%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP520-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 11:47:51 EDT 2022

% Result   : Unsatisfiable 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   11 (  11 unt;   0 nHn;  11 RR)
%            Number of literals    :   11 (   0 equ;   1 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;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(multiply(u,multiply(multiply(inverse(multiply(u,v)),w),v)),w),
    file('GRP520-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(multiply(b,a),multiply(a,b)),
    file('GRP520-1.p',unknown),
    [] ).

cnf(3,plain,
    equal(multiply(u,multiply(multiply(inverse(v),w),multiply(multiply(inverse(multiply(u,x)),v),x))),w),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(4,plain,
    equal(multiply(multiply(inverse(multiply(inverse(multiply(u,v)),w)),x),w),multiply(u,multiply(x,v))),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(15,plain,
    equal(multiply(multiply(inverse(u),v),u),v),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.0,3.0')] ).

cnf(22,plain,
    equal(multiply(multiply(inverse(multiply(inverse(u),v)),w),v),multiply(w,u)),
    inference(spr,[status(thm),theory(equality)],[1,15]),
    [iquote('0:SpR:1.0,15.0')] ).

cnf(23,plain,
    equal(multiply(multiply(inverse(u),v),multiply(multiply(inverse(multiply(inverse(w),x)),u),x)),multiply(v,w)),
    inference(spr,[status(thm),theory(equality)],[3,15]),
    [iquote('0:SpR:3.0,15.0')] ).

cnf(26,plain,
    equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
    inference(rew,[status(thm),theory(equality)],[22,4]),
    [iquote('0:Rew:22.0,4.0')] ).

cnf(28,plain,
    equal(multiply(u,multiply(multiply(inverse(u),v),w)),multiply(v,w)),
    inference(rew,[status(thm),theory(equality)],[26,23,22]),
    [iquote('0:Rew:26.0,23.0,22.0,23.0')] ).

cnf(70,plain,
    equal(multiply(u,v),multiply(v,u)),
    inference(spr,[status(thm),theory(equality)],[15,28]),
    [iquote('0:SpR:15.0,28.0')] ).

cnf(72,plain,
    $false,
    inference(unc,[status(thm)],[70,2]),
    [iquote('0:UnC:70.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP520-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n021.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 13:09:28 EDT 2022
% 0.13/0.33  % 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/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.41  SPASS derived 79 clauses, backtracked 0 clauses, performed 0 splits and kept 44 clauses.
% 0.18/0.41  SPASS allocated 63285 KBytes.
% 0.18/0.41  SPASS spent	0:00:00.07 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 4, length 11 :
% 0.18/0.41  % SZS output start Refutation
% See solution above
% 0.18/0.41  Formulae used in the proof : single_axiom prove_these_axioms_4
% 0.18/0.41  
%------------------------------------------------------------------------------