%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG235-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 : Thu Jul 14 18:03:09 EDT 2022

% Result   : Unsatisfiable 0.47s 0.66s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% 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    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(mult(u,mult(v,mult(u,v))),mult(u,v)),
    file('ALG235-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(mult(u,mult(v,mult(w,x))),mult(w,mult(v,mult(u,x)))),
    file('ALG235-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(mult(a,mult(b,mult(a,mult(c,mult(d,c))))),mult(a,mult(b,mult(d,c)))),
    file('ALG235-1.p',unknown),
    [] ).

cnf(25,plain,
    equal(mult(u,mult(v,mult(w,mult(x,mult(u,x))))),mult(w,mult(v,mult(u,x)))),
    inference(spr,[status(thm),theory(equality)],[1,2]),
    [iquote('0:SpR:1.0,2.0')] ).

cnf(789,plain,
    equal(mult(u,mult(v,mult(u,mult(w,mult(x,w))))),mult(x,mult(v,mult(u,w)))),
    inference(spr,[status(thm),theory(equality)],[2,25]),
    [iquote('0:SpR:2.0,25.0')] ).

cnf(816,plain,
    ~ equal(mult(d,mult(b,mult(a,c))),mult(a,mult(b,mult(d,c)))),
    inference(rew,[status(thm),theory(equality)],[789,4]),
    [iquote('0:Rew:789.0,4.0')] ).

cnf(817,plain,
    ~ equal(mult(a,mult(b,mult(d,c))),mult(a,mult(b,mult(d,c)))),
    inference(rew,[status(thm),theory(equality)],[2,816]),
    [iquote('0:Rew:2.0,816.0')] ).

cnf(818,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[817]),
    [iquote('0:Obv:817.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : ALG235-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun  8 16:20:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.47/0.66  
% 0.47/0.66  SPASS V 3.9 
% 0.47/0.66  SPASS beiseite: Proof found.
% 0.47/0.66  % SZS status Theorem
% 0.47/0.66  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.47/0.66  SPASS derived 530 clauses, backtracked 0 clauses, performed 0 splits and kept 151 clauses.
% 0.47/0.66  SPASS allocated 64843 KBytes.
% 0.47/0.66  SPASS spent	0:00:00.31 on the problem.
% 0.47/0.66  		0:00:00.03 for the input.
% 0.47/0.66  		0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.66  		0:00:00.01 for inferences.
% 0.47/0.66  		0:00:00.00 for the backtracking.
% 0.47/0.66  		0:00:00.25 for the reduction.
% 0.47/0.66  
% 0.47/0.66  
% 0.47/0.66  Here is a proof with depth 2, length 8 :
% 0.47/0.66  % SZS output start Refutation
% See solution above
% 0.47/0.66  Formulae used in the proof : c01 c02 goals
% 0.47/0.66  
%------------------------------------------------------------------------------