TSTP Solution File: GRP524-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 11:47:52 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   28 (  28 unt;   0 nHn;  28 RR)
%            Number of literals    :   28 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(divide(u,divide(v,divide(w,divide(u,v)))),w),
    file('GRP524-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
    file('GRP524-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(divide(u,u),v),inverse(v)),
    file('GRP524-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(multiply(b,a),multiply(a,b)),
    file('GRP524-1.p',unknown),
    [] ).

cnf(5,plain,
    equal(divide(u,inverse(v)),multiply(u,v)),
    inference(rew,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Rew:3.0,2.0')] ).

cnf(17,plain,
    equal(inverse(divide(u,divide(v,divide(divide(w,w),u)))),v),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.0,3.0')] ).

cnf(20,plain,
    equal(divide(u,divide(divide(v,divide(w,u)),v)),w),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(25,plain,
    equal(divide(u,divide(v,inverse(divide(u,v)))),divide(w,w)),
    inference(spr,[status(thm),theory(equality)],[3,1]),
    [iquote('0:SpR:3.0,1.0')] ).

cnf(29,plain,
    equal(inverse(divide(u,multiply(v,u))),v),
    inference(rew,[status(thm),theory(equality)],[5,17,3]),
    [iquote('0:Rew:5.0,17.0,3.0,17.0')] ).

cnf(31,plain,
    equal(divide(u,multiply(v,divide(u,v))),divide(w,w)),
    inference(rew,[status(thm),theory(equality)],[5,25]),
    [iquote('0:Rew:5.0,25.0')] ).

cnf(39,plain,
    equal(inverse(inverse(multiply(u,divide(v,v)))),u),
    inference(spr,[status(thm),theory(equality)],[3,29]),
    [iquote('0:SpR:3.0,29.0')] ).

cnf(63,plain,
    equal(multiply(u,inverse(multiply(v,divide(w,w)))),divide(u,v)),
    inference(spr,[status(thm),theory(equality)],[39,5]),
    [iquote('0:SpR:39.0,5.0')] ).

cnf(72,plain,
    equal(inverse(divide(divide(u,divide(v,divide(w,w))),u)),v),
    inference(spr,[status(thm),theory(equality)],[20,3]),
    [iquote('0:SpR:20.0,3.0')] ).

cnf(91,plain,
    equal(divide(u,inverse(divide(v,u))),v),
    inference(spr,[status(thm),theory(equality)],[3,20]),
    [iquote('0:SpR:3.0,20.0')] ).

cnf(92,plain,
    equal(multiply(u,divide(v,u)),v),
    inference(rew,[status(thm),theory(equality)],[5,91]),
    [iquote('0:Rew:5.0,91.0')] ).

cnf(93,plain,
    equal(divide(u,u),divide(v,v)),
    inference(rew,[status(thm),theory(equality)],[92,31]),
    [iquote('0:Rew:92.0,31.0')] ).

cnf(102,plain,
    equal(inverse(divide(divide(u,v),u)),v),
    inference(spr,[status(thm),theory(equality)],[92,29]),
    [iquote('0:SpR:92.0,29.0')] ).

cnf(103,plain,
    equal(inverse(inverse(u)),u),
    inference(spr,[status(thm),theory(equality)],[92,39]),
    [iquote('0:SpR:92.0,39.0')] ).

cnf(111,plain,
    equal(multiply(u,divide(v,v)),u),
    inference(rew,[status(thm),theory(equality)],[103,39]),
    [iquote('0:Rew:103.0,39.0')] ).

cnf(127,plain,
    equal(multiply(u,inverse(v)),divide(u,v)),
    inference(rew,[status(thm),theory(equality)],[111,63]),
    [iquote('0:Rew:111.0,63.0')] ).

cnf(130,plain,
    equal(divide(u,divide(v,v)),u),
    inference(rew,[status(thm),theory(equality)],[102,72]),
    [iquote('0:Rew:102.0,72.0')] ).

cnf(162,plain,
    equal(divide(u,divide(u,divide(v,divide(w,w)))),v),
    inference(spr,[status(thm),theory(equality)],[93,1]),
    [iquote('0:SpR:93.0,1.0')] ).

cnf(184,plain,
    equal(divide(u,divide(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[130,162]),
    [iquote('0:Rew:130.0,162.0')] ).

cnf(256,plain,
    equal(multiply(divide(u,v),v),u),
    inference(spr,[status(thm),theory(equality)],[184,92]),
    [iquote('0:SpR:184.0,92.0')] ).

cnf(287,plain,
    equal(multiply(multiply(u,v),inverse(v)),u),
    inference(spr,[status(thm),theory(equality)],[5,256]),
    [iquote('0:SpR:5.0,256.0')] ).

cnf(294,plain,
    equal(divide(multiply(u,v),v),u),
    inference(rew,[status(thm),theory(equality)],[127,287]),
    [iquote('0:Rew:127.0,287.0')] ).

cnf(301,plain,
    equal(multiply(u,v),multiply(v,u)),
    inference(spr,[status(thm),theory(equality)],[294,92]),
    [iquote('0:SpR:294.0,92.0')] ).

cnf(309,plain,
    $false,
    inference(unc,[status(thm)],[301,4]),
    [iquote('0:UnC:301.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP524-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.14/0.33  % Computer : n007.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Mon Jun 13 10:38:24 EDT 2022
% 0.14/0.34  % 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 241 clauses, backtracked 0 clauses, performed 0 splits and kept 84 clauses.
% 0.20/0.43  SPASS allocated 63351 KBytes.
% 0.20/0.43  SPASS spent	0:00:00.07 on the problem.
% 0.20/0.43  		0:00:00.04 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  		0:00:00.02 for the reduction.
% 0.20/0.43  
% 0.20/0.43  
% 0.20/0.43  Here is a proof with depth 5, length 28 :
% 0.20/0.43  % SZS output start Refutation
% See solution above
% 0.20/0.43  Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_4
% 0.20/0.43  
%------------------------------------------------------------------------------