%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : HEN002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 : Sat Jul 16 13:02:57 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% 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;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ quotient(zero,x__dfg,zero),
    file('HEN002-1.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ less_equal(u,v)
    | quotient(u,v,zero) ),
    file('HEN002-1.p',unknown),
    [] ).

cnf(6,axiom,
    less_equal(zero,u),
    file('HEN002-1.p',unknown),
    [] ).

cnf(11,plain,
    ~ less_equal(zero,x__dfg),
    inference(res,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Res:2.1,1.0')] ).

cnf(12,plain,
    $false,
    inference(mrr,[status(thm)],[11,6]),
    [iquote('0:MRR:11.0,6.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : HEN002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Fri Jul  1 13:52:48 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.41  
% 0.19/0.41  SPASS V 3.9 
% 0.19/0.41  SPASS beiseite: Proof found.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 1 clauses, backtracked 0 clauses, performed 0 splits and kept 11 clauses.
% 0.19/0.41  SPASS allocated 63084 KBytes.
% 0.19/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.41  		0:00:00.04 for the input.
% 0.19/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41  		0:00:00.00 for inferences.
% 0.19/0.41  		0:00:00.00 for the backtracking.
% 0.19/0.41  		0:00:00.00 for the reduction.
% 0.19/0.41  
% 0.19/0.41  
% 0.19/0.41  Here is a proof with depth 1, length 5 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : prove_zero_divide_anything_is_zero quotient_less_equal zero_is_smallest
% 0.19/0.41  
%------------------------------------------------------------------------------