TSTP Solution File: ALG402-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ALG402-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 17:40:08 EDT 2022
% Result : Unsatisfiable 115.40s 115.65s
% Output : CNFRefutation 115.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 27
% Syntax : Number of clauses : 64 ( 32 unt; 0 nHn; 38 RR)
% Number of literals : 107 ( 94 equ; 46 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 55 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_zero__neq__one_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_mult__1_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ).
cnf(cls_power__one_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ).
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_mult__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ).
cnf(refute_0_0,plain,
( ~ class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X_424,tc_Complex_Ocomplex) = X_424 ),
inference(subst,[],[cls_mult__1_0:[bind(T_a,$fot(tc_Complex_Ocomplex)),bind(V_a,$fot(X_424))]]) ).
cnf(refute_0_1,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X_424,tc_Complex_Ocomplex) = X_424,
inference(resolve,[$cnf( class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) )],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,refute_0_0]) ).
cnf(refute_0_2,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(subst,[],[refute_0_1:[bind(X_424,$fot(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)))]]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( c_HOL_Oone__class_Oone(tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(c_HOL_Oone__class_Oone(tc_nat))),bind(Y,$fot(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))]]) ).
cnf(refute_0_7,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
inference(resolve,[$cnf( $equal(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )],[cls_One__nat__def_0,refute_0_6]) ).
cnf(refute_0_8,plain,
c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
introduced(tautology,[refl,[$fot(c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))]]) ).
cnf(refute_0_9,plain,
( c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) != c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) ),[1,1],$fot(c_HOL_Oone__class_Oone(tc_nat))]]) ).
cnf(refute_0_10,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(resolve,[$cnf( $equal(c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(resolve,[$cnf( $equal(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_13,plain,
( c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) != c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex)) ),[1,1],$fot(c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat))]]) ).
cnf(refute_0_14,plain,
( c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) != c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_17,plain,
( c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),[1,1],$fot(c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_18,plain,
( c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),[0],$fot(c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_21,plain,
( c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_23,plain,
( c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) != c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex)) ),[1,1],$fot(c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat))]]) ).
cnf(refute_0_24,plain,
( c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) != c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )],[refute_0_11,refute_0_24]) ).
cnf(refute_0_26,plain,
c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_27,plain,
( c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),[1,1],$fot(c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_28,plain,
( c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),[0],$fot(c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_31,plain,
( c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_21,refute_0_31]) ).
cnf(refute_0_33,plain,
c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[cls_conjecture_0,refute_0_32]) ).
cnf(refute_0_34,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(subst,[],[refute_0_33:[bind(V_x,$fot(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),bind(V_xa,$fot(X_1098))]]) ).
cnf(refute_0_35,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)) ),[0],$fot(c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_36,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_2,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X_3087,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(subst,[],[cls_power__one_0:[bind(T_a,$fot(tc_Complex_Ocomplex)),bind(V_n,$fot(X_3087))]]) ).
cnf(refute_0_39,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X_3087,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolve,[$cnf( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) )],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,refute_0_38]) ).
cnf(refute_0_40,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(subst,[],[refute_0_39:[bind(X_3087,$fot(c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))]]) ).
cnf(refute_0_41,plain,
( c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),[0],$fot(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_42,plain,
( c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(X_1098,c_Power_Opower__class_Opower(X_1098,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(subst,[],[refute_0_43:[bind(X_1098,$fot(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)))]]) ).
cnf(refute_0_45,plain,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X_3664,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(subst,[],[cls_mult__eq__0__iff_1:[bind(T_a,$fot(tc_Complex_Ocomplex)),bind(V_b,$fot(X_3664))]]) ).
cnf(refute_0_46,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X_3664,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[$cnf( class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) )],[clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,refute_0_45]) ).
cnf(refute_0_47,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(subst,[],[refute_0_46:[bind(X_3664,$fot(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex)))]]) ).
cnf(refute_0_48,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),[0],$fot(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))]]) ).
cnf(refute_0_49,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) )],[refute_0_44,refute_0_49]) ).
cnf(refute_0_51,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
inference(subst,[],[cls_zero__neq__one_0:[bind(T_a,$fot(tc_Complex_Ocomplex))]]) ).
cnf(refute_0_52,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolve,[$cnf( class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) )],[clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,refute_0_51]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( $equal(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) )],[refute_0_50,refute_0_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG402-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 12:25:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 115.40/115.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 115.40/115.65
% 115.40/115.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 115.40/115.65
%------------------------------------------------------------------------------