%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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 05:23:26 EDT 2022

% Result   : Unsatisfiable 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   19 (  12 unt;   0 nHn;  10 RR)
%            Number of literals    :   28 (  14 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-4 aty)
%            Number of variables   :   45 (   8 sgn)

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

cnf(segment_construction1,axiom,
    between(X,Y,extension(X,Y,W,V)) ).

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

cnf(prove_b_between_a_and_b,negated_conjecture,
    ~ between(a,b,b) ).

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

cnf(refute_0_1,plain,
    equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14),
    inference(subst,[],[segment_construction2:[bind(V,$fot(X_14)),bind(W,$fot(X_14)),bind(Y,$fot(X_12))]]) ).

cnf(refute_0_2,plain,
    ( ~ equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14)
    | X_12 = extension(X,X_12,X_14,X_14) ),
    inference(subst,[],[identity_for_equidistance:[bind(X,$fot(X_12)),bind(Y,$fot(extension(X,X_12,X_14,X_14))),bind(Z,$fot(X_14))]]) ).

cnf(refute_0_3,plain,
    X_12 = extension(X,X_12,X_14,X_14),
    inference(resolve,[$cnf( equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    Y = extension(X,Y,V,V),
    inference(subst,[],[refute_0_3:[bind(X_12,$fot(Y)),bind(X_14,$fot(V))]]) ).

cnf(refute_0_5,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_6,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_7,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( Y != extension(X,Y,V,V)
    | extension(X,Y,V,V) = Y ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(Y)),bind(Y0,$fot(extension(X,Y,V,V)))]]) ).

cnf(refute_0_9,plain,
    extension(X,Y,V,V) = Y,
    inference(resolve,[$cnf( $equal(Y,extension(X,Y,V,V)) )],[refute_0_4,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( extension(X,Y,V,V) != Y
    | ~ between(X,Y,extension(X,Y,V,V))
    | between(X,Y,Y) ),
    introduced(tautology,[equality,[$cnf( between(X,Y,extension(X,Y,V,V)) ),[2],$fot(Y)]]) ).

cnf(refute_0_11,plain,
    ( ~ between(X,Y,extension(X,Y,V,V))
    | between(X,Y,Y) ),
    inference(resolve,[$cnf( $equal(extension(X,Y,V,V),Y) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    between(X,Y,Y),
    inference(resolve,[$cnf( between(X,Y,extension(X,Y,V,V)) )],[refute_0_0,refute_0_11]) ).

cnf(refute_0_13,plain,
    between(a,b,b),
    inference(subst,[],[refute_0_12:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( between(a,b,b) )],[refute_0_13,prove_b_between_a_and_b]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jun 17 20:35:01 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37  
% 0.13/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37  
%------------------------------------------------------------------------------