%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP702-11 : 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 11:49:03 EDT 2022

% Result   : Unsatisfiable 0.21s 0.42s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   8 unt;   0 nHn;   8 RR)
%            Number of literals    :    8 (   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;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(ld(u,mult(u,v)),v),
    file('GRP702-11.p',unknown),
    [] ).

cnf(9,axiom,
    equal(mult(mult(u,v),op_c),mult(u,mult(v,op_c))),
    file('GRP702-11.p',unknown),
    [] ).

cnf(11,axiom,
    equal(ld(u,mult(op_c,u)),op_d),
    file('GRP702-11.p',unknown),
    [] ).

cnf(14,axiom,
    ~ equal(mult(mult(x0__dfg,x1__dfg),op_d),mult(x0__dfg,mult(x1__dfg,op_d))),
    file('GRP702-11.p',unknown),
    [] ).

cnf(34,plain,
    equal(op_d,op_c),
    inference(spr,[status(thm),theory(equality)],[2,11]),
    [iquote('0:SpR:2.0,11.0')] ).

cnf(41,plain,
    ~ equal(mult(mult(x0__dfg,x1__dfg),op_c),mult(x0__dfg,mult(x1__dfg,op_c))),
    inference(rew,[status(thm),theory(equality)],[34,14]),
    [iquote('0:Rew:34.0,14.0')] ).

cnf(42,plain,
    ~ equal(mult(x0__dfg,mult(x1__dfg,op_c)),mult(x0__dfg,mult(x1__dfg,op_c))),
    inference(rew,[status(thm),theory(equality)],[9,41]),
    [iquote('0:Rew:9.0,41.0')] ).

cnf(43,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[42]),
    [iquote('0:Obv:42.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP702-11 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.15/0.34  % Computer : n006.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 600
% 0.15/0.35  % DateTime : Tue Jun 14 05:24:56 EDT 2022
% 0.15/0.35  % CPUTime  : 
% 0.21/0.42  
% 0.21/0.42  SPASS V 3.9 
% 0.21/0.42  SPASS beiseite: Proof found.
% 0.21/0.42  % SZS status Theorem
% 0.21/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.42  SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 23 clauses.
% 0.21/0.42  SPASS allocated 63121 KBytes.
% 0.21/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.21/0.42  		0:00:00.03 for the input.
% 0.21/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42  		0:00:00.00 for inferences.
% 0.21/0.42  		0:00:00.00 for the backtracking.
% 0.21/0.42  		0:00:00.00 for the reduction.
% 0.21/0.42  
% 0.21/0.42  
% 0.21/0.42  Here is a proof with depth 1, length 8 :
% 0.21/0.42  % SZS output start Refutation
% See solution above
% 0.21/0.42  Formulae used in the proof : f02 f09 f11 goal
% 0.21/0.42  
%------------------------------------------------------------------------------