%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP703-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 11:49:04 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (  11 unt;   0 nHn;  11 RR)
%            Number of literals    :   11 (   0 equ;   3 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    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    equal(mult(rd(u,v),v),u),
    file('GRP703-10.p',unknown),
    [] ).

cnf(5,axiom,
    equal(mult(u,unit),u),
    file('GRP703-10.p',unknown),
    [] ).

cnf(6,axiom,
    equal(mult(unit,u),u),
    file('GRP703-10.p',unknown),
    [] ).

cnf(8,axiom,
    equal(mult(mult(op_c,u),v),mult(op_c,mult(u,v))),
    file('GRP703-10.p',unknown),
    [] ).

cnf(12,axiom,
    equal(mult(mult(rd(op_c,mult(u,v)),v),u),op_e),
    file('GRP703-10.p',unknown),
    [] ).

cnf(14,axiom,
    ~ equal(mult(mult(op_e,x2__dfg),x3__dfg),mult(op_e,mult(x2__dfg,x3__dfg))),
    file('GRP703-10.p',unknown),
    [] ).

cnf(61,plain,
    equal(mult(rd(op_c,mult(unit,u)),u),op_e),
    inference(spr,[status(thm),theory(equality)],[12,5]),
    [iquote('0:SpR:12.0,5.0')] ).

cnf(70,plain,
    equal(op_e,op_c),
    inference(rew,[status(thm),theory(equality)],[3,61,6]),
    [iquote('0:Rew:3.0,61.0,6.0,61.0')] ).

cnf(72,plain,
    ~ equal(mult(mult(op_c,x2__dfg),x3__dfg),mult(op_c,mult(x2__dfg,x3__dfg))),
    inference(rew,[status(thm),theory(equality)],[70,14]),
    [iquote('0:Rew:70.0,14.0')] ).

cnf(81,plain,
    ~ equal(mult(op_c,mult(x2__dfg,x3__dfg)),mult(op_c,mult(x2__dfg,x3__dfg))),
    inference(rew,[status(thm),theory(equality)],[8,72]),
    [iquote('0:Rew:8.0,72.0')] ).

cnf(82,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[81]),
    [iquote('0:Obv:81.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRP703-10 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n006.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 10:54:56 EDT 2022
% 0.13/0.33  % 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 57 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.19/0.40  SPASS allocated 63160 KBytes.
% 0.19/0.40  SPASS spent	0:00:00.06 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 11 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.40  Formulae used in the proof : f03 f05 f06 f08 f12 goal
% 0.19/0.40  
%------------------------------------------------------------------------------