TSTP Solution File: GRP521-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP521-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:47:52 EDT 2022

% Result   : Unsatisfiable 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   25 (  25 unt;   0 nHn;  25 RR)
%            Number of literals    :   25 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   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('GRP521-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
    file('GRP521-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(divide(u,u),v),inverse(v)),
    file('GRP521-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
    file('GRP521-1.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(8,plain,
    equal(divide(multiply(inverse(u),u),v),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[5,3]),
    [iquote('0:SpR:5.0,3.0')] ).

cnf(10,plain,
    equal(multiply(divide(u,u),v),inverse(inverse(v))),
    inference(spr,[status(thm),theory(equality)],[5,3]),
    [iquote('0:SpR:5.0,3.0')] ).

cnf(51,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(70,plain,
    equal(divide(u,inverse(divide(v,divide(u,divide(w,w))))),v),
    inference(spr,[status(thm),theory(equality)],[3,1]),
    [iquote('0:SpR:3.0,1.0')] ).

cnf(75,plain,
    equal(inverse(divide(u,multiply(v,u))),v),
    inference(rew,[status(thm),theory(equality)],[5,51,3]),
    [iquote('0:Rew:5.0,51.0,3.0,51.0')] ).

cnf(78,plain,
    equal(multiply(u,divide(v,divide(u,divide(w,w)))),v),
    inference(rew,[status(thm),theory(equality)],[5,70]),
    [iquote('0:Rew:5.0,70.0')] ).

cnf(99,plain,
    equal(inverse(divide(u,inverse(inverse(u)))),divide(v,v)),
    inference(spr,[status(thm),theory(equality)],[10,75]),
    [iquote('0:SpR:10.0,75.0')] ).

cnf(106,plain,
    equal(inverse(multiply(u,inverse(u))),divide(v,v)),
    inference(rew,[status(thm),theory(equality)],[5,99]),
    [iquote('0:Rew:5.0,99.0')] ).

cnf(128,plain,
    equal(divide(u,u),divide(v,v)),
    inference(spr,[status(thm),theory(equality)],[106]),
    [iquote('0:SpR:106.0,106.0')] ).

cnf(140,plain,
    equal(divide(u,divide(u,divide(v,inverse(multiply(w,inverse(w)))))),v),
    inference(spr,[status(thm),theory(equality)],[106,1]),
    [iquote('0:SpR:106.0,1.0')] ).

cnf(143,plain,
    equal(divide(u,divide(v,inverse(multiply(w,inverse(w))))),divide(u,v)),
    inference(spr,[status(thm),theory(equality)],[106,1]),
    [iquote('0:SpR:106.0,1.0')] ).

cnf(149,plain,
    equal(divide(u,divide(u,multiply(v,multiply(w,inverse(w))))),v),
    inference(rew,[status(thm),theory(equality)],[5,140]),
    [iquote('0:Rew:5.0,140.0')] ).

cnf(150,plain,
    equal(divide(u,multiply(v,multiply(w,inverse(w)))),divide(u,v)),
    inference(rew,[status(thm),theory(equality)],[5,143]),
    [iquote('0:Rew:5.0,143.0')] ).

cnf(151,plain,
    equal(divide(u,divide(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[150,149]),
    [iquote('0:Rew:150.0,149.0')] ).

cnf(165,plain,
    equal(divide(u,divide(u,divide(v,divide(w,w)))),v),
    inference(spr,[status(thm),theory(equality)],[128,1]),
    [iquote('0:SpR:128.0,1.0')] ).

cnf(187,plain,
    equal(divide(u,divide(v,v)),u),
    inference(rew,[status(thm),theory(equality)],[151,165]),
    [iquote('0:Rew:151.0,165.0')] ).

cnf(188,plain,
    equal(multiply(u,divide(v,u)),v),
    inference(rew,[status(thm),theory(equality)],[187,78]),
    [iquote('0:Rew:187.0,78.0')] ).

cnf(321,plain,
    equal(multiply(divide(u,v),v),u),
    inference(spr,[status(thm),theory(equality)],[151,188]),
    [iquote('0:SpR:151.0,188.0')] ).

cnf(404,plain,
    equal(multiply(inverse(u),u),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[8,321]),
    [iquote('0:SpR:8.0,321.0')] ).

cnf(408,plain,
    $false,
    inference(unc,[status(thm)],[404,4]),
    [iquote('0:UnC:404.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP521-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 : Mon Jun 13 08:39:27 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.45  
% 0.20/0.45  SPASS V 3.9 
% 0.20/0.45  SPASS beiseite: Proof found.
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.45  SPASS derived 313 clauses, backtracked 0 clauses, performed 0 splits and kept 105 clauses.
% 0.20/0.45  SPASS allocated 63406 KBytes.
% 0.20/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.20/0.45  		0:00:00.04 for the input.
% 0.20/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45  		0:00:00.00 for inferences.
% 0.20/0.45  		0:00:00.00 for the backtracking.
% 0.20/0.45  		0:00:00.02 for the reduction.
% 0.20/0.45  
% 0.20/0.45  
% 0.20/0.45  Here is a proof with depth 5, length 25 :
% 0.20/0.45  % SZS output start Refutation
% See solution above
% 0.20/0.45  Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_1
% 0.20/0.45  
%------------------------------------------------------------------------------