%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : HEN005-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 13:03:03 EDT 2022

% Result   : Unsatisfiable 0.18s 0.42s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (  11 unt;   0 nHn;  16 RR)
%            Number of literals    :   23 (   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    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(divide(a,b),zero),
    file('HEN005-5.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(b,c),zero),
    file('HEN005-5.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(divide(a,c),zero),
    file('HEN005-5.p',unknown),
    [] ).

cnf(5,axiom,
    equal(divide(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),zero),
    file('HEN005-5.p',unknown),
    [] ).

cnf(6,axiom,
    equal(divide(zero,u),zero),
    file('HEN005-5.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ equal(divide(u,v),zero)
    | ~ equal(divide(v,u),zero)
    | equal(v,u) ),
    file('HEN005-5.p',unknown),
    [] ).

cnf(25,plain,
    ( ~ equal(zero,zero)
    | ~ equal(divide(u,zero),zero)
    | equal(u,zero) ),
    inference(spl,[status(thm),theory(equality)],[6,7]),
    [iquote('0:SpL:6.0,7.0')] ).

cnf(30,plain,
    ( ~ equal(divide(u,zero),zero)
    | equal(u,zero) ),
    inference(obv,[status(thm),theory(equality)],[25]),
    [iquote('0:Obv:25.0')] ).

cnf(40,plain,
    equal(divide(divide(divide(a,u),divide(b,u)),divide(zero,u)),zero),
    inference(spr,[status(thm),theory(equality)],[1,5]),
    [iquote('0:SpR:1.0,5.0')] ).

cnf(60,plain,
    equal(divide(divide(divide(a,u),divide(b,u)),zero),zero),
    inference(rew,[status(thm),theory(equality)],[6,40]),
    [iquote('0:Rew:6.0,40.0')] ).

cnf(117,plain,
    equal(divide(divide(divide(a,c),zero),zero),zero),
    inference(spr,[status(thm),theory(equality)],[2,60]),
    [iquote('0:SpR:2.0,60.0')] ).

cnf(139,plain,
    ( ~ equal(zero,zero)
    | equal(divide(divide(a,c),zero),zero) ),
    inference(spl,[status(thm),theory(equality)],[117,30]),
    [iquote('0:SpL:117.0,30.0')] ).

cnf(140,plain,
    equal(divide(divide(a,c),zero),zero),
    inference(obv,[status(thm),theory(equality)],[139]),
    [iquote('0:Obv:139.0')] ).

cnf(157,plain,
    ( ~ equal(zero,zero)
    | equal(divide(a,c),zero) ),
    inference(spl,[status(thm),theory(equality)],[140,30]),
    [iquote('0:SpL:140.0,30.0')] ).

cnf(158,plain,
    equal(divide(a,c),zero),
    inference(obv,[status(thm),theory(equality)],[157]),
    [iquote('0:Obv:157.0')] ).

cnf(159,plain,
    $false,
    inference(mrr,[status(thm)],[158,3]),
    [iquote('0:MRR:158.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : HEN005-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jul  1 13:01:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.42  
% 0.18/0.42  SPASS V 3.9 
% 0.18/0.42  SPASS beiseite: Proof found.
% 0.18/0.42  % SZS status Theorem
% 0.18/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.42  SPASS derived 98 clauses, backtracked 0 clauses, performed 0 splits and kept 41 clauses.
% 0.18/0.42  SPASS allocated 63301 KBytes.
% 0.18/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.18/0.42  		0:00:00.03 for the input.
% 0.18/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42  		0:00:00.00 for inferences.
% 0.18/0.42  		0:00:00.00 for the backtracking.
% 0.18/0.42  		0:00:00.01 for the reduction.
% 0.18/0.42  
% 0.18/0.42  
% 0.18/0.42  Here is a proof with depth 4, length 16 :
% 0.18/0.42  % SZS output start Refutation
% See solution above
% 0.18/0.42  Formulae used in the proof : a_divide_b_is_zero b_divide_c_is_zero prove_transitivity_of_divide_to_zero quotient_property zero_is_smallest divide_and_equal
% 0.18/0.42  
%------------------------------------------------------------------------------