%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP457-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 11:47:33 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   7 unt;   0 nHn;   7 RR)
%            Number of literals    :    7 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(divide(u,divide(identity,v)),multiply(u,v)),
    file('GRP457-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(identity,u),inverse(u)),
    file('GRP457-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(divide(u,u),identity),
    file('GRP457-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(inverse(a1),a1),identity),
    file('GRP457-1.p',unknown),
    [] ).

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

cnf(16,plain,
    $false,
    inference(unc,[status(thm)],[12,5]),
    [iquote('0:UnC:12.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP457-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n025.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 : Mon Jun 13 07:23:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.40  
% 0.19/0.40  SPASS V 3.9 
% 0.19/0.40  SPASS beiseite: Proof found.
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.40  SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.19/0.40  SPASS allocated 63098 KBytes.
% 0.19/0.40  SPASS spent	0:00:00.05 on the problem.
% 0.19/0.40  		0:00:00.03 for the input.
% 0.19/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40  		0:00:00.00 for inferences.
% 0.19/0.40  		0:00:00.00 for the backtracking.
% 0.19/0.40  		0:00:00.00 for the reduction.
% 0.19/0.40  
% 0.19/0.40  
% 0.19/0.40  Here is a proof with depth 1, length 7 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.40  Formulae used in the proof : multiply inverse identity prove_these_axioms_1
% 0.19/0.40  
%------------------------------------------------------------------------------