%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO018-3 : 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 05:23:37 EDT 2022

% Result   : Unsatisfiable 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   13 (   7 unt;   0 nHn;  13 RR)
%            Number of literals    :   19 (   0 equ;   7 neg)
%            Maximal clause size   :    2 (   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   :    8 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(d2,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(W,X,U,V) ) ).

cnf(d3,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(V,U,W,X) ) ).

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(u,v,x,w)
    | equidistant(v,u,x,w) ),
    inference(subst,[],[d3:[bind(U,$fot(u)),bind(V,$fot(v)),bind(W,$fot(x)),bind(X,$fot(w))]]) ).

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

cnf(refute_0_2,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_3,plain,
    equidistant(w,x,u,v),
    inference(resolve,[$cnf( equidistant(u,v,w,x) )],[u_to_v_equals_w_to_x,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ equidistant(w,x,u,v)
    | equidistant(x,w,u,v) ),
    inference(subst,[],[d3:[bind(U,$fot(w)),bind(V,$fot(x)),bind(W,$fot(u)),bind(X,$fot(v))]]) ).

cnf(refute_0_5,plain,
    equidistant(x,w,u,v),
    inference(resolve,[$cnf( equidistant(w,x,u,v) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    equidistant(u,v,x,w),
    inference(resolve,[$cnf( equidistant(x,w,u,v) )],[refute_0_5,refute_0_1]) ).

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

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( equidistant(v,u,x,w) )],[refute_0_7,prove_symmetry]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO018-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jun 17 21:14:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38  
% 0.13/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38  
%------------------------------------------------------------------------------