%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ANA021-2 : TPTP v8.1.0. Released v3.2.0.
% 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 19:28:48 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   6 unt;   1 nHn;   9 RR)
%            Number of literals    :   12 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_less(c_0,u,tc_nat)
    | equal(c_Suc(c_minus(u,c_1,tc_nat)),u) ),
    file('ANA021-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( equal(u,c_0)
    | c_less(c_0,u,tc_nat) ),
    file('ANA021-2.p',unknown),
    [] ).

cnf(3,axiom,
    c_lessequals(c_HOL_Oabs(v(c_Suc(u)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(u)),t_a),t_a),t_a),
    file('ANA021-2.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(v_x,c_0),
    file('ANA021-2.p',unknown),
    [] ).

cnf(5,axiom,
    ~ c_lessequals(c_HOL_Oabs(v(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
    file('ANA021-2.p',unknown),
    [] ).

cnf(7,plain,
    ( ~ c_less(c_0,u,tc_nat)
    | c_lessequals(c_HOL_Oabs(v(u),t_a),c_times(v_c,c_HOL_Oabs(v_h(u),t_a),t_a),t_a) ),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.1,3.0')] ).

cnf(9,plain,
    ~ c_less(c_0,v_x,tc_nat),
    inference(res,[status(thm),theory(equality)],[7,5]),
    [iquote('0:Res:7.1,5.0')] ).

cnf(10,plain,
    equal(v_x,c_0),
    inference(res,[status(thm),theory(equality)],[2,9]),
    [iquote('0:Res:2.1,9.0')] ).

cnf(11,plain,
    $false,
    inference(mrr,[status(thm)],[10,4]),
    [iquote('0:MRR:10.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ANA021-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % 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 : Fri Jul  8 04:47:25 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.42  
% 0.20/0.42  SPASS V 3.9 
% 0.20/0.42  SPASS beiseite: Proof found.
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.42  SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 8 clauses.
% 0.20/0.42  SPASS allocated 63092 KBytes.
% 0.20/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.42  		0:00:00.04 for the input.
% 0.20/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42  		0:00:00.00 for inferences.
% 0.20/0.42  		0:00:00.00 for the backtracking.
% 0.20/0.42  		0:00:00.00 for the reduction.
% 0.20/0.42  
% 0.20/0.42  
% 0.20/0.42  Here is a proof with depth 3, length 9 :
% 0.20/0.42  % SZS output start Refutation
% See solution above
% 0.20/0.42  Formulae used in the proof : cls_NatBin_OSuc__pred_H_0 cls_Nat_Onot__gr0_0 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4
% 0.20/0.42  
%------------------------------------------------------------------------------