%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GEO020-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 06:21:38 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   11 (   7 unt;   0 nHn;  11 RR)
%            Number of literals    :   16 (   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    :   10 (  10 usr;  10 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equidistant(u__dfg,v__dfg,w__dfg,x__dfg),
    file('GEO020-2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equidistant(x__dfg,w__dfg,u__dfg,v__dfg),
    file('GEO020-2.p',unknown),
    [] ).

cnf(3,axiom,
    equidistant(u,v,v,u),
    file('GEO020-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ equidistant(u,v,w,x)
    | ~ equidistant(u,v,y,z)
    | equidistant(y,z,w,x) ),
    file('GEO020-2.p',unknown),
    [] ).

cnf(21,plain,
    ( ~ equidistant(u,v,u__dfg,v__dfg)
    | ~ equidistant(u,v,x__dfg,w__dfg) ),
    inference(res,[status(thm),theory(equality)],[4,2]),
    [iquote('0:Res:4.2,2.0')] ).

cnf(30,plain,
    ~ equidistant(w__dfg,x__dfg,u__dfg,v__dfg),
    inference(res,[status(thm),theory(equality)],[3,21]),
    [iquote('0:Res:3.0,21.1')] ).

cnf(32,plain,
    ( ~ equidistant(u__dfg,v__dfg,u,v)
    | equidistant(u,v,w__dfg,x__dfg) ),
    inference(res,[status(thm),theory(equality)],[1,4]),
    [iquote('0:Res:1.0,4.0')] ).

cnf(33,plain,
    ( ~ equidistant(u,v,w,x)
    | equidistant(w,x,v,u) ),
    inference(res,[status(thm),theory(equality)],[3,4]),
    [iquote('0:Res:3.0,4.0')] ).

cnf(37,plain,
    equidistant(v__dfg,u__dfg,w__dfg,x__dfg),
    inference(res,[status(thm),theory(equality)],[3,32]),
    [iquote('0:Res:3.0,32.0')] ).

cnf(50,plain,
    equidistant(w__dfg,x__dfg,u__dfg,v__dfg),
    inference(res,[status(thm),theory(equality)],[37,33]),
    [iquote('0:Res:37.0,33.0')] ).

cnf(51,plain,
    $false,
    inference(mrr,[status(thm)],[50,30]),
    [iquote('0:MRR:50.0,30.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GEO020-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jun 17 16:11:26 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 30 clauses, backtracked 0 clauses, performed 0 splits and kept 40 clauses.
% 0.19/0.42  SPASS allocated 63141 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 3, length 11 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : u_to_v_equals_w_to_x prove_symmetry reflexivity_for_equidistance transitivity_for_equidistance
% 0.19/0.42  
%------------------------------------------------------------------------------