u) ),
    inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_23,refute_0_28]) ).

cnf(refute_0_30,plain,
    f(n2,f(n2,n2)) = f(u,u),
    inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(f(n2,n2),u)) )],[refute_0_27,refute_0_29]) ).

cnf(refute_0_31,plain,
    f(n2,f(n2,n2)) = f(n2,f(n2,n2)),
    introduced(tautology,[refl,[$fot(f(n2,f(n2,n2)))]]) ).

cnf(refute_0_32,plain,
    ( f(n2,f(n2,n2)) != f(n2,f(n2,n2))
    | f(n2,n2) != u
    | f(n2,f(n2,n2)) = f(n2,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n2,n2)),f(n2,f(n2,n2))) ),[1,1],$fot(u)]]) ).

cnf(refute_0_33,plain,
    ( f(n2,n2) != u
    | f(n2,f(n2,n2)) = f(n2,u) ),
    inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(n2,f(n2,n2))) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    f(n2,f(n2,n2)) = f(n2,u),
    inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_23,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( f(n2,f(n2,n2)) != f(n2,u)
    | f(n2,f(n2,n2)) != f(u,u)
    | f(n2,u) = f(u,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n2,n2)),f(u,u)) ),[0],$fot(f(n2,u))]]) ).

cnf(refute_0_36,plain,
    ( f(n2,f(n2,n2)) != f(u,u)
    | f(n2,u) = f(u,u) ),
    inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(n2,u)) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    ( uu != f(u,u)
    | f(u,u) = uu ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(uu)),bind(Y0,$fot(f(u,u)))]]) ).

cnf(refute_0_38,plain,
    f(u,u) = uu,
    inference(resolve,[$cnf( $equal(uu,f(u,u)) )],[clause_8,refute_0_37]) ).

cnf(refute_0_39,plain,
    ( f(n2,u) != f(u,u)
    | f(u,u) != uu
    | f(n2,u) = uu ),
    introduced(tautology,[equality,[$cnf( ~ $equal(f(n2,u),uu) ),[0],$fot(f(u,u))]]) ).

cnf(refute_0_40,plain,
    ( f(n2,u) != f(u,u)
    | f(n2,u) = uu ),
    inference(resolve,[$cnf( $equal(f(u,u),uu) )],[refute_0_38,refute_0_39]) ).

cnf(refute_0_41,plain,
    ( f(n2,f(n2,n2)) != f(u,u)
    | f(n2,u) = uu ),
    inference(resolve,[$cnf( $equal(f(n2,u),f(u,u)) )],[refute_0_36,refute_0_40]) ).

cnf(refute_0_42,plain,
    f(n2,u) = uu,
    inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(u,u)) )],[refute_0_30,refute_0_41]) ).

cnf(refute_0_43,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_44,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_43]) ).

cnf(refute_0_45,plain,
    ( f(n2,f(n2,n2)) != f(n2,u)
    | f(n2,u) != uu
    | f(n2,f(n2,n2)) = uu ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(n2,f(n2,n2)))),bind(Y0,$fot(f(n2,u))),bind(Z0,$fot(uu))]]) ).

cnf(refute_0_46,plain,
    ( f(n2,u) != uu
    | f(n2,f(n2,n2)) = uu ),
    inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),f(n2,u)) )],[refute_0_34,refute_0_45]) ).

cnf(refute_0_47,plain,
    f(n2,f(n2,n2)) = uu,
    inference(resolve,[$cnf( $equal(f(n2,u),uu) )],[refute_0_42,refute_0_46]) ).

cnf(refute_0_48,plain,
    f(n2,f(n2,X_2)) = f(f(n2,n2),f(n2,X_2)),
    inference(subst,[],[a1:[bind(X,$fot(n2)),bind(Y,$fot(n2)),bind(Z,$fot(X_2))]]) ).

cnf(refute_0_49,plain,
    ( f(n2,f(n2,X_2)) != f(f(n2,n2),f(n2,X_2))
    | f(n2,n2) != u
    | f(n2,f(n2,X_2)) = f(u,f(n2,X_2)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n2,X_2)),f(f(n2,n2),f(n2,X_2))) ),[1,0],$fot(u)]]) ).

cnf(refute_0_50,plain,
    ( f(n2,f(n2,X_2)) != f(f(n2,n2),f(n2,X_2))
    | f(n2,f(n2,X_2)) = f(u,f(n2,X_2)) ),
    inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_23,refute_0_49]) ).

cnf(refute_0_51,plain,
    f(n2,f(n2,X_2)) = f(u,f(n2,X_2)),
    inference(resolve,[$cnf( $equal(f(n2,f(n2,X_2)),f(f(n2,n2),f(n2,X_2))) )],[refute_0_48,refute_0_50]) ).

cnf(refute_0_52,plain,
    ( f(n2,f(n2,X_2)) != f(u,f(n2,X_2))
    | f(u,f(n2,X_2)) = f(n2,f(n2,X_2)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(n2,f(n2,X_2)))),bind(Y0,$fot(f(u,f(n2,X_2))))]]) ).

cnf(refute_0_53,plain,
    f(u,f(n2,X_2)) = f(n2,f(n2,X_2)),
    inference(resolve,[$cnf( $equal(f(n2,f(n2,X_2)),f(u,f(n2,X_2))) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    f(u,f(n2,n2)) = f(n2,f(n2,n2)),
    inference(subst,[],[refute_0_53:[bind(X_2,$fot(n2))]]) ).

cnf(refute_0_55,plain,
    ( f(n2,f(n2,n2)) != uu
    | f(u,f(n2,n2)) != f(n2,f(n2,n2))
    | f(u,f(n2,n2)) = uu ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(u,f(n2,n2)))),bind(Y0,$fot(f(n2,f(n2,n2)))),bind(Z0,$fot(uu))]]) ).

cnf(refute_0_56,plain,
    ( f(n2,f(n2,n2)) != uu
    | f(u,f(n2,n2)) = uu ),
    inference(resolve,[$cnf( $equal(f(u,f(n2,n2)),f(n2,f(n2,n2))) )],[refute_0_54,refute_0_55]) ).

cnf(refute_0_57,plain,
    f(u,f(n2,n2)) = uu,
    inference(resolve,[$cnf( $equal(f(n2,f(n2,n2)),uu) )],[refute_0_47,refute_0_56]) ).

cnf(refute_0_58,plain,
    ( f(u,f(n2,n2)) != f(u2,u2)
    | f(u,f(n2,n2)) != uu
    | uu = f(u2,u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n2,n2)),f(u2,u2)) ),[0],$fot(uu)]]) ).

cnf(refute_0_59,plain,
    ( f(u,f(n2,n2)) != f(u2,u2)
    | uu = f(u2,u2) ),
    inference(resolve,[$cnf( $equal(f(u,f(n2,n2)),uu) )],[refute_0_57,refute_0_58]) ).

cnf(refute_0_60,plain,
    uu = f(u2,u2),
    inference(resolve,[$cnf( $equal(f(u,f(n2,n2)),f(u2,u2)) )],[refute_0_20,refute_0_59]) ).

cnf(refute_0_61,plain,
    ( uu != f(u2,u2)
    | f(u2,u2) = uu ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(uu)),bind(Y0,$fot(f(u2,u2)))]]) ).

cnf(refute_0_62,plain,
    f(u2,u2) = uu,
    inference(resolve,[$cnf( $equal(uu,f(u2,u2)) )],[refute_0_60,refute_0_61]) ).

cnf(refute_0_63,plain,
    ( f(f(n3,n2),f(u2,u2)) != f(f(f(n3,n2),u2),a)
    | f(u2,u2) != uu
    | f(f(n3,n2),uu) = f(f(f(n3,n2),u2),a) ),
    introduced(tautology,[equality,[$cnf( $equal(f(f(n3,n2),f(u2,u2)),f(f(f(n3,n2),u2),a)) ),[0,1],$fot(uu)]]) ).

cnf(refute_0_64,plain,
    ( f(f(n3,n2),f(u2,u2)) != f(f(f(n3,n2),u2),a)
    | f(f(n3,n2),uu) = f(f(f(n3,n2),u2),a) ),
    inference(resolve,[$cnf( $equal(f(u2,u2),uu) )],[refute_0_62,refute_0_63]) ).

cnf(refute_0_65,plain,
    f(f(n3,n2),uu) = f(f(f(n3,n2),u2),a),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),f(u2,u2)),f(f(f(n3,n2),u2),a)) )],[refute_0_10,refute_0_64]) ).

cnf(refute_0_66,plain,
    f(u,f(X_1,u)) = f(f(u,X_1),f(u,u)),
    inference(subst,[],[a1:[bind(X,$fot(u)),bind(Y,$fot(X_1)),bind(Z,$fot(u))]]) ).

cnf(refute_0_67,plain,
    ( f(u,f(X_1,u)) != f(f(u,X_1),f(u,u))
    | f(u,u) != uu
    | f(u,f(X_1,u)) = f(f(u,X_1),uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(X_1,u)),f(f(u,X_1),f(u,u))) ),[1,1],$fot(uu)]]) ).

cnf(refute_0_68,plain,
    ( f(u,f(X_1,u)) != f(f(u,X_1),f(u,u))
    | f(u,f(X_1,u)) = f(f(u,X_1),uu) ),
    inference(resolve,[$cnf( $equal(f(u,u),uu) )],[refute_0_38,refute_0_67]) ).

cnf(refute_0_69,plain,
    f(u,f(X_1,u)) = f(f(u,X_1),uu),
    inference(resolve,[$cnf( $equal(f(u,f(X_1,u)),f(f(u,X_1),f(u,u))) )],[refute_0_66,refute_0_68]) ).

cnf(refute_0_70,plain,
    f(u,f(n1,u)) = f(f(u,n1),uu),
    inference(subst,[],[refute_0_69:[bind(X_1,$fot(n1))]]) ).

cnf(refute_0_71,plain,
    f(u,f(n1,n2)) = f(f(u,n1),u2),
    inference(subst,[],[refute_0_16:[bind(X_1,$fot(n1))]]) ).

cnf(refute_0_72,plain,
    f(n1,f(X_1,n1)) = f(f(n1,X_1),f(n1,n1)),
    inference(subst,[],[a1:[bind(X,$fot(n1)),bind(Y,$fot(X_1)),bind(Z,$fot(n1))]]) ).

cnf(refute_0_73,plain,
    ( n2 != f(n1,n1)
    | f(n1,n1) = n2 ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(n2)),bind(Y0,$fot(f(n1,n1)))]]) ).

cnf(refute_0_74,plain,
    f(n1,n1) = n2,
    inference(resolve,[$cnf( $equal(n2,f(n1,n1)) )],[clause_2,refute_0_73]) ).

cnf(refute_0_75,plain,
    ( f(n1,f(X_1,n1)) != f(f(n1,X_1),f(n1,n1))
    | f(n1,n1) != n2
    | f(n1,f(X_1,n1)) = f(f(n1,X_1),n2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(X_1,n1)),f(f(n1,X_1),f(n1,n1))) ),[1,1],$fot(n2)]]) ).

cnf(refute_0_76,plain,
    ( f(n1,f(X_1,n1)) != f(f(n1,X_1),f(n1,n1))
    | f(n1,f(X_1,n1)) = f(f(n1,X_1),n2) ),
    inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_74,refute_0_75]) ).

cnf(refute_0_77,plain,
    f(n1,f(X_1,n1)) = f(f(n1,X_1),n2),
    inference(resolve,[$cnf( $equal(f(n1,f(X_1,n1)),f(f(n1,X_1),f(n1,n1))) )],[refute_0_72,refute_0_76]) ).

cnf(refute_0_78,plain,
    f(n1,f(n1,n1)) = f(f(n1,n1),n2),
    inference(subst,[],[refute_0_77:[bind(X_1,$fot(n1))]]) ).

cnf(refute_0_79,plain,
    ( f(n1,f(n1,n1)) != f(f(n1,n1),n2)
    | f(n1,n1) != n2
    | f(n1,f(n1,n1)) = f(n2,n2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n1)),f(f(n1,n1),n2)) ),[1,0],$fot(n2)]]) ).

cnf(refute_0_80,plain,
    ( f(n1,f(n1,n1)) != f(f(n1,n1),n2)
    | f(n1,f(n1,n1)) = f(n2,n2) ),
    inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_74,refute_0_79]) ).

cnf(refute_0_81,plain,
    f(n1,f(n1,n1)) = f(n2,n2),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(f(n1,n1),n2)) )],[refute_0_78,refute_0_80]) ).

cnf(refute_0_82,plain,
    f(n1,f(n1,n1)) = f(n1,f(n1,n1)),
    introduced(tautology,[refl,[$fot(f(n1,f(n1,n1)))]]) ).

cnf(refute_0_83,plain,
    ( f(n1,f(n1,n1)) != f(n1,f(n1,n1))
    | f(n1,n1) != n2
    | f(n1,f(n1,n1)) = f(n1,n2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,f(n1,n1))) ),[1,1],$fot(n2)]]) ).

cnf(refute_0_84,plain,
    ( f(n1,n1) != n2
    | f(n1,f(n1,n1)) = f(n1,n2) ),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,f(n1,n1))) )],[refute_0_82,refute_0_83]) ).

cnf(refute_0_85,plain,
    f(n1,f(n1,n1)) = f(n1,n2),
    inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_74,refute_0_84]) ).

cnf(refute_0_86,plain,
    ( f(n1,f(n1,n1)) != f(n1,n2)
    | f(n1,f(n1,n1)) != f(n2,n2)
    | f(n1,n2) = f(n2,n2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n1)),f(n2,n2)) ),[0],$fot(f(n1,n2))]]) ).

cnf(refute_0_87,plain,
    ( f(n1,f(n1,n1)) != f(n2,n2)
    | f(n1,n2) = f(n2,n2) ),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n1,n2)) )],[refute_0_85,refute_0_86]) ).

cnf(refute_0_88,plain,
    ( f(n1,n2) != f(n2,n2)
    | f(n2,n2) != u
    | f(n1,n2) = u ),
    introduced(tautology,[equality,[$cnf( ~ $equal(f(n1,n2),u) ),[0],$fot(f(n2,n2))]]) ).

cnf(refute_0_89,plain,
    ( f(n1,n2) != f(n2,n2)
    | f(n1,n2) = u ),
    inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_23,refute_0_88]) ).

cnf(refute_0_90,plain,
    ( f(n1,f(n1,n1)) != f(n2,n2)
    | f(n1,n2) = u ),
    inference(resolve,[$cnf( $equal(f(n1,n2),f(n2,n2)) )],[refute_0_87,refute_0_89]) ).

cnf(refute_0_91,plain,
    f(n1,n2) = u,
    inference(resolve,[$cnf( $equal(f(n1,f(n1,n1)),f(n2,n2)) )],[refute_0_81,refute_0_90]) ).

cnf(refute_0_92,plain,
    ( f(n1,n2) != u
    | f(u,f(n1,n2)) != f(f(u,n1),u2)
    | f(u,u) = f(f(u,n1),u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n1,n2)),f(f(u,n1),u2)) ),[0,1],$fot(u)]]) ).

cnf(refute_0_93,plain,
    ( f(u,f(n1,n2)) != f(f(u,n1),u2)
    | f(u,u) = f(f(u,n1),u2) ),
    inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_91,refute_0_92]) ).

cnf(refute_0_94,plain,
    f(u,u) = f(f(u,n1),u2),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n2)),f(f(u,n1),u2)) )],[refute_0_71,refute_0_93]) ).

cnf(refute_0_95,plain,
    ( f(u,u) != f(f(u,n1),u2)
    | f(u,u) != uu
    | uu = f(f(u,n1),u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,u),f(f(u,n1),u2)) ),[0],$fot(uu)]]) ).

cnf(refute_0_96,plain,
    ( f(u,u) != f(f(u,n1),u2)
    | uu = f(f(u,n1),u2) ),
    inference(resolve,[$cnf( $equal(f(u,u),uu) )],[refute_0_38,refute_0_95]) ).

cnf(refute_0_97,plain,
    f(n1,f(n2,n2)) = f(n1,f(n2,n2)),
    introduced(tautology,[refl,[$fot(f(n1,f(n2,n2)))]]) ).

cnf(refute_0_98,plain,
    ( f(n1,f(n2,n2)) != f(n1,f(n2,n2))
    | f(n2,n2) != u
    | f(n1,f(n2,n2)) = f(n1,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n2,n2)),f(n1,f(n2,n2))) ),[1,1],$fot(u)]]) ).

cnf(refute_0_99,plain,
    ( f(n2,n2) != u
    | f(n1,f(n2,n2)) = f(n1,u) ),
    inference(resolve,[$cnf( $equal(f(n1,f(n2,n2)),f(n1,f(n2,n2))) )],[refute_0_97,refute_0_98]) ).

cnf(refute_0_100,plain,
    f(n1,f(n2,n2)) = f(n1,u),
    inference(resolve,[$cnf( $equal(f(n2,n2),u) )],[refute_0_23,refute_0_99]) ).

cnf(refute_0_101,plain,
    f(n1,f(n2,Z)) = f(f(n1,n2),f(n1,Z)),
    inference(subst,[],[a1:[bind(X,$fot(n1)),bind(Y,$fot(n2))]]) ).

cnf(refute_0_102,plain,
    ( f(n1,f(n2,Z)) != f(f(n1,n2),f(n1,Z))
    | f(n1,n2) != u
    | f(n1,f(n2,Z)) = f(u,f(n1,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n2,Z)),f(f(n1,n2),f(n1,Z))) ),[1,0],$fot(u)]]) ).

cnf(refute_0_103,plain,
    ( f(n1,f(n2,Z)) != f(f(n1,n2),f(n1,Z))
    | f(n1,f(n2,Z)) = f(u,f(n1,Z)) ),
    inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_91,refute_0_102]) ).

cnf(refute_0_104,plain,
    f(n1,f(n2,Z)) = f(u,f(n1,Z)),
    inference(resolve,[$cnf( $equal(f(n1,f(n2,Z)),f(f(n1,n2),f(n1,Z))) )],[refute_0_101,refute_0_103]) ).

cnf(refute_0_105,plain,
    ( f(n1,f(n2,Z)) != f(u,f(n1,Z))
    | f(u,f(n1,Z)) = f(n1,f(n2,Z)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(n1,f(n2,Z)))),bind(Y0,$fot(f(u,f(n1,Z))))]]) ).

cnf(refute_0_106,plain,
    f(u,f(n1,Z)) = f(n1,f(n2,Z)),
    inference(resolve,[$cnf( $equal(f(n1,f(n2,Z)),f(u,f(n1,Z))) )],[refute_0_104,refute_0_105]) ).

cnf(refute_0_107,plain,
    f(u,f(n1,n2)) = f(n1,f(n2,n2)),
    inference(subst,[],[refute_0_106:[bind(Z,$fot(n2))]]) ).

cnf(refute_0_108,plain,
    ( f(u,f(X_1,n2)) != f(f(u,X_1),u2)
    | f(f(u,X_1),u2) = f(u,f(X_1,n2)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(u,f(X_1,n2)))),bind(Y0,$fot(f(f(u,X_1),u2)))]]) ).

cnf(refute_0_109,plain,
    f(f(u,X_1),u2) = f(u,f(X_1,n2)),
    inference(resolve,[$cnf( $equal(f(u,f(X_1,n2)),f(f(u,X_1),u2)) )],[refute_0_16,refute_0_108]) ).

cnf(refute_0_110,plain,
    f(f(u,n1),u2) = f(u,f(n1,n2)),
    inference(subst,[],[refute_0_109:[bind(X_1,$fot(n1))]]) ).

cnf(refute_0_111,plain,
    ( f(f(u,n1),u2) != f(u,f(n1,n2))
    | f(u,f(n1,n2)) != f(n1,f(n2,n2))
    | f(f(u,n1),u2) = f(n1,f(n2,n2)) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(u,n1),u2))),bind(Y0,$fot(f(u,f(n1,n2)))),bind(Z0,$fot(f(n1,f(n2,n2))))]]) ).

cnf(refute_0_112,plain,
    ( f(u,f(n1,n2)) != f(n1,f(n2,n2))
    | f(f(u,n1),u2) = f(n1,f(n2,n2)) ),
    inference(resolve,[$cnf( $equal(f(f(u,n1),u2),f(u,f(n1,n2))) )],[refute_0_110,refute_0_111]) ).

cnf(refute_0_113,plain,
    f(f(u,n1),u2) = f(n1,f(n2,n2)),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n2)),f(n1,f(n2,n2))) )],[refute_0_107,refute_0_112]) ).

cnf(refute_0_114,plain,
    ( f(f(u,n1),u2) != f(n1,f(n2,n2))
    | f(n1,f(n2,n2)) != f(n1,u)
    | f(f(u,n1),u2) = f(n1,u) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(u,n1),u2))),bind(Y0,$fot(f(n1,f(n2,n2)))),bind(Z0,$fot(f(n1,u)))]]) ).

cnf(refute_0_115,plain,
    ( f(n1,f(n2,n2)) != f(n1,u)
    | f(f(u,n1),u2) = f(n1,u) ),
    inference(resolve,[$cnf( $equal(f(f(u,n1),u2),f(n1,f(n2,n2))) )],[refute_0_113,refute_0_114]) ).

cnf(refute_0_116,plain,
    f(f(u,n1),u2) = f(n1,u),
    inference(resolve,[$cnf( $equal(f(n1,f(n2,n2)),f(n1,u)) )],[refute_0_100,refute_0_115]) ).

cnf(refute_0_117,plain,
    ( f(f(u,n1),u2) != f(n1,u)
    | uu != f(f(u,n1),u2)
    | uu = f(n1,u) ),
    introduced(tautology,[equality,[$cnf( $equal(uu,f(f(u,n1),u2)) ),[1],$fot(f(n1,u))]]) ).

cnf(refute_0_118,plain,
    ( uu != f(f(u,n1),u2)
    | uu = f(n1,u) ),
    inference(resolve,[$cnf( $equal(f(f(u,n1),u2),f(n1,u)) )],[refute_0_116,refute_0_117]) ).

cnf(refute_0_119,plain,
    ( f(u,u) != f(f(u,n1),u2)
    | uu = f(n1,u) ),
    inference(resolve,[$cnf( $equal(uu,f(f(u,n1),u2)) )],[refute_0_96,refute_0_118]) ).

cnf(refute_0_120,plain,
    uu = f(n1,u),
    inference(resolve,[$cnf( $equal(f(u,u),f(f(u,n1),u2)) )],[refute_0_94,refute_0_119]) ).

cnf(refute_0_121,plain,
    ( uu != f(n1,u)
    | f(n1,u) = uu ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(uu)),bind(Y0,$fot(f(n1,u)))]]) ).

cnf(refute_0_122,plain,
    f(n1,u) = uu,
    inference(resolve,[$cnf( $equal(uu,f(n1,u)) )],[refute_0_120,refute_0_121]) ).

cnf(refute_0_123,plain,
    ( f(n1,u) != uu
    | f(u,f(n1,u)) != f(f(u,n1),uu)
    | f(u,uu) = f(f(u,n1),uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n1,u)),f(f(u,n1),uu)) ),[0,1],$fot(uu)]]) ).

cnf(refute_0_124,plain,
    ( f(u,f(n1,u)) != f(f(u,n1),uu)
    | f(u,uu) = f(f(u,n1),uu) ),
    inference(resolve,[$cnf( $equal(f(n1,u),uu) )],[refute_0_122,refute_0_123]) ).

cnf(refute_0_125,plain,
    f(u,uu) = f(f(u,n1),uu),
    inference(resolve,[$cnf( $equal(f(u,f(n1,u)),f(f(u,n1),uu)) )],[refute_0_70,refute_0_124]) ).

cnf(refute_0_126,plain,
    f(u,f(u,X_2)) = f(f(u,u),f(u,X_2)),
    inference(subst,[],[a1:[bind(X,$fot(u)),bind(Y,$fot(u)),bind(Z,$fot(X_2))]]) ).

cnf(refute_0_127,plain,
    ( f(u,f(u,X_2)) != f(f(u,u),f(u,X_2))
    | f(u,u) != uu
    | f(u,f(u,X_2)) = f(uu,f(u,X_2)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,X_2)),f(f(u,u),f(u,X_2))) ),[1,0],$fot(uu)]]) ).

cnf(refute_0_128,plain,
    ( f(u,f(u,X_2)) != f(f(u,u),f(u,X_2))
    | f(u,f(u,X_2)) = f(uu,f(u,X_2)) ),
    inference(resolve,[$cnf( $equal(f(u,u),uu) )],[refute_0_38,refute_0_127]) ).

cnf(refute_0_129,plain,
    f(u,f(u,X_2)) = f(uu,f(u,X_2)),
    inference(resolve,[$cnf( $equal(f(u,f(u,X_2)),f(f(u,u),f(u,X_2))) )],[refute_0_126,refute_0_128]) ).

cnf(refute_0_130,plain,
    f(u,f(u,u)) = f(uu,f(u,u)),
    inference(subst,[],[refute_0_129:[bind(X_2,$fot(u))]]) ).

cnf(refute_0_131,plain,
    ( f(u,f(u,u)) != f(uu,f(u,u))
    | f(u,u) != uu
    | f(u,f(u,u)) = f(uu,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,u)),f(uu,f(u,u))) ),[1,1],$fot(uu)]]) ).

cnf(refute_0_132,plain,
    ( f(u,f(u,u)) != f(uu,f(u,u))
    | f(u,f(u,u)) = f(uu,uu) ),
    inference(resolve,[$cnf( $equal(f(u,u),uu) )],[refute_0_38,refute_0_131]) ).

cnf(refute_0_133,plain,
    f(u,f(u,u)) = f(uu,uu),
    inference(resolve,[$cnf( $equal(f(u,f(u,u)),f(uu,f(u,u))) )],[refute_0_130,refute_0_132]) ).

cnf(refute_0_134,plain,
    f(u,f(u,u)) = f(u,f(u,u)),
    introduced(tautology,[refl,[$fot(f(u,f(u,u)))]]) ).

cnf(refute_0_135,plain,
    ( f(u,f(u,u)) != f(u,f(u,u))
    | f(u,u) != uu
    | f(u,f(u,u)) = f(u,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,u)),f(u,f(u,u))) ),[1,1],$fot(uu)]]) ).

cnf(refute_0_136,plain,
    ( f(u,u) != uu
    | f(u,f(u,u)) = f(u,uu) ),
    inference(resolve,[$cnf( $equal(f(u,f(u,u)),f(u,f(u,u))) )],[refute_0_134,refute_0_135]) ).

cnf(refute_0_137,plain,
    f(u,f(u,u)) = f(u,uu),
    inference(resolve,[$cnf( $equal(f(u,u),uu) )],[refute_0_38,refute_0_136]) ).

cnf(refute_0_138,plain,
    ( f(u,f(u,u)) != f(u,uu)
    | f(u,f(u,u)) != f(uu,uu)
    | f(u,uu) = f(uu,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,u)),f(uu,uu)) ),[0],$fot(f(u,uu))]]) ).

cnf(refute_0_139,plain,
    ( f(u,f(u,u)) != f(uu,uu)
    | f(u,uu) = f(uu,uu) ),
    inference(resolve,[$cnf( $equal(f(u,f(u,u)),f(u,uu)) )],[refute_0_137,refute_0_138]) ).

cnf(refute_0_140,plain,
    ( v != f(uu,uu)
    | f(uu,uu) = v ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(v)),bind(Y0,$fot(f(uu,uu)))]]) ).

cnf(refute_0_141,plain,
    f(uu,uu) = v,
    inference(resolve,[$cnf( $equal(v,f(uu,uu)) )],[clause_11,refute_0_140]) ).

cnf(refute_0_142,plain,
    ( f(u,uu) != f(uu,uu)
    | f(uu,uu) != v
    | f(u,uu) = v ),
    introduced(tautology,[equality,[$cnf( ~ $equal(f(u,uu),v) ),[0],$fot(f(uu,uu))]]) ).

cnf(refute_0_143,plain,
    ( f(u,uu) != f(uu,uu)
    | f(u,uu) = v ),
    inference(resolve,[$cnf( $equal(f(uu,uu),v) )],[refute_0_141,refute_0_142]) ).

cnf(refute_0_144,plain,
    ( f(u,f(u,u)) != f(uu,uu)
    | f(u,uu) = v ),
    inference(resolve,[$cnf( $equal(f(u,uu),f(uu,uu)) )],[refute_0_139,refute_0_143]) ).

cnf(refute_0_145,plain,
    f(u,uu) = v,
    inference(resolve,[$cnf( $equal(f(u,f(u,u)),f(uu,uu)) )],[refute_0_133,refute_0_144]) ).

cnf(refute_0_146,plain,
    ( f(u,uu) != f(f(u,n1),uu)
    | f(u,uu) != v
    | v = f(f(u,n1),uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,uu),f(f(u,n1),uu)) ),[0],$fot(v)]]) ).

cnf(refute_0_147,plain,
    ( f(u,uu) != f(f(u,n1),uu)
    | v = f(f(u,n1),uu) ),
    inference(resolve,[$cnf( $equal(f(u,uu),v) )],[refute_0_145,refute_0_146]) ).

cnf(refute_0_148,plain,
    f(n1,f(n2,u)) = f(n1,f(n2,u)),
    introduced(tautology,[refl,[$fot(f(n1,f(n2,u)))]]) ).

cnf(refute_0_149,plain,
    ( f(n1,f(n2,u)) != f(n1,f(n2,u))
    | f(n2,u) != uu
    | f(n1,f(n2,u)) = f(n1,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n2,u)),f(n1,f(n2,u))) ),[1,1],$fot(uu)]]) ).

cnf(refute_0_150,plain,
    ( f(n2,u) != uu
    | f(n1,f(n2,u)) = f(n1,uu) ),
    inference(resolve,[$cnf( $equal(f(n1,f(n2,u)),f(n1,f(n2,u))) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    f(n1,f(n2,u)) = f(n1,uu),
    inference(resolve,[$cnf( $equal(f(n2,u),uu) )],[refute_0_42,refute_0_150]) ).

cnf(refute_0_152,plain,
    f(u,f(n1,u)) = f(n1,f(n2,u)),
    inference(subst,[],[refute_0_106:[bind(Z,$fot(u))]]) ).

cnf(refute_0_153,plain,
    ( f(u,f(X_1,u)) != f(f(u,X_1),uu)
    | f(f(u,X_1),uu) = f(u,f(X_1,u)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(u,f(X_1,u)))),bind(Y0,$fot(f(f(u,X_1),uu)))]]) ).

cnf(refute_0_154,plain,
    f(f(u,X_1),uu) = f(u,f(X_1,u)),
    inference(resolve,[$cnf( $equal(f(u,f(X_1,u)),f(f(u,X_1),uu)) )],[refute_0_69,refute_0_153]) ).

cnf(refute_0_155,plain,
    f(f(u,n1),uu) = f(u,f(n1,u)),
    inference(subst,[],[refute_0_154:[bind(X_1,$fot(n1))]]) ).

cnf(refute_0_156,plain,
    ( f(f(u,n1),uu) != f(u,f(n1,u))
    | f(u,f(n1,u)) != f(n1,f(n2,u))
    | f(f(u,n1),uu) = f(n1,f(n2,u)) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(u,n1),uu))),bind(Y0,$fot(f(u,f(n1,u)))),bind(Z0,$fot(f(n1,f(n2,u))))]]) ).

cnf(refute_0_157,plain,
    ( f(u,f(n1,u)) != f(n1,f(n2,u))
    | f(f(u,n1),uu) = f(n1,f(n2,u)) ),
    inference(resolve,[$cnf( $equal(f(f(u,n1),uu),f(u,f(n1,u))) )],[refute_0_155,refute_0_156]) ).

cnf(refute_0_158,plain,
    f(f(u,n1),uu) = f(n1,f(n2,u)),
    inference(resolve,[$cnf( $equal(f(u,f(n1,u)),f(n1,f(n2,u))) )],[refute_0_152,refute_0_157]) ).

cnf(refute_0_159,plain,
    ( f(f(u,n1),uu) != f(n1,f(n2,u))
    | f(n1,f(n2,u)) != f(n1,uu)
    | f(f(u,n1),uu) = f(n1,uu) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(u,n1),uu))),bind(Y0,$fot(f(n1,f(n2,u)))),bind(Z0,$fot(f(n1,uu)))]]) ).

cnf(refute_0_160,plain,
    ( f(n1,f(n2,u)) != f(n1,uu)
    | f(f(u,n1),uu) = f(n1,uu) ),
    inference(resolve,[$cnf( $equal(f(f(u,n1),uu),f(n1,f(n2,u))) )],[refute_0_158,refute_0_159]) ).

cnf(refute_0_161,plain,
    f(f(u,n1),uu) = f(n1,uu),
    inference(resolve,[$cnf( $equal(f(n1,f(n2,u)),f(n1,uu)) )],[refute_0_151,refute_0_160]) ).

cnf(refute_0_162,plain,
    ( f(f(u,n1),uu) != f(n1,uu)
    | v != f(f(u,n1),uu)
    | v = f(n1,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(v,f(f(u,n1),uu)) ),[1],$fot(f(n1,uu))]]) ).

cnf(refute_0_163,plain,
    ( v != f(f(u,n1),uu)
    | v = f(n1,uu) ),
    inference(resolve,[$cnf( $equal(f(f(u,n1),uu),f(n1,uu)) )],[refute_0_161,refute_0_162]) ).

cnf(refute_0_164,plain,
    ( f(u,uu) != f(f(u,n1),uu)
    | v = f(n1,uu) ),
    inference(resolve,[$cnf( $equal(v,f(f(u,n1),uu)) )],[refute_0_147,refute_0_163]) ).

cnf(refute_0_165,plain,
    v = f(n1,uu),
    inference(resolve,[$cnf( $equal(f(u,uu),f(f(u,n1),uu)) )],[refute_0_125,refute_0_164]) ).

cnf(refute_0_166,plain,
    ( v != f(n1,uu)
    | f(n1,uu) = v ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(v)),bind(Y0,$fot(f(n1,uu)))]]) ).

cnf(refute_0_167,plain,
    f(n1,uu) = v,
    inference(resolve,[$cnf( $equal(v,f(n1,uu)) )],[refute_0_165,refute_0_166]) ).

cnf(refute_0_168,plain,
    f(n1,f(n1,u)) = f(n1,f(n1,u)),
    introduced(tautology,[refl,[$fot(f(n1,f(n1,u)))]]) ).

cnf(refute_0_169,plain,
    ( f(n1,f(n1,u)) != f(n1,f(n1,u))
    | f(n1,u) != uu
    | f(n1,f(n1,u)) = f(n1,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,u)),f(n1,f(n1,u))) ),[1,1],$fot(uu)]]) ).

cnf(refute_0_170,plain,
    ( f(n1,u) != uu
    | f(n1,f(n1,u)) = f(n1,uu) ),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,u)),f(n1,f(n1,u))) )],[refute_0_168,refute_0_169]) ).

cnf(refute_0_171,plain,
    f(n1,f(n1,u)) = f(n1,uu),
    inference(resolve,[$cnf( $equal(f(n1,u),uu) )],[refute_0_122,refute_0_170]) ).

cnf(refute_0_172,plain,
    ( f(n1,f(n1,u)) != f(n1,uu)
    | f(n1,uu) != v
    | f(n1,f(n1,u)) = v ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(n1,f(n1,u)))),bind(Y0,$fot(f(n1,uu))),bind(Z0,$fot(v))]]) ).

cnf(refute_0_173,plain,
    ( f(n1,uu) != v
    | f(n1,f(n1,u)) = v ),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,u)),f(n1,uu)) )],[refute_0_171,refute_0_172]) ).

cnf(refute_0_174,plain,
    f(n1,f(n1,u)) = v,
    inference(resolve,[$cnf( $equal(f(n1,uu),v) )],[refute_0_167,refute_0_173]) ).

cnf(refute_0_175,plain,
    f(n2,f(n1,X_2)) = f(f(n2,n1),f(n2,X_2)),
    inference(subst,[],[a1:[bind(X,$fot(n2)),bind(Y,$fot(n1)),bind(Z,$fot(X_2))]]) ).

cnf(refute_0_176,plain,
    ( n3 != f(n2,n1)
    | f(n2,n1) = n3 ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(n3)),bind(Y0,$fot(f(n2,n1)))]]) ).

cnf(refute_0_177,plain,
    f(n2,n1) = n3,
    inference(resolve,[$cnf( $equal(n3,f(n2,n1)) )],[clause_3,refute_0_176]) ).

cnf(refute_0_178,plain,
    ( f(n2,f(n1,X_2)) != f(f(n2,n1),f(n2,X_2))
    | f(n2,n1) != n3
    | f(n2,f(n1,X_2)) = f(n3,f(n2,X_2)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n1,X_2)),f(f(n2,n1),f(n2,X_2))) ),[1,0],$fot(n3)]]) ).

cnf(refute_0_179,plain,
    ( f(n2,f(n1,X_2)) != f(f(n2,n1),f(n2,X_2))
    | f(n2,f(n1,X_2)) = f(n3,f(n2,X_2)) ),
    inference(resolve,[$cnf( $equal(f(n2,n1),n3) )],[refute_0_177,refute_0_178]) ).

cnf(refute_0_180,plain,
    f(n2,f(n1,X_2)) = f(n3,f(n2,X_2)),
    inference(resolve,[$cnf( $equal(f(n2,f(n1,X_2)),f(f(n2,n1),f(n2,X_2))) )],[refute_0_175,refute_0_179]) ).

cnf(refute_0_181,plain,
    f(n1,f(n1,X_2)) = f(f(n1,n1),f(n1,X_2)),
    inference(subst,[],[a1:[bind(X,$fot(n1)),bind(Y,$fot(n1)),bind(Z,$fot(X_2))]]) ).

cnf(refute_0_182,plain,
    ( f(n1,f(n1,X_2)) != f(f(n1,n1),f(n1,X_2))
    | f(n1,n1) != n2
    | f(n1,f(n1,X_2)) = f(n2,f(n1,X_2)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,X_2)),f(f(n1,n1),f(n1,X_2))) ),[1,0],$fot(n2)]]) ).

cnf(refute_0_183,plain,
    ( f(n1,f(n1,X_2)) != f(f(n1,n1),f(n1,X_2))
    | f(n1,f(n1,X_2)) = f(n2,f(n1,X_2)) ),
    inference(resolve,[$cnf( $equal(f(n1,n1),n2) )],[refute_0_74,refute_0_182]) ).

cnf(refute_0_184,plain,
    f(n1,f(n1,X_2)) = f(n2,f(n1,X_2)),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,X_2)),f(f(n1,n1),f(n1,X_2))) )],[refute_0_181,refute_0_183]) ).

cnf(refute_0_185,plain,
    ( f(n1,f(n1,X_2)) != f(n2,f(n1,X_2))
    | f(n2,f(n1,X_2)) = f(n1,f(n1,X_2)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(n1,f(n1,X_2)))),bind(Y0,$fot(f(n2,f(n1,X_2))))]]) ).

cnf(refute_0_186,plain,
    f(n2,f(n1,X_2)) = f(n1,f(n1,X_2)),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,X_2)),f(n2,f(n1,X_2))) )],[refute_0_184,refute_0_185]) ).

cnf(refute_0_187,plain,
    ( f(n2,f(n1,X_2)) != f(n1,f(n1,X_2))
    | f(n2,f(n1,X_2)) != f(n3,f(n2,X_2))
    | f(n1,f(n1,X_2)) = f(n3,f(n2,X_2)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n1,X_2)),f(n3,f(n2,X_2))) ),[0],$fot(f(n1,f(n1,X_2)))]]) ).

cnf(refute_0_188,plain,
    ( f(n2,f(n1,X_2)) != f(n3,f(n2,X_2))
    | f(n1,f(n1,X_2)) = f(n3,f(n2,X_2)) ),
    inference(resolve,[$cnf( $equal(f(n2,f(n1,X_2)),f(n1,f(n1,X_2))) )],[refute_0_186,refute_0_187]) ).

cnf(refute_0_189,plain,
    f(n1,f(n1,X_2)) = f(n3,f(n2,X_2)),
    inference(resolve,[$cnf( $equal(f(n2,f(n1,X_2)),f(n3,f(n2,X_2))) )],[refute_0_180,refute_0_188]) ).

cnf(refute_0_190,plain,
    ( f(n1,f(n1,X_2)) != f(n3,f(n2,X_2))
    | f(n3,f(n2,X_2)) = f(n1,f(n1,X_2)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(n1,f(n1,X_2)))),bind(Y0,$fot(f(n3,f(n2,X_2))))]]) ).

cnf(refute_0_191,plain,
    f(n3,f(n2,X_2)) = f(n1,f(n1,X_2)),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,X_2)),f(n3,f(n2,X_2))) )],[refute_0_189,refute_0_190]) ).

cnf(refute_0_192,plain,
    f(n3,f(n2,u)) = f(n1,f(n1,u)),
    inference(subst,[],[refute_0_191:[bind(X_2,$fot(u))]]) ).

cnf(refute_0_193,plain,
    f(n3,f(Y,u)) = f(f(n3,Y),f(n3,u)),
    inference(subst,[],[a1:[bind(X,$fot(n3)),bind(Z,$fot(u))]]) ).

cnf(refute_0_194,plain,
    f(n2,f(n1,n2)) = f(f(n2,n1),u),
    inference(subst,[],[refute_0_26:[bind(X_1,$fot(n1))]]) ).

cnf(refute_0_195,plain,
    ( f(n2,f(n1,n2)) != f(f(n2,n1),u)
    | f(n2,n1) != n3
    | f(n2,f(n1,n2)) = f(n3,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n1,n2)),f(f(n2,n1),u)) ),[1,0],$fot(n3)]]) ).

cnf(refute_0_196,plain,
    ( f(n2,f(n1,n2)) != f(f(n2,n1),u)
    | f(n2,f(n1,n2)) = f(n3,u) ),
    inference(resolve,[$cnf( $equal(f(n2,n1),n3) )],[refute_0_177,refute_0_195]) ).

cnf(refute_0_197,plain,
    f(n2,f(n1,n2)) = f(n3,u),
    inference(resolve,[$cnf( $equal(f(n2,f(n1,n2)),f(f(n2,n1),u)) )],[refute_0_194,refute_0_196]) ).

cnf(refute_0_198,plain,
    f(n2,f(n1,n2)) = f(n1,f(n1,n2)),
    inference(subst,[],[refute_0_186:[bind(X_2,$fot(n2))]]) ).

cnf(refute_0_199,plain,
    ( f(n2,f(n1,n2)) != f(n1,f(n1,n2))
    | f(n2,f(n1,n2)) != f(n3,u)
    | f(n1,f(n1,n2)) = f(n3,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n1,n2)),f(n3,u)) ),[0],$fot(f(n1,f(n1,n2)))]]) ).

cnf(refute_0_200,plain,
    ( f(n2,f(n1,n2)) != f(n3,u)
    | f(n1,f(n1,n2)) = f(n3,u) ),
    inference(resolve,[$cnf( $equal(f(n2,f(n1,n2)),f(n1,f(n1,n2))) )],[refute_0_198,refute_0_199]) ).

cnf(refute_0_201,plain,
    f(n1,f(n1,n2)) = f(n3,u),
    inference(resolve,[$cnf( $equal(f(n2,f(n1,n2)),f(n3,u)) )],[refute_0_197,refute_0_200]) ).

cnf(refute_0_202,plain,
    f(n1,f(n1,n2)) = f(n1,f(n1,n2)),
    introduced(tautology,[refl,[$fot(f(n1,f(n1,n2)))]]) ).

cnf(refute_0_203,plain,
    ( f(n1,f(n1,n2)) != f(n1,f(n1,n2))
    | f(n1,n2) != u
    | f(n1,f(n1,n2)) = f(n1,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n2)),f(n1,f(n1,n2))) ),[1,1],$fot(u)]]) ).

cnf(refute_0_204,plain,
    ( f(n1,n2) != u
    | f(n1,f(n1,n2)) = f(n1,u) ),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,n2)),f(n1,f(n1,n2))) )],[refute_0_202,refute_0_203]) ).

cnf(refute_0_205,plain,
    f(n1,f(n1,n2)) = f(n1,u),
    inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_91,refute_0_204]) ).

cnf(refute_0_206,plain,
    ( f(n1,f(n1,n2)) != f(n1,u)
    | f(n1,f(n1,n2)) != f(n3,u)
    | f(n1,u) = f(n3,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n1,n2)),f(n3,u)) ),[0],$fot(f(n1,u))]]) ).

cnf(refute_0_207,plain,
    ( f(n1,f(n1,n2)) != f(n3,u)
    | f(n1,u) = f(n3,u) ),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,n2)),f(n1,u)) )],[refute_0_205,refute_0_206]) ).

cnf(refute_0_208,plain,
    f(n1,u) = f(n3,u),
    inference(resolve,[$cnf( $equal(f(n1,f(n1,n2)),f(n3,u)) )],[refute_0_201,refute_0_207]) ).

cnf(refute_0_209,plain,
    ( f(n1,u) != f(n3,u)
    | f(n1,u) != uu
    | uu = f(n3,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,u),f(n3,u)) ),[0],$fot(uu)]]) ).

cnf(refute_0_210,plain,
    ( f(n1,u) != f(n3,u)
    | uu = f(n3,u) ),
    inference(resolve,[$cnf( $equal(f(n1,u),uu) )],[refute_0_122,refute_0_209]) ).

cnf(refute_0_211,plain,
    uu = f(n3,u),
    inference(resolve,[$cnf( $equal(f(n1,u),f(n3,u)) )],[refute_0_208,refute_0_210]) ).

cnf(refute_0_212,plain,
    ( uu != f(n3,u)
    | f(n3,u) = uu ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(uu)),bind(Y0,$fot(f(n3,u)))]]) ).

cnf(refute_0_213,plain,
    f(n3,u) = uu,
    inference(resolve,[$cnf( $equal(uu,f(n3,u)) )],[refute_0_211,refute_0_212]) ).

cnf(refute_0_214,plain,
    ( f(n3,f(Y,u)) != f(f(n3,Y),f(n3,u))
    | f(n3,u) != uu
    | f(n3,f(Y,u)) = f(f(n3,Y),uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n3,f(Y,u)),f(f(n3,Y),f(n3,u))) ),[1,1],$fot(uu)]]) ).

cnf(refute_0_215,plain,
    ( f(n3,f(Y,u)) != f(f(n3,Y),f(n3,u))
    | f(n3,f(Y,u)) = f(f(n3,Y),uu) ),
    inference(resolve,[$cnf( $equal(f(n3,u),uu) )],[refute_0_213,refute_0_214]) ).

cnf(refute_0_216,plain,
    f(n3,f(Y,u)) = f(f(n3,Y),uu),
    inference(resolve,[$cnf( $equal(f(n3,f(Y,u)),f(f(n3,Y),f(n3,u))) )],[refute_0_193,refute_0_215]) ).

cnf(refute_0_217,plain,
    ( f(n3,f(Y,u)) != f(f(n3,Y),uu)
    | f(f(n3,Y),uu) = f(n3,f(Y,u)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(n3,f(Y,u)))),bind(Y0,$fot(f(f(n3,Y),uu)))]]) ).

cnf(refute_0_218,plain,
    f(f(n3,Y),uu) = f(n3,f(Y,u)),
    inference(resolve,[$cnf( $equal(f(n3,f(Y,u)),f(f(n3,Y),uu)) )],[refute_0_216,refute_0_217]) ).

cnf(refute_0_219,plain,
    f(f(n3,n2),uu) = f(n3,f(n2,u)),
    inference(subst,[],[refute_0_218:[bind(Y,$fot(n2))]]) ).

cnf(refute_0_220,plain,
    ( f(f(n3,n2),uu) != f(n3,f(n2,u))
    | f(n3,f(n2,u)) != f(n1,f(n1,u))
    | f(f(n3,n2),uu) = f(n1,f(n1,u)) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(n3,n2),uu))),bind(Y0,$fot(f(n3,f(n2,u)))),bind(Z0,$fot(f(n1,f(n1,u))))]]) ).

cnf(refute_0_221,plain,
    ( f(n3,f(n2,u)) != f(n1,f(n1,u))
    | f(f(n3,n2),uu) = f(n1,f(n1,u)) ),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),uu),f(n3,f(n2,u))) )],[refute_0_219,refute_0_220]) ).

cnf(refute_0_222,plain,
    f(f(n3,n2),uu) = f(n1,f(n1,u)),
    inference(resolve,[$cnf( $equal(f(n3,f(n2,u)),f(n1,f(n1,u))) )],[refute_0_192,refute_0_221]) ).

cnf(refute_0_223,plain,
    ( f(f(n3,n2),uu) != f(n1,f(n1,u))
    | f(n1,f(n1,u)) != v
    | f(f(n3,n2),uu) = v ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(n3,n2),uu))),bind(Y0,$fot(f(n1,f(n1,u)))),bind(Z0,$fot(v))]]) ).

cnf(refute_0_224,plain,
    ( f(n1,f(n1,u)) != v
    | f(f(n3,n2),uu) = v ),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),uu),f(n1,f(n1,u))) )],[refute_0_222,refute_0_223]) ).

cnf(refute_0_225,plain,
    f(f(n3,n2),uu) = v,
    inference(resolve,[$cnf( $equal(f(n1,f(n1,u)),v) )],[refute_0_174,refute_0_224]) ).

cnf(refute_0_226,plain,
    ( f(f(n3,n2),uu) != f(f(f(n3,n2),u2),a)
    | f(f(n3,n2),uu) != v
    | v = f(f(f(n3,n2),u2),a) ),
    introduced(tautology,[equality,[$cnf( $equal(f(f(n3,n2),uu),f(f(f(n3,n2),u2),a)) ),[0],$fot(v)]]) ).

cnf(refute_0_227,plain,
    ( f(f(n3,n2),uu) != f(f(f(n3,n2),u2),a)
    | v = f(f(f(n3,n2),u2),a) ),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),uu),v) )],[refute_0_225,refute_0_226]) ).

cnf(refute_0_228,plain,
    f(a,f(f(n3,n2),u2)) = f(a,f(f(n3,n2),u2)),
    introduced(tautology,[refl,[$fot(f(a,f(f(n3,n2),u2)))]]) ).

cnf(refute_0_229,plain,
    ( f(a,f(f(n3,n2),u2)) != f(a,f(f(n3,n2),u2))
    | f(f(n3,n2),u2) != a
    | f(a,f(f(n3,n2),u2)) = f(a,a) ),
    introduced(tautology,[equality,[$cnf( $equal(f(a,f(f(n3,n2),u2)),f(a,f(f(n3,n2),u2))) ),[1,1],$fot(a)]]) ).

cnf(refute_0_230,plain,
    ( f(f(n3,n2),u2) != a
    | f(a,f(f(n3,n2),u2)) = f(a,a) ),
    inference(resolve,[$cnf( $equal(f(a,f(f(n3,n2),u2)),f(a,f(f(n3,n2),u2))) )],[refute_0_228,refute_0_229]) ).

cnf(refute_0_231,plain,
    f(a,f(f(n3,n2),u2)) = f(a,a),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),u2),a) )],[refute_0_6,refute_0_230]) ).

cnf(refute_0_232,plain,
    f(f(n3,n2),f(u2,X_2)) = f(f(f(n3,n2),u2),f(f(n3,n2),X_2)),
    inference(subst,[],[a1:[bind(X,$fot(f(n3,n2))),bind(Y,$fot(u2)),bind(Z,$fot(X_2))]]) ).

cnf(refute_0_233,plain,
    ( f(f(n3,n2),f(u2,X_2)) != f(f(f(n3,n2),u2),f(f(n3,n2),X_2))
    | f(f(n3,n2),u2) != a
    | f(f(n3,n2),f(u2,X_2)) = f(a,f(f(n3,n2),X_2)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(f(n3,n2),f(u2,X_2)),f(f(f(n3,n2),u2),f(f(n3,n2),X_2))) ),[1,0],$fot(a)]]) ).

cnf(refute_0_234,plain,
    ( f(f(n3,n2),f(u2,X_2)) != f(f(f(n3,n2),u2),f(f(n3,n2),X_2))
    | f(f(n3,n2),f(u2,X_2)) = f(a,f(f(n3,n2),X_2)) ),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),u2),a) )],[refute_0_6,refute_0_233]) ).

cnf(refute_0_235,plain,
    f(f(n3,n2),f(u2,X_2)) = f(a,f(f(n3,n2),X_2)),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),f(u2,X_2)),f(f(f(n3,n2),u2),f(f(n3,n2),X_2))) )],[refute_0_232,refute_0_234]) ).

cnf(refute_0_236,plain,
    f(f(n3,n2),f(u2,u2)) = f(a,f(f(n3,n2),u2)),
    inference(subst,[],[refute_0_235:[bind(X_2,$fot(u2))]]) ).

cnf(refute_0_237,plain,
    ( f(f(n3,n2),f(X_1,u2)) != f(f(f(n3,n2),X_1),a)
    | f(f(f(n3,n2),X_1),a) = f(f(n3,n2),f(X_1,u2)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(f(n3,n2),f(X_1,u2)))),bind(Y0,$fot(f(f(f(n3,n2),X_1),a)))]]) ).

cnf(refute_0_238,plain,
    f(f(f(n3,n2),X_1),a) = f(f(n3,n2),f(X_1,u2)),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),f(X_1,u2)),f(f(f(n3,n2),X_1),a)) )],[refute_0_9,refute_0_237]) ).

cnf(refute_0_239,plain,
    f(f(f(n3,n2),u2),a) = f(f(n3,n2),f(u2,u2)),
    inference(subst,[],[refute_0_238:[bind(X_1,$fot(u2))]]) ).

cnf(refute_0_240,plain,
    ( f(f(f(n3,n2),u2),a) != f(f(n3,n2),f(u2,u2))
    | f(f(n3,n2),f(u2,u2)) != f(a,f(f(n3,n2),u2))
    | f(f(f(n3,n2),u2),a) = f(a,f(f(n3,n2),u2)) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(f(n3,n2),u2),a))),bind(Y0,$fot(f(f(n3,n2),f(u2,u2)))),bind(Z0,$fot(f(a,f(f(n3,n2),u2))))]]) ).

cnf(refute_0_241,plain,
    ( f(f(n3,n2),f(u2,u2)) != f(a,f(f(n3,n2),u2))
    | f(f(f(n3,n2),u2),a) = f(a,f(f(n3,n2),u2)) ),
    inference(resolve,[$cnf( $equal(f(f(f(n3,n2),u2),a),f(f(n3,n2),f(u2,u2))) )],[refute_0_239,refute_0_240]) ).

cnf(refute_0_242,plain,
    f(f(f(n3,n2),u2),a) = f(a,f(f(n3,n2),u2)),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),f(u2,u2)),f(a,f(f(n3,n2),u2))) )],[refute_0_236,refute_0_241]) ).

cnf(refute_0_243,plain,
    ( f(a,f(f(n3,n2),u2)) != f(a,a)
    | f(f(f(n3,n2),u2),a) != f(a,f(f(n3,n2),u2))
    | f(f(f(n3,n2),u2),a) = f(a,a) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(f(n3,n2),u2),a))),bind(Y0,$fot(f(a,f(f(n3,n2),u2)))),bind(Z0,$fot(f(a,a)))]]) ).

cnf(refute_0_244,plain,
    ( f(a,f(f(n3,n2),u2)) != f(a,a)
    | f(f(f(n3,n2),u2),a) = f(a,a) ),
    inference(resolve,[$cnf( $equal(f(f(f(n3,n2),u2),a),f(a,f(f(n3,n2),u2))) )],[refute_0_242,refute_0_243]) ).

cnf(refute_0_245,plain,
    f(f(f(n3,n2),u2),a) = f(a,a),
    inference(resolve,[$cnf( $equal(f(a,f(f(n3,n2),u2)),f(a,a)) )],[refute_0_231,refute_0_244]) ).

cnf(refute_0_246,plain,
    ( f(f(f(n3,n2),u2),a) != f(a,a)
    | v != f(f(f(n3,n2),u2),a)
    | v = f(a,a) ),
    introduced(tautology,[equality,[$cnf( $equal(v,f(f(f(n3,n2),u2),a)) ),[1],$fot(f(a,a))]]) ).

cnf(refute_0_247,plain,
    ( v != f(f(f(n3,n2),u2),a)
    | v = f(a,a) ),
    inference(resolve,[$cnf( $equal(f(f(f(n3,n2),u2),a),f(a,a)) )],[refute_0_245,refute_0_246]) ).

cnf(refute_0_248,plain,
    ( f(f(n3,n2),uu) != f(f(f(n3,n2),u2),a)
    | v = f(a,a) ),
    inference(resolve,[$cnf( $equal(v,f(f(f(n3,n2),u2),a)) )],[refute_0_227,refute_0_247]) ).

cnf(refute_0_249,plain,
    v = f(a,a),
    inference(resolve,[$cnf( $equal(f(f(n3,n2),uu),f(f(f(n3,n2),u2),a)) )],[refute_0_65,refute_0_248]) ).

cnf(refute_0_250,plain,
    ( v != f(a,a)
    | f(a,a) = v ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(v)),bind(Y0,$fot(f(a,a)))]]) ).

cnf(refute_0_251,plain,
    f(a,a) = v,
    inference(resolve,[$cnf( $equal(v,f(a,a)) )],[refute_0_249,refute_0_250]) ).

cnf(refute_0_252,plain,
    ( f(a,a) != v
    | f(a,f(a,Z)) != f(f(a,a),f(a,Z))
    | f(a,f(a,Z)) = f(v,f(a,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(a,f(a,Z)),f(f(a,a),f(a,Z))) ),[1,0],$fot(v)]]) ).

cnf(refute_0_253,plain,
    ( f(a,f(a,Z)) != f(f(a,a),f(a,Z))
    | f(a,f(a,Z)) = f(v,f(a,Z)) ),
    inference(resolve,[$cnf( $equal(f(a,a),v) )],[refute_0_251,refute_0_252]) ).

cnf(refute_0_254,plain,
    f(a,f(a,Z)) = f(v,f(a,Z)),
    inference(resolve,[$cnf( $equal(f(a,f(a,Z)),f(f(a,a),f(a,Z))) )],[refute_0_0,refute_0_253]) ).

cnf(refute_0_255,plain,
    f(a,f(a,a)) = f(v,f(a,a)),
    inference(subst,[],[refute_0_254:[bind(Z,$fot(a))]]) ).

cnf(refute_0_256,plain,
    ( f(a,a) != v
    | f(a,f(a,a)) != f(v,f(a,a))
    | f(a,f(a,a)) = f(v,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(a,f(a,a)),f(v,f(a,a))) ),[1,1],$fot(v)]]) ).

cnf(refute_0_257,plain,
    ( f(a,f(a,a)) != f(v,f(a,a))
    | f(a,f(a,a)) = f(v,v) ),
    inference(resolve,[$cnf( $equal(f(a,a),v) )],[refute_0_251,refute_0_256]) ).

cnf(refute_0_258,plain,
    f(a,f(a,a)) = f(v,v),
    inference(resolve,[$cnf( $equal(f(a,f(a,a)),f(v,f(a,a))) )],[refute_0_255,refute_0_257]) ).

cnf(refute_0_259,plain,
    f(a,f(a,a)) = f(a,f(a,a)),
    introduced(tautology,[refl,[$fot(f(a,f(a,a)))]]) ).

cnf(refute_0_260,plain,
    ( f(a,a) != v
    | f(a,f(a,a)) != f(a,f(a,a))
    | f(a,f(a,a)) = f(a,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(a,f(a,a)),f(a,f(a,a))) ),[1,1],$fot(v)]]) ).

cnf(refute_0_261,plain,
    ( f(a,a) != v
    | f(a,f(a,a)) = f(a,v) ),
    inference(resolve,[$cnf( $equal(f(a,f(a,a)),f(a,f(a,a))) )],[refute_0_259,refute_0_260]) ).

cnf(refute_0_262,plain,
    f(a,f(a,a)) = f(a,v),
    inference(resolve,[$cnf( $equal(f(a,a),v) )],[refute_0_251,refute_0_261]) ).

cnf(refute_0_263,plain,
    ( f(a,f(a,a)) != f(a,v)
    | f(a,f(a,a)) != f(v,v)
    | f(a,v) = f(v,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(a,f(a,a)),f(v,v)) ),[0],$fot(f(a,v))]]) ).

cnf(refute_0_264,plain,
    ( f(a,f(a,a)) != f(v,v)
    | f(a,v) = f(v,v) ),
    inference(resolve,[$cnf( $equal(f(a,f(a,a)),f(a,v)) )],[refute_0_262,refute_0_263]) ).

cnf(refute_0_265,plain,
    f(uu,f(uu,X_2)) = f(f(uu,uu),f(uu,X_2)),
    inference(subst,[],[a1:[bind(X,$fot(uu)),bind(Y,$fot(uu)),bind(Z,$fot(X_2))]]) ).

cnf(refute_0_266,plain,
    ( f(uu,f(uu,X_2)) != f(f(uu,uu),f(uu,X_2))
    | f(uu,uu) != v
    | f(uu,f(uu,X_2)) = f(v,f(uu,X_2)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,f(uu,X_2)),f(f(uu,uu),f(uu,X_2))) ),[1,0],$fot(v)]]) ).

cnf(refute_0_267,plain,
    ( f(uu,f(uu,X_2)) != f(f(uu,uu),f(uu,X_2))
    | f(uu,f(uu,X_2)) = f(v,f(uu,X_2)) ),
    inference(resolve,[$cnf( $equal(f(uu,uu),v) )],[refute_0_141,refute_0_266]) ).

cnf(refute_0_268,plain,
    f(uu,f(uu,X_2)) = f(v,f(uu,X_2)),
    inference(resolve,[$cnf( $equal(f(uu,f(uu,X_2)),f(f(uu,uu),f(uu,X_2))) )],[refute_0_265,refute_0_267]) ).

cnf(refute_0_269,plain,
    f(uu,f(uu,uu)) = f(v,f(uu,uu)),
    inference(subst,[],[refute_0_268:[bind(X_2,$fot(uu))]]) ).

cnf(refute_0_270,plain,
    ( f(uu,f(uu,uu)) != f(v,f(uu,uu))
    | f(uu,uu) != v
    | f(uu,f(uu,uu)) = f(v,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,f(uu,uu)),f(v,f(uu,uu))) ),[1,1],$fot(v)]]) ).

cnf(refute_0_271,plain,
    ( f(uu,f(uu,uu)) != f(v,f(uu,uu))
    | f(uu,f(uu,uu)) = f(v,v) ),
    inference(resolve,[$cnf( $equal(f(uu,uu),v) )],[refute_0_141,refute_0_270]) ).

cnf(refute_0_272,plain,
    f(uu,f(uu,uu)) = f(v,v),
    inference(resolve,[$cnf( $equal(f(uu,f(uu,uu)),f(v,f(uu,uu))) )],[refute_0_269,refute_0_271]) ).

cnf(refute_0_273,plain,
    f(u,f(u,uu)) = f(uu,f(u,uu)),
    inference(subst,[],[refute_0_129:[bind(X_2,$fot(uu))]]) ).

cnf(refute_0_274,plain,
    ( f(u,f(u,uu)) != f(uu,f(u,uu))
    | f(u,uu) != v
    | f(u,f(u,uu)) = f(uu,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,uu)),f(uu,f(u,uu))) ),[1,1],$fot(v)]]) ).

cnf(refute_0_275,plain,
    ( f(u,f(u,uu)) != f(uu,f(u,uu))
    | f(u,f(u,uu)) = f(uu,v) ),
    inference(resolve,[$cnf( $equal(f(u,uu),v) )],[refute_0_145,refute_0_274]) ).

cnf(refute_0_276,plain,
    f(u,f(u,uu)) = f(uu,v),
    inference(resolve,[$cnf( $equal(f(u,f(u,uu)),f(uu,f(u,uu))) )],[refute_0_273,refute_0_275]) ).

cnf(refute_0_277,plain,
    f(u,f(u,uu)) = f(u,f(u,uu)),
    introduced(tautology,[refl,[$fot(f(u,f(u,uu)))]]) ).

cnf(refute_0_278,plain,
    ( f(u,f(u,uu)) != f(u,f(u,uu))
    | f(u,uu) != v
    | f(u,f(u,uu)) = f(u,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,uu)),f(u,f(u,uu))) ),[1,1],$fot(v)]]) ).

cnf(refute_0_279,plain,
    ( f(u,uu) != v
    | f(u,f(u,uu)) = f(u,v) ),
    inference(resolve,[$cnf( $equal(f(u,f(u,uu)),f(u,f(u,uu))) )],[refute_0_277,refute_0_278]) ).

cnf(refute_0_280,plain,
    f(u,f(u,uu)) = f(u,v),
    inference(resolve,[$cnf( $equal(f(u,uu),v) )],[refute_0_145,refute_0_279]) ).

cnf(refute_0_281,plain,
    ( f(u,f(u,uu)) != f(u,v)
    | f(u,f(u,uu)) != f(uu,v)
    | f(u,v) = f(uu,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,uu)),f(uu,v)) ),[0],$fot(f(u,v))]]) ).

cnf(refute_0_282,plain,
    ( f(u,f(u,uu)) != f(uu,v)
    | f(u,v) = f(uu,v) ),
    inference(resolve,[$cnf( $equal(f(u,f(u,uu)),f(u,v)) )],[refute_0_280,refute_0_281]) ).

cnf(refute_0_283,plain,
    f(u,v) = f(uu,v),
    inference(resolve,[$cnf( $equal(f(u,f(u,uu)),f(uu,v)) )],[refute_0_276,refute_0_282]) ).

cnf(refute_0_284,plain,
    ( f(u,v) != f(uu,v)
    | f(uu,v) = f(u,v) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(u,v))),bind(Y0,$fot(f(uu,v)))]]) ).

cnf(refute_0_285,plain,
    f(uu,v) = f(u,v),
    inference(resolve,[$cnf( $equal(f(u,v),f(uu,v)) )],[refute_0_283,refute_0_284]) ).

cnf(refute_0_286,plain,
    f(uu,f(uu,uu)) = f(uu,f(uu,uu)),
    introduced(tautology,[refl,[$fot(f(uu,f(uu,uu)))]]) ).

cnf(refute_0_287,plain,
    ( f(uu,f(uu,uu)) != f(uu,f(uu,uu))
    | f(uu,uu) != v
    | f(uu,f(uu,uu)) = f(uu,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,f(uu,uu)),f(uu,f(uu,uu))) ),[1,1],$fot(v)]]) ).

cnf(refute_0_288,plain,
    ( f(uu,uu) != v
    | f(uu,f(uu,uu)) = f(uu,v) ),
    inference(resolve,[$cnf( $equal(f(uu,f(uu,uu)),f(uu,f(uu,uu))) )],[refute_0_286,refute_0_287]) ).

cnf(refute_0_289,plain,
    f(uu,f(uu,uu)) = f(uu,v),
    inference(resolve,[$cnf( $equal(f(uu,uu),v) )],[refute_0_141,refute_0_288]) ).

cnf(refute_0_290,plain,
    ( f(uu,f(uu,uu)) != f(uu,v)
    | f(uu,v) != f(u,v)
    | f(uu,f(uu,uu)) = f(u,v) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(uu,f(uu,uu)))),bind(Y0,$fot(f(uu,v))),bind(Z0,$fot(f(u,v)))]]) ).

cnf(refute_0_291,plain,
    ( f(uu,v) != f(u,v)
    | f(uu,f(uu,uu)) = f(u,v) ),
    inference(resolve,[$cnf( $equal(f(uu,f(uu,uu)),f(uu,v)) )],[refute_0_289,refute_0_290]) ).

cnf(refute_0_292,plain,
    f(uu,f(uu,uu)) = f(u,v),
    inference(resolve,[$cnf( $equal(f(uu,v),f(u,v)) )],[refute_0_285,refute_0_291]) ).

cnf(refute_0_293,plain,
    ( f(uu,f(uu,uu)) != f(u,v)
    | f(uu,f(uu,uu)) != f(v,v)
    | f(u,v) = f(v,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,f(uu,uu)),f(v,v)) ),[0],$fot(f(u,v))]]) ).

cnf(refute_0_294,plain,
    ( f(uu,f(uu,uu)) != f(v,v)
    | f(u,v) = f(v,v) ),
    inference(resolve,[$cnf( $equal(f(uu,f(uu,uu)),f(u,v)) )],[refute_0_292,refute_0_293]) ).

cnf(refute_0_295,plain,
    f(u,v) = f(v,v),
    inference(resolve,[$cnf( $equal(f(uu,f(uu,uu)),f(v,v)) )],[refute_0_272,refute_0_294]) ).

cnf(refute_0_296,plain,
    f(uu,f(X_1,uu)) = f(f(uu,X_1),f(uu,uu)),
    inference(subst,[],[a1:[bind(X,$fot(uu)),bind(Y,$fot(X_1)),bind(Z,$fot(uu))]]) ).

cnf(refute_0_297,plain,
    ( f(uu,f(X_1,uu)) != f(f(uu,X_1),f(uu,uu))
    | f(uu,uu) != v
    | f(uu,f(X_1,uu)) = f(f(uu,X_1),v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,f(X_1,uu)),f(f(uu,X_1),f(uu,uu))) ),[1,1],$fot(v)]]) ).

cnf(refute_0_298,plain,
    ( f(uu,f(X_1,uu)) != f(f(uu,X_1),f(uu,uu))
    | f(uu,f(X_1,uu)) = f(f(uu,X_1),v) ),
    inference(resolve,[$cnf( $equal(f(uu,uu),v) )],[refute_0_141,refute_0_297]) ).

cnf(refute_0_299,plain,
    f(uu,f(X_1,uu)) = f(f(uu,X_1),v),
    inference(resolve,[$cnf( $equal(f(uu,f(X_1,uu)),f(f(uu,X_1),f(uu,uu))) )],[refute_0_296,refute_0_298]) ).

cnf(refute_0_300,plain,
    f(uu,f(n1,uu)) = f(f(uu,n1),v),
    inference(subst,[],[refute_0_299:[bind(X_1,$fot(n1))]]) ).

cnf(refute_0_301,plain,
    ( f(n1,uu) != v
    | f(uu,f(n1,uu)) != f(f(uu,n1),v)
    | f(uu,v) = f(f(uu,n1),v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,f(n1,uu)),f(f(uu,n1),v)) ),[0,1],$fot(v)]]) ).

cnf(refute_0_302,plain,
    ( f(uu,f(n1,uu)) != f(f(uu,n1),v)
    | f(uu,v) = f(f(uu,n1),v) ),
    inference(resolve,[$cnf( $equal(f(n1,uu),v) )],[refute_0_167,refute_0_301]) ).

cnf(refute_0_303,plain,
    f(uu,v) = f(f(uu,n1),v),
    inference(resolve,[$cnf( $equal(f(uu,f(n1,uu)),f(f(uu,n1),v)) )],[refute_0_300,refute_0_302]) ).

cnf(refute_0_304,plain,
    ( f(uu,v) != f(f(uu,n1),v)
    | f(uu,v) != f(u,v)
    | f(u,v) = f(f(uu,n1),v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,v),f(f(uu,n1),v)) ),[0],$fot(f(u,v))]]) ).

cnf(refute_0_305,plain,
    ( f(uu,v) != f(f(uu,n1),v)
    | f(u,v) = f(f(uu,n1),v) ),
    inference(resolve,[$cnf( $equal(f(uu,v),f(u,v)) )],[refute_0_285,refute_0_304]) ).

cnf(refute_0_306,plain,
    f(n1,f(u,uu)) = f(n1,f(u,uu)),
    introduced(tautology,[refl,[$fot(f(n1,f(u,uu)))]]) ).

cnf(refute_0_307,plain,
    ( f(n1,f(u,uu)) != f(n1,f(u,uu))
    | f(u,uu) != v
    | f(n1,f(u,uu)) = f(n1,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(u,uu)),f(n1,f(u,uu))) ),[1,1],$fot(v)]]) ).

cnf(refute_0_308,plain,
    ( f(u,uu) != v
    | f(n1,f(u,uu)) = f(n1,v) ),
    inference(resolve,[$cnf( $equal(f(n1,f(u,uu)),f(n1,f(u,uu))) )],[refute_0_306,refute_0_307]) ).

cnf(refute_0_309,plain,
    f(n1,f(u,uu)) = f(n1,v),
    inference(resolve,[$cnf( $equal(f(u,uu),v) )],[refute_0_145,refute_0_308]) ).

cnf(refute_0_310,plain,
    f(n1,f(u,Z)) = f(f(n1,u),f(n1,Z)),
    inference(subst,[],[a1:[bind(X,$fot(n1)),bind(Y,$fot(u))]]) ).

cnf(refute_0_311,plain,
    ( f(n1,f(u,Z)) != f(f(n1,u),f(n1,Z))
    | f(n1,u) != uu
    | f(n1,f(u,Z)) = f(uu,f(n1,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(u,Z)),f(f(n1,u),f(n1,Z))) ),[1,0],$fot(uu)]]) ).

cnf(refute_0_312,plain,
    ( f(n1,f(u,Z)) != f(f(n1,u),f(n1,Z))
    | f(n1,f(u,Z)) = f(uu,f(n1,Z)) ),
    inference(resolve,[$cnf( $equal(f(n1,u),uu) )],[refute_0_122,refute_0_311]) ).

cnf(refute_0_313,plain,
    f(n1,f(u,Z)) = f(uu,f(n1,Z)),
    inference(resolve,[$cnf( $equal(f(n1,f(u,Z)),f(f(n1,u),f(n1,Z))) )],[refute_0_310,refute_0_312]) ).

cnf(refute_0_314,plain,
    ( f(n1,f(u,Z)) != f(uu,f(n1,Z))
    | f(uu,f(n1,Z)) = f(n1,f(u,Z)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(n1,f(u,Z)))),bind(Y0,$fot(f(uu,f(n1,Z))))]]) ).

cnf(refute_0_315,plain,
    f(uu,f(n1,Z)) = f(n1,f(u,Z)),
    inference(resolve,[$cnf( $equal(f(n1,f(u,Z)),f(uu,f(n1,Z))) )],[refute_0_313,refute_0_314]) ).

cnf(refute_0_316,plain,
    f(uu,f(n1,uu)) = f(n1,f(u,uu)),
    inference(subst,[],[refute_0_315:[bind(Z,$fot(uu))]]) ).

cnf(refute_0_317,plain,
    ( f(uu,f(X_1,uu)) != f(f(uu,X_1),v)
    | f(f(uu,X_1),v) = f(uu,f(X_1,uu)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(uu,f(X_1,uu)))),bind(Y0,$fot(f(f(uu,X_1),v)))]]) ).

cnf(refute_0_318,plain,
    f(f(uu,X_1),v) = f(uu,f(X_1,uu)),
    inference(resolve,[$cnf( $equal(f(uu,f(X_1,uu)),f(f(uu,X_1),v)) )],[refute_0_299,refute_0_317]) ).

cnf(refute_0_319,plain,
    f(f(uu,n1),v) = f(uu,f(n1,uu)),
    inference(subst,[],[refute_0_318:[bind(X_1,$fot(n1))]]) ).

cnf(refute_0_320,plain,
    ( f(f(uu,n1),v) != f(uu,f(n1,uu))
    | f(uu,f(n1,uu)) != f(n1,f(u,uu))
    | f(f(uu,n1),v) = f(n1,f(u,uu)) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(uu,n1),v))),bind(Y0,$fot(f(uu,f(n1,uu)))),bind(Z0,$fot(f(n1,f(u,uu))))]]) ).

cnf(refute_0_321,plain,
    ( f(uu,f(n1,uu)) != f(n1,f(u,uu))
    | f(f(uu,n1),v) = f(n1,f(u,uu)) ),
    inference(resolve,[$cnf( $equal(f(f(uu,n1),v),f(uu,f(n1,uu))) )],[refute_0_319,refute_0_320]) ).

cnf(refute_0_322,plain,
    f(f(uu,n1),v) = f(n1,f(u,uu)),
    inference(resolve,[$cnf( $equal(f(uu,f(n1,uu)),f(n1,f(u,uu))) )],[refute_0_316,refute_0_321]) ).

cnf(refute_0_323,plain,
    ( f(f(uu,n1),v) != f(n1,f(u,uu))
    | f(n1,f(u,uu)) != f(n1,v)
    | f(f(uu,n1),v) = f(n1,v) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(uu,n1),v))),bind(Y0,$fot(f(n1,f(u,uu)))),bind(Z0,$fot(f(n1,v)))]]) ).

cnf(refute_0_324,plain,
    ( f(n1,f(u,uu)) != f(n1,v)
    | f(f(uu,n1),v) = f(n1,v) ),
    inference(resolve,[$cnf( $equal(f(f(uu,n1),v),f(n1,f(u,uu))) )],[refute_0_322,refute_0_323]) ).

cnf(refute_0_325,plain,
    f(f(uu,n1),v) = f(n1,v),
    inference(resolve,[$cnf( $equal(f(n1,f(u,uu)),f(n1,v)) )],[refute_0_309,refute_0_324]) ).

cnf(refute_0_326,plain,
    ( f(f(uu,n1),v) != f(n1,v)
    | f(u,v) != f(f(uu,n1),v)
    | f(u,v) = f(n1,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,v),f(f(uu,n1),v)) ),[1],$fot(f(n1,v))]]) ).

cnf(refute_0_327,plain,
    ( f(u,v) != f(f(uu,n1),v)
    | f(u,v) = f(n1,v) ),
    inference(resolve,[$cnf( $equal(f(f(uu,n1),v),f(n1,v)) )],[refute_0_325,refute_0_326]) ).

cnf(refute_0_328,plain,
    ( f(uu,v) != f(f(uu,n1),v)
    | f(u,v) = f(n1,v) ),
    inference(resolve,[$cnf( $equal(f(u,v),f(f(uu,n1),v)) )],[refute_0_305,refute_0_327]) ).

cnf(refute_0_329,plain,
    f(u,v) = f(n1,v),
    inference(resolve,[$cnf( $equal(f(uu,v),f(f(uu,n1),v)) )],[refute_0_303,refute_0_328]) ).

cnf(refute_0_330,plain,
    f(uu,f(u2,uu)) = f(f(uu,u2),v),
    inference(subst,[],[refute_0_299:[bind(X_1,$fot(u2))]]) ).

cnf(refute_0_331,plain,
    f(u,f(n2,u)) = f(f(u,n2),uu),
    inference(subst,[],[refute_0_69:[bind(X_1,$fot(n2))]]) ).

cnf(refute_0_332,plain,
    ( f(u,f(n2,u)) != f(f(u,n2),uu)
    | f(u,n2) != u2
    | f(u,f(n2,u)) = f(u2,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n2,u)),f(f(u,n2),uu)) ),[1,0],$fot(u2)]]) ).

cnf(refute_0_333,plain,
    ( f(u,f(n2,u)) != f(f(u,n2),uu)
    | f(u,f(n2,u)) = f(u2,uu) ),
    inference(resolve,[$cnf( $equal(f(u,n2),u2) )],[refute_0_13,refute_0_332]) ).

cnf(refute_0_334,plain,
    f(u,f(n2,u)) = f(u2,uu),
    inference(resolve,[$cnf( $equal(f(u,f(n2,u)),f(f(u,n2),uu)) )],[refute_0_331,refute_0_333]) ).

cnf(refute_0_335,plain,
    ( f(n2,u) != uu
    | f(u,f(n2,u)) != f(f(u,n2),uu)
    | f(u,uu) = f(f(u,n2),uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n2,u)),f(f(u,n2),uu)) ),[0,1],$fot(uu)]]) ).

cnf(refute_0_336,plain,
    ( f(u,f(n2,u)) != f(f(u,n2),uu)
    | f(u,uu) = f(f(u,n2),uu) ),
    inference(resolve,[$cnf( $equal(f(n2,u),uu) )],[refute_0_42,refute_0_335]) ).

cnf(refute_0_337,plain,
    f(u,uu) = f(f(u,n2),uu),
    inference(resolve,[$cnf( $equal(f(u,f(n2,u)),f(f(u,n2),uu)) )],[refute_0_331,refute_0_336]) ).

cnf(refute_0_338,plain,
    ( f(u,uu) != f(f(u,n2),uu)
    | f(u,uu) != v
    | v = f(f(u,n2),uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,uu),f(f(u,n2),uu)) ),[0],$fot(v)]]) ).

cnf(refute_0_339,plain,
    ( f(u,uu) != f(f(u,n2),uu)
    | v = f(f(u,n2),uu) ),
    inference(resolve,[$cnf( $equal(f(u,uu),v) )],[refute_0_145,refute_0_338]) ).

cnf(refute_0_340,plain,
    f(n2,f(n2,u)) = f(n2,f(n2,u)),
    introduced(tautology,[refl,[$fot(f(n2,f(n2,u)))]]) ).

cnf(refute_0_341,plain,
    ( f(n2,f(n2,u)) != f(n2,f(n2,u))
    | f(n2,u) != uu
    | f(n2,f(n2,u)) = f(n2,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n2,f(n2,u)),f(n2,f(n2,u))) ),[1,1],$fot(uu)]]) ).

cnf(refute_0_342,plain,
    ( f(n2,u) != uu
    | f(n2,f(n2,u)) = f(n2,uu) ),
    inference(resolve,[$cnf( $equal(f(n2,f(n2,u)),f(n2,f(n2,u))) )],[refute_0_340,refute_0_341]) ).

cnf(refute_0_343,plain,
    f(n2,f(n2,u)) = f(n2,uu),
    inference(resolve,[$cnf( $equal(f(n2,u),uu) )],[refute_0_42,refute_0_342]) ).

cnf(refute_0_344,plain,
    f(u,f(n2,u)) = f(n2,f(n2,u)),
    inference(subst,[],[refute_0_53:[bind(X_2,$fot(u))]]) ).

cnf(refute_0_345,plain,
    f(f(u,n2),uu) = f(u,f(n2,u)),
    inference(subst,[],[refute_0_154:[bind(X_1,$fot(n2))]]) ).

cnf(refute_0_346,plain,
    ( f(f(u,n2),uu) != f(u,f(n2,u))
    | f(u,f(n2,u)) != f(n2,f(n2,u))
    | f(f(u,n2),uu) = f(n2,f(n2,u)) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(u,n2),uu))),bind(Y0,$fot(f(u,f(n2,u)))),bind(Z0,$fot(f(n2,f(n2,u))))]]) ).

cnf(refute_0_347,plain,
    ( f(u,f(n2,u)) != f(n2,f(n2,u))
    | f(f(u,n2),uu) = f(n2,f(n2,u)) ),
    inference(resolve,[$cnf( $equal(f(f(u,n2),uu),f(u,f(n2,u))) )],[refute_0_345,refute_0_346]) ).

cnf(refute_0_348,plain,
    f(f(u,n2),uu) = f(n2,f(n2,u)),
    inference(resolve,[$cnf( $equal(f(u,f(n2,u)),f(n2,f(n2,u))) )],[refute_0_344,refute_0_347]) ).

cnf(refute_0_349,plain,
    ( f(f(u,n2),uu) != f(n2,f(n2,u))
    | f(n2,f(n2,u)) != f(n2,uu)
    | f(f(u,n2),uu) = f(n2,uu) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(u,n2),uu))),bind(Y0,$fot(f(n2,f(n2,u)))),bind(Z0,$fot(f(n2,uu)))]]) ).

cnf(refute_0_350,plain,
    ( f(n2,f(n2,u)) != f(n2,uu)
    | f(f(u,n2),uu) = f(n2,uu) ),
    inference(resolve,[$cnf( $equal(f(f(u,n2),uu),f(n2,f(n2,u))) )],[refute_0_348,refute_0_349]) ).

cnf(refute_0_351,plain,
    f(f(u,n2),uu) = f(n2,uu),
    inference(resolve,[$cnf( $equal(f(n2,f(n2,u)),f(n2,uu)) )],[refute_0_343,refute_0_350]) ).

cnf(refute_0_352,plain,
    ( f(f(u,n2),uu) != f(n2,uu)
    | v != f(f(u,n2),uu)
    | v = f(n2,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(v,f(f(u,n2),uu)) ),[1],$fot(f(n2,uu))]]) ).

cnf(refute_0_353,plain,
    ( v != f(f(u,n2),uu)
    | v = f(n2,uu) ),
    inference(resolve,[$cnf( $equal(f(f(u,n2),uu),f(n2,uu)) )],[refute_0_351,refute_0_352]) ).

cnf(refute_0_354,plain,
    ( f(u,uu) != f(f(u,n2),uu)
    | v = f(n2,uu) ),
    inference(resolve,[$cnf( $equal(v,f(f(u,n2),uu)) )],[refute_0_339,refute_0_353]) ).

cnf(refute_0_355,plain,
    v = f(n2,uu),
    inference(resolve,[$cnf( $equal(f(u,uu),f(f(u,n2),uu)) )],[refute_0_337,refute_0_354]) ).

cnf(refute_0_356,plain,
    ( v != f(n2,uu)
    | f(n2,uu) = v ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(v)),bind(Y0,$fot(f(n2,uu)))]]) ).

cnf(refute_0_357,plain,
    f(n2,uu) = v,
    inference(resolve,[$cnf( $equal(v,f(n2,uu)) )],[refute_0_355,refute_0_356]) ).

cnf(refute_0_358,plain,
    ( f(n2,f(n2,u)) != f(n2,uu)
    | f(n2,uu) != v
    | f(n2,f(n2,u)) = v ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(n2,f(n2,u)))),bind(Y0,$fot(f(n2,uu))),bind(Z0,$fot(v))]]) ).

cnf(refute_0_359,plain,
    ( f(n2,uu) != v
    | f(n2,f(n2,u)) = v ),
    inference(resolve,[$cnf( $equal(f(n2,f(n2,u)),f(n2,uu)) )],[refute_0_343,refute_0_358]) ).

cnf(refute_0_360,plain,
    f(n2,f(n2,u)) = v,
    inference(resolve,[$cnf( $equal(f(n2,uu),v) )],[refute_0_357,refute_0_359]) ).

cnf(refute_0_361,plain,
    ( f(n2,f(n2,u)) != v
    | f(u,f(n2,u)) != f(n2,f(n2,u))
    | f(u,f(n2,u)) = v ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(u,f(n2,u)))),bind(Y0,$fot(f(n2,f(n2,u)))),bind(Z0,$fot(v))]]) ).

cnf(refute_0_362,plain,
    ( f(n2,f(n2,u)) != v
    | f(u,f(n2,u)) = v ),
    inference(resolve,[$cnf( $equal(f(u,f(n2,u)),f(n2,f(n2,u))) )],[refute_0_344,refute_0_361]) ).

cnf(refute_0_363,plain,
    f(u,f(n2,u)) = v,
    inference(resolve,[$cnf( $equal(f(n2,f(n2,u)),v) )],[refute_0_360,refute_0_362]) ).

cnf(refute_0_364,plain,
    ( f(u,f(n2,u)) != f(u2,uu)
    | f(u,f(n2,u)) != v
    | v = f(u2,uu) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n2,u)),f(u2,uu)) ),[0],$fot(v)]]) ).

cnf(refute_0_365,plain,
    ( f(u,f(n2,u)) != f(u2,uu)
    | v = f(u2,uu) ),
    inference(resolve,[$cnf( $equal(f(u,f(n2,u)),v) )],[refute_0_363,refute_0_364]) ).

cnf(refute_0_366,plain,
    v = f(u2,uu),
    inference(resolve,[$cnf( $equal(f(u,f(n2,u)),f(u2,uu)) )],[refute_0_334,refute_0_365]) ).

cnf(refute_0_367,plain,
    ( v != f(u2,uu)
    | f(u2,uu) = v ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(v)),bind(Y0,$fot(f(u2,uu)))]]) ).

cnf(refute_0_368,plain,
    f(u2,uu) = v,
    inference(resolve,[$cnf( $equal(v,f(u2,uu)) )],[refute_0_366,refute_0_367]) ).

cnf(refute_0_369,plain,
    ( f(u2,uu) != v
    | f(uu,f(u2,uu)) != f(f(uu,u2),v)
    | f(uu,v) = f(f(uu,u2),v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,f(u2,uu)),f(f(uu,u2),v)) ),[0,1],$fot(v)]]) ).

cnf(refute_0_370,plain,
    ( f(uu,f(u2,uu)) != f(f(uu,u2),v)
    | f(uu,v) = f(f(uu,u2),v) ),
    inference(resolve,[$cnf( $equal(f(u2,uu),v) )],[refute_0_368,refute_0_369]) ).

cnf(refute_0_371,plain,
    f(uu,v) = f(f(uu,u2),v),
    inference(resolve,[$cnf( $equal(f(uu,f(u2,uu)),f(f(uu,u2),v)) )],[refute_0_330,refute_0_370]) ).

cnf(refute_0_372,plain,
    ( f(u,v) != f(n1,v)
    | f(uu,v) != f(u,v)
    | f(uu,v) = f(n1,v) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(uu,v))),bind(Y0,$fot(f(u,v))),bind(Z0,$fot(f(n1,v)))]]) ).

cnf(refute_0_373,plain,
    ( f(u,v) != f(n1,v)
    | f(uu,v) = f(n1,v) ),
    inference(resolve,[$cnf( $equal(f(uu,v),f(u,v)) )],[refute_0_285,refute_0_372]) ).

cnf(refute_0_374,plain,
    f(uu,v) = f(n1,v),
    inference(resolve,[$cnf( $equal(f(u,v),f(n1,v)) )],[refute_0_329,refute_0_373]) ).

cnf(refute_0_375,plain,
    ( f(uu,v) != f(f(uu,u2),v)
    | f(uu,v) != f(n1,v)
    | f(n1,v) = f(f(uu,u2),v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,v),f(f(uu,u2),v)) ),[0],$fot(f(n1,v))]]) ).

cnf(refute_0_376,plain,
    ( f(uu,v) != f(f(uu,u2),v)
    | f(n1,v) = f(f(uu,u2),v) ),
    inference(resolve,[$cnf( $equal(f(uu,v),f(n1,v)) )],[refute_0_374,refute_0_375]) ).

cnf(refute_0_377,plain,
    f(b,f(uu,uu)) = f(b,f(uu,uu)),
    introduced(tautology,[refl,[$fot(f(b,f(uu,uu)))]]) ).

cnf(refute_0_378,plain,
    ( f(b,f(uu,uu)) != f(b,f(uu,uu))
    | f(uu,uu) != v
    | f(b,f(uu,uu)) = f(b,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(b,f(uu,uu)),f(b,f(uu,uu))) ),[1,1],$fot(v)]]) ).

cnf(refute_0_379,plain,
    ( f(uu,uu) != v
    | f(b,f(uu,uu)) = f(b,v) ),
    inference(resolve,[$cnf( $equal(f(b,f(uu,uu)),f(b,f(uu,uu))) )],[refute_0_377,refute_0_378]) ).

cnf(refute_0_380,plain,
    f(b,f(uu,uu)) = f(b,v),
    inference(resolve,[$cnf( $equal(f(uu,uu),v) )],[refute_0_141,refute_0_379]) ).

cnf(refute_0_381,plain,
    f(u2,f(u2,Z)) = f(f(u2,u2),f(u2,Z)),
    inference(subst,[],[a1:[bind(X,$fot(u2)),bind(Y,$fot(u2))]]) ).

cnf(refute_0_382,plain,
    ( f(u2,f(u2,Z)) != f(f(u2,u2),f(u2,Z))
    | f(u2,u2) != uu
    | f(u2,f(u2,Z)) = f(uu,f(u2,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u2,f(u2,Z)),f(f(u2,u2),f(u2,Z))) ),[1,0],$fot(uu)]]) ).

cnf(refute_0_383,plain,
    ( f(u2,f(u2,Z)) != f(f(u2,u2),f(u2,Z))
    | f(u2,f(u2,Z)) = f(uu,f(u2,Z)) ),
    inference(resolve,[$cnf( $equal(f(u2,u2),uu) )],[refute_0_62,refute_0_382]) ).

cnf(refute_0_384,plain,
    f(u2,f(u2,Z)) = f(uu,f(u2,Z)),
    inference(resolve,[$cnf( $equal(f(u2,f(u2,Z)),f(f(u2,u2),f(u2,Z))) )],[refute_0_381,refute_0_383]) ).

cnf(refute_0_385,plain,
    f(uu,f(u2,Z)) = f(f(uu,u2),f(uu,Z)),
    inference(subst,[],[a1:[bind(X,$fot(uu)),bind(Y,$fot(u2))]]) ).

cnf(refute_0_386,plain,
    f(u,f(u,n2)) = f(f(u,u),u2),
    inference(subst,[],[refute_0_16:[bind(X_1,$fot(u))]]) ).

cnf(refute_0_387,plain,
    ( f(u,f(u,n2)) != f(f(u,u),u2)
    | f(u,u) != uu
    | f(u,f(u,n2)) = f(uu,u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,n2)),f(f(u,u),u2)) ),[1,0],$fot(uu)]]) ).

cnf(refute_0_388,plain,
    ( f(u,f(u,n2)) != f(f(u,u),u2)
    | f(u,f(u,n2)) = f(uu,u2) ),
    inference(resolve,[$cnf( $equal(f(u,u),uu) )],[refute_0_38,refute_0_387]) ).

cnf(refute_0_389,plain,
    f(u,f(u,n2)) = f(uu,u2),
    inference(resolve,[$cnf( $equal(f(u,f(u,n2)),f(f(u,u),u2)) )],[refute_0_386,refute_0_388]) ).

cnf(refute_0_390,plain,
    f(u,f(u,n2)) = f(u,f(u,n2)),
    introduced(tautology,[refl,[$fot(f(u,f(u,n2)))]]) ).

cnf(refute_0_391,plain,
    ( f(u,f(u,n2)) != f(u,f(u,n2))
    | f(u,n2) != u2
    | f(u,f(u,n2)) = f(u,u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,n2)),f(u,f(u,n2))) ),[1,1],$fot(u2)]]) ).

cnf(refute_0_392,plain,
    ( f(u,n2) != u2
    | f(u,f(u,n2)) = f(u,u2) ),
    inference(resolve,[$cnf( $equal(f(u,f(u,n2)),f(u,f(u,n2))) )],[refute_0_390,refute_0_391]) ).

cnf(refute_0_393,plain,
    f(u,f(u,n2)) = f(u,u2),
    inference(resolve,[$cnf( $equal(f(u,n2),u2) )],[refute_0_13,refute_0_392]) ).

cnf(refute_0_394,plain,
    ( f(u,f(u,n2)) != f(u,u2)
    | f(u,f(u,n2)) != f(uu,u2)
    | f(u,u2) = f(uu,u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(u,n2)),f(uu,u2)) ),[0],$fot(f(u,u2))]]) ).

cnf(refute_0_395,plain,
    ( f(u,f(u,n2)) != f(uu,u2)
    | f(u,u2) = f(uu,u2) ),
    inference(resolve,[$cnf( $equal(f(u,f(u,n2)),f(u,u2)) )],[refute_0_393,refute_0_394]) ).

cnf(refute_0_396,plain,
    f(u,u2) = f(uu,u2),
    inference(resolve,[$cnf( $equal(f(u,f(u,n2)),f(uu,u2)) )],[refute_0_389,refute_0_395]) ).

cnf(refute_0_397,plain,
    ( f(u,u2) != f(uu,u2)
    | f(uu,u2) = f(u,u2) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(u,u2))),bind(Y0,$fot(f(uu,u2)))]]) ).

cnf(refute_0_398,plain,
    f(uu,u2) = f(u,u2),
    inference(resolve,[$cnf( $equal(f(u,u2),f(uu,u2)) )],[refute_0_396,refute_0_397]) ).

cnf(refute_0_399,plain,
    ( f(uu,f(u2,Z)) != f(f(uu,u2),f(uu,Z))
    | f(uu,u2) != f(u,u2)
    | f(uu,f(u2,Z)) = f(f(u,u2),f(uu,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,f(u2,Z)),f(f(uu,u2),f(uu,Z))) ),[1,0],$fot(f(u,u2))]]) ).

cnf(refute_0_400,plain,
    ( f(uu,f(u2,Z)) != f(f(uu,u2),f(uu,Z))
    | f(uu,f(u2,Z)) = f(f(u,u2),f(uu,Z)) ),
    inference(resolve,[$cnf( $equal(f(uu,u2),f(u,u2)) )],[refute_0_398,refute_0_399]) ).

cnf(refute_0_401,plain,
    f(uu,f(u2,Z)) = f(f(u,u2),f(uu,Z)),
    inference(resolve,[$cnf( $equal(f(uu,f(u2,Z)),f(f(uu,u2),f(uu,Z))) )],[refute_0_385,refute_0_400]) ).

cnf(refute_0_402,plain,
    ( f(u2,f(u2,Z)) != f(uu,f(u2,Z))
    | f(uu,f(u2,Z)) = f(u2,f(u2,Z)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(u2,f(u2,Z)))),bind(Y0,$fot(f(uu,f(u2,Z))))]]) ).

cnf(refute_0_403,plain,
    f(uu,f(u2,Z)) = f(u2,f(u2,Z)),
    inference(resolve,[$cnf( $equal(f(u2,f(u2,Z)),f(uu,f(u2,Z))) )],[refute_0_384,refute_0_402]) ).

cnf(refute_0_404,plain,
    ( f(uu,f(u2,Z)) != f(f(u,u2),f(uu,Z))
    | f(uu,f(u2,Z)) != f(u2,f(u2,Z))
    | f(u2,f(u2,Z)) = f(f(u,u2),f(uu,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(uu,f(u2,Z)),f(f(u,u2),f(uu,Z))) ),[0],$fot(f(u2,f(u2,Z)))]]) ).

cnf(refute_0_405,plain,
    ( f(uu,f(u2,Z)) != f(f(u,u2),f(uu,Z))
    | f(u2,f(u2,Z)) = f(f(u,u2),f(uu,Z)) ),
    inference(resolve,[$cnf( $equal(f(uu,f(u2,Z)),f(u2,f(u2,Z))) )],[refute_0_403,refute_0_404]) ).

cnf(refute_0_406,plain,
    f(u2,f(u2,Z)) = f(f(u,u2),f(uu,Z)),
    inference(resolve,[$cnf( $equal(f(uu,f(u2,Z)),f(f(u,u2),f(uu,Z))) )],[refute_0_401,refute_0_405]) ).

cnf(refute_0_407,plain,
    f(u,f(f(n1,n2),n2)) = f(f(u,f(n1,n2)),u2),
    inference(subst,[],[refute_0_16:[bind(X_1,$fot(f(n1,n2)))]]) ).

cnf(refute_0_408,plain,
    ( u1 != f(u,n1)
    | f(u,n1) = u1 ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(u1)),bind(Y0,$fot(f(u,n1)))]]) ).

cnf(refute_0_409,plain,
    f(u,n1) = u1,
    inference(resolve,[$cnf( $equal(u1,f(u,n1)) )],[clause_5,refute_0_408]) ).

cnf(refute_0_410,plain,
    ( f(u,f(n1,n2)) != f(f(u,n1),u2)
    | f(u,n1) != u1
    | f(u,f(n1,n2)) = f(u1,u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n1,n2)),f(f(u,n1),u2)) ),[1,0],$fot(u1)]]) ).

cnf(refute_0_411,plain,
    ( f(u,f(n1,n2)) != f(f(u,n1),u2)
    | f(u,f(n1,n2)) = f(u1,u2) ),
    inference(resolve,[$cnf( $equal(f(u,n1),u1) )],[refute_0_409,refute_0_410]) ).

cnf(refute_0_412,plain,
    f(u,f(n1,n2)) = f(u1,u2),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n2)),f(f(u,n1),u2)) )],[refute_0_71,refute_0_411]) ).

cnf(refute_0_413,plain,
    ( f(u,f(f(n1,n2),n2)) != f(f(u,f(n1,n2)),u2)
    | f(u,f(n1,n2)) != f(u1,u2)
    | f(u,f(f(n1,n2),n2)) = f(f(u1,u2),u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(f(n1,n2),n2)),f(f(u,f(n1,n2)),u2)) ),[1,0],$fot(f(u1,u2))]]) ).

cnf(refute_0_414,plain,
    ( f(u,f(f(n1,n2),n2)) != f(f(u,f(n1,n2)),u2)
    | f(u,f(f(n1,n2),n2)) = f(f(u1,u2),u2) ),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n2)),f(u1,u2)) )],[refute_0_412,refute_0_413]) ).

cnf(refute_0_415,plain,
    f(u,f(f(n1,n2),n2)) = f(f(u1,u2),u2),
    inference(resolve,[$cnf( $equal(f(u,f(f(n1,n2),n2)),f(f(u,f(n1,n2)),u2)) )],[refute_0_407,refute_0_414]) ).

cnf(refute_0_416,plain,
    f(n1,f(n2,n1)) = f(n1,f(n2,n1)),
    introduced(tautology,[refl,[$fot(f(n1,f(n2,n1)))]]) ).

cnf(refute_0_417,plain,
    ( f(n1,f(n2,n1)) != f(n1,f(n2,n1))
    | f(n2,n1) != n3
    | f(n1,f(n2,n1)) = f(n1,n3) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,f(n2,n1)),f(n1,f(n2,n1))) ),[1,1],$fot(n3)]]) ).

cnf(refute_0_418,plain,
    ( f(n2,n1) != n3
    | f(n1,f(n2,n1)) = f(n1,n3) ),
    inference(resolve,[$cnf( $equal(f(n1,f(n2,n1)),f(n1,f(n2,n1))) )],[refute_0_416,refute_0_417]) ).

cnf(refute_0_419,plain,
    f(n1,f(n2,n1)) = f(n1,n3),
    inference(resolve,[$cnf( $equal(f(n2,n1),n3) )],[refute_0_177,refute_0_418]) ).

cnf(refute_0_420,plain,
    ( f(n1,f(X_1,n1)) != f(f(n1,X_1),n2)
    | f(f(n1,X_1),n2) = f(n1,f(X_1,n1)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(n1,f(X_1,n1)))),bind(Y0,$fot(f(f(n1,X_1),n2)))]]) ).

cnf(refute_0_421,plain,
    f(f(n1,X_1),n2) = f(n1,f(X_1,n1)),
    inference(resolve,[$cnf( $equal(f(n1,f(X_1,n1)),f(f(n1,X_1),n2)) )],[refute_0_77,refute_0_420]) ).

cnf(refute_0_422,plain,
    f(f(n1,n2),n2) = f(n1,f(n2,n1)),
    inference(subst,[],[refute_0_421:[bind(X_1,$fot(n2))]]) ).

cnf(refute_0_423,plain,
    ( f(f(n1,n2),n2) != f(n1,f(n2,n1))
    | f(n1,f(n2,n1)) != f(n1,n3)
    | f(f(n1,n2),n2) = f(n1,n3) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(n1,n2),n2))),bind(Y0,$fot(f(n1,f(n2,n1)))),bind(Z0,$fot(f(n1,n3)))]]) ).

cnf(refute_0_424,plain,
    ( f(n1,f(n2,n1)) != f(n1,n3)
    | f(f(n1,n2),n2) = f(n1,n3) ),
    inference(resolve,[$cnf( $equal(f(f(n1,n2),n2),f(n1,f(n2,n1))) )],[refute_0_422,refute_0_423]) ).

cnf(refute_0_425,plain,
    f(f(n1,n2),n2) = f(n1,n3),
    inference(resolve,[$cnf( $equal(f(n1,f(n2,n1)),f(n1,n3)) )],[refute_0_419,refute_0_424]) ).

cnf(refute_0_426,plain,
    f(u,f(f(n1,n2),n2)) = f(u,f(f(n1,n2),n2)),
    introduced(tautology,[refl,[$fot(f(u,f(f(n1,n2),n2)))]]) ).

cnf(refute_0_427,plain,
    ( f(f(n1,n2),n2) != f(n1,n3)
    | f(u,f(f(n1,n2),n2)) != f(u,f(f(n1,n2),n2))
    | f(u,f(f(n1,n2),n2)) = f(u,f(n1,n3)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(f(n1,n2),n2)),f(u,f(f(n1,n2),n2))) ),[1,1],$fot(f(n1,n3))]]) ).

cnf(refute_0_428,plain,
    ( f(f(n1,n2),n2) != f(n1,n3)
    | f(u,f(f(n1,n2),n2)) = f(u,f(n1,n3)) ),
    inference(resolve,[$cnf( $equal(f(u,f(f(n1,n2),n2)),f(u,f(f(n1,n2),n2))) )],[refute_0_426,refute_0_427]) ).

cnf(refute_0_429,plain,
    f(u,f(f(n1,n2),n2)) = f(u,f(n1,n3)),
    inference(resolve,[$cnf( $equal(f(f(n1,n2),n2),f(n1,n3)) )],[refute_0_425,refute_0_428]) ).

cnf(refute_0_430,plain,
    ( f(u,f(f(n1,n2),n2)) != f(f(u1,u2),u2)
    | f(u,f(f(n1,n2),n2)) != f(u,f(n1,n3))
    | f(u,f(n1,n3)) = f(f(u1,u2),u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(f(n1,n2),n2)),f(f(u1,u2),u2)) ),[0],$fot(f(u,f(n1,n3)))]]) ).

cnf(refute_0_431,plain,
    ( f(u,f(f(n1,n2),n2)) != f(f(u1,u2),u2)
    | f(u,f(n1,n3)) = f(f(u1,u2),u2) ),
    inference(resolve,[$cnf( $equal(f(u,f(f(n1,n2),n2)),f(u,f(n1,n3))) )],[refute_0_429,refute_0_430]) ).

cnf(refute_0_432,plain,
    f(u,f(n1,n3)) = f(f(u1,u2),u2),
    inference(resolve,[$cnf( $equal(f(u,f(f(n1,n2),n2)),f(f(u1,u2),u2)) )],[refute_0_415,refute_0_431]) ).

cnf(refute_0_433,plain,
    f(u,f(X_1,n3)) = f(f(u,X_1),f(u,n3)),
    inference(subst,[],[a1:[bind(X,$fot(u)),bind(Y,$fot(X_1)),bind(Z,$fot(n3))]]) ).

cnf(refute_0_434,plain,
    ( u3 != f(u,n3)
    | f(u,n3) = u3 ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(u3)),bind(Y0,$fot(f(u,n3)))]]) ).

cnf(refute_0_435,plain,
    f(u,n3) = u3,
    inference(resolve,[$cnf( $equal(u3,f(u,n3)) )],[clause_7,refute_0_434]) ).

cnf(refute_0_436,plain,
    ( f(u,f(X_1,n3)) != f(f(u,X_1),f(u,n3))
    | f(u,n3) != u3
    | f(u,f(X_1,n3)) = f(f(u,X_1),u3) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(X_1,n3)),f(f(u,X_1),f(u,n3))) ),[1,1],$fot(u3)]]) ).

cnf(refute_0_437,plain,
    ( f(u,f(X_1,n3)) != f(f(u,X_1),f(u,n3))
    | f(u,f(X_1,n3)) = f(f(u,X_1),u3) ),
    inference(resolve,[$cnf( $equal(f(u,n3),u3) )],[refute_0_435,refute_0_436]) ).

cnf(refute_0_438,plain,
    f(u,f(X_1,n3)) = f(f(u,X_1),u3),
    inference(resolve,[$cnf( $equal(f(u,f(X_1,n3)),f(f(u,X_1),f(u,n3))) )],[refute_0_433,refute_0_437]) ).

cnf(refute_0_439,plain,
    f(u,f(n1,n3)) = f(f(u,n1),u3),
    inference(subst,[],[refute_0_438:[bind(X_1,$fot(n1))]]) ).

cnf(refute_0_440,plain,
    ( f(u,f(n1,n3)) != f(f(u,n1),u3)
    | f(u,n1) != u1
    | f(u,f(n1,n3)) = f(u1,u3) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n1,n3)),f(f(u,n1),u3)) ),[1,0],$fot(u1)]]) ).

cnf(refute_0_441,plain,
    ( f(u,f(n1,n3)) != f(f(u,n1),u3)
    | f(u,f(n1,n3)) = f(u1,u3) ),
    inference(resolve,[$cnf( $equal(f(u,n1),u1) )],[refute_0_409,refute_0_440]) ).

cnf(refute_0_442,plain,
    f(u,f(n1,n3)) = f(u1,u3),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n3)),f(f(u,n1),u3)) )],[refute_0_439,refute_0_441]) ).

cnf(refute_0_443,plain,
    ( b != f(u1,u3)
    | f(u1,u3) = b ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(b)),bind(Y0,$fot(f(u1,u3)))]]) ).

cnf(refute_0_444,plain,
    f(u1,u3) = b,
    inference(resolve,[$cnf( $equal(b,f(u1,u3)) )],[clause_10,refute_0_443]) ).

cnf(refute_0_445,plain,
    ( f(u,f(n1,n3)) != f(u1,u3)
    | f(u1,u3) != b
    | f(u,f(n1,n3)) = b ),
    introduced(tautology,[equality,[$cnf( ~ $equal(f(u,f(n1,n3)),b) ),[0],$fot(f(u1,u3))]]) ).

cnf(refute_0_446,plain,
    ( f(u,f(n1,n3)) != f(u1,u3)
    | f(u,f(n1,n3)) = b ),
    inference(resolve,[$cnf( $equal(f(u1,u3),b) )],[refute_0_444,refute_0_445]) ).

cnf(refute_0_447,plain,
    f(u,f(n1,n3)) = b,
    inference(resolve,[$cnf( $equal(f(u,f(n1,n3)),f(u1,u3)) )],[refute_0_442,refute_0_446]) ).

cnf(refute_0_448,plain,
    ( f(u,f(n1,n3)) != b
    | f(u,f(n1,n3)) != f(f(u1,u2),u2)
    | b = f(f(u1,u2),u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n1,n3)),f(f(u1,u2),u2)) ),[0],$fot(b)]]) ).

cnf(refute_0_449,plain,
    ( f(u,f(n1,n3)) != f(f(u1,u2),u2)
    | b = f(f(u1,u2),u2) ),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n3)),b) )],[refute_0_447,refute_0_448]) ).

cnf(refute_0_450,plain,
    b = f(f(u1,u2),u2),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n3)),f(f(u1,u2),u2)) )],[refute_0_432,refute_0_449]) ).

cnf(refute_0_451,plain,
    f(u,f(n1,n2)) = f(u,f(n1,n2)),
    introduced(tautology,[refl,[$fot(f(u,f(n1,n2)))]]) ).

cnf(refute_0_452,plain,
    ( f(n1,n2) != u
    | f(u,f(n1,n2)) != f(u,f(n1,n2))
    | f(u,f(n1,n2)) = f(u,u) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n1,n2)),f(u,f(n1,n2))) ),[1,1],$fot(u)]]) ).

cnf(refute_0_453,plain,
    ( f(n1,n2) != u
    | f(u,f(n1,n2)) = f(u,u) ),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n2)),f(u,f(n1,n2))) )],[refute_0_451,refute_0_452]) ).

cnf(refute_0_454,plain,
    f(u,f(n1,n2)) = f(u,u),
    inference(resolve,[$cnf( $equal(f(n1,n2),u) )],[refute_0_91,refute_0_453]) ).

cnf(refute_0_455,plain,
    ( f(u,f(n1,n2)) != f(u,u)
    | f(u,u) != uu
    | f(u,f(n1,n2)) = uu ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(u,f(n1,n2)))),bind(Y0,$fot(f(u,u))),bind(Z0,$fot(uu))]]) ).

cnf(refute_0_456,plain,
    ( f(u,u) != uu
    | f(u,f(n1,n2)) = uu ),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n2)),f(u,u)) )],[refute_0_454,refute_0_455]) ).

cnf(refute_0_457,plain,
    f(u,f(n1,n2)) = uu,
    inference(resolve,[$cnf( $equal(f(u,u),uu) )],[refute_0_38,refute_0_456]) ).

cnf(refute_0_458,plain,
    ( f(u,f(n1,n2)) != f(u1,u2)
    | f(u,f(n1,n2)) != uu
    | uu = f(u1,u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,f(n1,n2)),f(u1,u2)) ),[0],$fot(uu)]]) ).

cnf(refute_0_459,plain,
    ( f(u,f(n1,n2)) != f(u1,u2)
    | uu = f(u1,u2) ),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n2)),uu) )],[refute_0_457,refute_0_458]) ).

cnf(refute_0_460,plain,
    uu = f(u1,u2),
    inference(resolve,[$cnf( $equal(f(u,f(n1,n2)),f(u1,u2)) )],[refute_0_412,refute_0_459]) ).

cnf(refute_0_461,plain,
    ( uu != f(u1,u2)
    | f(u1,u2) = uu ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(uu)),bind(Y0,$fot(f(u1,u2)))]]) ).

cnf(refute_0_462,plain,
    f(u1,u2) = uu,
    inference(resolve,[$cnf( $equal(uu,f(u1,u2)) )],[refute_0_460,refute_0_461]) ).

cnf(refute_0_463,plain,
    f(f(u1,u2),u2) = f(f(u1,u2),u2),
    introduced(tautology,[refl,[$fot(f(f(u1,u2),u2))]]) ).

cnf(refute_0_464,plain,
    ( f(f(u1,u2),u2) != f(f(u1,u2),u2)
    | f(u1,u2) != uu
    | f(f(u1,u2),u2) = f(uu,u2) ),
    introduced(tautology,[equality,[$cnf( $equal(f(f(u1,u2),u2),f(f(u1,u2),u2)) ),[1,0],$fot(uu)]]) ).

cnf(refute_0_465,plain,
    ( f(u1,u2) != uu
    | f(f(u1,u2),u2) = f(uu,u2) ),
    inference(resolve,[$cnf( $equal(f(f(u1,u2),u2),f(f(u1,u2),u2)) )],[refute_0_463,refute_0_464]) ).

cnf(refute_0_466,plain,
    f(f(u1,u2),u2) = f(uu,u2),
    inference(resolve,[$cnf( $equal(f(u1,u2),uu) )],[refute_0_462,refute_0_465]) ).

cnf(refute_0_467,plain,
    ( f(f(u1,u2),u2) != f(uu,u2)
    | f(uu,u2) != f(u,u2)
    | f(f(u1,u2),u2) = f(u,u2) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(u1,u2),u2))),bind(Y0,$fot(f(uu,u2))),bind(Z0,$fot(f(u,u2)))]]) ).

cnf(refute_0_468,plain,
    ( f(uu,u2) != f(u,u2)
    | f(f(u1,u2),u2) = f(u,u2) ),
    inference(resolve,[$cnf( $equal(f(f(u1,u2),u2),f(uu,u2)) )],[refute_0_466,refute_0_467]) ).

cnf(refute_0_469,plain,
    f(f(u1,u2),u2) = f(u,u2),
    inference(resolve,[$cnf( $equal(f(uu,u2),f(u,u2)) )],[refute_0_398,refute_0_468]) ).

cnf(refute_0_470,plain,
    ( b != f(f(u1,u2),u2)
    | f(f(u1,u2),u2) != f(u,u2)
    | b = f(u,u2) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(b,f(u,u2)) ),[0],$fot(f(f(u1,u2),u2))]]) ).

cnf(refute_0_471,plain,
    ( b != f(f(u1,u2),u2)
    | b = f(u,u2) ),
    inference(resolve,[$cnf( $equal(f(f(u1,u2),u2),f(u,u2)) )],[refute_0_469,refute_0_470]) ).

cnf(refute_0_472,plain,
    b = f(u,u2),
    inference(resolve,[$cnf( $equal(b,f(f(u1,u2),u2)) )],[refute_0_450,refute_0_471]) ).

cnf(refute_0_473,plain,
    ( b != f(u,u2)
    | f(u,u2) = b ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(b)),bind(Y0,$fot(f(u,u2)))]]) ).

cnf(refute_0_474,plain,
    f(u,u2) = b,
    inference(resolve,[$cnf( $equal(b,f(u,u2)) )],[refute_0_472,refute_0_473]) ).

cnf(refute_0_475,plain,
    f(f(u,u2),f(uu,Z)) = f(f(u,u2),f(uu,Z)),
    introduced(tautology,[refl,[$fot(f(f(u,u2),f(uu,Z)))]]) ).

cnf(refute_0_476,plain,
    ( f(f(u,u2),f(uu,Z)) != f(f(u,u2),f(uu,Z))
    | f(u,u2) != b
    | f(f(u,u2),f(uu,Z)) = f(b,f(uu,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(f(u,u2),f(uu,Z)),f(f(u,u2),f(uu,Z))) ),[1,0],$fot(b)]]) ).

cnf(refute_0_477,plain,
    ( f(u,u2) != b
    | f(f(u,u2),f(uu,Z)) = f(b,f(uu,Z)) ),
    inference(resolve,[$cnf( $equal(f(f(u,u2),f(uu,Z)),f(f(u,u2),f(uu,Z))) )],[refute_0_475,refute_0_476]) ).

cnf(refute_0_478,plain,
    f(f(u,u2),f(uu,Z)) = f(b,f(uu,Z)),
    inference(resolve,[$cnf( $equal(f(u,u2),b) )],[refute_0_474,refute_0_477]) ).

cnf(refute_0_479,plain,
    ( f(f(u,u2),f(uu,Z)) != f(b,f(uu,Z))
    | f(u2,f(u2,Z)) != f(f(u,u2),f(uu,Z))
    | f(u2,f(u2,Z)) = f(b,f(uu,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u2,f(u2,Z)),f(f(u,u2),f(uu,Z))) ),[1],$fot(f(b,f(uu,Z)))]]) ).

cnf(refute_0_480,plain,
    ( f(u2,f(u2,Z)) != f(f(u,u2),f(uu,Z))
    | f(u2,f(u2,Z)) = f(b,f(uu,Z)) ),
    inference(resolve,[$cnf( $equal(f(f(u,u2),f(uu,Z)),f(b,f(uu,Z))) )],[refute_0_478,refute_0_479]) ).

cnf(refute_0_481,plain,
    f(u2,f(u2,Z)) = f(b,f(uu,Z)),
    inference(resolve,[$cnf( $equal(f(u2,f(u2,Z)),f(f(u,u2),f(uu,Z))) )],[refute_0_406,refute_0_480]) ).

cnf(refute_0_482,plain,
    ( f(u2,f(u2,Z)) != f(b,f(uu,Z))
    | f(u2,f(u2,Z)) != f(uu,f(u2,Z))
    | f(b,f(uu,Z)) = f(uu,f(u2,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u2,f(u2,Z)),f(uu,f(u2,Z))) ),[0],$fot(f(b,f(uu,Z)))]]) ).

cnf(refute_0_483,plain,
    ( f(u2,f(u2,Z)) != f(uu,f(u2,Z))
    | f(b,f(uu,Z)) = f(uu,f(u2,Z)) ),
    inference(resolve,[$cnf( $equal(f(u2,f(u2,Z)),f(b,f(uu,Z))) )],[refute_0_481,refute_0_482]) ).

cnf(refute_0_484,plain,
    f(b,f(uu,Z)) = f(uu,f(u2,Z)),
    inference(resolve,[$cnf( $equal(f(u2,f(u2,Z)),f(uu,f(u2,Z))) )],[refute_0_384,refute_0_483]) ).

cnf(refute_0_485,plain,
    ( f(b,f(uu,Z)) != f(uu,f(u2,Z))
    | f(uu,f(u2,Z)) = f(b,f(uu,Z)) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(b,f(uu,Z)))),bind(Y0,$fot(f(uu,f(u2,Z))))]]) ).

cnf(refute_0_486,plain,
    f(uu,f(u2,Z)) = f(b,f(uu,Z)),
    inference(resolve,[$cnf( $equal(f(b,f(uu,Z)),f(uu,f(u2,Z))) )],[refute_0_484,refute_0_485]) ).

cnf(refute_0_487,plain,
    f(uu,f(u2,uu)) = f(b,f(uu,uu)),
    inference(subst,[],[refute_0_486:[bind(Z,$fot(uu))]]) ).

cnf(refute_0_488,plain,
    f(f(uu,u2),v) = f(uu,f(u2,uu)),
    inference(subst,[],[refute_0_318:[bind(X_1,$fot(u2))]]) ).

cnf(refute_0_489,plain,
    ( f(f(uu,u2),v) != f(uu,f(u2,uu))
    | f(uu,f(u2,uu)) != f(b,f(uu,uu))
    | f(f(uu,u2),v) = f(b,f(uu,uu)) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(uu,u2),v))),bind(Y0,$fot(f(uu,f(u2,uu)))),bind(Z0,$fot(f(b,f(uu,uu))))]]) ).

cnf(refute_0_490,plain,
    ( f(uu,f(u2,uu)) != f(b,f(uu,uu))
    | f(f(uu,u2),v) = f(b,f(uu,uu)) ),
    inference(resolve,[$cnf( $equal(f(f(uu,u2),v),f(uu,f(u2,uu))) )],[refute_0_488,refute_0_489]) ).

cnf(refute_0_491,plain,
    f(f(uu,u2),v) = f(b,f(uu,uu)),
    inference(resolve,[$cnf( $equal(f(uu,f(u2,uu)),f(b,f(uu,uu))) )],[refute_0_487,refute_0_490]) ).

cnf(refute_0_492,plain,
    ( f(b,f(uu,uu)) != f(b,v)
    | f(f(uu,u2),v) != f(b,f(uu,uu))
    | f(f(uu,u2),v) = f(b,v) ),
    inference(subst,[],[refute_0_44:[bind(X0,$fot(f(f(uu,u2),v))),bind(Y0,$fot(f(b,f(uu,uu)))),bind(Z0,$fot(f(b,v)))]]) ).

cnf(refute_0_493,plain,
    ( f(b,f(uu,uu)) != f(b,v)
    | f(f(uu,u2),v) = f(b,v) ),
    inference(resolve,[$cnf( $equal(f(f(uu,u2),v),f(b,f(uu,uu))) )],[refute_0_491,refute_0_492]) ).

cnf(refute_0_494,plain,
    f(f(uu,u2),v) = f(b,v),
    inference(resolve,[$cnf( $equal(f(b,f(uu,uu)),f(b,v)) )],[refute_0_380,refute_0_493]) ).

cnf(refute_0_495,plain,
    ( f(f(uu,u2),v) != f(b,v)
    | f(n1,v) != f(f(uu,u2),v)
    | f(n1,v) = f(b,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(n1,v),f(f(uu,u2),v)) ),[1],$fot(f(b,v))]]) ).

cnf(refute_0_496,plain,
    ( f(n1,v) != f(f(uu,u2),v)
    | f(n1,v) = f(b,v) ),
    inference(resolve,[$cnf( $equal(f(f(uu,u2),v),f(b,v)) )],[refute_0_494,refute_0_495]) ).

cnf(refute_0_497,plain,
    ( f(uu,v) != f(f(uu,u2),v)
    | f(n1,v) = f(b,v) ),
    inference(resolve,[$cnf( $equal(f(n1,v),f(f(uu,u2),v)) )],[refute_0_376,refute_0_496]) ).

cnf(refute_0_498,plain,
    f(n1,v) = f(b,v),
    inference(resolve,[$cnf( $equal(f(uu,v),f(f(uu,u2),v)) )],[refute_0_371,refute_0_497]) ).

cnf(refute_0_499,plain,
    ( f(n1,v) != f(b,v)
    | f(u,v) != f(n1,v)
    | f(u,v) = f(b,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,v),f(n1,v)) ),[1],$fot(f(b,v))]]) ).

cnf(refute_0_500,plain,
    ( f(u,v) != f(n1,v)
    | f(u,v) = f(b,v) ),
    inference(resolve,[$cnf( $equal(f(n1,v),f(b,v)) )],[refute_0_498,refute_0_499]) ).

cnf(refute_0_501,plain,
    f(u,v) = f(b,v),
    inference(resolve,[$cnf( $equal(f(u,v),f(n1,v)) )],[refute_0_329,refute_0_500]) ).

cnf(refute_0_502,plain,
    ( f(u,v) != f(b,v)
    | f(u,v) != f(v,v)
    | f(b,v) = f(v,v) ),
    introduced(tautology,[equality,[$cnf( $equal(f(u,v),f(v,v)) ),[0],$fot(f(b,v))]]) ).

cnf(refute_0_503,plain,
    ( f(u,v) != f(v,v)
    | f(b,v) = f(v,v) ),
    inference(resolve,[$cnf( $equal(f(u,v),f(b,v)) )],[refute_0_501,refute_0_502]) ).

cnf(refute_0_504,plain,
    f(b,v) = f(v,v),
    inference(resolve,[$cnf( $equal(f(u,v),f(v,v)) )],[refute_0_295,refute_0_503]) ).

cnf(refute_0_505,plain,
    ( f(b,v) != f(v,v)
    | f(v,v) = f(b,v) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(f(b,v))),bind(Y0,$fot(f(v,v)))]]) ).

cnf(refute_0_506,plain,
    f(v,v) = f(b,v),
    inference(resolve,[$cnf( $equal(f(b,v),f(v,v)) )],[refute_0_504,refute_0_505]) ).

cnf(refute_0_507,plain,
    ( f(a,v) != f(v,v)
    | f(v,v) != f(b,v)
    | f(a,v) = f(b,v) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(f(a,v),f(b,v)) ),[0],$fot(f(v,v))]]) ).

cnf(refute_0_508,plain,
    ( f(a,v) != f(v,v)
    | f(a,v) = f(b,v) ),
    inference(resolve,[$cnf( $equal(f(v,v),f(b,v)) )],[refute_0_506,refute_0_507]) ).

cnf(refute_0_509,plain,
    ( f(a,f(a,a)) != f(v,v)
    | f(a,v) = f(b,v) ),
    inference(resolve,[$cnf( $equal(f(a,v),f(v,v)) )],[refute_0_264,refute_0_508]) ).

cnf(refute_0_510,plain,
    f(a,v) = f(b,v),
    inference(resolve,[$cnf( $equal(f(a,f(a,a)),f(v,v)) )],[refute_0_258,refute_0_509]) ).

cnf(refute_0_511,plain,
    $false,
    inference(resolve,[$cnf( $equal(f(a,v),f(b,v)) )],[refute_0_510,prove_equation]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n020.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 May 30 03:00:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.52/0.72  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.72  
% 0.52/0.72  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.59/0.77  
%------------------------------------------------------------------------------