TSTP Solution File: GRP446-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP446-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 11:47:31 EDT 2022

% Result   : Unsatisfiable 0.20s 0.46s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   22 (  22 unt;   0 nHn;  22 RR)
%            Number of literals    :   22 (   0 equ;   2 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(divide(divide(divide(u,u),v),w),divide(divide(divide(u,u),u),w))),v),
    file('GRP446-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
    file('GRP446-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(divide(u,u),v),inverse(v)),
    file('GRP446-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP446-1.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(6,plain,
    equal(divide(u,divide(divide(inverse(v),w),divide(inverse(u),w))),v),
    inference(rew,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Rew:3.0,1.0,3.0,1.0')] ).

cnf(7,plain,
    equal(divide(inverse(divide(u,u)),v),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[3]),
    [iquote('0:SpR:3.0,3.0')] ).

cnf(9,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(24,plain,
    equal(divide(divide(u,u),divide(divide(inverse(v),w),inverse(w))),v),
    inference(spr,[status(thm),theory(equality)],[7,6]),
    [iquote('0:SpR:7.0,6.0')] ).

cnf(27,plain,
    equal(divide(u,inverse(divide(inverse(u),inverse(v)))),v),
    inference(spr,[status(thm),theory(equality)],[3,6]),
    [iquote('0:SpR:3.0,6.0')] ).

cnf(28,plain,
    equal(multiply(u,multiply(inverse(u),v)),v),
    inference(rew,[status(thm),theory(equality)],[5,27]),
    [iquote('0:Rew:5.0,27.0,5.0,27.0')] ).

cnf(29,plain,
    equal(inverse(multiply(divide(inverse(u),v),v)),u),
    inference(rew,[status(thm),theory(equality)],[3,24,5]),
    [iquote('0:Rew:3.0,24.0,5.0,24.0')] ).

cnf(36,plain,
    equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
    inference(spr,[status(thm),theory(equality)],[28]),
    [iquote('0:SpR:28.0,28.0')] ).

cnf(39,plain,
    equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
    inference(spr,[status(thm),theory(equality)],[9,5]),
    [iquote('0:SpR:9.0,5.0')] ).

cnf(42,plain,
    ~ equal(inverse(inverse(a2)),a2),
    inference(rew,[status(thm),theory(equality)],[39,4]),
    [iquote('0:Rew:39.0,4.0')] ).

cnf(105,plain,
    equal(inverse(multiply(inverse(u),u)),divide(v,v)),
    inference(spr,[status(thm),theory(equality)],[7,29]),
    [iquote('0:SpR:7.0,29.0')] ).

cnf(164,plain,
    equal(divide(u,u),divide(v,v)),
    inference(spr,[status(thm),theory(equality)],[105]),
    [iquote('0:SpR:105.0,105.0')] ).

cnf(187,plain,
    equal(divide(u,u),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[164,5]),
    [iquote('0:SpR:164.0,5.0')] ).

cnf(250,plain,
    equal(multiply(u,divide(v,v)),u),
    inference(spr,[status(thm),theory(equality)],[187,28]),
    [iquote('0:SpR:187.0,28.0')] ).

cnf(362,plain,
    equal(multiply(u,divide(v,v)),inverse(inverse(u))),
    inference(spr,[status(thm),theory(equality)],[250,36]),
    [iquote('0:SpR:250.0,36.0')] ).

cnf(373,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[250,362]),
    [iquote('0:Rew:250.0,362.0')] ).

cnf(374,plain,
    $false,
    inference(unc,[status(thm)],[373,42]),
    [iquote('0:UnC:373.0,42.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP446-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n020.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 : Tue Jun 14 03:47:35 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.46  
% 0.20/0.46  SPASS V 3.9 
% 0.20/0.46  SPASS beiseite: Proof found.
% 0.20/0.46  % SZS status Theorem
% 0.20/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.46  SPASS derived 248 clauses, backtracked 0 clauses, performed 0 splits and kept 89 clauses.
% 0.20/0.46  SPASS allocated 63667 KBytes.
% 0.20/0.46  SPASS spent	0:00:00.09 on the problem.
% 0.20/0.46  		0:00:00.03 for the input.
% 0.20/0.46  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.46  		0:00:00.00 for inferences.
% 0.20/0.46  		0:00:00.00 for the backtracking.
% 0.20/0.46  		0:00:00.03 for the reduction.
% 0.20/0.46  
% 0.20/0.46  
% 0.20/0.46  Here is a proof with depth 7, length 22 :
% 0.20/0.46  % SZS output start Refutation
% See solution above
% 0.20/0.46  Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_2
% 0.20/0.46  
%------------------------------------------------------------------------------