%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO016-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 06:21:36 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 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :   10 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;  10 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    equidistant(u__dfg,v__dfg,w__dfg,x__dfg),
    file('GEO016-3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equidistant(v__dfg,u__dfg,w__dfg,x__dfg),
    file('GEO016-3.p',unknown),
    [] ).

cnf(5,axiom,
    equidistant(u,v,v,u),
    file('GEO016-3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ equidistant(u,v,w,x)
    | ~ equidistant(u,v,y,z)
    | equidistant(y,z,w,x) ),
    file('GEO016-3.p',unknown),
    [] ).

cnf(24,plain,
    ( ~ equidistant(u,v,w__dfg,x__dfg)
    | ~ equidistant(u,v,v__dfg,u__dfg) ),
    inference(res,[status(thm),theory(equality)],[6,4]),
    [iquote('0:Res:6.2,4.0')] ).

cnf(42,plain,
    ~ equidistant(u__dfg,v__dfg,v__dfg,u__dfg),
    inference(res,[status(thm),theory(equality)],[3,24]),
    [iquote('0:Res:3.0,24.0')] ).

cnf(46,plain,
    $false,
    inference(mrr,[status(thm)],[42,5]),
    [iquote('0:MRR:42.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO016-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n028.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 12:43:59 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/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.40  SPASS derived 23 clauses, backtracked 0 clauses, performed 0 splits and kept 33 clauses.
% 0.18/0.40  SPASS allocated 63134 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 2, length 7 :
% 0.18/0.40  % SZS output start Refutation
% See solution above
% 0.18/0.40  Formulae used in the proof : u_to_v_equals_w_to_x prove_symmetry reflexivity_for_equidistance transitivity_for_equidistance
% 0.18/0.40  
%------------------------------------------------------------------------------