%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO038-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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 05:23:46 EDT 2022

% Result   : Unsatisfiable 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   8 unt;   0 nHn;  11 RR)
%            Number of literals    :   20 (  11 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-4 aty)
%            Number of variables   :    9 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(segment_construction1,axiom,
    between(X,Y,extension(X,Y,W,V)) ).

cnf(y_is_extension,hypothesis,
    y = extension(u,v,w,x) ).

cnf(prove_corollary,negated_conjecture,
    ~ between(u,v,y) ).

cnf(refute_0_0,plain,
    between(u,v,extension(u,v,w,x)),
    inference(subst,[],[segment_construction1:[bind(V,$fot(x)),bind(W,$fot(w)),bind(X,$fot(u)),bind(Y,$fot(v))]]) ).

cnf(refute_0_1,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_3,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( y != extension(u,v,w,x)
    | extension(u,v,w,x) = y ),
    inference(subst,[],[refute_0_3:[bind(X0,$fot(y)),bind(Y0,$fot(extension(u,v,w,x)))]]) ).

cnf(refute_0_5,plain,
    extension(u,v,w,x) = y,
    inference(resolve,[$cnf( $equal(y,extension(u,v,w,x)) )],[y_is_extension,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( extension(u,v,w,x) != y
    | ~ between(u,v,extension(u,v,w,x))
    | between(u,v,y) ),
    introduced(tautology,[equality,[$cnf( between(u,v,extension(u,v,w,x)) ),[2],$fot(y)]]) ).

cnf(refute_0_7,plain,
    ( ~ between(u,v,extension(u,v,w,x))
    | between(u,v,y) ),
    inference(resolve,[$cnf( $equal(extension(u,v,w,x),y) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    between(u,v,y),
    inference(resolve,[$cnf( between(u,v,extension(u,v,w,x)) )],[refute_0_0,refute_0_7]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( between(u,v,y) )],[refute_0_8,prove_corollary]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO038-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n013.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 12:55:14 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38  
% 0.13/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38  
%------------------------------------------------------------------------------