%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO018-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n005.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 0.71s 0.93s
% Output   : CNFRefutation 0.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   15 (   8 unt;   0 nHn;  14 RR)
%            Number of literals    :   25 (   0 equ;  11 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(u_to_v_equals_w_to_x,hypothesis,
    equidistant(u,v,w,x) ).

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

cnf(refute_0_0,plain,
    equidistant(w,x,x,w),
    inference(subst,[],[reflexivity_for_equidistance:[bind(X,$fot(w)),bind(Y,$fot(x))]]) ).

cnf(refute_0_1,plain,
    ( ~ equidistant(w,x,V2,W)
    | ~ equidistant(w,x,v,u)
    | equidistant(v,u,V2,W) ),
    inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(u)),bind(X,$fot(w)),bind(Y,$fot(x)),bind(Z,$fot(v))]]) ).

cnf(refute_0_2,plain,
    equidistant(u,v,v,u),
    inference(subst,[],[reflexivity_for_equidistance:[bind(X,$fot(u)),bind(Y,$fot(v))]]) ).

cnf(refute_0_3,plain,
    ( ~ equidistant(u,v,X_582,X_583)
    | ~ equidistant(u,v,w,x)
    | equidistant(w,x,X_582,X_583) ),
    inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(x)),bind(V2,$fot(X_582)),bind(W,$fot(X_583)),bind(X,$fot(u)),bind(Y,$fot(v)),bind(Z,$fot(w))]]) ).

cnf(refute_0_4,plain,
    ( ~ equidistant(u,v,X_582,X_583)
    | equidistant(w,x,X_582,X_583) ),
    inference(resolve,[$cnf( equidistant(u,v,w,x) )],[u_to_v_equals_w_to_x,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ equidistant(u,v,v,u)
    | equidistant(w,x,v,u) ),
    inference(subst,[],[refute_0_4:[bind(X_582,$fot(v)),bind(X_583,$fot(u))]]) ).

cnf(refute_0_6,plain,
    equidistant(w,x,v,u),
    inference(resolve,[$cnf( equidistant(u,v,v,u) )],[refute_0_2,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ equidistant(w,x,V2,W)
    | equidistant(v,u,V2,W) ),
    inference(resolve,[$cnf( equidistant(w,x,v,u) )],[refute_0_6,refute_0_1]) ).

cnf(refute_0_8,plain,
    ( ~ equidistant(w,x,x,w)
    | equidistant(v,u,x,w) ),
    inference(subst,[],[refute_0_7:[bind(V2,$fot(x)),bind(W,$fot(w))]]) ).

cnf(refute_0_9,plain,
    equidistant(v,u,x,w),
    inference(resolve,[$cnf( equidistant(w,x,x,w) )],[refute_0_0,refute_0_8]) ).

cnf(refute_0_10,plain,
    $false,
    inference(resolve,[$cnf( equidistant(v,u,x,w) )],[refute_0_9,prove_symmetry]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO018-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jun 18 14:18:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.71/0.93  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.71/0.93  
% 0.71/0.93  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.71/0.93  
%------------------------------------------------------------------------------