%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG023-7 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:41:14 EDT 2022

% Result   : Unsatisfiable 0.20s 0.48s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   9 unt;   0 nHn;   9 RR)
%            Number of literals    :    9 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(8,axiom,
    ~ equal(associator(x__dfg,x__dfg,y__dfg),additive_identity),
    file('RNG023-7.p',unknown),
    [] ).

cnf(14,axiom,
    equal(add(u,additive_inverse(u)),additive_identity),
    file('RNG023-7.p',unknown),
    [] ).

cnf(18,axiom,
    equal(add(u,v),add(v,u)),
    file('RNG023-7.p',unknown),
    [] ).

cnf(21,axiom,
    equal(multiply(multiply(u,u),v),multiply(u,multiply(u,v))),
    file('RNG023-7.p',unknown),
    [] ).

cnf(22,axiom,
    equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
    file('RNG023-7.p',unknown),
    [] ).

cnf(30,plain,
    equal(add(additive_inverse(multiply(u,multiply(v,w))),multiply(multiply(u,v),w)),associator(u,v,w)),
    inference(rew,[status(thm),theory(equality)],[18,22]),
    [iquote('0:Rew:18.0,22.0')] ).

cnf(480,plain,
    equal(add(additive_inverse(multiply(u,multiply(u,v))),multiply(u,multiply(u,v))),associator(u,u,v)),
    inference(spr,[status(thm),theory(equality)],[21,30]),
    [iquote('0:SpR:21.0,30.0')] ).

cnf(505,plain,
    equal(associator(u,u,v),additive_identity),
    inference(rew,[status(thm),theory(equality)],[14,480,18]),
    [iquote('0:Rew:14.0,480.0,18.0,480.0')] ).

cnf(506,plain,
    $false,
    inference(unc,[status(thm)],[505,8]),
    [iquote('0:UnC:505.0,8.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG023-7 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon May 30 22:26:06 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.48  
% 0.20/0.48  SPASS V 3.9 
% 0.20/0.48  SPASS beiseite: Proof found.
% 0.20/0.48  % SZS status Theorem
% 0.20/0.48  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.48  SPASS derived 302 clauses, backtracked 0 clauses, performed 0 splits and kept 93 clauses.
% 0.20/0.48  SPASS allocated 63975 KBytes.
% 0.20/0.48  SPASS spent	0:00:00.12 on the problem.
% 0.20/0.48  		0:00:00.04 for the input.
% 0.20/0.48  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48  		0:00:00.00 for inferences.
% 0.20/0.48  		0:00:00.00 for the backtracking.
% 0.20/0.48  		0:00:00.05 for the reduction.
% 0.20/0.48  
% 0.20/0.48  
% 0.20/0.48  Here is a proof with depth 1, length 9 :
% 0.20/0.48  % SZS output start Refutation
% See solution above
% 0.20/0.48  Formulae used in the proof : prove_left_alternative right_additive_inverse commutativity_for_addition left_alternative associator
% 0.20/0.48  
%------------------------------------------------------------------------------