%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO022-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 0.20s 0.40s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   8 unt;   0 nHn;  12 RR)
%            Number of literals    :   17 (   0 equ;   8 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(7,axiom,
    ( ~ equidistant(u,v,w,x)
    | equidistant(x,w,u,v) ),
    file('GEO022-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ equidistant(u,v,w,x)
    | equidistant(x,w,v,u) ),
    file('GEO022-3.p',unknown),
    [] ).

cnf(9,axiom,
    equidistant(u__dfg,v__dfg,w__dfg,x__dfg),
    file('GEO022-3.p',unknown),
    [] ).

cnf(10,axiom,
    equidistant(w__dfg,x__dfg,y__dfg,z__dfg),
    file('GEO022-3.p',unknown),
    [] ).

cnf(11,axiom,
    ~ equidistant(u__dfg,v__dfg,y__dfg,z__dfg),
    file('GEO022-3.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ equidistant(u,v,w,x)
    | ~ equidistant(u,v,y,z)
    | equidistant(y,z,w,x) ),
    file('GEO022-3.p',unknown),
    [] ).

cnf(35,plain,
    ( ~ equidistant(u,v,y__dfg,z__dfg)
    | ~ equidistant(u,v,u__dfg,v__dfg) ),
    inference(res,[status(thm),theory(equality)],[13,11]),
    [iquote('0:Res:13.2,11.0')] ).

cnf(43,plain,
    equidistant(x__dfg,w__dfg,v__dfg,u__dfg),
    inference(res,[status(thm),theory(equality)],[9,8]),
    [iquote('0:Res:9.0,8.0')] ).

cnf(58,plain,
    equidistant(u__dfg,v__dfg,x__dfg,w__dfg),
    inference(res,[status(thm),theory(equality)],[43,7]),
    [iquote('0:Res:43.0,7.0')] ).

cnf(64,plain,
    equidistant(w__dfg,x__dfg,u__dfg,v__dfg),
    inference(res,[status(thm),theory(equality)],[58,7]),
    [iquote('0:Res:58.0,7.0')] ).

cnf(246,plain,
    ~ equidistant(w__dfg,x__dfg,u__dfg,v__dfg),
    inference(res,[status(thm),theory(equality)],[10,35]),
    [iquote('0:Res:10.0,35.0')] ).

cnf(254,plain,
    $false,
    inference(mrr,[status(thm)],[246,64]),
    [iquote('0:MRR:246.0,64.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO022-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n008.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 : Sat Jun 18 10:00:07 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.40  
% 0.20/0.40  SPASS V 3.9 
% 0.20/0.40  SPASS beiseite: Proof found.
% 0.20/0.40  % SZS status Theorem
% 0.20/0.40  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.40  SPASS derived 224 clauses, backtracked 0 clauses, performed 0 splits and kept 68 clauses.
% 0.20/0.40  SPASS allocated 63223 KBytes.
% 0.20/0.40  SPASS spent	0:00:00.05 on the problem.
% 0.20/0.40  		0:00:00.03 for the input.
% 0.20/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.40  		0:00:00.00 for inferences.
% 0.20/0.40  		0:00:00.00 for the backtracking.
% 0.20/0.40  		0:00:00.00 for the reduction.
% 0.20/0.40  
% 0.20/0.40  
% 0.20/0.40  Here is a proof with depth 3, length 12 :
% 0.20/0.40  % SZS output start Refutation
% See solution above
% 0.20/0.40  Formulae used in the proof : d4_4 d4_5 u_to_v_equals_w_to_x w_to_x_equals_y_to_z prove_transitivity transitivity_for_equidistance
% 0.20/0.40  
%------------------------------------------------------------------------------