%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO016-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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 05:23:36 EDT 2022

% Result   : Unsatisfiable 0.67s 0.83s
% Output   : CNFRefutation 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   21 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-4 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   16 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(reflexivity_for_equidistance,axiom,
    equidistant(X,Y,Y,X) ).

cnf(transitivity_for_equidistance,axiom,
    ( ~ equidistant(X,Y,Z,V)
    | ~ equidistant(X,Y,V2,W)
    | equidistant(Z,V,V2,W) ) ).

cnf(d2,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(W,X,U,V) ) ).

cnf(u_to_v_equals_w_to_x,hypothesis,
    equidistant(u,v,w,x) ).

cnf(prove_symmetry,negated_conjecture,
    ~ equidistant(v,u,w,x) ).

cnf(refute_0_0,plain,
    ( ~ equidistant(w,x,v,u)
    | equidistant(v,u,w,x) ),
    inference(subst,[],[d2:[bind(U,$fot(w)),bind(V,$fot(x)),bind(W,$fot(v)),bind(X,$fot(u))]]) ).

cnf(refute_0_1,plain,
    equidistant(u,v,v,u),
    inference(subst,[],[reflexivity_for_equidistance:[bind(X,$fot(u)),bind(Y,$fot(v))]]) ).

cnf(refute_0_2,plain,
    ( ~ equidistant(u,v,X_490,X_491)
    | ~ equidistant(u,v,w,x)
    | equidistant(w,x,X_490,X_491) ),
    inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(x)),bind(V2,$fot(X_490)),bind(W,$fot(X_491)),bind(X,$fot(u)),bind(Y,$fot(v)),bind(Z,$fot(w))]]) ).

cnf(refute_0_3,plain,
    ( ~ equidistant(u,v,X_490,X_491)
    | equidistant(w,x,X_490,X_491) ),
    inference(resolve,[$cnf( equidistant(u,v,w,x) )],[u_to_v_equals_w_to_x,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ equidistant(u,v,v,u)
    | equidistant(w,x,v,u) ),
    inference(subst,[],[refute_0_3:[bind(X_490,$fot(v)),bind(X_491,$fot(u))]]) ).

cnf(refute_0_5,plain,
    equidistant(w,x,v,u),
    inference(resolve,[$cnf( equidistant(u,v,v,u) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    equidistant(v,u,w,x),
    inference(resolve,[$cnf( equidistant(w,x,v,u) )],[refute_0_5,refute_0_0]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( equidistant(v,u,w,x) )],[refute_0_6,prove_symmetry]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO016-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun 18 12:57:49 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.67/0.83  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.67/0.83  
% 0.67/0.83  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.67/0.84  
%------------------------------------------------------------------------------