%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO056-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 : Sat Jul 16 06:21:57 EDT 2022

% Result   : Unsatisfiable 0.18s 0.40s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :    8 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(13,axiom,
    equidistant(u,reflection(v,u),v,u),
    file('GEO056-3.p',unknown),
    [] ).

cnf(14,axiom,
    equal(v__dfg,u__dfg),
    file('GEO056-3.p',unknown),
    [] ).

cnf(15,axiom,
    ~ equal(reflection(u__dfg,v__dfg),v__dfg),
    file('GEO056-3.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ equidistant(u,v,w,w)
    | equal(u,v) ),
    file('GEO056-3.p',unknown),
    [] ).

cnf(35,plain,
    ~ equal(reflection(u__dfg,u__dfg),u__dfg),
    inference(rew,[status(thm),theory(equality)],[14,15]),
    [iquote('0:Rew:14.0,15.0')] ).

cnf(47,plain,
    ~ equidistant(u__dfg,reflection(u__dfg,u__dfg),u,u),
    inference(res,[status(thm),theory(equality)],[18,35]),
    [iquote('0:Res:18.1,35.0')] ).

cnf(50,plain,
    $false,
    inference(unc,[status(thm)],[47,13]),
    [iquote('0:UnC:47.0,13.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GEO056-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n022.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 : Sat Jun 18 10:18:32 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.40  
% 0.18/0.40  SPASS V 3.9 
% 0.18/0.40  SPASS beiseite: Proof found.
% 0.18/0.40  % SZS status Theorem
% 0.18/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.40  SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 37 clauses.
% 0.18/0.40  SPASS allocated 63141 KBytes.
% 0.18/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.40  		0:00:00.04 for the input.
% 0.18/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40  		0:00:00.00 for inferences.
% 0.18/0.40  		0:00:00.00 for the backtracking.
% 0.18/0.40  		0:00:00.00 for the reduction.
% 0.18/0.40  
% 0.18/0.40  
% 0.18/0.40  Here is a proof with depth 1, length 7 :
% 0.18/0.40  % SZS output start Refutation
% See solution above
% 0.18/0.40  Formulae used in the proof : r2_2 u_equals_v prove_v_equals_reflection identity_for_equidistance
% 0.18/0.40  
%------------------------------------------------------------------------------