%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP549-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 11:47:59 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   9 unt;   0 nHn;   9 RR)
%            Number of literals    :    9 (   0 equ;   3 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    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(divide(u,divide(identity,v)),multiply(u,v)),
    file('GRP549-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(identity,u),inverse(u)),
    file('GRP549-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(divide(u,u),identity),
    file('GRP549-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
    file('GRP549-1.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,
    ~ equal(multiply(inverse(a1),a1),identity),
    inference(rew,[status(thm),theory(equality)],[12,5]),
    [iquote('0:Rew:12.0,5.0')] ).

cnf(17,plain,
    ~ equal(identity,identity),
    inference(rew,[status(thm),theory(equality)],[12,16]),
    [iquote('0:Rew:12.0,16.0')] ).

cnf(18,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[17]),
    [iquote('0:Obv:17.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP549-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 14 10:15:22 EDT 2022
% 0.13/0.34  % 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/sandbox/benchmark/theBenchmark.p 
% 0.19/0.40  SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 10 clauses.
% 0.19/0.40  SPASS allocated 63097 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 9 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : multiply inverse identity prove_these_axioms_1
% 0.19/0.41  
%------------------------------------------------------------------------------