%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ROB021-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 20:56:16 EDT 2022

% Result   : Unsatisfiable 0.39s 0.63s
% Output   : Refutation 0.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ equal(negate(u),negate(v))
    | equal(u,v) ),
    file('ROB021-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
    file('ROB021-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(add(u,v),add(v,u)),
    file('ROB021-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
    file('ROB021-1.p',unknown),
    [] ).

cnf(66,plain,
    ( ~ equal(negate(u),v)
    | equal(u,add(negate(add(v,w)),negate(add(v,negate(w))))) ),
    inference(spl,[status(thm),theory(equality)],[5,1]),
    [iquote('0:SpL:5.0,1.0')] ).

cnf(816,plain,
    equal(add(negate(add(negate(u),v)),negate(add(negate(u),negate(v)))),u),
    inference(eqr,[status(thm),theory(equality)],[66]),
    [iquote('0:EqR:66.0')] ).

cnf(854,plain,
    equal(add(negate(add(negate(u),v)),negate(add(negate(v),negate(u)))),u),
    inference(spr,[status(thm),theory(equality)],[3,816]),
    [iquote('0:SpR:3.0,816.0')] ).

cnf(967,plain,
    equal(add(negate(add(u,negate(v))),negate(add(negate(u),negate(v)))),v),
    inference(spr,[status(thm),theory(equality)],[3,854]),
    [iquote('0:SpR:3.0,854.0')] ).

cnf(986,plain,
    $false,
    inference(unc,[status(thm)],[967,2]),
    [iquote('0:UnC:967.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ROB021-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun  9 14:56:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.39/0.63  
% 0.39/0.63  SPASS V 3.9 
% 0.39/0.63  SPASS beiseite: Proof found.
% 0.39/0.63  % SZS status Theorem
% 0.39/0.63  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.39/0.63  SPASS derived 685 clauses, backtracked 0 clauses, performed 0 splits and kept 203 clauses.
% 0.39/0.63  SPASS allocated 64364 KBytes.
% 0.39/0.63  SPASS spent	0:00:00.26 on the problem.
% 0.39/0.63  		0:00:00.03 for the input.
% 0.39/0.63  		0:00:00.00 for the FLOTTER CNF translation.
% 0.39/0.63  		0:00:00.01 for inferences.
% 0.39/0.63  		0:00:00.00 for the backtracking.
% 0.39/0.63  		0:00:00.20 for the reduction.
% 0.39/0.63  
% 0.39/0.63  
% 0.39/0.63  Here is a proof with depth 4, length 9 :
% 0.39/0.63  % SZS output start Refutation
% See solution above
% 0.39/0.63  Formulae used in the proof : negative_equality_implies_positive_equality prove_huntingtons_axiom commutativity_of_add robbins_axiom
% 0.39/0.63  
%------------------------------------------------------------------------------