%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO022-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n032.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 06:21:39 EDT 2022

% Result   : Unsatisfiable 0.14s 0.33s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   8 unt;   0 nHn;  12 RR)
%            Number of literals    :   17 (   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    :   12 (  12 usr;  12 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equidistant(u__dfg,v__dfg,w__dfg,x__dfg),
    file('GEO022-2.p',unknown),
    [] ).

cnf(2,axiom,
    equidistant(w__dfg,x__dfg,y__dfg,z__dfg),
    file('GEO022-2.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equidistant(u__dfg,v__dfg,y__dfg,z__dfg),
    file('GEO022-2.p',unknown),
    [] ).

cnf(4,axiom,
    equidistant(u,v,v,u),
    file('GEO022-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ equidistant(u,v,w,x)
    | ~ equidistant(u,v,y,z)
    | equidistant(y,z,w,x) ),
    file('GEO022-2.p',unknown),
    [] ).

cnf(31,plain,
    ( ~ equidistant(w__dfg,x__dfg,u,v)
    | equidistant(u,v,y__dfg,z__dfg) ),
    inference(res,[status(thm),theory(equality)],[2,5]),
    [iquote('0:Res:2.0,5.0')] ).

cnf(32,plain,
    ( ~ equidistant(u__dfg,v__dfg,u,v)
    | equidistant(u,v,w__dfg,x__dfg) ),
    inference(res,[status(thm),theory(equality)],[1,5]),
    [iquote('0:Res:1.0,5.0')] ).

cnf(33,plain,
    ( ~ equidistant(u,v,w,x)
    | equidistant(w,x,v,u) ),
    inference(res,[status(thm),theory(equality)],[4,5]),
    [iquote('0:Res:4.0,5.0')] ).

cnf(41,plain,
    equidistant(v__dfg,u__dfg,w__dfg,x__dfg),
    inference(res,[status(thm),theory(equality)],[4,32]),
    [iquote('0:Res:4.0,32.0')] ).

cnf(72,plain,
    equidistant(w__dfg,x__dfg,u__dfg,v__dfg),
    inference(res,[status(thm),theory(equality)],[41,33]),
    [iquote('0:Res:41.0,33.0')] ).

cnf(84,plain,
    equidistant(u__dfg,v__dfg,y__dfg,z__dfg),
    inference(res,[status(thm),theory(equality)],[72,31]),
    [iquote('0:Res:72.0,31.0')] ).

cnf(87,plain,
    $false,
    inference(mrr,[status(thm)],[84,3]),
    [iquote('0:MRR:84.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : GEO022-2 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10  % Command  : run_spass %d %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 600
% 0.09/0.28  % DateTime : Fri Jun 17 19:19:31 EDT 2022
% 0.09/0.28  % CPUTime  : 
% 0.14/0.33  
% 0.14/0.33  SPASS V 3.9 
% 0.14/0.33  SPASS beiseite: Proof found.
% 0.14/0.33  % SZS status Theorem
% 0.14/0.33  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.14/0.33  SPASS derived 65 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses.
% 0.14/0.33  SPASS allocated 63163 KBytes.
% 0.14/0.33  SPASS spent	0:00:00.04 on the problem.
% 0.14/0.33  		0:00:00.02 for the input.
% 0.14/0.33  		0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.33  		0:00:00.00 for inferences.
% 0.14/0.33  		0:00:00.00 for the backtracking.
% 0.14/0.33  		0:00:00.00 for the reduction.
% 0.14/0.33  
% 0.14/0.33  
% 0.14/0.33  Here is a proof with depth 4, length 12 :
% 0.14/0.33  % SZS output start Refutation
% See solution above
% 0.14/0.33  Formulae used in the proof : u_to_v_equals_w_to_x w_to_x_equals_y_to_z prove_transitivity reflexivity_for_equidistance transitivity_for_equidistance
% 0.14/0.33  
%------------------------------------------------------------------------------