%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ROB009-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:56:13 EDT 2022

% Result   : Unsatisfiable 0.18s 0.44s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (  10 unt;   0 nHn;  10 RR)
%            Number of literals    :   10 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(negate(add(b,negate(add(a,c)))),negate(add(a,negate(add(b,c))))),
    file('ROB009-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(b,a),
    file('ROB009-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(add(u,v),add(v,u)),
    file('ROB009-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(add(add(u,v),w),add(u,add(v,w))),
    file('ROB009-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
    file('ROB009-1.p',unknown),
    [] ).

cnf(14,plain,
    equal(add(add(u,v),w),add(v,add(u,w))),
    inference(spr,[status(thm),theory(equality)],[3,4]),
    [iquote('0:SpR:3.0,4.0')] ).

cnf(16,plain,
    equal(add(u,add(v,w)),add(v,add(u,w))),
    inference(rew,[status(thm),theory(equality)],[4,14]),
    [iquote('0:Rew:4.0,14.0')] ).

cnf(331,plain,
    equal(negate(add(negate(add(b,add(a,c))),negate(add(a,negate(add(b,c)))))),b),
    inference(spr,[status(thm),theory(equality)],[1,5]),
    [iquote('0:SpR:1.0,5.0')] ).

cnf(335,plain,
    equal(b,a),
    inference(rew,[status(thm),theory(equality)],[5,331,16]),
    [iquote('0:Rew:5.0,331.0,16.0,331.0')] ).

cnf(336,plain,
    $false,
    inference(mrr,[status(thm)],[335,2]),
    [iquote('0:MRR:335.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : ROB009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % 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 : Thu Jun  9 14:36:06 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  
% 0.18/0.44  SPASS V 3.9 
% 0.18/0.44  SPASS beiseite: Proof found.
% 0.18/0.44  % SZS status Theorem
% 0.18/0.44  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.44  SPASS derived 226 clauses, backtracked 0 clauses, performed 0 splits and kept 56 clauses.
% 0.18/0.44  SPASS allocated 63455 KBytes.
% 0.18/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.18/0.44  		0:00:00.03 for the input.
% 0.18/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.44  		0:00:00.00 for inferences.
% 0.18/0.44  		0:00:00.00 for the backtracking.
% 0.18/0.44  		0:00:00.04 for the reduction.
% 0.18/0.44  
% 0.18/0.44  
% 0.18/0.44  Here is a proof with depth 1, length 10 :
% 0.18/0.44  % SZS output start Refutation
% See solution above
% 0.18/0.44  Formulae used in the proof : condition prove_result commutativity_of_add associativity_of_add robbins_axiom
% 0.18/0.44  
%------------------------------------------------------------------------------