TSTP Solution File: SWV633-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV633-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 : Wed Jul 20 20:39:43 EDT 2022
% Result : Unsatisfiable 1.02s 1.19s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 36
% Syntax : Number of clauses : 103 ( 50 unt; 0 nHn; 94 RR)
% Number of literals : 182 ( 181 equ; 81 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_One__nat__def_0,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).
cnf(cls_numeral__2__eq__2_0,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ).
cnf(cls_nat__mult__2__right_0,axiom,
c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ).
cnf(cls_nat__mult__assoc_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ).
cnf(cls_nat__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( c_HOL_Oone__class_Oone(tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(c_HOL_Oone__class_Oone(tc_nat))),bind(Y,$fot(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))]]) ).
cnf(refute_0_4,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )],[cls_One__nat__def_0,refute_0_3]) ).
cnf(refute_0_5,plain,
c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
introduced(tautology,[refl,[$fot(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))]]) ).
cnf(refute_0_6,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oone__class_Oone(tc_nat)
| c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) != c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
| c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))) ),[1,0],$fot(c_HOL_Oone__class_Oone(tc_nat))]]) ).
cnf(refute_0_7,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oone__class_Oone(tc_nat)
| c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)) ),
inference(resolve,[$cnf( $equal(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)),
inference(resolve,[$cnf( $equal(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
| c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) != c_Suc(c_HOL_Oone__class_Oone(tc_nat))
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat))) ),[0],$fot(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))]]) ).
cnf(refute_0_10,plain,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)) ),
inference(resolve,[$cnf( $equal(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Oone__class_Oone(tc_nat))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)),
inference(resolve,[$cnf( $equal(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))) )],[cls_numeral__2__eq__2_0,refute_0_10]) ).
cnf(refute_0_12,plain,
c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
introduced(tautology,[refl,[$fot(c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))]]) ).
cnf(refute_0_13,plain,
( c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Suc(c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_z,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) ),[1,1],$fot(c_Suc(c_HOL_Oone__class_Oone(tc_nat)))]]) ).
cnf(refute_0_14,plain,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Suc(c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_z,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_z,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(resolve,[$cnf( $equal(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat)
| c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(V_z,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| c_HOL_Otimes__class_Otimes(V_z,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat)) ),[0],$fot(c_HOL_Otimes__class_Otimes(V_z,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat))]]) ).
cnf(refute_0_17,plain,
( c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat)
| c_HOL_Otimes__class_Otimes(V_z,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(V_z,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
c_HOL_Otimes__class_Otimes(V_z,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat)) )],[cls_nat__mult__2__right_0,refute_0_17]) ).
cnf(refute_0_19,plain,
c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),
inference(subst,[],[refute_0_18:[bind(V_z,$fot(v_j))]]) ).
cnf(refute_0_20,plain,
c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
introduced(tautology,[refl,[$fot(c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))]]) ).
cnf(refute_0_21,plain,
( c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Suc(c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) ),[1,1],$fot(c_Suc(c_HOL_Oone__class_Oone(tc_nat)))]]) ).
cnf(refute_0_22,plain,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Suc(c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(resolve,[$cnf( $equal(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat))) )],[refute_0_11,refute_0_22]) ).
cnf(refute_0_24,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_25,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_24]) ).
cnf(refute_0_26,plain,
( c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) != c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)
| c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))),bind(Y,$fot(c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat))),bind(Z,$fot(c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)))]]) ).
cnf(refute_0_27,plain,
( c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) != c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)
| c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)) )],[refute_0_19,refute_0_27]) ).
cnf(refute_0_29,plain,
( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat)
| c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat))),bind(Y,$fot(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat)))]]) ).
cnf(refute_0_30,plain,
c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat)) )],[cls_nat__mult__commute_0,refute_0_29]) ).
cnf(refute_0_31,plain,
c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat) = c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
inference(subst,[],[refute_0_30:[bind(V_m,$fot(v_j)),bind(V_n,$fot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))]]) ).
cnf(refute_0_32,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat) != c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat) = c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat))),bind(Y,$fot(c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))),bind(Z,$fot(c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)))]]) ).
cnf(refute_0_33,plain,
( c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat) = c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat) = c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),
introduced(tautology,[refl,[$fot(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat))]]) ).
cnf(refute_0_36,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat) != c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)
| c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat)) ),[1,1],$fot(c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat))]]) ).
cnf(refute_0_37,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat) != c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)
| c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_40,plain,
( c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) ),[1,1],$fot(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat))]]) ).
cnf(refute_0_41,plain,
( c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat),
inference(subst,[],[refute_0_18:[bind(V_z,$fot(v_m))]]) ).
cnf(refute_0_44,plain,
c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
introduced(tautology,[refl,[$fot(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))]]) ).
cnf(refute_0_45,plain,
( c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Suc(c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) ),[1,1],$fot(c_Suc(c_HOL_Oone__class_Oone(tc_nat)))]]) ).
cnf(refute_0_46,plain,
( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) != c_Suc(c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(resolve,[$cnf( $equal(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat))) )],[refute_0_11,refute_0_46]) ).
cnf(refute_0_48,plain,
( c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) != c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)
| c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))),bind(Y,$fot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat))),bind(Z,$fot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)))]]) ).
cnf(refute_0_49,plain,
( c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) != c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)
| c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)) )],[refute_0_43,refute_0_49]) ).
cnf(refute_0_51,plain,
c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat) = c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
inference(subst,[],[refute_0_30:[bind(V_m,$fot(v_m)),bind(V_n,$fot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))]]) ).
cnf(refute_0_52,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat) != c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat) = c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat))),bind(Y,$fot(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))),bind(Z,$fot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)))]]) ).
cnf(refute_0_53,plain,
( c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat) = c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat),c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat) = c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)) = c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),
introduced(tautology,[refl,[$fot(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)))]]) ).
cnf(refute_0_56,plain,
( c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)) != c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat))
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat) != c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)
| c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)) = c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat))) ),[1,0],$fot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat))]]) ).
cnf(refute_0_57,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat) != c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)
| c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)) = c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)) ),
inference(resolve,[$cnf( $equal(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)) = c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat),c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_60,plain,
( c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)) != c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat))
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) ),[1,0],$fot(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)))]]) ).
cnf(refute_0_61,plain,
( c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)) != c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat))
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))),bind(Y,$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))),bind(Z,$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)))]]) ).
cnf(refute_0_64,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_42,refute_0_64]) ).
cnf(refute_0_66,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) ),[1],$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_67,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat),
introduced(tautology,[refl,[$fot(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat))]]) ).
cnf(refute_0_69,plain,
( c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)
| c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)) ),[1,1],$fot(c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat))]]) ).
cnf(refute_0_70,plain,
( c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)
| c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat)) )],[refute_0_28,refute_0_70]) ).
cnf(refute_0_72,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat),
inference(subst,[],[cls_nat__mult__assoc_0:[bind(V_k,$fot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),bind(V_m,$fot(v_i)),bind(V_n,$fot(v_j))]]) ).
cnf(refute_0_73,plain,
c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
inference(subst,[],[refute_0_30:[bind(V_m,$fot(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat))),bind(V_n,$fot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))]]) ).
cnf(refute_0_74,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat))),bind(Y,$fot(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat))),bind(Z,$fot(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)))]]) ).
cnf(refute_0_75,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat))),bind(Y,$fot(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat))),bind(Z,$fot(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)))]]) ).
cnf(refute_0_78,plain,
( c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)) )],[refute_0_71,refute_0_78]) ).
cnf(refute_0_80,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_81,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) ),[1,1],$fot(c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat))]]) ).
cnf(refute_0_82,plain,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) != c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat)) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_85,plain,
( c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)) != c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat))
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) ),[1,0],$fot(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)))]]) ).
cnf(refute_0_86,plain,
( c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)) != c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat))
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat))) )],[refute_0_58,refute_0_86]) ).
cnf(refute_0_88,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))),bind(Y,$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))),bind(Z,$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)))]]) ).
cnf(refute_0_89,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_83,refute_0_89]) ).
cnf(refute_0_91,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) ),[1],$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_92,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_92,refute_0_67]) ).
cnf(refute_0_94,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_93,cls_conjecture_0]) ).
cnf(refute_0_95,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_96,plain,
$false,
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_95,refute_0_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV633-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 15 10:28:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.02/1.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.02/1.19
% 1.02/1.19 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.02/1.21
%------------------------------------------------------------------------------