%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV675-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 21:44:46 EDT 2022

% Result   : Unsatisfiable 0.61s 0.81s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    5 (   4 unt;   0 nHn;   5 RR)
%            Number of literals    :    6 (   0 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(812,axiom,
    ~ c_HOL_Oord__class_Oless(u,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('SWV675-1.p',unknown),
    [] ).

cnf(951,axiom,
    ( ~ c_lessequals(c_Suc(u),v,tc_nat)
    | c_HOL_Oord__class_Oless(u,v,tc_nat) ),
    file('SWV675-1.p',unknown),
    [] ).

cnf(1388,axiom,
    c_lessequals(c_Suc(v_y),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('SWV675-1.p',unknown),
    [] ).

cnf(1670,plain,
    c_HOL_Oord__class_Oless(v_y,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(res,[status(thm),theory(equality)],[1388,951]),
    [iquote('0:Res:1388.0,951.0')] ).

cnf(1901,plain,
    $false,
    inference(mrr,[status(thm)],[1670,812]),
    [iquote('0:MRR:1670.0,812.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SWV675-1 : TPTP v8.1.0. Released v4.1.0.
% 0.13/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35  % CPULimit : 300
% 0.20/0.35  % WCLimit  : 600
% 0.20/0.35  % DateTime : Wed Jun 15 11:41:22 EDT 2022
% 0.20/0.35  % CPUTime  : 
% 0.61/0.81  
% 0.61/0.81  SPASS V 3.9 
% 0.61/0.81  SPASS beiseite: Proof found.
% 0.61/0.81  % SZS status Theorem
% 0.61/0.81  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.61/0.81  SPASS derived 203 clauses, backtracked 0 clauses, performed 0 splits and kept 1065 clauses.
% 0.61/0.81  SPASS allocated 78095 KBytes.
% 0.61/0.81  SPASS spent	0:00:00.43 on the problem.
% 0.61/0.81  		0:00:00.11 for the input.
% 0.61/0.81  		0:00:00.00 for the FLOTTER CNF translation.
% 0.61/0.81  		0:00:00.00 for inferences.
% 0.61/0.81  		0:00:00.00 for the backtracking.
% 0.61/0.81  		0:00:00.20 for the reduction.
% 0.61/0.81  
% 0.61/0.81  
% 0.61/0.81  Here is a proof with depth 1, length 5 :
% 0.61/0.81  % SZS output start Refutation
% See solution above
% 0.61/0.81  Formulae used in the proof : cls_gr__implies__not0_0 cls_Suc__le__eq_0 cls_conjecture_0
% 0.61/0.81  
%------------------------------------------------------------------------------