%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : BOO003-4 : TPTP v8.1.0. Released v1.1.0.
% 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 23:49:22 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (  14 unt;   0 nHn;  14 RR)
%            Number of literals    :   14 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(multiply(a,a),a),
    file('BOO003-4.p',unknown),
    [] ).

cnf(2,axiom,
    equal(add(u,v),add(v,u)),
    file('BOO003-4.p',unknown),
    [] ).

cnf(5,axiom,
    equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
    file('BOO003-4.p',unknown),
    [] ).

cnf(6,axiom,
    equal(add(u,additive_identity),u),
    file('BOO003-4.p',unknown),
    [] ).

cnf(7,axiom,
    equal(multiply(u,multiplicative_identity),u),
    file('BOO003-4.p',unknown),
    [] ).

cnf(8,axiom,
    equal(add(u,inverse(u)),multiplicative_identity),
    file('BOO003-4.p',unknown),
    [] ).

cnf(9,axiom,
    equal(multiply(u,inverse(u)),additive_identity),
    file('BOO003-4.p',unknown),
    [] ).

cnf(30,plain,
    equal(add(additive_identity,u),u),
    inference(spr,[status(thm),theory(equality)],[2,6]),
    [iquote('0:SpR:2.0,6.0')] ).

cnf(40,plain,
    equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
    inference(spr,[status(thm),theory(equality)],[9,5]),
    [iquote('0:SpR:9.0,5.0')] ).

cnf(53,plain,
    equal(multiply(u,add(v,inverse(u))),add(additive_identity,multiply(u,v))),
    inference(rew,[status(thm),theory(equality)],[2,40]),
    [iquote('0:Rew:2.0,40.0')] ).

cnf(54,plain,
    equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
    inference(rew,[status(thm),theory(equality)],[30,53]),
    [iquote('0:Rew:30.0,53.0')] ).

cnf(72,plain,
    equal(multiply(u,multiplicative_identity),multiply(u,u)),
    inference(spr,[status(thm),theory(equality)],[8,54]),
    [iquote('0:SpR:8.0,54.0')] ).

cnf(76,plain,
    equal(multiply(u,u),u),
    inference(rew,[status(thm),theory(equality)],[7,72]),
    [iquote('0:Rew:7.0,72.0')] ).

cnf(77,plain,
    $false,
    inference(unc,[status(thm)],[76,1]),
    [iquote('0:UnC:76.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : BOO003-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n020.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  1 18:37:38 EDT 2022
% 0.12/0.33  % 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 25 clauses.
% 0.19/0.40  SPASS allocated 63159 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 2, length 14 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.40  Formulae used in the proof : prove_a_times_a_is_a commutativity_of_add distributivity2 additive_id1 multiplicative_id1 additive_inverse1 multiplicative_inverse1
% 0.19/0.40  
%------------------------------------------------------------------------------