%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO064-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n032.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 05:24:00 EDT 2022

% Result   : Unsatisfiable 0.14s 0.47s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   5 unt;   0 nHn;   9 RR)
%            Number of literals    :   13 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :    6 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(colinearity1,axiom,
    ( ~ between(X,Y,Z)
    | colinear(X,Y,Z) ) ).

cnf(t1,axiom,
    ( ~ between(U,V,W)
    | between(W,V,U) ) ).

cnf(v_between_w_and_u,hypothesis,
    between(w,v,u) ).

cnf(prove_uvw_colinear,negated_conjecture,
    ~ colinear(u,v,w) ).

cnf(refute_0_0,plain,
    ( ~ between(u,v,w)
    | colinear(u,v,w) ),
    inference(subst,[],[colinearity1:[bind(X,$fot(u)),bind(Y,$fot(v)),bind(Z,$fot(w))]]) ).

cnf(refute_0_1,plain,
    ( ~ between(w,v,u)
    | between(u,v,w) ),
    inference(subst,[],[t1:[bind(U,$fot(w)),bind(V,$fot(v)),bind(W,$fot(u))]]) ).

cnf(refute_0_2,plain,
    between(u,v,w),
    inference(resolve,[$cnf( between(w,v,u) )],[v_between_w_and_u,refute_0_1]) ).

cnf(refute_0_3,plain,
    colinear(u,v,w),
    inference(resolve,[$cnf( between(u,v,w) )],[refute_0_2,refute_0_0]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( colinear(u,v,w) )],[refute_0_3,prove_uvw_colinear]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : GEO064-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.09  % Command  : metis --show proof --show saturation %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 600
% 0.09/0.28  % DateTime : Sat Jun 18 03:00:16 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.09/0.29  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.47  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.47  
% 0.14/0.47  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.47  
%------------------------------------------------------------------------------