%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG384-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 18:03:32 EDT 2022

% Result   : Unsatisfiable 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    6 (   4 unt;   1 nHn;   6 RR)
%            Number of literals    :    9 (   0 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(485,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(u)
    | equal(v,c_HOL_Ozero__class_Ozero(u))
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v,u),tc_RealDef_Oreal) ),
    file('ALG384-1.p',unknown),
    [] ).

cnf(496,axiom,
    ~ equal(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_c____),
    file('ALG384-1.p',unknown),
    [] ).

cnf(562,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('ALG384-1.p',unknown),
    [] ).

cnf(574,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    file('ALG384-1.p',unknown),
    [] ).

cnf(608,plain,
    ( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | equal(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_c____) ),
    inference(res,[status(thm),theory(equality)],[485,574]),
    [iquote('0:Res:485.1,574.0')] ).

cnf(682,plain,
    $false,
    inference(mrr,[status(thm)],[608,562,496]),
    [iquote('0:MRR:608.0,608.1,562.0,496.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ALG384-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Wed Jun  8 12:04:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.54  
% 0.20/0.54  SPASS V 3.9 
% 0.20/0.54  SPASS beiseite: Proof found.
% 0.20/0.54  % SZS status Theorem
% 0.20/0.54  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.54  SPASS derived 20 clauses, backtracked 0 clauses, performed 0 splits and kept 502 clauses.
% 0.20/0.54  SPASS allocated 76497 KBytes.
% 0.20/0.54  SPASS spent	0:00:00.19 on the problem.
% 0.20/0.54  		0:00:00.06 for the input.
% 0.20/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.54  		0:00:00.00 for inferences.
% 0.20/0.54  		0:00:00.00 for the backtracking.
% 0.20/0.54  		0:00:00.08 for the reduction.
% 0.20/0.54  
% 0.20/0.54  
% 0.20/0.54  Here is a proof with depth 1, length 6 :
% 0.20/0.54  % SZS output start Refutation
% See solution above
% 0.20/0.54  Formulae used in the proof : cls_zero__less__norm__iff_1 cls_CHAINED_0 clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector cls_conjecture_0
% 0.20/0.54  
%------------------------------------------------------------------------------