%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO024-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n003.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 05:23:40 EDT 2022

% Result   : Unsatisfiable 0.11s 0.35s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   15 (  10 unt;   0 nHn;   8 RR)
%            Number of literals    :   22 (  12 equ;   8 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    :    3 (   3 usr;   2 con; 0-4 aty)
%            Number of variables   :   32 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(segment_construction2,axiom,
    equidistant(Y,extension(X,Y,W,V),W,V) ).

cnf(e1,axiom,
    V = extension(U,V,W,W) ).

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

cnf(refute_0_0,plain,
    equidistant(X_18,extension(X_17,X_18,X_15,X_15),X_15,X_15),
    inference(subst,[],[segment_construction2:[bind(V,$fot(X_15)),bind(W,$fot(X_15)),bind(X,$fot(X_17)),bind(Y,$fot(X_18))]]) ).

cnf(refute_0_1,plain,
    X_18 = extension(X_17,X_18,X_15,X_15),
    inference(subst,[],[e1:[bind(U,$fot(X_17)),bind(V,$fot(X_18)),bind(W,$fot(X_15))]]) ).

cnf(refute_0_2,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_3,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_4,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( X_18 != extension(X_17,X_18,X_15,X_15)
    | extension(X_17,X_18,X_15,X_15) = X_18 ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(X_18)),bind(Y0,$fot(extension(X_17,X_18,X_15,X_15)))]]) ).

cnf(refute_0_6,plain,
    extension(X_17,X_18,X_15,X_15) = X_18,
    inference(resolve,[$cnf( $equal(X_18,extension(X_17,X_18,X_15,X_15)) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( extension(X_17,X_18,X_15,X_15) != X_18
    | ~ equidistant(X_18,extension(X_17,X_18,X_15,X_15),X_15,X_15)
    | equidistant(X_18,X_18,X_15,X_15) ),
    introduced(tautology,[equality,[$cnf( equidistant(X_18,extension(X_17,X_18,X_15,X_15),X_15,X_15) ),[1],$fot(X_18)]]) ).

cnf(refute_0_8,plain,
    ( ~ equidistant(X_18,extension(X_17,X_18,X_15,X_15),X_15,X_15)
    | equidistant(X_18,X_18,X_15,X_15) ),
    inference(resolve,[$cnf( $equal(extension(X_17,X_18,X_15,X_15),X_18) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    equidistant(X_18,X_18,X_15,X_15),
    inference(resolve,[$cnf( equidistant(X_18,extension(X_17,X_18,X_15,X_15),X_15,X_15) )],[refute_0_0,refute_0_8]) ).

cnf(refute_0_10,plain,
    equidistant(u,u,v,v),
    inference(subst,[],[refute_0_9:[bind(X_15,$fot(v)),bind(X_18,$fot(u))]]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( equidistant(u,u,v,v) )],[refute_0_10,prove_congruence]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : GEO024-3 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.11  % Command  : metis --show proof --show saturation %s
% 0.11/0.32  % Computer : n003.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sat Jun 18 14:17:28 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35  
% 0.11/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.11/0.35  
%------------------------------------------------------------------------------