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