TSTP Solution File: GRP522-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   21 (  21 unt;   0 nHn;  21 RR)
%            Number of literals    :   21 (   0 equ;   2 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('GRP522-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
    file('GRP522-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(divide(u,u),v),inverse(v)),
    file('GRP522-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP522-1.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(inverse(divide(u,u)),v),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[3]),
    [iquote('0:SpR:3.0,3.0')] ).

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(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(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(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(43,plain,
    equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
    inference(spr,[status(thm),theory(equality)],[8,5]),
    [iquote('0:SpR:8.0,5.0')] ).

cnf(51,plain,
    ~ equal(inverse(inverse(a2)),a2),
    inference(rew,[status(thm),theory(equality)],[43,4]),
    [iquote('0:Rew:43.0,4.0')] ).

cnf(65,plain,
    equal(inverse(divide(divide(u,divide(v,inverse(divide(w,w)))),u)),v),
    inference(spr,[status(thm),theory(equality)],[20,6]),
    [iquote('0:SpR:20.0,6.0')] ).

cnf(83,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(84,plain,
    equal(multiply(u,divide(v,u)),v),
    inference(rew,[status(thm),theory(equality)],[5,83]),
    [iquote('0:Rew:5.0,83.0')] ).

cnf(89,plain,
    equal(inverse(divide(divide(u,multiply(v,divide(w,w))),u)),v),
    inference(rew,[status(thm),theory(equality)],[5,65]),
    [iquote('0:Rew:5.0,65.0')] ).

cnf(94,plain,
    equal(inverse(divide(divide(u,v),u)),v),
    inference(spr,[status(thm),theory(equality)],[84,29]),
    [iquote('0:SpR:84.0,29.0')] ).

cnf(102,plain,
    equal(multiply(u,divide(v,v)),u),
    inference(rew,[status(thm),theory(equality)],[94,89]),
    [iquote('0:Rew:94.0,89.0')] ).

cnf(107,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[102,39]),
    [iquote('0:Rew:102.0,39.0')] ).

cnf(108,plain,
    $false,
    inference(unc,[status(thm)],[107,51]),
    [iquote('0:UnC:107.0,51.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n010.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 : Tue Jun 14 07:48:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.41  
% 0.18/0.41  SPASS V 3.9 
% 0.18/0.41  SPASS beiseite: Proof found.
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.41  SPASS derived 86 clauses, backtracked 0 clauses, performed 0 splits and kept 63 clauses.
% 0.18/0.41  SPASS allocated 63252 KBytes.
% 0.18/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.41  		0:00:00.03 for the input.
% 0.18/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41  		0:00:00.00 for inferences.
% 0.18/0.41  		0:00:00.00 for the backtracking.
% 0.18/0.41  		0:00:00.01 for the reduction.
% 0.18/0.41  
% 0.18/0.41  
% 0.18/0.41  Here is a proof with depth 3, length 21 :
% 0.18/0.41  % SZS output start Refutation
% See solution above
% 0.18/0.41  Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_2
% 0.18/0.41  
%------------------------------------------------------------------------------