%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : BOO009-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 23:49:24 EDT 2022

% Result   : Unsatisfiable 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (  15 unt;   0 nHn;  15 RR)
%            Number of literals    :   15 (   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,add(a,b)),a),
    file('BOO009-4.p',unknown),
    [] ).

cnf(2,axiom,
    equal(add(u,v),add(v,u)),
    file('BOO009-4.p',unknown),
    [] ).

cnf(3,axiom,
    equal(multiply(u,v),multiply(v,u)),
    file('BOO009-4.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
    file('BOO009-4.p',unknown),
    [] ).

cnf(5,axiom,
    equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
    file('BOO009-4.p',unknown),
    [] ).

cnf(6,axiom,
    equal(add(u,additive_identity),u),
    file('BOO009-4.p',unknown),
    [] ).

cnf(9,axiom,
    equal(multiply(u,inverse(u)),additive_identity),
    file('BOO009-4.p',unknown),
    [] ).

cnf(28,plain,
    equal(add(additive_identity,u),u),
    inference(spr,[status(thm),theory(equality)],[2,6]),
    [iquote('0:SpR:2.0,6.0')] ).

cnf(46,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(59,plain,
    equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
    inference(rew,[status(thm),theory(equality)],[28,46,2]),
    [iquote('0:Rew:28.0,46.0,2.0,46.0')] ).

cnf(72,plain,
    equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
    inference(spr,[status(thm),theory(equality)],[28,59]),
    [iquote('0:SpR:28.0,59.0')] ).

cnf(75,plain,
    equal(multiply(u,additive_identity),additive_identity),
    inference(rew,[status(thm),theory(equality)],[9,72]),
    [iquote('0:Rew:9.0,72.0')] ).

cnf(94,plain,
    equal(multiply(add(u,v),u),add(u,multiply(v,additive_identity))),
    inference(spr,[status(thm),theory(equality)],[6,4]),
    [iquote('0:SpR:6.0,4.0')] ).

cnf(106,plain,
    equal(multiply(u,add(u,v)),u),
    inference(rew,[status(thm),theory(equality)],[3,94,6,75]),
    [iquote('0:Rew:3.0,94.0,6.0,94.0,75.0,94.0')] ).

cnf(107,plain,
    $false,
    inference(unc,[status(thm)],[106,1]),
    [iquote('0:UnC:106.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem  : BOO009-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Wed Jun  1 23:49:51 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.20/0.41  
% 0.20/0.41  SPASS V 3.9 
% 0.20/0.41  SPASS beiseite: Proof found.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.41  SPASS derived 80 clauses, backtracked 0 clauses, performed 0 splits and kept 38 clauses.
% 0.20/0.41  SPASS allocated 63212 KBytes.
% 0.20/0.41  SPASS spent	0:00:00.04 on the problem.
% 0.20/0.41  		0:00:00.02 for the input.
% 0.20/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41  		0:00:00.00 for inferences.
% 0.20/0.41  		0:00:00.00 for the backtracking.
% 0.20/0.41  		0:00:00.00 for the reduction.
% 0.20/0.41  
% 0.20/0.41  
% 0.20/0.41  Here is a proof with depth 2, length 15 :
% 0.20/0.41  % SZS output start Refutation
% See solution above
% 0.20/0.41  Formulae used in the proof : prove_operation commutativity_of_add commutativity_of_multiply distributivity1 distributivity2 additive_id1 multiplicative_inverse1
% 0.20/0.41  
%------------------------------------------------------------------------------