%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO022-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 05:23:39 EDT 2022

% Result   : Unsatisfiable 0.88s 1.04s
% Output   : CNFRefutation 0.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   14 (   7 unt;   0 nHn;  14 RR)
%            Number of literals    :   23 (   0 equ;  10 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    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   14 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
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(w_to_x_equals_y_to_z,hypothesis,
    equidistant(w,x,y,z) ).

cnf(prove_transitivity,negated_conjecture,
    ~ equidistant(u,v,y,z) ).

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

cnf(refute_0_1,plain,
    ( ~ equidistant(u,v,w,x)
    | equidistant(w,x,u,v) ),
    inference(subst,[],[d2:[bind(U,$fot(u)),bind(V,$fot(v)),bind(W,$fot(w)),bind(X,$fot(x))]]) ).

cnf(refute_0_2,plain,
    equidistant(w,x,u,v),
    inference(resolve,[$cnf( equidistant(u,v,w,x) )],[u_to_v_equals_w_to_x,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ equidistant(w,x,X_715,X_710)
    | ~ equidistant(w,x,u,v)
    | equidistant(X_715,X_710,u,v) ),
    inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_710)),bind(V2,$fot(u)),bind(W,$fot(v)),bind(X,$fot(w)),bind(Y,$fot(x)),bind(Z,$fot(X_715))]]) ).

cnf(refute_0_4,plain,
    ( ~ equidistant(w,x,X_715,X_710)
    | equidistant(X_715,X_710,u,v) ),
    inference(resolve,[$cnf( equidistant(w,x,u,v) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ equidistant(w,x,y,z)
    | equidistant(y,z,u,v) ),
    inference(subst,[],[refute_0_4:[bind(X_710,$fot(z)),bind(X_715,$fot(y))]]) ).

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

cnf(refute_0_7,plain,
    equidistant(u,v,y,z),
    inference(resolve,[$cnf( equidistant(y,z,u,v) )],[refute_0_6,refute_0_0]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( equidistant(u,v,y,z) )],[refute_0_7,prove_transitivity]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : GEO022-3 : TPTP v8.1.0. Released v1.0.0.
% 0.14/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.36  % Computer : n029.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sat Jun 18 10:04:44 EDT 2022
% 0.21/0.36  % CPUTime  : 
% 0.21/0.37  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.88/1.04  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.88/1.04  
% 0.88/1.04  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.88/1.04  
%------------------------------------------------------------------------------