%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : BOO021-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 23:49:28 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% 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;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(multiply(add(u,v),v),v),
    file('BOO021-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(add(multiply(u,v),multiply(w,v)),multiply(v,add(u,w))),
    file('BOO021-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(add(multiply(u,v),v),v),
    file('BOO021-1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(multiply(a,b),multiply(b,a)),
    file('BOO021-1.p',unknown),
    [] ).

cnf(14,plain,
    equal(add(u,u),u),
    inference(spr,[status(thm),theory(equality)],[1,4]),
    [iquote('0:SpR:1.0,4.0')] ).

cnf(106,plain,
    equal(multiply(u,add(v,v)),multiply(v,u)),
    inference(spr,[status(thm),theory(equality)],[2,14]),
    [iquote('0:SpR:2.0,14.0')] ).

cnf(123,plain,
    equal(multiply(u,v),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[14,106]),
    [iquote('0:Rew:14.0,106.0')] ).

cnf(124,plain,
    $false,
    inference(unc,[status(thm)],[123,7]),
    [iquote('0:UnC:123.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : BOO021-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n020.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 : Wed Jun  1 22:55:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 109 clauses, backtracked 0 clauses, performed 0 splits and kept 64 clauses.
% 0.19/0.42  SPASS allocated 63253 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.01 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 2, length 8 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : multiply_add multiply_add_property add_multiply prove_commutativity_of_multiply
% 0.19/0.42  
%------------------------------------------------------------------------------