%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG041-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 : Mon Jul 18 20:41:18 EDT 2022

% Result   : Unsatisfiable 0.18s 0.45s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   15 (   9 unt;   1 nHn;  15 RR)
%            Number of literals    :   25 (   0 equ;  13 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;  10 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    product(additive_identity,u,additive_identity),
    file('RNG041-1.p',unknown),
    [] ).

cnf(3,axiom,
    product(u,multiplicative_identity,u),
    file('RNG041-1.p',unknown),
    [] ).

cnf(5,axiom,
    ( equal(u,additive_identity)
    | product(u,h(u),multiplicative_identity) ),
    file('RNG041-1.p',unknown),
    [] ).

cnf(7,axiom,
    product(a,b,additive_identity),
    file('RNG041-1.p',unknown),
    [] ).

cnf(8,axiom,
    ~ equal(a,additive_identity),
    file('RNG041-1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(b,additive_identity),
    file('RNG041-1.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ product(u,v,w)
    | ~ product(x,y,v)
    | ~ product(u,x,z)
    | product(z,y,w) ),
    file('RNG041-1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equal(x,w) ),
    file('RNG041-1.p',unknown),
    [] ).

cnf(27,plain,
    product(b,h(b),multiplicative_identity),
    inference(res,[status(thm),theory(equality)],[5,9]),
    [iquote('0:Res:5.1,9.0')] ).

cnf(36,plain,
    ( ~ product(u,v,additive_identity)
    | ~ product(u,v,a) ),
    inference(res,[status(thm),theory(equality)],[26,8]),
    [iquote('0:Res:26.2,8.0')] ).

cnf(44,plain,
    ( ~ product(a,u,v)
    | ~ product(b,w,u)
    | product(additive_identity,w,v) ),
    inference(res,[status(thm),theory(equality)],[7,20]),
    [iquote('0:Res:7.0,20.0')] ).

cnf(371,plain,
    ( ~ product(b,u,multiplicative_identity)
    | product(additive_identity,u,a) ),
    inference(res,[status(thm),theory(equality)],[3,44]),
    [iquote('0:Res:3.0,44.0')] ).

cnf(374,plain,
    product(additive_identity,h(b),a),
    inference(res,[status(thm),theory(equality)],[27,371]),
    [iquote('0:Res:27.0,371.0')] ).

cnf(383,plain,
    ~ product(additive_identity,h(b),additive_identity),
    inference(res,[status(thm),theory(equality)],[374,36]),
    [iquote('0:Res:374.0,36.1')] ).

cnf(387,plain,
    $false,
    inference(mrr,[status(thm)],[383,1]),
    [iquote('0:MRR:383.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : RNG041-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n019.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 : Mon May 30 04:43:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.45  
% 0.18/0.45  SPASS V 3.9 
% 0.18/0.45  SPASS beiseite: Proof found.
% 0.18/0.45  % SZS status Theorem
% 0.18/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.45  SPASS derived 352 clauses, backtracked 19 clauses, performed 1 splits and kept 212 clauses.
% 0.18/0.45  SPASS allocated 63370 KBytes.
% 0.18/0.45  SPASS spent	0:00:00.10 on the problem.
% 0.18/0.45  		0:00:00.04 for the input.
% 0.18/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.45  		0:00:00.00 for inferences.
% 0.18/0.45  		0:00:00.00 for the backtracking.
% 0.18/0.45  		0:00:00.04 for the reduction.
% 0.18/0.45  
% 0.18/0.45  
% 0.18/0.45  Here is a proof with depth 4, length 15 :
% 0.18/0.45  % SZS output start Refutation
% See solution above
% 0.18/0.45  Formulae used in the proof : multiplicative_identity1 right_multiplicative_identity clause41 a_times_b a_not_additive_identity prove_b_is_additive_identity associativity_of_multiplication2 multiplication_is_well_defined
% 0.18/0.45  
%------------------------------------------------------------------------------