%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG341-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 18:03:24 EDT 2022

% Result   : Unsatisfiable 0.17s 0.52s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :   10 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(465,axiom,
    ( ~ c_lessequals(u,v,tc_RealDef_Oreal)
    | ~ c_lessequals(v,w,tc_RealDef_Oreal)
    | c_lessequals(u,w,tc_RealDef_Oreal) ),
    file('ALG341-1.p',unknown),
    [] ).

cnf(472,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    file('ALG341-1.p',unknown),
    [] ).

cnf(473,axiom,
    c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
    file('ALG341-1.p',unknown),
    [] ).

cnf(595,axiom,
    ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
    file('ALG341-1.p',unknown),
    [] ).

cnf(636,plain,
    ( ~ c_lessequals(u,v_r,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal) ),
    inference(res,[status(thm),theory(equality)],[465,595]),
    [iquote('0:Res:465.2,595.0')] ).

cnf(772,plain,
    ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
    inference(res,[status(thm),theory(equality)],[472,636]),
    [iquote('0:Res:472.0,636.1')] ).

cnf(794,plain,
    $false,
    inference(mrr,[status(thm)],[772,473]),
    [iquote('0:MRR:772.0,473.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : ALG341-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.32  % Computer : n027.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Wed Jun  8 11:33:56 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.17/0.52  
% 0.17/0.52  SPASS V 3.9 
% 0.17/0.52  SPASS beiseite: Proof found.
% 0.17/0.52  % SZS status Theorem
% 0.17/0.52  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.17/0.52  SPASS derived 145 clauses, backtracked 0 clauses, performed 0 splits and kept 572 clauses.
% 0.17/0.52  SPASS allocated 76645 KBytes.
% 0.17/0.52  SPASS spent	0:00:00.19 on the problem.
% 0.17/0.52  		0:00:00.06 for the input.
% 0.17/0.52  		0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.52  		0:00:00.00 for inferences.
% 0.17/0.52  		0:00:00.00 for the backtracking.
% 0.17/0.52  		0:00:00.07 for the reduction.
% 0.17/0.52  
% 0.17/0.52  
% 0.17/0.52  Here is a proof with depth 2, length 7 :
% 0.17/0.52  % SZS output start Refutation
% See solution above
% 0.17/0.52  Formulae used in the proof : cls_real__le__trans_0 cls_CHAINED_0 cls_CHAINED_0_01 cls_conjecture_0
% 0.17/0.52  
%------------------------------------------------------------------------------