TSTP Solution File: ALG340-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : ALG340-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 17:40:01 EDT 2022

% Result   : Unsatisfiable 2.58s 2.79s
% Output   : CNFRefutation 2.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   23
% Syntax   : Number of clauses     :   76 (  38 unt;   0 nHn;  40 RR)
%            Number of literals    :  128 (  88 equ;  56 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-3 aty)
%            Number of variables   :  142 (   8 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_real__of__preal__zero__less_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_m),tc_RealDef_Oreal) ).

cnf(cls_real__mult__order_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_real__mult__commute_0,axiom,
    c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal) ).

cnf(cls_real__mult__assoc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_z1,V_z2,tc_RealDef_Oreal),V_z3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_z1,c_HOL_Otimes__class_Otimes(V_z2,V_z3,tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_real__less__def_0,axiom,
    ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_norm__zero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_order__root_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_conjecture_1,negated_conjecture,
    ( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_xa,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal) ) ).

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ).

cnf(refute_0_0,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(subst,[],[cls_real__less__def_0:[bind(V_x,$fot(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),bind(V_y,$fot(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)))]]) ).

cnf(refute_0_1,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(subst,[],[cls_real__mult__order_0:[bind(V_x,$fot(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal))),bind(V_y,$fot(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal)))]]) ).

cnf(refute_0_2,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_m),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(V_m),c_RealDef_Oreal__of__preal(V_m),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(subst,[],[cls_real__mult__order_0:[bind(V_x,$fot(c_RealDef_Oreal__of__preal(V_m))),bind(V_y,$fot(c_RealDef_Oreal__of__preal(V_m)))]]) ).

cnf(refute_0_3,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(V_m),c_RealDef_Oreal__of__preal(V_m),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_m),tc_RealDef_Oreal) )],[cls_real__of__preal__zero__less_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[refute_0_3:[bind(V_m,$fot(X_137))]]) ).

cnf(refute_0_5,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal) )],[refute_0_4,refute_0_1]) ).

cnf(refute_0_6,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[cls_real__mult__commute_0:[bind(V_z,$fot(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal)))]]) ).

cnf(refute_0_7,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[cls_real__mult__commute_0:[bind(V_z,$fot(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal)))]]) ).

cnf(refute_0_8,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[cls_real__mult__assoc_0:[bind(V_z1,$fot(X_51)),bind(V_z2,$fot(X_52)),bind(V_z3,$fot(X_53))]]) ).

cnf(refute_0_9,plain,
    c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal),
    inference(subst,[],[cls_real__mult__commute_0:[bind(V_w,$fot(X_51)),bind(V_z,$fot(X_52))]]) ).

cnf(refute_0_10,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_11,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_12,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal) ),
    inference(subst,[],[refute_0_12:[bind(X,$fot(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal))),bind(Y,$fot(c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal)))]]) ).

cnf(refute_0_14,plain,
    c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal)) )],[refute_0_9,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),[0,0],$fot(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal))]]) ).

cnf(refute_0_16,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal)) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_51,X_52,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_8,refute_0_16]) ).

cnf(refute_0_18,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_52,c_HOL_Otimes__class_Otimes(X_51,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[cls_real__mult__assoc_0:[bind(V_z1,$fot(X_52)),bind(V_z2,$fot(X_51)),bind(V_z3,$fot(X_53))]]) ).

cnf(refute_0_19,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_52,c_HOL_Otimes__class_Otimes(X_51,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(X_52,c_HOL_Otimes__class_Otimes(X_51,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),[0],$fot(c_HOL_Otimes__class_Otimes(X_52,c_HOL_Otimes__class_Otimes(X_51,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal))]]) ).

cnf(refute_0_20,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(X_52,c_HOL_Otimes__class_Otimes(X_51,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_52,c_HOL_Otimes__class_Otimes(X_51,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    c_HOL_Otimes__class_Otimes(X_52,c_HOL_Otimes__class_Otimes(X_51,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_52,X_51,tc_RealDef_Oreal),X_53,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_51,c_HOL_Otimes__class_Otimes(X_52,X_53,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_17,refute_0_20]) ).

cnf(refute_0_22,plain,
    c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[refute_0_21:[bind(X_51,$fot(X_112)),bind(X_52,$fot(V_w)),bind(X_53,$fot(X_114))]]) ).

cnf(refute_0_23,plain,
    ( c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),[1],$fot(c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal))]]) ).

cnf(refute_0_24,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_7,refute_0_24]) ).

cnf(refute_0_26,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(X_114,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[cls_real__mult__assoc_0:[bind(V_z1,$fot(X_112)),bind(V_z2,$fot(X_114)),bind(V_z3,$fot(V_w))]]) ).

cnf(refute_0_27,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(X_114,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(X_114,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),[0],$fot(c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(X_114,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal))]]) ).

cnf(refute_0_28,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(X_114,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(X_114,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(X_114,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_112,X_114,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_112,c_HOL_Otimes__class_Otimes(V_w,X_114,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_25,refute_0_28]) ).

cnf(refute_0_30,plain,
    c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[refute_0_29:[bind(V_w,$fot(X_115)),bind(X_112,$fot(V_w)),bind(X_114,$fot(X_117))]]) ).

cnf(refute_0_31,plain,
    ( c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),[1],$fot(c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal))]]) ).

cnf(refute_0_32,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_6,refute_0_32]) ).

cnf(refute_0_34,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[cls_real__mult__assoc_0:[bind(V_z1,$fot(X_117)),bind(V_z2,$fot(X_115)),bind(V_z3,$fot(V_w))]]) ).

cnf(refute_0_35,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),[0],$fot(c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal))]]) ).

cnf(refute_0_36,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X_117,X_115,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_33,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(subst,[],[refute_0_12:[bind(X,$fot(c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal))),bind(Y,$fot(c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal)))]]) ).

cnf(refute_0_39,plain,
    c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(X_117,c_HOL_Otimes__class_Otimes(X_115,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_w,c_HOL_Otimes__class_Otimes(X_115,X_117,tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[refute_0_39:[bind(V_w,$fot(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal))),bind(X_115,$fot(c_RealDef_Oreal__of__preal(X_137))),bind(X_117,$fot(c_RealDef_Oreal__of__preal(X_137)))]]) ).

cnf(refute_0_41,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(tautology,[equality,[$cnf( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),[1],$fot(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))]]) ).

cnf(refute_0_42,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_137),c_RealDef_Oreal__of__preal(X_137),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )],[refute_0_5,refute_0_42]) ).

cnf(refute_0_44,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(subst,[],[refute_0_43:[bind(X_137,$fot(X_142))]]) ).

cnf(refute_0_45,plain,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )],[refute_0_44,refute_0_0]) ).

cnf(refute_0_46,plain,
    ( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(subst,[],[cls_norm__zero_0:[bind(T_a,$fot(tc_Complex_Ocomplex))]]) ).

cnf(refute_0_47,plain,
    c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(resolve,[$cnf( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) )],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
    | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X_147,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(subst,[],[cls_order__root_1:[bind(T_a,$fot(tc_Complex_Ocomplex)),bind(V_a,$fot(X_147))]]) ).

cnf(refute_0_49,plain,
    c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X_147,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(resolve,[$cnf( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )],[clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,refute_0_48]) ).

cnf(refute_0_50,plain,
    c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(subst,[],[refute_0_49:[bind(X_147,$fot(v_x(V_xa)))]]) ).

cnf(refute_0_51,plain,
    c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    introduced(tautology,[refl,[$fot(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex))]]) ).

cnf(refute_0_52,plain,
    ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(tautology,[equality,[$cnf( $equal(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),[1,0],$fot(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))]]) ).

cnf(refute_0_53,plain,
    ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    inference(resolve,[$cnf( $equal(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(resolve,[$cnf( $equal(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) )],[refute_0_50,refute_0_53]) ).

cnf(refute_0_55,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_56,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_12,refute_0_55]) ).

cnf(refute_0_57,plain,
    ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(subst,[],[refute_0_56:[bind(X,$fot(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex))),bind(Y,$fot(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex))),bind(Z,$fot(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)))]]) ).

cnf(refute_0_58,plain,
    ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( $equal(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_54,refute_0_57]) ).

cnf(refute_0_59,plain,
    c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(resolve,[$cnf( $equal(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) )],[refute_0_47,refute_0_58]) ).

cnf(refute_0_60,plain,
    ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_xa,tc_RealDef_Oreal) ),
    introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_xa,tc_RealDef_Oreal) ),[0],$fot(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))]]) ).

cnf(refute_0_61,plain,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_xa,tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( $equal(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) )],[refute_0_59,refute_0_60]) ).

cnf(refute_0_62,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal) ),
    inference(resolve,[$cnf( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_xa,tc_RealDef_Oreal) )],[refute_0_61,cls_conjecture_1]) ).

cnf(refute_0_63,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(subst,[],[refute_0_62:[bind(V_xa,$fot(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)))]]) ).

cnf(refute_0_64,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolve,[$cnf( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )],[refute_0_45,refute_0_63]) ).

cnf(refute_0_65,plain,
    $false,
    inference(resolve,[$cnf( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal__of__preal(X_142),c_RealDef_Oreal__of__preal(X_142),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )],[refute_0_44,refute_0_64]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : ALG340-1 : TPTP v8.1.0. Released v4.1.0.
% 0.02/0.10  % Command  : metis --show proof --show saturation %s
% 0.10/0.30  % Computer : n024.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Wed Jun  8 19:16:49 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 0.10/0.31  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.58/2.79  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.58/2.79  
% 2.58/2.79  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.58/2.80  
%------------------------------------------------------------------------------