TSTP Solution File: HEN009-5 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : HEN009-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 13:03:11 EDT 2022

% Result   : Unsatisfiable 9.52s 9.76s
% Output   : Refutation 9.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   21 (   8 unt;   0 nHn;  21 RR)
%            Number of literals    :   40 (   0 equ;  20 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ equal(divide(divide(u,v),w),zero)
    | equal(divide(divide(u,w),v),zero) ),
    file('HEN009-5.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ equal(divide(u,v),zero)
    | equal(divide(divide(w,v),divide(w,u)),zero) ),
    file('HEN009-5.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)),
    file('HEN009-5.p',unknown),
    [] ).

cnf(5,axiom,
    equal(divide(divide(u,v),u),zero),
    file('HEN009-5.p',unknown),
    [] ).

cnf(7,axiom,
    equal(divide(zero,u),zero),
    file('HEN009-5.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ equal(divide(u,v),zero)
    | ~ equal(divide(v,u),zero)
    | equal(v,u) ),
    file('HEN009-5.p',unknown),
    [] ).

cnf(20,plain,
    ( ~ equal(zero,zero)
    | ~ equal(divide(u,zero),zero)
    | equal(u,zero) ),
    inference(spl,[status(thm),theory(equality)],[7,8]),
    [iquote('0:SpL:7.0,8.0')] ).

cnf(23,plain,
    ( ~ equal(divide(u,zero),zero)
    | equal(u,zero) ),
    inference(obv,[status(thm),theory(equality)],[20]),
    [iquote('0:Obv:20.0')] ).

cnf(47,plain,
    ( ~ equal(divide(u,v),zero)
    | ~ equal(zero,zero)
    | ~ equal(divide(divide(w,u),divide(w,v)),zero)
    | equal(divide(w,u),divide(w,v)) ),
    inference(spl,[status(thm),theory(equality)],[3,8]),
    [iquote('0:SpL:3.1,8.0')] ).

cnf(50,plain,
    ( ~ equal(divide(u,v),zero)
    | ~ equal(divide(divide(w,u),divide(w,v)),zero)
    | equal(divide(w,u),divide(w,v)) ),
    inference(obv,[status(thm),theory(equality)],[47]),
    [iquote('0:Obv:47.1')] ).

cnf(55,plain,
    ( ~ equal(zero,zero)
    | equal(divide(divide(u,u),v),zero) ),
    inference(spl,[status(thm),theory(equality)],[5,2]),
    [iquote('0:SpL:5.0,2.0')] ).

cnf(58,plain,
    equal(divide(divide(u,u),v),zero),
    inference(obv,[status(thm),theory(equality)],[55]),
    [iquote('0:Obv:55.0')] ).

cnf(81,plain,
    ( ~ equal(zero,zero)
    | equal(divide(u,u),zero) ),
    inference(spl,[status(thm),theory(equality)],[58,23]),
    [iquote('0:SpL:58.0,23.0')] ).

cnf(84,plain,
    equal(divide(u,u),zero),
    inference(obv,[status(thm),theory(equality)],[81]),
    [iquote('0:Obv:81.0')] ).

cnf(110,plain,
    ( ~ equal(zero,zero)
    | equal(divide(divide(u,divide(u,v)),v),zero) ),
    inference(spl,[status(thm),theory(equality)],[84,2]),
    [iquote('0:SpL:84.0,2.0')] ).

cnf(112,plain,
    equal(divide(divide(u,divide(u,v)),v),zero),
    inference(obv,[status(thm),theory(equality)],[110]),
    [iquote('0:Obv:110.0')] ).

cnf(28763,plain,
    ( ~ equal(divide(divide(u,divide(u,v)),v),zero)
    | ~ equal(zero,zero)
    | equal(divide(u,divide(u,divide(u,v))),divide(u,v)) ),
    inference(spl,[status(thm),theory(equality)],[112,50]),
    [iquote('0:SpL:112.0,50.1')] ).

cnf(28819,plain,
    ( ~ equal(divide(divide(u,divide(u,v)),v),zero)
    | equal(divide(u,divide(u,divide(u,v))),divide(u,v)) ),
    inference(obv,[status(thm),theory(equality)],[28763]),
    [iquote('0:Obv:28763.1')] ).

cnf(28820,plain,
    ( ~ equal(zero,zero)
    | equal(divide(u,divide(u,divide(u,v))),divide(u,v)) ),
    inference(rew,[status(thm),theory(equality)],[112,28819]),
    [iquote('0:Rew:112.0,28819.0')] ).

cnf(28821,plain,
    equal(divide(u,divide(u,divide(u,v))),divide(u,v)),
    inference(obv,[status(thm),theory(equality)],[28820]),
    [iquote('0:Obv:28820.0')] ).

cnf(28822,plain,
    $false,
    inference(unc,[status(thm)],[28821,4]),
    [iquote('0:UnC:28821.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : HEN009-5 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.09/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n009.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 13:11:52 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 9.52/9.76  
% 9.52/9.76  SPASS V 3.9 
% 9.52/9.76  SPASS beiseite: Proof found.
% 9.52/9.76  % SZS status Theorem
% 9.52/9.76  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 9.52/9.76  SPASS derived 17779 clauses, backtracked 0 clauses, performed 0 splits and kept 1611 clauses.
% 9.52/9.76  SPASS allocated 86311 KBytes.
% 9.52/9.76  SPASS spent	0:00:08.63 on the problem.
% 9.52/9.76  		0:00:00.04 for the input.
% 9.52/9.76  		0:00:00.00 for the FLOTTER CNF translation.
% 9.52/9.76  		0:00:00.12 for inferences.
% 9.52/9.76  		0:00:00.00 for the backtracking.
% 9.52/9.76  		0:00:08.45 for the reduction.
% 9.52/9.76  
% 9.52/9.76  
% 9.52/9.76  Here is a proof with depth 4, length 21 :
% 9.52/9.76  % SZS output start Refutation
% See solution above
% 9.52/9.76  Formulae used in the proof : property_of_divide1 property_of_divide2 prove_this quotient_smaller_than_numerator zero_is_smallest divide_and_equal
% 9.52/9.76  
%------------------------------------------------------------------------------