%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP671-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 11:48:53 EDT 2022

% Result   : Unsatisfiable 0.21s 0.43s
% Output   : Refutation 0.21s
% 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    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    equal(mult(u,unit),u),
    file('GRP671-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(mult(unit,u),u),
    file('GRP671-1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(mult(mult(mult(u,mult(v,w)),u),v),mult(mult(u,v),mult(w,mult(u,v)))),
    file('GRP671-1.p',unknown),
    [] ).

cnf(10,axiom,
    ~ equal(mult(mult(a,b),a),mult(a,mult(b,a))),
    file('GRP671-1.p',unknown),
    [] ).

cnf(110,plain,
    equal(mult(mult(u,unit),mult(v,mult(u,unit))),mult(mult(u,mult(unit,v)),u)),
    inference(spr,[status(thm),theory(equality)],[9,5]),
    [iquote('0:SpR:9.0,5.0')] ).

cnf(124,plain,
    equal(mult(mult(u,v),u),mult(u,mult(v,u))),
    inference(rew,[status(thm),theory(equality)],[5,110,6]),
    [iquote('0:Rew:5.0,110.0,6.0,110.0')] ).

cnf(125,plain,
    $false,
    inference(unc,[status(thm)],[124,10]),
    [iquote('0:UnC:124.0,10.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GRP671-1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun 13 08:55:07 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.43  
% 0.21/0.43  SPASS V 3.9 
% 0.21/0.43  SPASS beiseite: Proof found.
% 0.21/0.43  % SZS status Theorem
% 0.21/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.43  SPASS derived 101 clauses, backtracked 0 clauses, performed 0 splits and kept 45 clauses.
% 0.21/0.43  SPASS allocated 63224 KBytes.
% 0.21/0.43  SPASS spent	0:00:00.06 on the problem.
% 0.21/0.43  		0:00:00.04 for the input.
% 0.21/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43  		0:00:00.00 for inferences.
% 0.21/0.43  		0:00:00.00 for the backtracking.
% 0.21/0.43  		0:00:00.01 for the reduction.
% 0.21/0.43  
% 0.21/0.43  
% 0.21/0.43  Here is a proof with depth 1, length 7 :
% 0.21/0.43  % SZS output start Refutation
% See solution above
% 0.21/0.43  Formulae used in the proof : c05 c06 c09 goals
% 0.21/0.43  
%------------------------------------------------------------------------------