%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 13:03:00 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   14 (   9 unt;   0 nHn;  14 RR)
%            Number of literals    :   21 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(divide(a,a),zero),
    file('HEN003-5.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(divide(u,v),u),zero),
    file('HEN003-5.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),zero),
    file('HEN003-5.p',unknown),
    [] ).

cnf(4,axiom,
    equal(divide(zero,u),zero),
    file('HEN003-5.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ equal(divide(u,v),zero)
    | ~ equal(divide(v,u),zero)
    | equal(v,u) ),
    file('HEN003-5.p',unknown),
    [] ).

cnf(17,plain,
    ( ~ equal(zero,zero)
    | ~ equal(divide(u,zero),zero)
    | equal(u,zero) ),
    inference(spl,[status(thm),theory(equality)],[4,5]),
    [iquote('0:SpL:4.0,5.0')] ).

cnf(20,plain,
    ( ~ equal(divide(u,zero),zero)
    | equal(u,zero) ),
    inference(obv,[status(thm),theory(equality)],[17]),
    [iquote('0:Obv:17.0')] ).

cnf(43,plain,
    equal(divide(divide(divide(u,u),divide(v,u)),zero),zero),
    inference(spr,[status(thm),theory(equality)],[2,3]),
    [iquote('0:SpR:2.0,3.0')] ).

cnf(120,plain,
    equal(divide(divide(divide(u,u),zero),zero),zero),
    inference(spr,[status(thm),theory(equality)],[4,43]),
    [iquote('0:SpR:4.0,43.0')] ).

cnf(155,plain,
    ( ~ equal(zero,zero)
    | equal(divide(divide(u,u),zero),zero) ),
    inference(spl,[status(thm),theory(equality)],[120,20]),
    [iquote('0:SpL:120.0,20.0')] ).

cnf(156,plain,
    equal(divide(divide(u,u),zero),zero),
    inference(obv,[status(thm),theory(equality)],[155]),
    [iquote('0:Obv:155.0')] ).

cnf(181,plain,
    ( ~ equal(zero,zero)
    | equal(divide(u,u),zero) ),
    inference(spl,[status(thm),theory(equality)],[156,20]),
    [iquote('0:SpL:156.0,20.0')] ).

cnf(182,plain,
    equal(divide(u,u),zero),
    inference(obv,[status(thm),theory(equality)],[181]),
    [iquote('0:Obv:181.0')] ).

cnf(183,plain,
    $false,
    inference(unc,[status(thm)],[182,1]),
    [iquote('0:UnC:182.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Fri Jul  1 14:34:29 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.43  
% 0.20/0.43  SPASS V 3.9 
% 0.20/0.43  SPASS beiseite: Proof found.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.43  SPASS derived 122 clauses, backtracked 0 clauses, performed 0 splits and kept 33 clauses.
% 0.20/0.43  SPASS allocated 63301 KBytes.
% 0.20/0.43  SPASS spent	0:00:00.07 on the problem.
% 0.20/0.43  		0:00:00.03 for the input.
% 0.20/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43  		0:00:00.00 for inferences.
% 0.20/0.43  		0:00:00.00 for the backtracking.
% 0.20/0.43  		0:00:00.01 for the reduction.
% 0.20/0.43  
% 0.20/0.43  
% 0.20/0.43  Here is a proof with depth 4, length 14 :
% 0.20/0.43  % SZS output start Refutation
% See solution above
% 0.20/0.43  Formulae used in the proof : prove_x_divide_x_is_zero quotient_smaller_than_numerator quotient_property zero_is_smallest divide_and_equal
% 0.20/0.43  
%------------------------------------------------------------------------------