%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO035-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n025.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 05:23:45 EDT 2022

% Result   : Unsatisfiable 0.20s 0.37s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   17 (  10 unt;   0 nHn;  12 RR)
%            Number of literals    :   26 (  21 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-4 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-4 aty)
%            Number of variables   :   27 (   4 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(identity_for_equidistance,axiom,
    ( ~ equidistant(X,Y,Z,Z)
    | X = Y ) ).

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

cnf(prove_null_extension,negated_conjecture,
    v != extension(u,v,w,w) ).

cnf(refute_0_0,plain,
    equidistant(X_14,extension(X,X_14,X_16,X_16),X_16,X_16),
    inference(subst,[],[segment_construction2:[bind(V,$fot(X_16)),bind(W,$fot(X_16)),bind(Y,$fot(X_14))]]) ).

cnf(refute_0_1,plain,
    ( ~ equidistant(X_14,extension(X,X_14,X_16,X_16),X_16,X_16)
    | X_14 = extension(X,X_14,X_16,X_16) ),
    inference(subst,[],[identity_for_equidistance:[bind(X,$fot(X_14)),bind(Y,$fot(extension(X,X_14,X_16,X_16))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_2,plain,
    X_14 = extension(X,X_14,X_16,X_16),
    inference(resolve,[$cnf( equidistant(X_14,extension(X,X_14,X_16,X_16),X_16,X_16) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_4,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_5,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( X_14 != extension(X,X_14,X_16,X_16)
    | extension(X,X_14,X_16,X_16) = X_14 ),
    inference(subst,[],[refute_0_5:[bind(X0,$fot(X_14)),bind(Y0,$fot(extension(X,X_14,X_16,X_16)))]]) ).

cnf(refute_0_7,plain,
    extension(X,X_14,X_16,X_16) = X_14,
    inference(resolve,[$cnf( $equal(X_14,extension(X,X_14,X_16,X_16)) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    extension(u,v,w,w) = v,
    inference(subst,[],[refute_0_7:[bind(X,$fot(u)),bind(X_14,$fot(v)),bind(X_16,$fot(w))]]) ).

cnf(refute_0_9,plain,
    ( extension(u,v,w,w) != v
    | v != v
    | v = extension(u,v,w,w) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(v,extension(u,v,w,w)) ),[1],$fot(v)]]) ).

cnf(refute_0_10,plain,
    ( v != v
    | v = extension(u,v,w,w) ),
    inference(resolve,[$cnf( $equal(extension(u,v,w,w),v) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    v != v,
    inference(resolve,[$cnf( $equal(v,extension(u,v,w,w)) )],[refute_0_10,prove_null_extension]) ).

cnf(refute_0_12,plain,
    v = v,
    introduced(tautology,[refl,[$fot(v)]]) ).

cnf(refute_0_13,plain,
    $false,
    inference(resolve,[$cnf( $equal(v,v) )],[refute_0_12,refute_0_11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO035-3 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n025.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 : Fri Jun 17 23:18:27 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.37  
% 0.20/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.38  
%------------------------------------------------------------------------------