%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP493-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 11:47:44 EDT 2022

% Result   : Unsatisfiable 0.20s 0.40s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   16 (  16 unt;   0 nHn;  16 RR)
%            Number of literals    :   16 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   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(double_divide(double_divide(identity,u),double_divide(double_divide(double_divide(v,w),double_divide(identity,identity)),double_divide(u,w))),v),
    file('GRP493-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
    file('GRP493-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(double_divide(u,identity),inverse(u)),
    file('GRP493-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(double_divide(u,inverse(u)),identity),
    file('GRP493-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(inverse(a1),a1),identity),
    file('GRP493-1.p',unknown),
    [] ).

cnf(6,plain,
    equal(inverse(double_divide(u,v)),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Rew:3.0,2.0')] ).

cnf(7,plain,
    equal(double_divide(double_divide(identity,u),double_divide(double_divide(double_divide(v,w),inverse(identity)),double_divide(u,w))),v),
    inference(rew,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Rew:3.0,1.0')] ).

cnf(12,plain,
    equal(multiply(inverse(u),u),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[4,6]),
    [iquote('0:SpR:4.0,6.0')] ).

cnf(14,plain,
    ~ equal(inverse(identity),identity),
    inference(rew,[status(thm),theory(equality)],[12,5]),
    [iquote('0:Rew:12.0,5.0')] ).

cnf(54,plain,
    equal(double_divide(double_divide(identity,u),double_divide(double_divide(identity,inverse(identity)),double_divide(u,inverse(v)))),v),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(61,plain,
    equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(u,inverse(v)))),v),
    inference(rew,[status(thm),theory(equality)],[4,54]),
    [iquote('0:Rew:4.0,54.0')] ).

cnf(74,plain,
    equal(double_divide(double_divide(identity,u),double_divide(identity,identity)),u),
    inference(spr,[status(thm),theory(equality)],[4,61]),
    [iquote('0:SpR:4.0,61.0')] ).

cnf(77,plain,
    equal(double_divide(double_divide(identity,u),inverse(identity)),u),
    inference(rew,[status(thm),theory(equality)],[3,74]),
    [iquote('0:Rew:3.0,74.0')] ).

cnf(88,plain,
    equal(double_divide(identity,inverse(identity)),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[4,77]),
    [iquote('0:SpR:4.0,77.0')] ).

cnf(90,plain,
    equal(inverse(identity),identity),
    inference(rew,[status(thm),theory(equality)],[4,88]),
    [iquote('0:Rew:4.0,88.0')] ).

cnf(91,plain,
    $false,
    inference(mrr,[status(thm)],[90,14]),
    [iquote('0:MRR:90.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP493-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n014.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 : Tue Jun 14 13:20:06 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.20/0.40  
% 0.20/0.40  SPASS V 3.9 
% 0.20/0.40  SPASS beiseite: Proof found.
% 0.20/0.40  % SZS status Theorem
% 0.20/0.40  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.40  SPASS derived 59 clauses, backtracked 0 clauses, performed 0 splits and kept 33 clauses.
% 0.20/0.40  SPASS allocated 63229 KBytes.
% 0.20/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.40  		0:00:00.03 for the input.
% 0.20/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.40  		0:00:00.00 for inferences.
% 0.20/0.40  		0:00:00.00 for the backtracking.
% 0.20/0.40  		0:00:00.01 for the reduction.
% 0.20/0.40  
% 0.20/0.40  
% 0.20/0.40  Here is a proof with depth 3, length 16 :
% 0.20/0.40  % SZS output start Refutation
% See solution above
% 0.20/0.40  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_1
% 0.20/0.40  
%------------------------------------------------------------------------------