%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : BOO012-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 : Thu Jul 14 23:44:35 EDT 2022

% Result   : Unsatisfiable 0.18s 0.52s
% Output   : CNFRefutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   61
%            Number of leaves      :   97
% Syntax   : Number of clauses     :  424 ( 224 unt;   0 nHn; 202 RR)
%            Number of literals    :  712 ( 711 equ; 290 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  578 (  23 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
    add(X,Y) = add(Y,X) ).

cnf(commutativity_of_multiply,axiom,
    multiply(X,Y) = multiply(Y,X) ).

cnf(distributivity1,axiom,
    add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).

cnf(distributivity2,axiom,
    multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).

cnf(additive_id1,axiom,
    add(X,additive_identity) = X ).

cnf(multiplicative_id1,axiom,
    multiply(X,multiplicative_identity) = X ).

cnf(additive_inverse1,axiom,
    add(X,inverse(X)) = multiplicative_identity ).

cnf(multiplicative_inverse1,axiom,
    multiply(X,inverse(X)) = additive_identity ).

cnf(prove_inverse_is_an_involution,negated_conjecture,
    inverse(inverse(x)) != x ).

cnf(refute_0_0,plain,
    multiply(X_36,add(inverse(X_36),X_38)) = add(multiply(X_36,inverse(X_36)),multiply(X_36,X_38)),
    inference(subst,[],[distributivity2:[bind(X,$fot(X_36)),bind(Y,$fot(inverse(X_36))),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_1,plain,
    multiply(X_36,inverse(X_36)) = additive_identity,
    inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_36))]]) ).

cnf(refute_0_2,plain,
    ( multiply(X_36,add(inverse(X_36),X_38)) != add(multiply(X_36,inverse(X_36)),multiply(X_36,X_38))
    | multiply(X_36,inverse(X_36)) != additive_identity
    | multiply(X_36,add(inverse(X_36),X_38)) = add(additive_identity,multiply(X_36,X_38)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_36,add(inverse(X_36),X_38)),add(multiply(X_36,inverse(X_36)),multiply(X_36,X_38))) ),[1,0],$fot(additive_identity)]]) ).

cnf(refute_0_3,plain,
    ( multiply(X_36,add(inverse(X_36),X_38)) != add(multiply(X_36,inverse(X_36)),multiply(X_36,X_38))
    | multiply(X_36,add(inverse(X_36),X_38)) = add(additive_identity,multiply(X_36,X_38)) ),
    inference(resolve,[$cnf( $equal(multiply(X_36,inverse(X_36)),additive_identity) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    multiply(X_36,add(inverse(X_36),X_38)) = add(additive_identity,multiply(X_36,X_38)),
    inference(resolve,[$cnf( $equal(multiply(X_36,add(inverse(X_36),X_38)),add(multiply(X_36,inverse(X_36)),multiply(X_36,X_38))) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    add(X,additive_identity) = add(additive_identity,X),
    inference(subst,[],[commutativity_of_add:[bind(Y,$fot(additive_identity))]]) ).

cnf(refute_0_6,plain,
    ( add(X,additive_identity) != X
    | add(X,additive_identity) != add(additive_identity,X)
    | add(additive_identity,X) = X ),
    introduced(tautology,[equality,[$cnf( $equal(add(X,additive_identity),X) ),[0],$fot(add(additive_identity,X))]]) ).

cnf(refute_0_7,plain,
    ( add(X,additive_identity) != X
    | add(additive_identity,X) = X ),
    inference(resolve,[$cnf( $equal(add(X,additive_identity),add(additive_identity,X)) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    add(additive_identity,X) = X,
    inference(resolve,[$cnf( $equal(add(X,additive_identity),X) )],[additive_id1,refute_0_7]) ).

cnf(refute_0_9,plain,
    add(additive_identity,multiply(X_36,X_38)) = multiply(X_36,X_38),
    inference(subst,[],[refute_0_8:[bind(X,$fot(multiply(X_36,X_38)))]]) ).

cnf(refute_0_10,plain,
    ( multiply(X_36,add(inverse(X_36),X_38)) != add(additive_identity,multiply(X_36,X_38))
    | add(additive_identity,multiply(X_36,X_38)) != multiply(X_36,X_38)
    | multiply(X_36,add(inverse(X_36),X_38)) = multiply(X_36,X_38) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_36,add(inverse(X_36),X_38)),multiply(X_36,X_38)) ),[0],$fot(add(additive_identity,multiply(X_36,X_38)))]]) ).

cnf(refute_0_11,plain,
    ( multiply(X_36,add(inverse(X_36),X_38)) != add(additive_identity,multiply(X_36,X_38))
    | multiply(X_36,add(inverse(X_36),X_38)) = multiply(X_36,X_38) ),
    inference(resolve,[$cnf( $equal(add(additive_identity,multiply(X_36,X_38)),multiply(X_36,X_38)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    multiply(X_36,add(inverse(X_36),X_38)) = multiply(X_36,X_38),
    inference(resolve,[$cnf( $equal(multiply(X_36,add(inverse(X_36),X_38)),add(additive_identity,multiply(X_36,X_38))) )],[refute_0_4,refute_0_11]) ).

cnf(refute_0_13,plain,
    multiply(X_51,add(inverse(X_51),inverse(inverse(X_51)))) = multiply(X_51,inverse(inverse(X_51))),
    inference(subst,[],[refute_0_12:[bind(X_36,$fot(X_51)),bind(X_38,$fot(inverse(inverse(X_51))))]]) ).

cnf(refute_0_14,plain,
    add(inverse(X_51),inverse(inverse(X_51))) = multiplicative_identity,
    inference(subst,[],[additive_inverse1:[bind(X,$fot(inverse(X_51)))]]) ).

cnf(refute_0_15,plain,
    ( multiply(X_51,add(inverse(X_51),inverse(inverse(X_51)))) != multiply(X_51,inverse(inverse(X_51)))
    | add(inverse(X_51),inverse(inverse(X_51))) != multiplicative_identity
    | multiply(X_51,multiplicative_identity) = multiply(X_51,inverse(inverse(X_51))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_51,add(inverse(X_51),inverse(inverse(X_51)))),multiply(X_51,inverse(inverse(X_51)))) ),[0,1],$fot(multiplicative_identity)]]) ).

cnf(refute_0_16,plain,
    ( multiply(X_51,add(inverse(X_51),inverse(inverse(X_51)))) != multiply(X_51,inverse(inverse(X_51)))
    | multiply(X_51,multiplicative_identity) = multiply(X_51,inverse(inverse(X_51))) ),
    inference(resolve,[$cnf( $equal(add(inverse(X_51),inverse(inverse(X_51))),multiplicative_identity) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    multiply(X_51,multiplicative_identity) = multiply(X_51,inverse(inverse(X_51))),
    inference(resolve,[$cnf( $equal(multiply(X_51,add(inverse(X_51),inverse(inverse(X_51)))),multiply(X_51,inverse(inverse(X_51)))) )],[refute_0_13,refute_0_16]) ).

cnf(refute_0_18,plain,
    multiply(X_51,multiplicative_identity) = X_51,
    inference(subst,[],[multiplicative_id1:[bind(X,$fot(X_51))]]) ).

cnf(refute_0_19,plain,
    ( multiply(X_51,multiplicative_identity) != X_51
    | multiply(X_51,multiplicative_identity) != multiply(X_51,inverse(inverse(X_51)))
    | X_51 = multiply(X_51,inverse(inverse(X_51))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_51,multiplicative_identity),multiply(X_51,inverse(inverse(X_51)))) ),[0],$fot(X_51)]]) ).

cnf(refute_0_20,plain,
    ( multiply(X_51,multiplicative_identity) != multiply(X_51,inverse(inverse(X_51)))
    | X_51 = multiply(X_51,inverse(inverse(X_51))) ),
    inference(resolve,[$cnf( $equal(multiply(X_51,multiplicative_identity),X_51) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),add(X_10,additive_identity)),
    inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(additive_identity))]]) ).

cnf(refute_0_22,plain,
    add(X_10,additive_identity) = X_10,
    inference(subst,[],[additive_id1:[bind(X,$fot(X_10))]]) ).

cnf(refute_0_23,plain,
    ( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),add(X_10,additive_identity))
    | add(X_10,additive_identity) != X_10
    | add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),add(X_10,additive_identity))) ),[1,1],$fot(X_10)]]) ).

cnf(refute_0_24,plain,
    ( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),add(X_10,additive_identity))
    | add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10) ),
    inference(resolve,[$cnf( $equal(add(X_10,additive_identity),X_10) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10),
    inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),add(X_10,additive_identity))) )],[refute_0_21,refute_0_24]) ).

cnf(refute_0_26,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_27,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_28,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( multiply(X,Y) != multiply(Y,X)
    | multiply(Y,X) = multiply(X,Y) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(Y,X)))]]) ).

cnf(refute_0_30,plain,
    multiply(Y,X) = multiply(X,Y),
    inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(Y,X)) )],[commutativity_of_multiply,refute_0_29]) ).

cnf(refute_0_31,plain,
    multiply(add(X_10,X_11),X_10) = multiply(X_10,add(X_10,X_11)),
    inference(subst,[],[refute_0_30:[bind(X,$fot(X_10)),bind(Y,$fot(add(X_10,X_11)))]]) ).

cnf(refute_0_32,plain,
    ( multiply(add(X_10,X_11),X_10) != multiply(X_10,add(X_10,X_11))
    | add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),X_10)
    | add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),X_10)) ),[1],$fot(multiply(X_10,add(X_10,X_11)))]]) ).

cnf(refute_0_33,plain,
    ( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),X_10)
    | add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)) ),
    inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),X_10),multiply(X_10,add(X_10,X_11))) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)),
    inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),X_10)) )],[refute_0_25,refute_0_33]) ).

cnf(refute_0_35,plain,
    add(X_28,multiply(X_29,additive_identity)) = multiply(X_28,add(X_28,X_29)),
    inference(subst,[],[refute_0_34:[bind(X_10,$fot(X_28)),bind(X_11,$fot(X_29))]]) ).

cnf(refute_0_36,plain,
    add(X_29,X_28) = add(X_28,X_29),
    inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_29)),bind(Y,$fot(X_28))]]) ).

cnf(refute_0_37,plain,
    ( add(X_29,X_28) != add(X_28,X_29)
    | add(X_28,X_29) = add(X_29,X_28) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(add(X_29,X_28))),bind(Y0,$fot(add(X_28,X_29)))]]) ).

cnf(refute_0_38,plain,
    add(X_28,X_29) = add(X_29,X_28),
    inference(resolve,[$cnf( $equal(add(X_29,X_28),add(X_28,X_29)) )],[refute_0_36,refute_0_37]) ).

cnf(refute_0_39,plain,
    ( add(X_28,X_29) != add(X_29,X_28)
    | add(X_28,multiply(X_29,additive_identity)) != multiply(X_28,add(X_28,X_29))
    | add(X_28,multiply(X_29,additive_identity)) = multiply(X_28,add(X_29,X_28)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_28,multiply(X_29,additive_identity)),multiply(X_28,add(X_28,X_29))) ),[1,1],$fot(add(X_29,X_28))]]) ).

cnf(refute_0_40,plain,
    ( add(X_28,multiply(X_29,additive_identity)) != multiply(X_28,add(X_28,X_29))
    | add(X_28,multiply(X_29,additive_identity)) = multiply(X_28,add(X_29,X_28)) ),
    inference(resolve,[$cnf( $equal(add(X_28,X_29),add(X_29,X_28)) )],[refute_0_38,refute_0_39]) ).

cnf(refute_0_41,plain,
    add(X_28,multiply(X_29,additive_identity)) = multiply(X_28,add(X_29,X_28)),
    inference(resolve,[$cnf( $equal(add(X_28,multiply(X_29,additive_identity)),multiply(X_28,add(X_28,X_29))) )],[refute_0_35,refute_0_40]) ).

cnf(refute_0_42,plain,
    add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = multiply(inverse(inverse(X_35)),add(X_35,inverse(inverse(X_35)))),
    inference(subst,[],[refute_0_41:[bind(X_28,$fot(inverse(inverse(X_35)))),bind(X_29,$fot(X_35))]]) ).

cnf(refute_0_43,plain,
    add(X_10,multiply(inverse(X_10),X_12)) = multiply(add(X_10,inverse(X_10)),add(X_10,X_12)),
    inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(inverse(X_10))),bind(Z,$fot(X_12))]]) ).

cnf(refute_0_44,plain,
    add(X_10,inverse(X_10)) = multiplicative_identity,
    inference(subst,[],[additive_inverse1:[bind(X,$fot(X_10))]]) ).

cnf(refute_0_45,plain,
    ( add(X_10,multiply(inverse(X_10),X_12)) != multiply(add(X_10,inverse(X_10)),add(X_10,X_12))
    | add(X_10,inverse(X_10)) != multiplicative_identity
    | add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(add(X_10,inverse(X_10)),add(X_10,X_12))) ),[1,0],$fot(multiplicative_identity)]]) ).

cnf(refute_0_46,plain,
    ( add(X_10,multiply(inverse(X_10),X_12)) != multiply(add(X_10,inverse(X_10)),add(X_10,X_12))
    | add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)) ),
    inference(resolve,[$cnf( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_44,refute_0_45]) ).

cnf(refute_0_47,plain,
    add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)),
    inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(add(X_10,inverse(X_10)),add(X_10,X_12))) )],[refute_0_43,refute_0_46]) ).

cnf(refute_0_48,plain,
    multiply(X,multiplicative_identity) = multiply(multiplicative_identity,X),
    inference(subst,[],[commutativity_of_multiply:[bind(Y,$fot(multiplicative_identity))]]) ).

cnf(refute_0_49,plain,
    ( multiply(X,multiplicative_identity) != X
    | multiply(X,multiplicative_identity) != multiply(multiplicative_identity,X)
    | multiply(multiplicative_identity,X) = X ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiplicative_identity),X) ),[0],$fot(multiply(multiplicative_identity,X))]]) ).

cnf(refute_0_50,plain,
    ( multiply(X,multiplicative_identity) != X
    | multiply(multiplicative_identity,X) = X ),
    inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),multiply(multiplicative_identity,X)) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    multiply(multiplicative_identity,X) = X,
    inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),X) )],[multiplicative_id1,refute_0_50]) ).

cnf(refute_0_52,plain,
    multiply(multiplicative_identity,add(X_10,X_12)) = add(X_10,X_12),
    inference(subst,[],[refute_0_51:[bind(X,$fot(add(X_10,X_12)))]]) ).

cnf(refute_0_53,plain,
    ( multiply(multiplicative_identity,add(X_10,X_12)) != add(X_10,X_12)
    | add(X_10,multiply(inverse(X_10),X_12)) != multiply(multiplicative_identity,add(X_10,X_12))
    | add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(multiplicative_identity,add(X_10,X_12))) ),[1],$fot(add(X_10,X_12))]]) ).

cnf(refute_0_54,plain,
    ( add(X_10,multiply(inverse(X_10),X_12)) != multiply(multiplicative_identity,add(X_10,X_12))
    | add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12) ),
    inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_10,X_12)),add(X_10,X_12)) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12),
    inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(multiplicative_identity,add(X_10,X_12))) )],[refute_0_47,refute_0_54]) ).

cnf(refute_0_56,plain,
    add(X_24,multiply(inverse(X_24),inverse(inverse(X_24)))) = add(X_24,inverse(inverse(X_24))),
    inference(subst,[],[refute_0_55:[bind(X_10,$fot(X_24)),bind(X_12,$fot(inverse(inverse(X_24))))]]) ).

cnf(refute_0_57,plain,
    multiply(inverse(X_24),inverse(inverse(X_24))) = additive_identity,
    inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(inverse(X_24)))]]) ).

cnf(refute_0_58,plain,
    ( multiply(inverse(X_24),inverse(inverse(X_24))) != additive_identity
    | add(X_24,multiply(inverse(X_24),inverse(inverse(X_24)))) != add(X_24,inverse(inverse(X_24)))
    | add(X_24,additive_identity) = add(X_24,inverse(inverse(X_24))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_24,multiply(inverse(X_24),inverse(inverse(X_24)))),add(X_24,inverse(inverse(X_24)))) ),[0,1],$fot(additive_identity)]]) ).

cnf(refute_0_59,plain,
    ( add(X_24,multiply(inverse(X_24),inverse(inverse(X_24)))) != add(X_24,inverse(inverse(X_24)))
    | add(X_24,additive_identity) = add(X_24,inverse(inverse(X_24))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_24),inverse(inverse(X_24))),additive_identity) )],[refute_0_57,refute_0_58]) ).

cnf(refute_0_60,plain,
    add(X_24,additive_identity) = add(X_24,inverse(inverse(X_24))),
    inference(resolve,[$cnf( $equal(add(X_24,multiply(inverse(X_24),inverse(inverse(X_24)))),add(X_24,inverse(inverse(X_24)))) )],[refute_0_56,refute_0_59]) ).

cnf(refute_0_61,plain,
    add(X_24,additive_identity) = X_24,
    inference(subst,[],[additive_id1:[bind(X,$fot(X_24))]]) ).

cnf(refute_0_62,plain,
    ( add(X_24,additive_identity) != X_24
    | add(X_24,additive_identity) != add(X_24,inverse(inverse(X_24)))
    | X_24 = add(X_24,inverse(inverse(X_24))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_24,additive_identity),add(X_24,inverse(inverse(X_24)))) ),[0],$fot(X_24)]]) ).

cnf(refute_0_63,plain,
    ( add(X_24,additive_identity) != add(X_24,inverse(inverse(X_24)))
    | X_24 = add(X_24,inverse(inverse(X_24))) ),
    inference(resolve,[$cnf( $equal(add(X_24,additive_identity),X_24) )],[refute_0_61,refute_0_62]) ).

cnf(refute_0_64,plain,
    X_24 = add(X_24,inverse(inverse(X_24))),
    inference(resolve,[$cnf( $equal(add(X_24,additive_identity),add(X_24,inverse(inverse(X_24)))) )],[refute_0_60,refute_0_63]) ).

cnf(refute_0_65,plain,
    X_35 = add(X_35,inverse(inverse(X_35))),
    inference(subst,[],[refute_0_64:[bind(X_24,$fot(X_35))]]) ).

cnf(refute_0_66,plain,
    ( X_35 != add(X_35,inverse(inverse(X_35)))
    | add(X_35,inverse(inverse(X_35))) = X_35 ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(X_35)),bind(Y0,$fot(add(X_35,inverse(inverse(X_35)))))]]) ).

cnf(refute_0_67,plain,
    add(X_35,inverse(inverse(X_35))) = X_35,
    inference(resolve,[$cnf( $equal(X_35,add(X_35,inverse(inverse(X_35)))) )],[refute_0_65,refute_0_66]) ).

cnf(refute_0_68,plain,
    ( add(X_35,inverse(inverse(X_35))) != X_35
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) != multiply(inverse(inverse(X_35)),add(X_35,inverse(inverse(X_35))))
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = multiply(inverse(inverse(X_35)),X_35) ),
    introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),multiply(inverse(inverse(X_35)),add(X_35,inverse(inverse(X_35))))) ),[1,1],$fot(X_35)]]) ).

cnf(refute_0_69,plain,
    ( add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) != multiply(inverse(inverse(X_35)),add(X_35,inverse(inverse(X_35))))
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = multiply(inverse(inverse(X_35)),X_35) ),
    inference(resolve,[$cnf( $equal(add(X_35,inverse(inverse(X_35))),X_35) )],[refute_0_67,refute_0_68]) ).

cnf(refute_0_70,plain,
    add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = multiply(inverse(inverse(X_35)),X_35),
    inference(resolve,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),multiply(inverse(inverse(X_35)),add(X_35,inverse(inverse(X_35))))) )],[refute_0_42,refute_0_69]) ).

cnf(refute_0_71,plain,
    multiply(inverse(inverse(X_35)),X_35) = multiply(X_35,inverse(inverse(X_35))),
    inference(subst,[],[refute_0_30:[bind(X,$fot(X_35)),bind(Y,$fot(inverse(inverse(X_35))))]]) ).

cnf(refute_0_72,plain,
    ( multiply(inverse(inverse(X_35)),X_35) != multiply(X_35,inverse(inverse(X_35)))
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) != multiply(inverse(inverse(X_35)),X_35)
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = multiply(X_35,inverse(inverse(X_35))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),multiply(inverse(inverse(X_35)),X_35)) ),[1],$fot(multiply(X_35,inverse(inverse(X_35))))]]) ).

cnf(refute_0_73,plain,
    ( add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) != multiply(inverse(inverse(X_35)),X_35)
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = multiply(X_35,inverse(inverse(X_35))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_35)),X_35),multiply(X_35,inverse(inverse(X_35)))) )],[refute_0_71,refute_0_72]) ).

cnf(refute_0_74,plain,
    add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = multiply(X_35,inverse(inverse(X_35))),
    inference(resolve,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),multiply(inverse(inverse(X_35)),X_35)) )],[refute_0_70,refute_0_73]) ).

cnf(refute_0_75,plain,
    add(inverse(inverse(X_35)),additive_identity) = inverse(inverse(X_35)),
    inference(subst,[],[additive_id1:[bind(X,$fot(inverse(inverse(X_35))))]]) ).

cnf(refute_0_76,plain,
    add(multiply(X_29,additive_identity),Y) = add(Y,multiply(X_29,additive_identity)),
    inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(X_29,additive_identity)))]]) ).

cnf(refute_0_77,plain,
    add(Y,multiply(X_29,additive_identity)) = multiply(Y,add(Y,X_29)),
    inference(subst,[],[refute_0_34:[bind(X_10,$fot(Y)),bind(X_11,$fot(X_29))]]) ).

cnf(refute_0_78,plain,
    ( add(Y,multiply(X_29,additive_identity)) != multiply(Y,add(Y,X_29))
    | add(multiply(X_29,additive_identity),Y) != add(Y,multiply(X_29,additive_identity))
    | add(multiply(X_29,additive_identity),Y) = multiply(Y,add(Y,X_29)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_29,additive_identity),Y),add(Y,multiply(X_29,additive_identity))) ),[1],$fot(multiply(Y,add(Y,X_29)))]]) ).

cnf(refute_0_79,plain,
    ( add(multiply(X_29,additive_identity),Y) != add(Y,multiply(X_29,additive_identity))
    | add(multiply(X_29,additive_identity),Y) = multiply(Y,add(Y,X_29)) ),
    inference(resolve,[$cnf( $equal(add(Y,multiply(X_29,additive_identity)),multiply(Y,add(Y,X_29))) )],[refute_0_77,refute_0_78]) ).

cnf(refute_0_80,plain,
    add(multiply(X_29,additive_identity),Y) = multiply(Y,add(Y,X_29)),
    inference(resolve,[$cnf( $equal(add(multiply(X_29,additive_identity),Y),add(Y,multiply(X_29,additive_identity))) )],[refute_0_76,refute_0_79]) ).

cnf(refute_0_81,plain,
    add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))) = multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31)),
    inference(subst,[],[refute_0_80:[bind(Y,$fot(inverse(inverse(multiply(X_31,additive_identity))))),bind(X_29,$fot(X_31))]]) ).

cnf(refute_0_82,plain,
    multiply(X_31,additive_identity) = add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))),
    inference(subst,[],[refute_0_64:[bind(X_24,$fot(multiply(X_31,additive_identity)))]]) ).

cnf(refute_0_83,plain,
    ( multiply(X_31,additive_identity) != add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity))))
    | add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))) = multiply(X_31,additive_identity) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X_31,additive_identity))),bind(Y0,$fot(add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity))))))]]) ).

cnf(refute_0_84,plain,
    add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))) = multiply(X_31,additive_identity),
    inference(resolve,[$cnf( $equal(multiply(X_31,additive_identity),add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity))))) )],[refute_0_82,refute_0_83]) ).

cnf(refute_0_85,plain,
    ( add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))) != multiply(X_31,additive_identity)
    | add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))) != multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31))
    | multiply(X_31,additive_identity) = multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))),multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31))) ),[0],$fot(multiply(X_31,additive_identity))]]) ).

cnf(refute_0_86,plain,
    ( add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))) != multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31))
    | multiply(X_31,additive_identity) = multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31)) ),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))),multiply(X_31,additive_identity)) )],[refute_0_84,refute_0_85]) ).

cnf(refute_0_87,plain,
    multiply(X_31,additive_identity) = multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31)),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),inverse(inverse(multiply(X_31,additive_identity)))),multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31))) )],[refute_0_81,refute_0_86]) ).

cnf(refute_0_88,plain,
    add(multiply(X_31,additive_identity),X_30) = multiply(X_30,add(X_30,X_31)),
    inference(subst,[],[refute_0_80:[bind(Y,$fot(X_30)),bind(X_29,$fot(X_31))]]) ).

cnf(refute_0_89,plain,
    multiply(additive_identity,X_31) = multiply(X_31,additive_identity),
    inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_31))]]) ).

cnf(refute_0_90,plain,
    ( multiply(additive_identity,X_31) != multiply(X_31,additive_identity)
    | multiply(X_31,additive_identity) = multiply(additive_identity,X_31) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(additive_identity,X_31))),bind(Y0,$fot(multiply(X_31,additive_identity)))]]) ).

cnf(refute_0_91,plain,
    multiply(X_31,additive_identity) = multiply(additive_identity,X_31),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,X_31),multiply(X_31,additive_identity)) )],[refute_0_89,refute_0_90]) ).

cnf(refute_0_92,plain,
    ( multiply(X_31,additive_identity) != multiply(additive_identity,X_31)
    | add(multiply(X_31,additive_identity),X_30) != multiply(X_30,add(X_30,X_31))
    | add(multiply(additive_identity,X_31),X_30) = multiply(X_30,add(X_30,X_31)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_31,additive_identity),X_30),multiply(X_30,add(X_30,X_31))) ),[0,0],$fot(multiply(additive_identity,X_31))]]) ).

cnf(refute_0_93,plain,
    ( add(multiply(X_31,additive_identity),X_30) != multiply(X_30,add(X_30,X_31))
    | add(multiply(additive_identity,X_31),X_30) = multiply(X_30,add(X_30,X_31)) ),
    inference(resolve,[$cnf( $equal(multiply(X_31,additive_identity),multiply(additive_identity,X_31)) )],[refute_0_91,refute_0_92]) ).

cnf(refute_0_94,plain,
    add(multiply(additive_identity,X_31),X_30) = multiply(X_30,add(X_30,X_31)),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),X_30),multiply(X_30,add(X_30,X_31))) )],[refute_0_88,refute_0_93]) ).

cnf(refute_0_95,plain,
    ( add(multiply(additive_identity,X_31),X_30) != multiply(X_30,add(X_30,X_31))
    | multiply(X_30,add(X_30,X_31)) = add(multiply(additive_identity,X_31),X_30) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(add(multiply(additive_identity,X_31),X_30))),bind(Y0,$fot(multiply(X_30,add(X_30,X_31))))]]) ).

cnf(refute_0_96,plain,
    multiply(X_30,add(X_30,X_31)) = add(multiply(additive_identity,X_31),X_30),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),X_30),multiply(X_30,add(X_30,X_31))) )],[refute_0_94,refute_0_95]) ).

cnf(refute_0_97,plain,
    multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31)) = add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))),
    inference(subst,[],[refute_0_96:[bind(X_30,$fot(inverse(inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_98,plain,
    ( multiply(X_31,additive_identity) != multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31))
    | multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31)) != add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity))))
    | multiply(X_31,additive_identity) = add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_31,additive_identity),add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity))))) ),[0],$fot(multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31)))]]) ).

cnf(refute_0_99,plain,
    ( multiply(X_31,additive_identity) != multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31))
    | multiply(X_31,additive_identity) = add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31)),add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity))))) )],[refute_0_97,refute_0_98]) ).

cnf(refute_0_100,plain,
    multiply(X_31,additive_identity) = add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))),
    inference(resolve,[$cnf( $equal(multiply(X_31,additive_identity),multiply(inverse(inverse(multiply(X_31,additive_identity))),add(inverse(inverse(multiply(X_31,additive_identity))),X_31))) )],[refute_0_87,refute_0_99]) ).

cnf(refute_0_101,plain,
    add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),add(X_10,inverse(X_10))),
    inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_10)))]]) ).

cnf(refute_0_102,plain,
    ( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
    | add(X_10,inverse(X_10)) != multiplicative_identity
    | add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) ),[1,1],$fot(multiplicative_identity)]]) ).

cnf(refute_0_103,plain,
    ( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
    | add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_44,refute_0_102]) ).

cnf(refute_0_104,plain,
    add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity),
    inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) )],[refute_0_101,refute_0_103]) ).

cnf(refute_0_105,plain,
    multiply(add(X_10,X_11),multiplicative_identity) = add(X_10,X_11),
    inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,X_11)))]]) ).

cnf(refute_0_106,plain,
    ( multiply(add(X_10,X_11),multiplicative_identity) != add(X_10,X_11)
    | add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),multiplicative_identity)
    | add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) ),[1],$fot(add(X_10,X_11))]]) ).

cnf(refute_0_107,plain,
    ( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),multiplicative_identity)
    | add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11) ),
    inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),multiplicative_identity),add(X_10,X_11)) )],[refute_0_105,refute_0_106]) ).

cnf(refute_0_108,plain,
    add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11),
    inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) )],[refute_0_104,refute_0_107]) ).

cnf(refute_0_109,plain,
    add(X_19,multiply(X_19,inverse(X_19))) = add(X_19,X_19),
    inference(subst,[],[refute_0_108:[bind(X_10,$fot(X_19)),bind(X_11,$fot(X_19))]]) ).

cnf(refute_0_110,plain,
    multiply(X_19,inverse(X_19)) = additive_identity,
    inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_19))]]) ).

cnf(refute_0_111,plain,
    ( multiply(X_19,inverse(X_19)) != additive_identity
    | add(X_19,multiply(X_19,inverse(X_19))) != add(X_19,X_19)
    | add(X_19,additive_identity) = add(X_19,X_19) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_19,multiply(X_19,inverse(X_19))),add(X_19,X_19)) ),[0,1],$fot(additive_identity)]]) ).

cnf(refute_0_112,plain,
    ( add(X_19,multiply(X_19,inverse(X_19))) != add(X_19,X_19)
    | add(X_19,additive_identity) = add(X_19,X_19) ),
    inference(resolve,[$cnf( $equal(multiply(X_19,inverse(X_19)),additive_identity) )],[refute_0_110,refute_0_111]) ).

cnf(refute_0_113,plain,
    add(X_19,additive_identity) = add(X_19,X_19),
    inference(resolve,[$cnf( $equal(add(X_19,multiply(X_19,inverse(X_19))),add(X_19,X_19)) )],[refute_0_109,refute_0_112]) ).

cnf(refute_0_114,plain,
    add(X_19,additive_identity) = X_19,
    inference(subst,[],[additive_id1:[bind(X,$fot(X_19))]]) ).

cnf(refute_0_115,plain,
    ( add(X_19,additive_identity) != X_19
    | add(X_19,additive_identity) != add(X_19,X_19)
    | X_19 = add(X_19,X_19) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_19,additive_identity),add(X_19,X_19)) ),[0],$fot(X_19)]]) ).

cnf(refute_0_116,plain,
    ( add(X_19,additive_identity) != add(X_19,X_19)
    | X_19 = add(X_19,X_19) ),
    inference(resolve,[$cnf( $equal(add(X_19,additive_identity),X_19) )],[refute_0_114,refute_0_115]) ).

cnf(refute_0_117,plain,
    X_19 = add(X_19,X_19),
    inference(resolve,[$cnf( $equal(add(X_19,additive_identity),add(X_19,X_19)) )],[refute_0_113,refute_0_116]) ).

cnf(refute_0_118,plain,
    ( X_19 != add(X_19,X_19)
    | add(X_19,X_19) = X_19 ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(X_19)),bind(Y0,$fot(add(X_19,X_19)))]]) ).

cnf(refute_0_119,plain,
    add(X_19,X_19) = X_19,
    inference(resolve,[$cnf( $equal(X_19,add(X_19,X_19)) )],[refute_0_117,refute_0_118]) ).

cnf(refute_0_120,plain,
    add(additive_identity,additive_identity) = additive_identity,
    inference(subst,[],[refute_0_119:[bind(X_19,$fot(additive_identity))]]) ).

cnf(refute_0_121,plain,
    multiply(multiplicative_identity,inverse(multiplicative_identity)) = additive_identity,
    inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(multiplicative_identity))]]) ).

cnf(refute_0_122,plain,
    multiply(multiplicative_identity,inverse(multiplicative_identity)) = inverse(multiplicative_identity),
    inference(subst,[],[refute_0_51:[bind(X,$fot(inverse(multiplicative_identity)))]]) ).

cnf(refute_0_123,plain,
    ( multiply(multiplicative_identity,inverse(multiplicative_identity)) != additive_identity
    | multiply(multiplicative_identity,inverse(multiplicative_identity)) != inverse(multiplicative_identity)
    | inverse(multiplicative_identity) = additive_identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiplicative_identity,inverse(multiplicative_identity)),additive_identity) ),[0],$fot(inverse(multiplicative_identity))]]) ).

cnf(refute_0_124,plain,
    ( multiply(multiplicative_identity,inverse(multiplicative_identity)) != additive_identity
    | inverse(multiplicative_identity) = additive_identity ),
    inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(multiplicative_identity)),inverse(multiplicative_identity)) )],[refute_0_122,refute_0_123]) ).

cnf(refute_0_125,plain,
    inverse(multiplicative_identity) = additive_identity,
    inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(multiplicative_identity)),additive_identity) )],[refute_0_121,refute_0_124]) ).

cnf(refute_0_126,plain,
    add(multiply(X_31,additive_identity),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31)),
    inference(subst,[],[refute_0_80:[bind(Y,$fot(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))),bind(X_29,$fot(X_31))]]) ).

cnf(refute_0_127,plain,
    add(X_19,multiply(inverse(X_19),inverse(X_19))) = add(X_19,inverse(X_19)),
    inference(subst,[],[refute_0_108:[bind(X_10,$fot(X_19)),bind(X_11,$fot(inverse(X_19)))]]) ).

cnf(refute_0_128,plain,
    add(multiply(additive_identity,additive_identity),Y) = add(Y,multiply(additive_identity,additive_identity)),
    inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,additive_identity)))]]) ).

cnf(refute_0_129,plain,
    add(X_10,multiply(additive_identity,X_12)) = multiply(add(X_10,additive_identity),add(X_10,X_12)),
    inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).

cnf(refute_0_130,plain,
    ( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
    | add(X_10,additive_identity) != X_10
    | add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) ),[1,0],$fot(X_10)]]) ).

cnf(refute_0_131,plain,
    ( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
    | add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
    inference(resolve,[$cnf( $equal(add(X_10,additive_identity),X_10) )],[refute_0_22,refute_0_130]) ).

cnf(refute_0_132,plain,
    add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)),
    inference(resolve,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) )],[refute_0_129,refute_0_131]) ).

cnf(refute_0_133,plain,
    add(X_13,multiply(additive_identity,additive_identity)) = multiply(X_13,add(X_13,additive_identity)),
    inference(subst,[],[refute_0_132:[bind(X_10,$fot(X_13)),bind(X_12,$fot(additive_identity))]]) ).

cnf(refute_0_134,plain,
    add(X_13,additive_identity) = X_13,
    inference(subst,[],[additive_id1:[bind(X,$fot(X_13))]]) ).

cnf(refute_0_135,plain,
    ( add(X_13,multiply(additive_identity,additive_identity)) != multiply(X_13,add(X_13,additive_identity))
    | add(X_13,additive_identity) != X_13
    | add(X_13,multiply(additive_identity,additive_identity)) = multiply(X_13,X_13) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_13,multiply(additive_identity,additive_identity)),multiply(X_13,add(X_13,additive_identity))) ),[1,1],$fot(X_13)]]) ).

cnf(refute_0_136,plain,
    ( add(X_13,multiply(additive_identity,additive_identity)) != multiply(X_13,add(X_13,additive_identity))
    | add(X_13,multiply(additive_identity,additive_identity)) = multiply(X_13,X_13) ),
    inference(resolve,[$cnf( $equal(add(X_13,additive_identity),X_13) )],[refute_0_134,refute_0_135]) ).

cnf(refute_0_137,plain,
    add(X_13,multiply(additive_identity,additive_identity)) = multiply(X_13,X_13),
    inference(resolve,[$cnf( $equal(add(X_13,multiply(additive_identity,additive_identity)),multiply(X_13,add(X_13,additive_identity))) )],[refute_0_133,refute_0_136]) ).

cnf(refute_0_138,plain,
    add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y),
    inference(subst,[],[refute_0_137:[bind(X_13,$fot(Y))]]) ).

cnf(refute_0_139,plain,
    ( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,Y)
    | add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
    | add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) ),[1],$fot(multiply(Y,Y))]]) ).

cnf(refute_0_140,plain,
    ( add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
    | add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
    inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,Y)) )],[refute_0_138,refute_0_139]) ).

cnf(refute_0_141,plain,
    add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_128,refute_0_140]) ).

cnf(refute_0_142,plain,
    add(multiply(additive_identity,additive_identity),inverse(X_19)) = multiply(inverse(X_19),inverse(X_19)),
    inference(subst,[],[refute_0_141:[bind(Y,$fot(inverse(X_19)))]]) ).

cnf(refute_0_143,plain,
    ( add(multiply(additive_identity,additive_identity),inverse(X_19)) != multiply(inverse(X_19),inverse(X_19))
    | multiply(inverse(X_19),inverse(X_19)) = add(multiply(additive_identity,additive_identity),inverse(X_19)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),inverse(X_19)))),bind(Y0,$fot(multiply(inverse(X_19),inverse(X_19))))]]) ).

cnf(refute_0_144,plain,
    multiply(inverse(X_19),inverse(X_19)) = add(multiply(additive_identity,additive_identity),inverse(X_19)),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),inverse(X_19)),multiply(inverse(X_19),inverse(X_19))) )],[refute_0_142,refute_0_143]) ).

cnf(refute_0_145,plain,
    ( multiply(inverse(X_19),inverse(X_19)) != add(multiply(additive_identity,additive_identity),inverse(X_19))
    | add(X_19,multiply(inverse(X_19),inverse(X_19))) != add(X_19,inverse(X_19))
    | add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))) = add(X_19,inverse(X_19)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_19,multiply(inverse(X_19),inverse(X_19))),add(X_19,inverse(X_19))) ),[0,1],$fot(add(multiply(additive_identity,additive_identity),inverse(X_19)))]]) ).

cnf(refute_0_146,plain,
    ( add(X_19,multiply(inverse(X_19),inverse(X_19))) != add(X_19,inverse(X_19))
    | add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))) = add(X_19,inverse(X_19)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_19),inverse(X_19)),add(multiply(additive_identity,additive_identity),inverse(X_19))) )],[refute_0_144,refute_0_145]) ).

cnf(refute_0_147,plain,
    add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))) = add(X_19,inverse(X_19)),
    inference(resolve,[$cnf( $equal(add(X_19,multiply(inverse(X_19),inverse(X_19))),add(X_19,inverse(X_19))) )],[refute_0_127,refute_0_146]) ).

cnf(refute_0_148,plain,
    add(X_19,inverse(X_19)) = multiplicative_identity,
    inference(subst,[],[additive_inverse1:[bind(X,$fot(X_19))]]) ).

cnf(refute_0_149,plain,
    ( add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))) != add(X_19,inverse(X_19))
    | add(X_19,inverse(X_19)) != multiplicative_identity
    | add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))) = multiplicative_identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))),multiplicative_identity) ),[0],$fot(add(X_19,inverse(X_19)))]]) ).

cnf(refute_0_150,plain,
    ( add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))) != add(X_19,inverse(X_19))
    | add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))) = multiplicative_identity ),
    inference(resolve,[$cnf( $equal(add(X_19,inverse(X_19)),multiplicative_identity) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))) = multiplicative_identity,
    inference(resolve,[$cnf( $equal(add(X_19,add(multiply(additive_identity,additive_identity),inverse(X_19))),add(X_19,inverse(X_19))) )],[refute_0_147,refute_0_150]) ).

cnf(refute_0_152,plain,
    add(multiply(X_31,additive_identity),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = multiplicative_identity,
    inference(subst,[],[refute_0_151:[bind(X_19,$fot(multiply(X_31,additive_identity)))]]) ).

cnf(refute_0_153,plain,
    ( add(multiply(X_31,additive_identity),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31))
    | add(multiply(X_31,additive_identity),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != multiplicative_identity
    | multiplicative_identity = multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_31,additive_identity),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31))) ),[0],$fot(multiplicative_identity)]]) ).

cnf(refute_0_154,plain,
    ( add(multiply(X_31,additive_identity),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31))
    | multiplicative_identity = multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31)) ),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),multiplicative_identity) )],[refute_0_152,refute_0_153]) ).

cnf(refute_0_155,plain,
    multiplicative_identity = multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31)),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31))) )],[refute_0_126,refute_0_154]) ).

cnf(refute_0_156,plain,
    multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31)) = add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),
    inference(subst,[],[refute_0_96:[bind(X_30,$fot(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_157,plain,
    ( multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31)) != add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))
    | multiplicative_identity != multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31))
    | multiplicative_identity = add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiplicative_identity,multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31))) ),[1],$fot(add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_158,plain,
    ( multiplicative_identity != multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31))
    | multiplicative_identity = add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31)),add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))) )],[refute_0_156,refute_0_157]) ).

cnf(refute_0_159,plain,
    multiplicative_identity = add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),
    inference(resolve,[$cnf( $equal(multiplicative_identity,multiply(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),add(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),X_31))) )],[refute_0_155,refute_0_158]) ).

cnf(refute_0_160,plain,
    add(additive_identity,inverse(multiply(X_31,additive_identity))) = inverse(multiply(X_31,additive_identity)),
    inference(subst,[],[refute_0_8:[bind(X,$fot(inverse(multiply(X_31,additive_identity))))]]) ).

cnf(refute_0_161,plain,
    add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = multiply(add(multiply(X_33,additive_identity),Y),add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))),
    inference(subst,[],[distributivity1:[bind(X,$fot(multiply(X_33,additive_identity))),bind(Z,$fot(inverse(multiply(additive_identity,X_33))))]]) ).

cnf(refute_0_162,plain,
    add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) = add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity))),
    inference(subst,[],[refute_0_55:[bind(X_10,$fot(multiply(additive_identity,X_32))),bind(X_12,$fot(inverse(multiply(X_32,additive_identity))))]]) ).

cnf(refute_0_163,plain,
    add(multiply(X_31,additive_identity),inverse(multiply(X_31,additive_identity))) = multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31)),
    inference(subst,[],[refute_0_80:[bind(Y,$fot(inverse(multiply(X_31,additive_identity)))),bind(X_29,$fot(X_31))]]) ).

cnf(refute_0_164,plain,
    add(multiply(X_31,additive_identity),inverse(multiply(X_31,additive_identity))) = multiplicative_identity,
    inference(subst,[],[additive_inverse1:[bind(X,$fot(multiply(X_31,additive_identity)))]]) ).

cnf(refute_0_165,plain,
    ( add(multiply(X_31,additive_identity),inverse(multiply(X_31,additive_identity))) != multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31))
    | add(multiply(X_31,additive_identity),inverse(multiply(X_31,additive_identity))) != multiplicative_identity
    | multiplicative_identity = multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_31,additive_identity),inverse(multiply(X_31,additive_identity))),multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31))) ),[0],$fot(multiplicative_identity)]]) ).

cnf(refute_0_166,plain,
    ( add(multiply(X_31,additive_identity),inverse(multiply(X_31,additive_identity))) != multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31))
    | multiplicative_identity = multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31)) ),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),inverse(multiply(X_31,additive_identity))),multiplicative_identity) )],[refute_0_164,refute_0_165]) ).

cnf(refute_0_167,plain,
    multiplicative_identity = multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31)),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),inverse(multiply(X_31,additive_identity))),multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31))) )],[refute_0_163,refute_0_166]) ).

cnf(refute_0_168,plain,
    multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31)) = add(multiply(additive_identity,X_31),inverse(multiply(X_31,additive_identity))),
    inference(subst,[],[refute_0_96:[bind(X_30,$fot(inverse(multiply(X_31,additive_identity))))]]) ).

cnf(refute_0_169,plain,
    ( multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31)) != add(multiply(additive_identity,X_31),inverse(multiply(X_31,additive_identity)))
    | multiplicative_identity != multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31))
    | multiplicative_identity = add(multiply(additive_identity,X_31),inverse(multiply(X_31,additive_identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiplicative_identity,multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31))) ),[1],$fot(add(multiply(additive_identity,X_31),inverse(multiply(X_31,additive_identity))))]]) ).

cnf(refute_0_170,plain,
    ( multiplicative_identity != multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31))
    | multiplicative_identity = add(multiply(additive_identity,X_31),inverse(multiply(X_31,additive_identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31)),add(multiply(additive_identity,X_31),inverse(multiply(X_31,additive_identity)))) )],[refute_0_168,refute_0_169]) ).

cnf(refute_0_171,plain,
    multiplicative_identity = add(multiply(additive_identity,X_31),inverse(multiply(X_31,additive_identity))),
    inference(resolve,[$cnf( $equal(multiplicative_identity,multiply(inverse(multiply(X_31,additive_identity)),add(inverse(multiply(X_31,additive_identity)),X_31))) )],[refute_0_167,refute_0_170]) ).

cnf(refute_0_172,plain,
    multiplicative_identity = add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity))),
    inference(subst,[],[refute_0_171:[bind(X_31,$fot(X_32))]]) ).

cnf(refute_0_173,plain,
    ( multiplicative_identity != add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity)))
    | add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity))) = multiplicative_identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity)))))]]) ).

cnf(refute_0_174,plain,
    add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity))) = multiplicative_identity,
    inference(resolve,[$cnf( $equal(multiplicative_identity,add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity)))) )],[refute_0_172,refute_0_173]) ).

cnf(refute_0_175,plain,
    ( add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) != add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity)))
    | add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity))) != multiplicative_identity
    | add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) = multiplicative_identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))),multiplicative_identity) ),[0],$fot(add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity))))]]) ).

cnf(refute_0_176,plain,
    ( add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) != add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity)))
    | add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) = multiplicative_identity ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity))),multiplicative_identity) )],[refute_0_174,refute_0_175]) ).

cnf(refute_0_177,plain,
    add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) = multiplicative_identity,
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))),add(multiply(additive_identity,X_32),inverse(multiply(X_32,additive_identity)))) )],[refute_0_162,refute_0_176]) ).

cnf(refute_0_178,plain,
    add(multiply(X_31,additive_identity),multiply(X_11,inverse(multiply(X_31,additive_identity)))) = multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31)),
    inference(subst,[],[refute_0_80:[bind(Y,$fot(multiply(X_11,inverse(multiply(X_31,additive_identity))))),bind(X_29,$fot(X_31))]]) ).

cnf(refute_0_179,plain,
    add(multiply(X_31,additive_identity),multiply(X_11,inverse(multiply(X_31,additive_identity)))) = add(multiply(X_31,additive_identity),X_11),
    inference(subst,[],[refute_0_108:[bind(X_10,$fot(multiply(X_31,additive_identity)))]]) ).

cnf(refute_0_180,plain,
    ( add(multiply(X_31,additive_identity),multiply(X_11,inverse(multiply(X_31,additive_identity)))) != multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31))
    | add(multiply(X_31,additive_identity),multiply(X_11,inverse(multiply(X_31,additive_identity)))) != add(multiply(X_31,additive_identity),X_11)
    | add(multiply(X_31,additive_identity),X_11) = multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(X_11,inverse(multiply(X_31,additive_identity)))),multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31))) ),[0],$fot(add(multiply(X_31,additive_identity),X_11))]]) ).

cnf(refute_0_181,plain,
    ( add(multiply(X_31,additive_identity),multiply(X_11,inverse(multiply(X_31,additive_identity)))) != multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31))
    | add(multiply(X_31,additive_identity),X_11) = multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31)) ),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(X_11,inverse(multiply(X_31,additive_identity)))),add(multiply(X_31,additive_identity),X_11)) )],[refute_0_179,refute_0_180]) ).

cnf(refute_0_182,plain,
    add(multiply(X_31,additive_identity),X_11) = multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31)),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(X_11,inverse(multiply(X_31,additive_identity)))),multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31))) )],[refute_0_178,refute_0_181]) ).

cnf(refute_0_183,plain,
    multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31)) = add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity)))),
    inference(subst,[],[refute_0_96:[bind(X_30,$fot(multiply(X_11,inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_184,plain,
    ( multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31)) != add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity))))
    | add(multiply(X_31,additive_identity),X_11) != multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31))
    | add(multiply(X_31,additive_identity),X_11) = add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_31,additive_identity),X_11),multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31))) ),[1],$fot(add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_185,plain,
    ( add(multiply(X_31,additive_identity),X_11) != multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31))
    | add(multiply(X_31,additive_identity),X_11) = add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31)),add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity))))) )],[refute_0_183,refute_0_184]) ).

cnf(refute_0_186,plain,
    add(multiply(X_31,additive_identity),X_11) = add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity)))),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),X_11),multiply(multiply(X_11,inverse(multiply(X_31,additive_identity))),add(multiply(X_11,inverse(multiply(X_31,additive_identity))),X_31))) )],[refute_0_182,refute_0_185]) ).

cnf(refute_0_187,plain,
    ( add(multiply(X_31,additive_identity),X_11) != add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity))))
    | add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity)))) = add(multiply(X_31,additive_identity),X_11) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(add(multiply(X_31,additive_identity),X_11))),bind(Y0,$fot(add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity))))))]]) ).

cnf(refute_0_188,plain,
    add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity)))) = add(multiply(X_31,additive_identity),X_11),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),X_11),add(multiply(additive_identity,X_31),multiply(X_11,inverse(multiply(X_31,additive_identity))))) )],[refute_0_186,refute_0_187]) ).

cnf(refute_0_189,plain,
    add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) = add(multiply(X_32,additive_identity),inverse(multiply(additive_identity,X_32))),
    inference(subst,[],[refute_0_188:[bind(X_11,$fot(inverse(multiply(additive_identity,X_32)))),bind(X_31,$fot(X_32))]]) ).

cnf(refute_0_190,plain,
    ( add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) != add(multiply(X_32,additive_identity),inverse(multiply(additive_identity,X_32)))
    | add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) != multiplicative_identity
    | add(multiply(X_32,additive_identity),inverse(multiply(additive_identity,X_32))) = multiplicative_identity ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))),multiplicative_identity) ),[0],$fot(add(multiply(X_32,additive_identity),inverse(multiply(additive_identity,X_32))))]]) ).

cnf(refute_0_191,plain,
    ( add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))) != multiplicative_identity
    | add(multiply(X_32,additive_identity),inverse(multiply(additive_identity,X_32))) = multiplicative_identity ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))),add(multiply(X_32,additive_identity),inverse(multiply(additive_identity,X_32)))) )],[refute_0_189,refute_0_190]) ).

cnf(refute_0_192,plain,
    add(multiply(X_32,additive_identity),inverse(multiply(additive_identity,X_32))) = multiplicative_identity,
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_32),multiply(inverse(multiply(additive_identity,X_32)),inverse(multiply(X_32,additive_identity)))),multiplicative_identity) )],[refute_0_177,refute_0_191]) ).

cnf(refute_0_193,plain,
    add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))) = multiplicative_identity,
    inference(subst,[],[refute_0_192:[bind(X_32,$fot(X_33))]]) ).

cnf(refute_0_194,plain,
    ( add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) != multiply(add(multiply(X_33,additive_identity),Y),add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))))
    | add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))) != multiplicative_identity
    | add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))),multiply(add(multiply(X_33,additive_identity),Y),add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))))) ),[1,1],$fot(multiplicative_identity)]]) ).

cnf(refute_0_195,plain,
    ( add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) != multiply(add(multiply(X_33,additive_identity),Y),add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))))
    | add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))),multiplicative_identity) )],[refute_0_193,refute_0_194]) ).

cnf(refute_0_196,plain,
    add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity),
    inference(resolve,[$cnf( $equal(add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))),multiply(add(multiply(X_33,additive_identity),Y),add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))))) )],[refute_0_161,refute_0_195]) ).

cnf(refute_0_197,plain,
    multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity) = add(multiply(X_33,additive_identity),Y),
    inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(multiply(X_33,additive_identity),Y)))]]) ).

cnf(refute_0_198,plain,
    ( multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity) != add(multiply(X_33,additive_identity),Y)
    | add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) != multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity)
    | add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = add(multiply(X_33,additive_identity),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))),multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity)) ),[1],$fot(add(multiply(X_33,additive_identity),Y))]]) ).

cnf(refute_0_199,plain,
    ( add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) != multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity)
    | add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = add(multiply(X_33,additive_identity),Y) ),
    inference(resolve,[$cnf( $equal(multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity),add(multiply(X_33,additive_identity),Y)) )],[refute_0_197,refute_0_198]) ).

cnf(refute_0_200,plain,
    add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = add(multiply(X_33,additive_identity),Y),
    inference(resolve,[$cnf( $equal(add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))),multiply(add(multiply(X_33,additive_identity),Y),multiplicative_identity)) )],[refute_0_196,refute_0_199]) ).

cnf(refute_0_201,plain,
    multiply(Y,multiplicative_identity) = Y,
    inference(subst,[],[multiplicative_id1:[bind(X,$fot(Y))]]) ).

cnf(refute_0_202,plain,
    multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) = multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))),
    introduced(tautology,[refl,[$fot(multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))))]]) ).

cnf(refute_0_203,plain,
    ( multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) != multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))))
    | add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))) != multiplicative_identity
    | multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) = multiply(Y,multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))),multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))))) ),[1,1],$fot(multiplicative_identity)]]) ).

cnf(refute_0_204,plain,
    ( add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))) != multiplicative_identity
    | multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) = multiply(Y,multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))),multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))))) )],[refute_0_202,refute_0_203]) ).

cnf(refute_0_205,plain,
    multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) = multiply(Y,multiplicative_identity),
    inference(resolve,[$cnf( $equal(add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))),multiplicative_identity) )],[refute_0_193,refute_0_204]) ).

cnf(refute_0_206,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_207,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_28,refute_0_206]) ).

cnf(refute_0_208,plain,
    ( multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) != multiply(Y,multiplicative_identity)
    | multiply(Y,multiplicative_identity) != Y
    | multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) = Y ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))))),bind(Y0,$fot(multiply(Y,multiplicative_identity))),bind(Z0,$fot(Y))]]) ).

cnf(refute_0_209,plain,
    ( multiply(Y,multiplicative_identity) != Y
    | multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) = Y ),
    inference(resolve,[$cnf( $equal(multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))),multiply(Y,multiplicative_identity)) )],[refute_0_205,refute_0_208]) ).

cnf(refute_0_210,plain,
    multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) = Y,
    inference(resolve,[$cnf( $equal(multiply(Y,multiplicative_identity),Y) )],[refute_0_201,refute_0_209]) ).

cnf(refute_0_211,plain,
    add(multiply(X_31,additive_identity),multiply(Y,Z)) = multiply(add(multiply(X_31,additive_identity),Y),add(multiply(X_31,additive_identity),Z)),
    inference(subst,[],[distributivity1:[bind(X,$fot(multiply(X_31,additive_identity)))]]) ).

cnf(refute_0_212,plain,
    add(multiply(X_31,additive_identity),Y) = multiply(Y,add(Y,X_31)),
    inference(subst,[],[refute_0_80:[bind(X_29,$fot(X_31))]]) ).

cnf(refute_0_213,plain,
    ( add(multiply(X_31,additive_identity),Y) != multiply(Y,add(Y,X_31))
    | add(multiply(X_31,additive_identity),multiply(Y,Z)) != multiply(add(multiply(X_31,additive_identity),Y),add(multiply(X_31,additive_identity),Z))
    | add(multiply(X_31,additive_identity),multiply(Y,Z)) = multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(Y,Z)),multiply(add(multiply(X_31,additive_identity),Y),add(multiply(X_31,additive_identity),Z))) ),[1,0],$fot(multiply(Y,add(Y,X_31)))]]) ).

cnf(refute_0_214,plain,
    ( add(multiply(X_31,additive_identity),multiply(Y,Z)) != multiply(add(multiply(X_31,additive_identity),Y),add(multiply(X_31,additive_identity),Z))
    | add(multiply(X_31,additive_identity),multiply(Y,Z)) = multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)) ),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),Y),multiply(Y,add(Y,X_31))) )],[refute_0_212,refute_0_213]) ).

cnf(refute_0_215,plain,
    add(multiply(X_31,additive_identity),multiply(Y,Z)) = multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(Y,Z)),multiply(add(multiply(X_31,additive_identity),Y),add(multiply(X_31,additive_identity),Z))) )],[refute_0_211,refute_0_214]) ).

cnf(refute_0_216,plain,
    multiply(X_36,add(X_37,multiplicative_identity)) = add(multiply(X_36,X_37),multiply(X_36,multiplicative_identity)),
    inference(subst,[],[distributivity2:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(multiplicative_identity))]]) ).

cnf(refute_0_217,plain,
    multiply(X_36,multiplicative_identity) = X_36,
    inference(subst,[],[multiplicative_id1:[bind(X,$fot(X_36))]]) ).

cnf(refute_0_218,plain,
    ( multiply(X_36,add(X_37,multiplicative_identity)) != add(multiply(X_36,X_37),multiply(X_36,multiplicative_identity))
    | multiply(X_36,multiplicative_identity) != X_36
    | multiply(X_36,add(X_37,multiplicative_identity)) = add(multiply(X_36,X_37),X_36) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_36,add(X_37,multiplicative_identity)),add(multiply(X_36,X_37),multiply(X_36,multiplicative_identity))) ),[1,1],$fot(X_36)]]) ).

cnf(refute_0_219,plain,
    ( multiply(X_36,add(X_37,multiplicative_identity)) != add(multiply(X_36,X_37),multiply(X_36,multiplicative_identity))
    | multiply(X_36,add(X_37,multiplicative_identity)) = add(multiply(X_36,X_37),X_36) ),
    inference(resolve,[$cnf( $equal(multiply(X_36,multiplicative_identity),X_36) )],[refute_0_217,refute_0_218]) ).

cnf(refute_0_220,plain,
    multiply(X_36,add(X_37,multiplicative_identity)) = add(multiply(X_36,X_37),X_36),
    inference(resolve,[$cnf( $equal(multiply(X_36,add(X_37,multiplicative_identity)),add(multiply(X_36,X_37),multiply(X_36,multiplicative_identity))) )],[refute_0_216,refute_0_219]) ).

cnf(refute_0_221,plain,
    add(X_19,multiply(multiplicative_identity,inverse(X_19))) = add(X_19,multiplicative_identity),
    inference(subst,[],[refute_0_108:[bind(X_10,$fot(X_19)),bind(X_11,$fot(multiplicative_identity))]]) ).

cnf(refute_0_222,plain,
    multiply(multiplicative_identity,inverse(X_19)) = inverse(X_19),
    inference(subst,[],[refute_0_51:[bind(X,$fot(inverse(X_19)))]]) ).

cnf(refute_0_223,plain,
    ( multiply(multiplicative_identity,inverse(X_19)) != inverse(X_19)
    | add(X_19,multiply(multiplicative_identity,inverse(X_19))) != add(X_19,multiplicative_identity)
    | add(X_19,inverse(X_19)) = add(X_19,multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_19,multiply(multiplicative_identity,inverse(X_19))),add(X_19,multiplicative_identity)) ),[0,1],$fot(inverse(X_19))]]) ).

cnf(refute_0_224,plain,
    ( add(X_19,multiply(multiplicative_identity,inverse(X_19))) != add(X_19,multiplicative_identity)
    | add(X_19,inverse(X_19)) = add(X_19,multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(X_19)),inverse(X_19)) )],[refute_0_222,refute_0_223]) ).

cnf(refute_0_225,plain,
    add(X_19,inverse(X_19)) = add(X_19,multiplicative_identity),
    inference(resolve,[$cnf( $equal(add(X_19,multiply(multiplicative_identity,inverse(X_19))),add(X_19,multiplicative_identity)) )],[refute_0_221,refute_0_224]) ).

cnf(refute_0_226,plain,
    ( add(X_19,inverse(X_19)) != add(X_19,multiplicative_identity)
    | add(X_19,inverse(X_19)) != multiplicative_identity
    | multiplicative_identity = add(X_19,multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_19,inverse(X_19)),add(X_19,multiplicative_identity)) ),[0],$fot(multiplicative_identity)]]) ).

cnf(refute_0_227,plain,
    ( add(X_19,inverse(X_19)) != add(X_19,multiplicative_identity)
    | multiplicative_identity = add(X_19,multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(add(X_19,inverse(X_19)),multiplicative_identity) )],[refute_0_148,refute_0_226]) ).

cnf(refute_0_228,plain,
    multiplicative_identity = add(X_19,multiplicative_identity),
    inference(resolve,[$cnf( $equal(add(X_19,inverse(X_19)),add(X_19,multiplicative_identity)) )],[refute_0_225,refute_0_227]) ).

cnf(refute_0_229,plain,
    ( multiplicative_identity != add(X_19,multiplicative_identity)
    | add(X_19,multiplicative_identity) = multiplicative_identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_19,multiplicative_identity)))]]) ).

cnf(refute_0_230,plain,
    add(X_19,multiplicative_identity) = multiplicative_identity,
    inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_19,multiplicative_identity)) )],[refute_0_228,refute_0_229]) ).

cnf(refute_0_231,plain,
    add(X_37,multiplicative_identity) = multiplicative_identity,
    inference(subst,[],[refute_0_230:[bind(X_19,$fot(X_37))]]) ).

cnf(refute_0_232,plain,
    multiply(X_36,add(X_37,multiplicative_identity)) = multiply(X_36,add(X_37,multiplicative_identity)),
    introduced(tautology,[refl,[$fot(multiply(X_36,add(X_37,multiplicative_identity)))]]) ).

cnf(refute_0_233,plain,
    ( multiply(X_36,add(X_37,multiplicative_identity)) != multiply(X_36,add(X_37,multiplicative_identity))
    | add(X_37,multiplicative_identity) != multiplicative_identity
    | multiply(X_36,add(X_37,multiplicative_identity)) = multiply(X_36,multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_36,add(X_37,multiplicative_identity)),multiply(X_36,add(X_37,multiplicative_identity))) ),[1,1],$fot(multiplicative_identity)]]) ).

cnf(refute_0_234,plain,
    ( add(X_37,multiplicative_identity) != multiplicative_identity
    | multiply(X_36,add(X_37,multiplicative_identity)) = multiply(X_36,multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_36,add(X_37,multiplicative_identity)),multiply(X_36,add(X_37,multiplicative_identity))) )],[refute_0_232,refute_0_233]) ).

cnf(refute_0_235,plain,
    multiply(X_36,add(X_37,multiplicative_identity)) = multiply(X_36,multiplicative_identity),
    inference(resolve,[$cnf( $equal(add(X_37,multiplicative_identity),multiplicative_identity) )],[refute_0_231,refute_0_234]) ).

cnf(refute_0_236,plain,
    ( multiply(X_36,add(X_37,multiplicative_identity)) != multiply(X_36,multiplicative_identity)
    | multiply(X_36,multiplicative_identity) != X_36
    | multiply(X_36,add(X_37,multiplicative_identity)) = X_36 ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(multiply(X_36,add(X_37,multiplicative_identity)))),bind(Y0,$fot(multiply(X_36,multiplicative_identity))),bind(Z0,$fot(X_36))]]) ).

cnf(refute_0_237,plain,
    ( multiply(X_36,multiplicative_identity) != X_36
    | multiply(X_36,add(X_37,multiplicative_identity)) = X_36 ),
    inference(resolve,[$cnf( $equal(multiply(X_36,add(X_37,multiplicative_identity)),multiply(X_36,multiplicative_identity)) )],[refute_0_235,refute_0_236]) ).

cnf(refute_0_238,plain,
    multiply(X_36,add(X_37,multiplicative_identity)) = X_36,
    inference(resolve,[$cnf( $equal(multiply(X_36,multiplicative_identity),X_36) )],[refute_0_217,refute_0_237]) ).

cnf(refute_0_239,plain,
    ( multiply(X_36,add(X_37,multiplicative_identity)) != X_36
    | multiply(X_36,add(X_37,multiplicative_identity)) != add(multiply(X_36,X_37),X_36)
    | X_36 = add(multiply(X_36,X_37),X_36) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_36,add(X_37,multiplicative_identity)),add(multiply(X_36,X_37),X_36)) ),[0],$fot(X_36)]]) ).

cnf(refute_0_240,plain,
    ( multiply(X_36,add(X_37,multiplicative_identity)) != add(multiply(X_36,X_37),X_36)
    | X_36 = add(multiply(X_36,X_37),X_36) ),
    inference(resolve,[$cnf( $equal(multiply(X_36,add(X_37,multiplicative_identity)),X_36) )],[refute_0_238,refute_0_239]) ).

cnf(refute_0_241,plain,
    add(Y,multiply(Y,Z)) = multiply(add(Y,Y),add(Y,Z)),
    inference(subst,[],[distributivity1:[bind(X,$fot(Y))]]) ).

cnf(refute_0_242,plain,
    Y = add(Y,Y),
    inference(subst,[],[refute_0_117:[bind(X_19,$fot(Y))]]) ).

cnf(refute_0_243,plain,
    ( Y != add(Y,Y)
    | add(Y,Y) = Y ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(Y)),bind(Y0,$fot(add(Y,Y)))]]) ).

cnf(refute_0_244,plain,
    add(Y,Y) = Y,
    inference(resolve,[$cnf( $equal(Y,add(Y,Y)) )],[refute_0_242,refute_0_243]) ).

cnf(refute_0_245,plain,
    ( add(Y,Y) != Y
    | add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
    | add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) ),[1,0],$fot(Y)]]) ).

cnf(refute_0_246,plain,
    ( add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
    | add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
    inference(resolve,[$cnf( $equal(add(Y,Y),Y) )],[refute_0_244,refute_0_245]) ).

cnf(refute_0_247,plain,
    add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)),
    inference(resolve,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) )],[refute_0_241,refute_0_246]) ).

cnf(refute_0_248,plain,
    add(X_36,multiply(X_36,X_37)) = multiply(X_36,add(X_36,X_37)),
    inference(subst,[],[refute_0_247:[bind(Y,$fot(X_36)),bind(Z,$fot(X_37))]]) ).

cnf(refute_0_249,plain,
    ( add(X,Y) != add(Y,X)
    | add(Y,X) = add(X,Y) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).

cnf(refute_0_250,plain,
    add(Y,X) = add(X,Y),
    inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_249]) ).

cnf(refute_0_251,plain,
    add(multiply(X_36,X_37),X_36) = add(X_36,multiply(X_36,X_37)),
    inference(subst,[],[refute_0_250:[bind(X,$fot(X_36)),bind(Y,$fot(multiply(X_36,X_37)))]]) ).

cnf(refute_0_252,plain,
    ( add(X_36,multiply(X_36,X_37)) != multiply(X_36,add(X_36,X_37))
    | add(multiply(X_36,X_37),X_36) != add(X_36,multiply(X_36,X_37))
    | add(multiply(X_36,X_37),X_36) = multiply(X_36,add(X_36,X_37)) ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(add(multiply(X_36,X_37),X_36))),bind(Y0,$fot(add(X_36,multiply(X_36,X_37)))),bind(Z0,$fot(multiply(X_36,add(X_36,X_37))))]]) ).

cnf(refute_0_253,plain,
    ( add(X_36,multiply(X_36,X_37)) != multiply(X_36,add(X_36,X_37))
    | add(multiply(X_36,X_37),X_36) = multiply(X_36,add(X_36,X_37)) ),
    inference(resolve,[$cnf( $equal(add(multiply(X_36,X_37),X_36),add(X_36,multiply(X_36,X_37))) )],[refute_0_251,refute_0_252]) ).

cnf(refute_0_254,plain,
    add(multiply(X_36,X_37),X_36) = multiply(X_36,add(X_36,X_37)),
    inference(resolve,[$cnf( $equal(add(X_36,multiply(X_36,X_37)),multiply(X_36,add(X_36,X_37))) )],[refute_0_248,refute_0_253]) ).

cnf(refute_0_255,plain,
    ( X_36 != add(multiply(X_36,X_37),X_36)
    | add(multiply(X_36,X_37),X_36) != multiply(X_36,add(X_36,X_37))
    | X_36 = multiply(X_36,add(X_36,X_37)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_36,multiply(X_36,add(X_36,X_37))) ),[0],$fot(add(multiply(X_36,X_37),X_36))]]) ).

cnf(refute_0_256,plain,
    ( X_36 != add(multiply(X_36,X_37),X_36)
    | X_36 = multiply(X_36,add(X_36,X_37)) ),
    inference(resolve,[$cnf( $equal(add(multiply(X_36,X_37),X_36),multiply(X_36,add(X_36,X_37))) )],[refute_0_254,refute_0_255]) ).

cnf(refute_0_257,plain,
    ( multiply(X_36,add(X_37,multiplicative_identity)) != add(multiply(X_36,X_37),X_36)
    | X_36 = multiply(X_36,add(X_36,X_37)) ),
    inference(resolve,[$cnf( $equal(X_36,add(multiply(X_36,X_37),X_36)) )],[refute_0_240,refute_0_256]) ).

cnf(refute_0_258,plain,
    X_36 = multiply(X_36,add(X_36,X_37)),
    inference(resolve,[$cnf( $equal(multiply(X_36,add(X_37,multiplicative_identity)),add(multiply(X_36,X_37),X_36)) )],[refute_0_220,refute_0_257]) ).

cnf(refute_0_259,plain,
    ( X_36 != multiply(X_36,add(X_36,X_37))
    | multiply(X_36,add(X_36,X_37)) = X_36 ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(X_36)),bind(Y0,$fot(multiply(X_36,add(X_36,X_37))))]]) ).

cnf(refute_0_260,plain,
    multiply(X_36,add(X_36,X_37)) = X_36,
    inference(resolve,[$cnf( $equal(X_36,multiply(X_36,add(X_36,X_37))) )],[refute_0_258,refute_0_259]) ).

cnf(refute_0_261,plain,
    multiply(Y,add(Y,X_31)) = Y,
    inference(subst,[],[refute_0_260:[bind(X_36,$fot(Y)),bind(X_37,$fot(X_31))]]) ).

cnf(refute_0_262,plain,
    multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)) = multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)),
    introduced(tautology,[refl,[$fot(multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)))]]) ).

cnf(refute_0_263,plain,
    ( multiply(Y,add(Y,X_31)) != Y
    | multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)) != multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z))
    | multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)) = multiply(Y,add(multiply(X_31,additive_identity),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)),multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z))) ),[1,0],$fot(Y)]]) ).

cnf(refute_0_264,plain,
    ( multiply(Y,add(Y,X_31)) != Y
    | multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)) = multiply(Y,add(multiply(X_31,additive_identity),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)),multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z))) )],[refute_0_262,refute_0_263]) ).

cnf(refute_0_265,plain,
    multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)) = multiply(Y,add(multiply(X_31,additive_identity),Z)),
    inference(resolve,[$cnf( $equal(multiply(Y,add(Y,X_31)),Y) )],[refute_0_261,refute_0_264]) ).

cnf(refute_0_266,plain,
    ( multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)) != multiply(Y,add(multiply(X_31,additive_identity),Z))
    | add(multiply(X_31,additive_identity),multiply(Y,Z)) != multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z))
    | add(multiply(X_31,additive_identity),multiply(Y,Z)) = multiply(Y,add(multiply(X_31,additive_identity),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(Y,Z)),multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z))) ),[1],$fot(multiply(Y,add(multiply(X_31,additive_identity),Z)))]]) ).

cnf(refute_0_267,plain,
    ( add(multiply(X_31,additive_identity),multiply(Y,Z)) != multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z))
    | add(multiply(X_31,additive_identity),multiply(Y,Z)) = multiply(Y,add(multiply(X_31,additive_identity),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z)),multiply(Y,add(multiply(X_31,additive_identity),Z))) )],[refute_0_265,refute_0_266]) ).

cnf(refute_0_268,plain,
    add(multiply(X_31,additive_identity),multiply(Y,Z)) = multiply(Y,add(multiply(X_31,additive_identity),Z)),
    inference(resolve,[$cnf( $equal(add(multiply(X_31,additive_identity),multiply(Y,Z)),multiply(multiply(Y,add(Y,X_31)),add(multiply(X_31,additive_identity),Z))) )],[refute_0_215,refute_0_267]) ).

cnf(refute_0_269,plain,
    add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))),
    inference(subst,[],[refute_0_268:[bind(Z,$fot(inverse(multiply(additive_identity,X_33)))),bind(X_31,$fot(X_33))]]) ).

cnf(refute_0_270,plain,
    ( multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) != Y
    | add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) != multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))))
    | add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = Y ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))))),bind(Y0,$fot(multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))))),bind(Z0,$fot(Y))]]) ).

cnf(refute_0_271,plain,
    ( multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))) != Y
    | add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = Y ),
    inference(resolve,[$cnf( $equal(add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))),multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33))))) )],[refute_0_269,refute_0_270]) ).

cnf(refute_0_272,plain,
    add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) = Y,
    inference(resolve,[$cnf( $equal(multiply(Y,add(multiply(X_33,additive_identity),inverse(multiply(additive_identity,X_33)))),Y) )],[refute_0_210,refute_0_271]) ).

cnf(refute_0_273,plain,
    ( add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) != Y
    | add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) != add(multiply(X_33,additive_identity),Y)
    | Y = add(multiply(X_33,additive_identity),Y) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))),add(multiply(X_33,additive_identity),Y)) ),[0],$fot(Y)]]) ).

cnf(refute_0_274,plain,
    ( add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))) != add(multiply(X_33,additive_identity),Y)
    | Y = add(multiply(X_33,additive_identity),Y) ),
    inference(resolve,[$cnf( $equal(add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))),Y) )],[refute_0_272,refute_0_273]) ).

cnf(refute_0_275,plain,
    Y = add(multiply(X_33,additive_identity),Y),
    inference(resolve,[$cnf( $equal(add(multiply(X_33,additive_identity),multiply(Y,inverse(multiply(additive_identity,X_33)))),add(multiply(X_33,additive_identity),Y)) )],[refute_0_200,refute_0_274]) ).

cnf(refute_0_276,plain,
    ( Y != add(multiply(X_33,additive_identity),Y)
    | add(multiply(X_33,additive_identity),Y) = Y ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(Y)),bind(Y0,$fot(add(multiply(X_33,additive_identity),Y)))]]) ).

cnf(refute_0_277,plain,
    add(multiply(X_33,additive_identity),Y) = Y,
    inference(resolve,[$cnf( $equal(Y,add(multiply(X_33,additive_identity),Y)) )],[refute_0_275,refute_0_276]) ).

cnf(refute_0_278,plain,
    add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))) = inverse(multiply(X_31,additive_identity)),
    inference(subst,[],[refute_0_277:[bind(Y,$fot(inverse(multiply(X_31,additive_identity)))),bind(X_33,$fot(additive_identity))]]) ).

cnf(refute_0_279,plain,
    add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),
    introduced(tautology,[refl,[$fot(add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_280,plain,
    ( add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))) != inverse(multiply(X_31,additive_identity))
    | add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))
    | add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(multiply(X_31,additive_identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))) ),[1,1],$fot(inverse(multiply(X_31,additive_identity)))]]) ).

cnf(refute_0_281,plain,
    ( add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))) != inverse(multiply(X_31,additive_identity))
    | add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(multiply(X_31,additive_identity))) ),
    inference(resolve,[$cnf( $equal(add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))) )],[refute_0_279,refute_0_280]) ).

cnf(refute_0_282,plain,
    add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(multiply(X_31,additive_identity))),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))),inverse(multiply(X_31,additive_identity))) )],[refute_0_278,refute_0_281]) ).

cnf(refute_0_283,plain,
    multiply(additive_identity,add(additive_identity,X_38)) = add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_38)),
    inference(subst,[],[distributivity2:[bind(X,$fot(additive_identity)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_38))]]) ).

cnf(refute_0_284,plain,
    add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_38)) = multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38)),
    inference(subst,[],[refute_0_141:[bind(Y,$fot(multiply(additive_identity,X_38)))]]) ).

cnf(refute_0_285,plain,
    ( multiply(additive_identity,add(additive_identity,X_38)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_38))
    | add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_38)) != multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))
    | multiply(additive_identity,add(additive_identity,X_38)) = multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(additive_identity,add(additive_identity,X_38)),multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))) ),[0],$fot(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_38)))]]) ).

cnf(refute_0_286,plain,
    ( multiply(additive_identity,add(additive_identity,X_38)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_38))
    | multiply(additive_identity,add(additive_identity,X_38)) = multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38)) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_38)),multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))) )],[refute_0_284,refute_0_285]) ).

cnf(refute_0_287,plain,
    multiply(additive_identity,add(additive_identity,X_38)) = multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38)),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_38)),add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_38))) )],[refute_0_283,refute_0_286]) ).

cnf(refute_0_288,plain,
    multiply(additive_identity,add(additive_identity,X_38)) = additive_identity,
    inference(subst,[],[refute_0_260:[bind(X_36,$fot(additive_identity)),bind(X_37,$fot(X_38))]]) ).

cnf(refute_0_289,plain,
    ( multiply(additive_identity,add(additive_identity,X_38)) != multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))
    | multiply(additive_identity,add(additive_identity,X_38)) != additive_identity
    | additive_identity = multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_38)),multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))) ),[0],$fot(additive_identity)]]) ).

cnf(refute_0_290,plain,
    ( multiply(additive_identity,add(additive_identity,X_38)) != multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))
    | additive_identity = multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38)) ),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_38)),additive_identity) )],[refute_0_288,refute_0_289]) ).

cnf(refute_0_291,plain,
    add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
    inference(subst,[],[refute_0_132:[bind(X_10,$fot(multiply(additive_identity,additive_identity)))]]) ).

cnf(refute_0_292,plain,
    add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),
    inference(subst,[],[refute_0_141:[bind(Y,$fot(multiply(additive_identity,X_12)))]]) ).

cnf(refute_0_293,plain,
    ( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))
    | add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
    | multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) ),[0],$fot(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)))]]) ).

cnf(refute_0_294,plain,
    ( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
    | multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))) )],[refute_0_292,refute_0_293]) ).

cnf(refute_0_295,plain,
    multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_291,refute_0_294]) ).

cnf(refute_0_296,plain,
    add(X_13,multiply(additive_identity,X_14)) = multiply(X_13,add(X_13,X_14)),
    inference(subst,[],[refute_0_132:[bind(X_10,$fot(X_13)),bind(X_12,$fot(X_14))]]) ).

cnf(refute_0_297,plain,
    multiply(X_14,additive_identity) = multiply(additive_identity,X_14),
    inference(subst,[],[commutativity_of_multiply:[bind(X,$fot(X_14)),bind(Y,$fot(additive_identity))]]) ).

cnf(refute_0_298,plain,
    ( multiply(X_14,additive_identity) != multiply(additive_identity,X_14)
    | multiply(additive_identity,X_14) = multiply(X_14,additive_identity) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X_14,additive_identity))),bind(Y0,$fot(multiply(additive_identity,X_14)))]]) ).

cnf(refute_0_299,plain,
    multiply(additive_identity,X_14) = multiply(X_14,additive_identity),
    inference(resolve,[$cnf( $equal(multiply(X_14,additive_identity),multiply(additive_identity,X_14)) )],[refute_0_297,refute_0_298]) ).

cnf(refute_0_300,plain,
    ( multiply(additive_identity,X_14) != multiply(X_14,additive_identity)
    | add(X_13,multiply(additive_identity,X_14)) != multiply(X_13,add(X_13,X_14))
    | add(X_13,multiply(X_14,additive_identity)) = multiply(X_13,add(X_13,X_14)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(X_13,multiply(additive_identity,X_14)),multiply(X_13,add(X_13,X_14))) ),[0,1],$fot(multiply(X_14,additive_identity))]]) ).

cnf(refute_0_301,plain,
    ( add(X_13,multiply(additive_identity,X_14)) != multiply(X_13,add(X_13,X_14))
    | add(X_13,multiply(X_14,additive_identity)) = multiply(X_13,add(X_13,X_14)) ),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,X_14),multiply(X_14,additive_identity)) )],[refute_0_299,refute_0_300]) ).

cnf(refute_0_302,plain,
    add(X_13,multiply(X_14,additive_identity)) = multiply(X_13,add(X_13,X_14)),
    inference(resolve,[$cnf( $equal(add(X_13,multiply(additive_identity,X_14)),multiply(X_13,add(X_13,X_14))) )],[refute_0_296,refute_0_301]) ).

cnf(refute_0_303,plain,
    ( add(X_13,multiply(X_14,additive_identity)) != multiply(X_13,add(X_13,X_14))
    | multiply(X_13,add(X_13,X_14)) = add(X_13,multiply(X_14,additive_identity)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(add(X_13,multiply(X_14,additive_identity)))),bind(Y0,$fot(multiply(X_13,add(X_13,X_14))))]]) ).

cnf(refute_0_304,plain,
    multiply(X_13,add(X_13,X_14)) = add(X_13,multiply(X_14,additive_identity)),
    inference(resolve,[$cnf( $equal(add(X_13,multiply(X_14,additive_identity)),multiply(X_13,add(X_13,X_14))) )],[refute_0_302,refute_0_303]) ).

cnf(refute_0_305,plain,
    multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity)),
    inference(subst,[],[refute_0_304:[bind(X_13,$fot(multiply(additive_identity,additive_identity))),bind(X_14,$fot(X_12))]]) ).

cnf(refute_0_306,plain,
    ( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
    | multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity))
    | multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity))) ),[0],$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))]]) ).

cnf(refute_0_307,plain,
    ( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
    | multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity)) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity))) )],[refute_0_305,refute_0_306]) ).

cnf(refute_0_308,plain,
    multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity)),
    inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_295,refute_0_307]) ).

cnf(refute_0_309,plain,
    add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_29)),
    inference(subst,[],[refute_0_34:[bind(X_10,$fot(multiply(additive_identity,additive_identity))),bind(X_11,$fot(X_29))]]) ).

cnf(refute_0_310,plain,
    add(multiply(additive_identity,additive_identity),X_29) = multiply(X_29,X_29),
    inference(subst,[],[refute_0_141:[bind(Y,$fot(X_29))]]) ).

cnf(refute_0_311,plain,
    ( add(multiply(additive_identity,additive_identity),X_29) != multiply(X_29,X_29)
    | add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_29))
    | add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) = multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_29))) ),[1,1],$fot(multiply(X_29,X_29))]]) ).

cnf(refute_0_312,plain,
    ( add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_29))
    | add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) = multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29)) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_29),multiply(X_29,X_29)) )],[refute_0_310,refute_0_311]) ).

cnf(refute_0_313,plain,
    add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) = multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29)),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_29))) )],[refute_0_309,refute_0_312]) ).

cnf(refute_0_314,plain,
    add(multiply(additive_identity,additive_identity),X_12) = multiply(X_12,X_12),
    inference(subst,[],[refute_0_141:[bind(Y,$fot(X_12))]]) ).

cnf(refute_0_315,plain,
    ( add(multiply(additive_identity,additive_identity),X_12) != multiply(X_12,X_12)
    | add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
    | add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) ),[1,1],$fot(multiply(X_12,X_12))]]) ).

cnf(refute_0_316,plain,
    ( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
    | add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12)) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_12),multiply(X_12,X_12)) )],[refute_0_314,refute_0_315]) ).

cnf(refute_0_317,plain,
    add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12)),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_291,refute_0_316]) ).

cnf(refute_0_318,plain,
    add(additive_identity,X_12) = X_12,
    inference(subst,[],[refute_0_8:[bind(X,$fot(X_12))]]) ).

cnf(refute_0_319,plain,
    multiply(additive_identity,add(additive_identity,X_12)) = multiply(additive_identity,add(additive_identity,X_12)),
    introduced(tautology,[refl,[$fot(multiply(additive_identity,add(additive_identity,X_12)))]]) ).

cnf(refute_0_320,plain,
    ( multiply(additive_identity,add(additive_identity,X_12)) != multiply(additive_identity,add(additive_identity,X_12))
    | add(additive_identity,X_12) != X_12
    | multiply(additive_identity,add(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_12)),multiply(additive_identity,add(additive_identity,X_12))) ),[1,1],$fot(X_12)]]) ).

cnf(refute_0_321,plain,
    ( add(additive_identity,X_12) != X_12
    | multiply(additive_identity,add(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_12)),multiply(additive_identity,add(additive_identity,X_12))) )],[refute_0_319,refute_0_320]) ).

cnf(refute_0_322,plain,
    multiply(additive_identity,add(additive_identity,X_12)) = multiply(additive_identity,X_12),
    inference(resolve,[$cnf( $equal(add(additive_identity,X_12),X_12) )],[refute_0_318,refute_0_321]) ).

cnf(refute_0_323,plain,
    ( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
    | add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).

cnf(refute_0_324,plain,
    add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distributivity2,refute_0_323]) ).

cnf(refute_0_325,plain,
    add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(additive_identity,add(additive_identity,X_12)),
    inference(subst,[],[refute_0_324:[bind(X,$fot(additive_identity)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).

cnf(refute_0_326,plain,
    ( multiply(additive_identity,add(additive_identity,X_12)) != multiply(additive_identity,X_12)
    | add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(additive_identity,add(additive_identity,X_12))
    | add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)))),bind(Y0,$fot(multiply(additive_identity,add(additive_identity,X_12)))),bind(Z0,$fot(multiply(additive_identity,X_12)))]]) ).

cnf(refute_0_327,plain,
    ( multiply(additive_identity,add(additive_identity,X_12)) != multiply(additive_identity,X_12)
    | add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(additive_identity,add(additive_identity,X_12))) )],[refute_0_325,refute_0_326]) ).

cnf(refute_0_328,plain,
    add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_12)),multiply(additive_identity,X_12)) )],[refute_0_322,refute_0_327]) ).

cnf(refute_0_329,plain,
    ( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12))
    | add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(additive_identity,X_12)
    | multiply(additive_identity,X_12) = multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12)) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12))) ),[0],$fot(multiply(additive_identity,X_12))]]) ).

cnf(refute_0_330,plain,
    ( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12))
    | multiply(additive_identity,X_12) = multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12)) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(additive_identity,X_12)) )],[refute_0_328,refute_0_329]) ).

cnf(refute_0_331,plain,
    multiply(additive_identity,X_12) = multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12)),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12))) )],[refute_0_317,refute_0_330]) ).

cnf(refute_0_332,plain,
    ( multiply(additive_identity,X_12) != multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12))
    | multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12)) = multiply(additive_identity,X_12) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiply(additive_identity,X_12))),bind(Y0,$fot(multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12))))]]) ).

cnf(refute_0_333,plain,
    multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12)) = multiply(additive_identity,X_12),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,X_12),multiply(multiply(additive_identity,additive_identity),multiply(X_12,X_12))) )],[refute_0_331,refute_0_332]) ).

cnf(refute_0_334,plain,
    multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29)) = multiply(additive_identity,X_29),
    inference(subst,[],[refute_0_333:[bind(X_12,$fot(X_29))]]) ).

cnf(refute_0_335,plain,
    ( multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29)) != multiply(additive_identity,X_29)
    | add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) != multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29))
    | add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) = multiply(additive_identity,X_29) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)),multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29))) ),[1],$fot(multiply(additive_identity,X_29))]]) ).

cnf(refute_0_336,plain,
    ( add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) != multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29))
    | add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) = multiply(additive_identity,X_29) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29)),multiply(additive_identity,X_29)) )],[refute_0_334,refute_0_335]) ).

cnf(refute_0_337,plain,
    add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)) = multiply(additive_identity,X_29),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_29,additive_identity)),multiply(multiply(additive_identity,additive_identity),multiply(X_29,X_29))) )],[refute_0_313,refute_0_336]) ).

cnf(refute_0_338,plain,
    add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity)) = multiply(additive_identity,X_12),
    inference(subst,[],[refute_0_337:[bind(X_29,$fot(X_12))]]) ).

cnf(refute_0_339,plain,
    ( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity))
    | add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity)) != multiply(additive_identity,X_12)
    | multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),multiply(additive_identity,X_12)) ),[0],$fot(add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity)))]]) ).

cnf(refute_0_340,plain,
    ( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity))
    | multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity)),multiply(additive_identity,X_12)) )],[refute_0_338,refute_0_339]) ).

cnf(refute_0_341,plain,
    multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12),
    inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),add(multiply(additive_identity,additive_identity),multiply(X_12,additive_identity))) )],[refute_0_308,refute_0_340]) ).

cnf(refute_0_342,plain,
    multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38)) = multiply(additive_identity,X_38),
    inference(subst,[],[refute_0_341:[bind(X_12,$fot(X_38))]]) ).

cnf(refute_0_343,plain,
    ( multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38)) != multiply(additive_identity,X_38)
    | additive_identity != multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))
    | additive_identity = multiply(additive_identity,X_38) ),
    introduced(tautology,[equality,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))) ),[1],$fot(multiply(additive_identity,X_38))]]) ).

cnf(refute_0_344,plain,
    ( additive_identity != multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))
    | additive_identity = multiply(additive_identity,X_38) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38)),multiply(additive_identity,X_38)) )],[refute_0_342,refute_0_343]) ).

cnf(refute_0_345,plain,
    ( multiply(additive_identity,add(additive_identity,X_38)) != multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))
    | additive_identity = multiply(additive_identity,X_38) ),
    inference(resolve,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))) )],[refute_0_290,refute_0_344]) ).

cnf(refute_0_346,plain,
    additive_identity = multiply(additive_identity,X_38),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_38)),multiply(multiply(additive_identity,X_38),multiply(additive_identity,X_38))) )],[refute_0_287,refute_0_345]) ).

cnf(refute_0_347,plain,
    ( additive_identity != multiply(additive_identity,X_38)
    | multiply(additive_identity,X_38) = additive_identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(additive_identity,X_38)))]]) ).

cnf(refute_0_348,plain,
    multiply(additive_identity,X_38) = additive_identity,
    inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,X_38)) )],[refute_0_346,refute_0_347]) ).

cnf(refute_0_349,plain,
    multiply(additive_identity,X_31) = additive_identity,
    inference(subst,[],[refute_0_348:[bind(X_38,$fot(X_31))]]) ).

cnf(refute_0_350,plain,
    add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),
    introduced(tautology,[refl,[$fot(add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_351,plain,
    ( multiply(additive_identity,X_31) != additive_identity
    | add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))
    | add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))) ),[1,0],$fot(additive_identity)]]) ).

cnf(refute_0_352,plain,
    ( multiply(additive_identity,X_31) != additive_identity
    | add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))) )],[refute_0_350,refute_0_351]) ).

cnf(refute_0_353,plain,
    add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,X_31),additive_identity) )],[refute_0_349,refute_0_352]) ).

cnf(refute_0_354,plain,
    ( add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))
    | add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != add(additive_identity,inverse(multiply(X_31,additive_identity)))
    | add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(multiply(X_31,additive_identity))) ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))))),bind(Y0,$fot(add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))))),bind(Z0,$fot(add(additive_identity,inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_355,plain,
    ( add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != add(additive_identity,inverse(multiply(X_31,additive_identity)))
    | add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(multiply(X_31,additive_identity))) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))) )],[refute_0_353,refute_0_354]) ).

cnf(refute_0_356,plain,
    add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(multiply(X_31,additive_identity))),
    inference(resolve,[$cnf( $equal(add(additive_identity,add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),add(additive_identity,inverse(multiply(X_31,additive_identity)))) )],[refute_0_282,refute_0_355]) ).

cnf(refute_0_357,plain,
    ( add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != add(additive_identity,inverse(multiply(X_31,additive_identity)))
    | add(additive_identity,inverse(multiply(X_31,additive_identity))) != inverse(multiply(X_31,additive_identity))
    | add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = inverse(multiply(X_31,additive_identity)) ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))))),bind(Y0,$fot(add(additive_identity,inverse(multiply(X_31,additive_identity))))),bind(Z0,$fot(inverse(multiply(X_31,additive_identity))))]]) ).

cnf(refute_0_358,plain,
    ( add(additive_identity,inverse(multiply(X_31,additive_identity))) != inverse(multiply(X_31,additive_identity))
    | add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = inverse(multiply(X_31,additive_identity)) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),add(additive_identity,inverse(multiply(X_31,additive_identity)))) )],[refute_0_356,refute_0_357]) ).

cnf(refute_0_359,plain,
    add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) = inverse(multiply(X_31,additive_identity)),
    inference(resolve,[$cnf( $equal(add(additive_identity,inverse(multiply(X_31,additive_identity))),inverse(multiply(X_31,additive_identity))) )],[refute_0_160,refute_0_358]) ).

cnf(refute_0_360,plain,
    ( add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))) != inverse(multiply(X_31,additive_identity))
    | multiplicative_identity != add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))
    | multiplicative_identity = inverse(multiply(X_31,additive_identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiplicative_identity,add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))) ),[1],$fot(inverse(multiply(X_31,additive_identity)))]]) ).

cnf(refute_0_361,plain,
    ( multiplicative_identity != add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))
    | multiplicative_identity = inverse(multiply(X_31,additive_identity)) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity)))),inverse(multiply(X_31,additive_identity))) )],[refute_0_359,refute_0_360]) ).

cnf(refute_0_362,plain,
    multiplicative_identity = inverse(multiply(X_31,additive_identity)),
    inference(resolve,[$cnf( $equal(multiplicative_identity,add(multiply(additive_identity,X_31),add(multiply(additive_identity,additive_identity),inverse(multiply(X_31,additive_identity))))) )],[refute_0_159,refute_0_361]) ).

cnf(refute_0_363,plain,
    ( multiplicative_identity != inverse(multiply(X_31,additive_identity))
    | inverse(multiply(X_31,additive_identity)) = multiplicative_identity ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(inverse(multiply(X_31,additive_identity))))]]) ).

cnf(refute_0_364,plain,
    inverse(multiply(X_31,additive_identity)) = multiplicative_identity,
    inference(resolve,[$cnf( $equal(multiplicative_identity,inverse(multiply(X_31,additive_identity))) )],[refute_0_362,refute_0_363]) ).

cnf(refute_0_365,plain,
    inverse(inverse(multiply(X_31,additive_identity))) = inverse(inverse(multiply(X_31,additive_identity))),
    introduced(tautology,[refl,[$fot(inverse(inverse(multiply(X_31,additive_identity))))]]) ).

cnf(refute_0_366,plain,
    ( inverse(multiply(X_31,additive_identity)) != multiplicative_identity
    | inverse(inverse(multiply(X_31,additive_identity))) != inverse(inverse(multiply(X_31,additive_identity)))
    | inverse(inverse(multiply(X_31,additive_identity))) = inverse(multiplicative_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_31,additive_identity))),inverse(inverse(multiply(X_31,additive_identity)))) ),[1,0],$fot(multiplicative_identity)]]) ).

cnf(refute_0_367,plain,
    ( inverse(multiply(X_31,additive_identity)) != multiplicative_identity
    | inverse(inverse(multiply(X_31,additive_identity))) = inverse(multiplicative_identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_31,additive_identity))),inverse(inverse(multiply(X_31,additive_identity)))) )],[refute_0_365,refute_0_366]) ).

cnf(refute_0_368,plain,
    inverse(inverse(multiply(X_31,additive_identity))) = inverse(multiplicative_identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_31,additive_identity)),multiplicative_identity) )],[refute_0_364,refute_0_367]) ).

cnf(refute_0_369,plain,
    ( inverse(inverse(multiply(X_31,additive_identity))) != inverse(multiplicative_identity)
    | inverse(multiplicative_identity) != additive_identity
    | inverse(inverse(multiply(X_31,additive_identity))) = additive_identity ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(inverse(inverse(multiply(X_31,additive_identity))))),bind(Y0,$fot(inverse(multiplicative_identity))),bind(Z0,$fot(additive_identity))]]) ).

cnf(refute_0_370,plain,
    ( inverse(multiplicative_identity) != additive_identity
    | inverse(inverse(multiply(X_31,additive_identity))) = additive_identity ),
    inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_31,additive_identity))),inverse(multiplicative_identity)) )],[refute_0_368,refute_0_369]) ).

cnf(refute_0_371,plain,
    inverse(inverse(multiply(X_31,additive_identity))) = additive_identity,
    inference(resolve,[$cnf( $equal(inverse(multiplicative_identity),additive_identity) )],[refute_0_125,refute_0_370]) ).

cnf(refute_0_372,plain,
    add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))),
    introduced(tautology,[refl,[$fot(add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_373,plain,
    ( add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))) != add(additive_identity,inverse(inverse(multiply(X_31,additive_identity))))
    | inverse(inverse(multiply(X_31,additive_identity))) != additive_identity
    | add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,additive_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))),add(additive_identity,inverse(inverse(multiply(X_31,additive_identity))))) ),[1,1],$fot(additive_identity)]]) ).

cnf(refute_0_374,plain,
    ( inverse(inverse(multiply(X_31,additive_identity))) != additive_identity
    | add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,additive_identity) ),
    inference(resolve,[$cnf( $equal(add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))),add(additive_identity,inverse(inverse(multiply(X_31,additive_identity))))) )],[refute_0_372,refute_0_373]) ).

cnf(refute_0_375,plain,
    add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,additive_identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_31,additive_identity))),additive_identity) )],[refute_0_371,refute_0_374]) ).

cnf(refute_0_376,plain,
    add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))),
    introduced(tautology,[refl,[$fot(add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_377,plain,
    ( multiply(additive_identity,X_31) != additive_identity
    | add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) != add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity))))
    | add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))),add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity))))) ),[1,0],$fot(additive_identity)]]) ).

cnf(refute_0_378,plain,
    ( multiply(additive_identity,X_31) != additive_identity
    | add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))),add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity))))) )],[refute_0_376,refute_0_377]) ).

cnf(refute_0_379,plain,
    add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))),
    inference(resolve,[$cnf( $equal(multiply(additive_identity,X_31),additive_identity) )],[refute_0_349,refute_0_378]) ).

cnf(refute_0_380,plain,
    ( add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) != add(additive_identity,inverse(inverse(multiply(X_31,additive_identity))))
    | add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))) != add(additive_identity,additive_identity)
    | add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,additive_identity) ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))))),bind(Y0,$fot(add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))))),bind(Z0,$fot(add(additive_identity,additive_identity)))]]) ).

cnf(refute_0_381,plain,
    ( add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))) != add(additive_identity,additive_identity)
    | add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,additive_identity) ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))),add(additive_identity,inverse(inverse(multiply(X_31,additive_identity))))) )],[refute_0_379,refute_0_380]) ).

cnf(refute_0_382,plain,
    add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = add(additive_identity,additive_identity),
    inference(resolve,[$cnf( $equal(add(additive_identity,inverse(inverse(multiply(X_31,additive_identity)))),add(additive_identity,additive_identity)) )],[refute_0_375,refute_0_381]) ).

cnf(refute_0_383,plain,
    ( add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) != add(additive_identity,additive_identity)
    | add(additive_identity,additive_identity) != additive_identity
    | add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = additive_identity ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))))),bind(Y0,$fot(add(additive_identity,additive_identity))),bind(Z0,$fot(additive_identity))]]) ).

cnf(refute_0_384,plain,
    ( add(additive_identity,additive_identity) != additive_identity
    | add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = additive_identity ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))),add(additive_identity,additive_identity)) )],[refute_0_382,refute_0_383]) ).

cnf(refute_0_385,plain,
    add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) = additive_identity,
    inference(resolve,[$cnf( $equal(add(additive_identity,additive_identity),additive_identity) )],[refute_0_120,refute_0_384]) ).

cnf(refute_0_386,plain,
    ( multiply(X_31,additive_identity) != add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity))))
    | add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))) != additive_identity
    | multiply(X_31,additive_identity) = additive_identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_31,additive_identity),additive_identity) ),[0],$fot(add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))))]]) ).

cnf(refute_0_387,plain,
    ( multiply(X_31,additive_identity) != add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity))))
    | multiply(X_31,additive_identity) = additive_identity ),
    inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity)))),additive_identity) )],[refute_0_385,refute_0_386]) ).

cnf(refute_0_388,plain,
    multiply(X_31,additive_identity) = additive_identity,
    inference(resolve,[$cnf( $equal(multiply(X_31,additive_identity),add(multiply(additive_identity,X_31),inverse(inverse(multiply(X_31,additive_identity))))) )],[refute_0_100,refute_0_387]) ).

cnf(refute_0_389,plain,
    multiply(X_35,additive_identity) = additive_identity,
    inference(subst,[],[refute_0_388:[bind(X_31,$fot(X_35))]]) ).

cnf(refute_0_390,plain,
    add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),
    introduced(tautology,[refl,[$fot(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)))]]) ).

cnf(refute_0_391,plain,
    ( multiply(X_35,additive_identity) != additive_identity
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) != add(inverse(inverse(X_35)),multiply(X_35,additive_identity))
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = add(inverse(inverse(X_35)),additive_identity) ),
    introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),add(inverse(inverse(X_35)),multiply(X_35,additive_identity))) ),[1,1],$fot(additive_identity)]]) ).

cnf(refute_0_392,plain,
    ( multiply(X_35,additive_identity) != additive_identity
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = add(inverse(inverse(X_35)),additive_identity) ),
    inference(resolve,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),add(inverse(inverse(X_35)),multiply(X_35,additive_identity))) )],[refute_0_390,refute_0_391]) ).

cnf(refute_0_393,plain,
    add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = add(inverse(inverse(X_35)),additive_identity),
    inference(resolve,[$cnf( $equal(multiply(X_35,additive_identity),additive_identity) )],[refute_0_389,refute_0_392]) ).

cnf(refute_0_394,plain,
    ( add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) != add(inverse(inverse(X_35)),additive_identity)
    | add(inverse(inverse(X_35)),additive_identity) != inverse(inverse(X_35))
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = inverse(inverse(X_35)) ),
    inference(subst,[],[refute_0_207:[bind(X0,$fot(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)))),bind(Y0,$fot(add(inverse(inverse(X_35)),additive_identity))),bind(Z0,$fot(inverse(inverse(X_35))))]]) ).

cnf(refute_0_395,plain,
    ( add(inverse(inverse(X_35)),additive_identity) != inverse(inverse(X_35))
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = inverse(inverse(X_35)) ),
    inference(resolve,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),add(inverse(inverse(X_35)),additive_identity)) )],[refute_0_393,refute_0_394]) ).

cnf(refute_0_396,plain,
    add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) = inverse(inverse(X_35)),
    inference(resolve,[$cnf( $equal(add(inverse(inverse(X_35)),additive_identity),inverse(inverse(X_35))) )],[refute_0_75,refute_0_395]) ).

cnf(refute_0_397,plain,
    ( add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) != multiply(X_35,inverse(inverse(X_35)))
    | add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) != inverse(inverse(X_35))
    | inverse(inverse(X_35)) = multiply(X_35,inverse(inverse(X_35))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),multiply(X_35,inverse(inverse(X_35)))) ),[0],$fot(inverse(inverse(X_35)))]]) ).

cnf(refute_0_398,plain,
    ( add(inverse(inverse(X_35)),multiply(X_35,additive_identity)) != multiply(X_35,inverse(inverse(X_35)))
    | inverse(inverse(X_35)) = multiply(X_35,inverse(inverse(X_35))) ),
    inference(resolve,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),inverse(inverse(X_35))) )],[refute_0_396,refute_0_397]) ).

cnf(refute_0_399,plain,
    inverse(inverse(X_35)) = multiply(X_35,inverse(inverse(X_35))),
    inference(resolve,[$cnf( $equal(add(inverse(inverse(X_35)),multiply(X_35,additive_identity)),multiply(X_35,inverse(inverse(X_35)))) )],[refute_0_74,refute_0_398]) ).

cnf(refute_0_400,plain,
    ( inverse(inverse(X_35)) != multiply(X_35,inverse(inverse(X_35)))
    | multiply(X_35,inverse(inverse(X_35))) = inverse(inverse(X_35)) ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(inverse(inverse(X_35)))),bind(Y0,$fot(multiply(X_35,inverse(inverse(X_35)))))]]) ).

cnf(refute_0_401,plain,
    multiply(X_35,inverse(inverse(X_35))) = inverse(inverse(X_35)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),multiply(X_35,inverse(inverse(X_35)))) )],[refute_0_399,refute_0_400]) ).

cnf(refute_0_402,plain,
    multiply(X_51,inverse(inverse(X_51))) = inverse(inverse(X_51)),
    inference(subst,[],[refute_0_401:[bind(X_35,$fot(X_51))]]) ).

cnf(refute_0_403,plain,
    ( X_51 != multiply(X_51,inverse(inverse(X_51)))
    | multiply(X_51,inverse(inverse(X_51))) != inverse(inverse(X_51))
    | X_51 = inverse(inverse(X_51)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_51,inverse(inverse(X_51))) ),[0],$fot(multiply(X_51,inverse(inverse(X_51))))]]) ).

cnf(refute_0_404,plain,
    ( X_51 != multiply(X_51,inverse(inverse(X_51)))
    | X_51 = inverse(inverse(X_51)) ),
    inference(resolve,[$cnf( $equal(multiply(X_51,inverse(inverse(X_51))),inverse(inverse(X_51))) )],[refute_0_402,refute_0_403]) ).

cnf(refute_0_405,plain,
    ( multiply(X_51,multiplicative_identity) != multiply(X_51,inverse(inverse(X_51)))
    | X_51 = inverse(inverse(X_51)) ),
    inference(resolve,[$cnf( $equal(X_51,multiply(X_51,inverse(inverse(X_51)))) )],[refute_0_20,refute_0_404]) ).

cnf(refute_0_406,plain,
    X_51 = inverse(inverse(X_51)),
    inference(resolve,[$cnf( $equal(multiply(X_51,multiplicative_identity),multiply(X_51,inverse(inverse(X_51)))) )],[refute_0_17,refute_0_405]) ).

cnf(refute_0_407,plain,
    ( X_51 != inverse(inverse(X_51))
    | inverse(inverse(X_51)) = X_51 ),
    inference(subst,[],[refute_0_28:[bind(X0,$fot(X_51)),bind(Y0,$fot(inverse(inverse(X_51))))]]) ).

cnf(refute_0_408,plain,
    inverse(inverse(X_51)) = X_51,
    inference(resolve,[$cnf( $equal(X_51,inverse(inverse(X_51))) )],[refute_0_406,refute_0_407]) ).

cnf(refute_0_409,plain,
    inverse(inverse(x)) = x,
    inference(subst,[],[refute_0_408:[bind(X_51,$fot(x))]]) ).

cnf(refute_0_410,plain,
    ( inverse(inverse(x)) != x
    | x != x
    | inverse(inverse(x)) = x ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(inverse(x)),x) ),[0],$fot(x)]]) ).

cnf(refute_0_411,plain,
    ( x != x
    | inverse(inverse(x)) = x ),
    inference(resolve,[$cnf( $equal(inverse(inverse(x)),x) )],[refute_0_409,refute_0_410]) ).

cnf(refute_0_412,plain,
    x != x,
    inference(resolve,[$cnf( $equal(inverse(inverse(x)),x) )],[refute_0_411,prove_inverse_is_an_involution]) ).

cnf(refute_0_413,plain,
    x = x,
    introduced(tautology,[refl,[$fot(x)]]) ).

cnf(refute_0_414,plain,
    $false,
    inference(resolve,[$cnf( $equal(x,x) )],[refute_0_413,refute_0_412]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : BOO012-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Wed Jun  1 17:43:19 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.52  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.52  
% 0.18/0.52  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.38/0.56  
%------------------------------------------------------------------------------