%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO014-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n004.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 05:23:34 EDT 2022

% Result   : Unsatisfiable 0.19s 0.36s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   5 RR)
%            Number of literals    :   11 (   0 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-4 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-4 aty)
%            Number of variables   :   20 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(transitivity_for_equidistance,axiom,
    ( ~ equidistant(X,Y,Z,V)
    | ~ equidistant(X,Y,V2,W)
    | equidistant(Z,V,V2,W) ) ).

cnf(segment_construction2,axiom,
    equidistant(Y,extension(X,Y,W,V),W,V) ).

cnf(prove_reflexivity,negated_conjecture,
    ~ equidistant(u,v,u,v) ).

cnf(refute_0_0,plain,
    equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22),
    inference(subst,[],[segment_construction2:[bind(V,$fot(X_22)),bind(W,$fot(X_25)),bind(Y,$fot(X_23))]]) ).

cnf(refute_0_1,plain,
    ( ~ equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22)
    | equidistant(X_25,X_22,X_25,X_22) ),
    inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_22)),bind(V2,$fot(X_25)),bind(W,$fot(X_22)),bind(X,$fot(X_23)),bind(Y,$fot(extension(X,X_23,X_25,X_22))),bind(Z,$fot(X_25))]]) ).

cnf(refute_0_2,plain,
    equidistant(X_25,X_22,X_25,X_22),
    inference(resolve,[$cnf( equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    equidistant(u,v,u,v),
    inference(subst,[],[refute_0_2:[bind(X_22,$fot(v)),bind(X_25,$fot(u))]]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( equidistant(u,v,u,v) )],[refute_0_3,prove_reflexivity]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n004.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 09:16:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.36  
% 0.19/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36  
%------------------------------------------------------------------------------