%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO039-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n014.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 05:23:47 EDT 2022

% Result   : Unsatisfiable 0.20s 0.40s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   25 (  13 unt;   0 nHn;  23 RR)
%            Number of literals    :   41 (  19 equ;  19 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :    9 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(identity_for_betweeness,axiom,
    ( ~ between(X,Y,X)
    | X = Y ) ).

cnf(t3,axiom,
    between(U,V,V) ).

cnf(w_between_u_and_x,hypothesis,
    between(u,w,x) ).

cnf(u_is_x,hypothesis,
    u = x ).

cnf(prove_corollary,negated_conjecture,
    ~ between(v,w,x) ).

cnf(refute_0_0,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_1,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( u != x
    | x = u ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(u)),bind(Y0,$fot(x))]]) ).

cnf(refute_0_4,plain,
    x = u,
    inference(resolve,[$cnf( $equal(u,x) )],[u_is_x,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( x != u
    | ~ between(v,w,u)
    | between(v,w,x) ),
    introduced(tautology,[equality,[$cnf( ~ between(v,w,x) ),[2],$fot(u)]]) ).

cnf(refute_0_6,plain,
    ( ~ between(v,w,u)
    | between(v,w,x) ),
    inference(resolve,[$cnf( $equal(x,u) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ~ between(v,w,u),
    inference(resolve,[$cnf( between(v,w,x) )],[refute_0_6,prove_corollary]) ).

cnf(refute_0_8,plain,
    ( x != u
    | ~ between(u,w,x)
    | between(u,w,u) ),
    introduced(tautology,[equality,[$cnf( between(u,w,x) ),[2],$fot(u)]]) ).

cnf(refute_0_9,plain,
    ( ~ between(u,w,x)
    | between(u,w,u) ),
    inference(resolve,[$cnf( $equal(x,u) )],[refute_0_4,refute_0_8]) ).

cnf(refute_0_10,plain,
    between(u,w,u),
    inference(resolve,[$cnf( between(u,w,x) )],[w_between_u_and_x,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ between(u,w,u)
    | u = w ),
    inference(subst,[],[identity_for_betweeness:[bind(X,$fot(u)),bind(Y,$fot(w))]]) ).

cnf(refute_0_12,plain,
    u = w,
    inference(resolve,[$cnf( between(u,w,u) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( u != w
    | w = u ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(u)),bind(Y0,$fot(w))]]) ).

cnf(refute_0_14,plain,
    w = u,
    inference(resolve,[$cnf( $equal(u,w) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( w != u
    | ~ between(v,u,u)
    | between(v,w,u) ),
    introduced(tautology,[equality,[$cnf( ~ between(v,w,u) ),[1],$fot(u)]]) ).

cnf(refute_0_16,plain,
    ( ~ between(v,u,u)
    | between(v,w,u) ),
    inference(resolve,[$cnf( $equal(w,u) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    ~ between(v,u,u),
    inference(resolve,[$cnf( between(v,w,u) )],[refute_0_16,refute_0_7]) ).

cnf(refute_0_18,plain,
    between(v,u,u),
    inference(subst,[],[t3:[bind(U,$fot(v)),bind(V,$fot(u))]]) ).

cnf(refute_0_19,plain,
    $false,
    inference(resolve,[$cnf( between(v,u,u) )],[refute_0_18,refute_0_17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GEO039-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sat Jun 18 05:25:19 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.40  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.40  
% 0.20/0.40  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.41  
%------------------------------------------------------------------------------