%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO020-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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 05:23:38 EDT 2022

% Result   : Unsatisfiable 0.76s 0.95s
% Output   : CNFRefutation 0.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   19 (  11 unt;   0 nHn;  15 RR)
%            Number of literals    :   30 (   0 equ;  12 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-4 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-4 aty)
%            Number of variables   :   30 (   3 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(segment_construction2,axiom,
    equidistant(Y,extension(X,Y,W,V),W,V) ).

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

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

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

cnf(refute_0_2,plain,
    equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22),
    inference(subst,[],[segment_construction2:[bind(V,$fot(X_22)),bind(W,$fot(X_25)),bind(Y,$fot(X_23))]]) ).

cnf(refute_0_3,plain,
    ( ~ equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22)
    | equidistant(X_25,X_22,X_25,X_22) ),
    inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_22)),bind(V2,$fot(X_25)),bind(W,$fot(X_22)),bind(X,$fot(X_23)),bind(Y,$fot(extension(X,X_23,X_25,X_22))),bind(Z,$fot(X_25))]]) ).

cnf(refute_0_4,plain,
    equidistant(X_25,X_22,X_25,X_22),
    inference(resolve,[$cnf( equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    equidistant(u,v,u,v),
    inference(subst,[],[refute_0_4:[bind(X_22,$fot(v)),bind(X_25,$fot(u))]]) ).

cnf(refute_0_6,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_7,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_6]) ).

cnf(refute_0_8,plain,
    ( ~ equidistant(u,v,u,v)
    | equidistant(w,x,u,v) ),
    inference(subst,[],[refute_0_7:[bind(X_582,$fot(u)),bind(X_583,$fot(v))]]) ).

cnf(refute_0_9,plain,
    equidistant(w,x,u,v),
    inference(resolve,[$cnf( equidistant(u,v,u,v) )],[refute_0_5,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ equidistant(w,x,Z,V)
    | equidistant(Z,V,u,v) ),
    inference(resolve,[$cnf( equidistant(w,x,u,v) )],[refute_0_9,refute_0_1]) ).

cnf(refute_0_11,plain,
    ( ~ equidistant(w,x,x,w)
    | equidistant(x,w,u,v) ),
    inference(subst,[],[refute_0_10:[bind(V,$fot(w)),bind(Z,$fot(x))]]) ).

cnf(refute_0_12,plain,
    equidistant(x,w,u,v),
    inference(resolve,[$cnf( equidistant(w,x,x,w) )],[refute_0_0,refute_0_11]) ).

cnf(refute_0_13,plain,
    $false,
    inference(resolve,[$cnf( equidistant(x,w,u,v) )],[refute_0_12,prove_symmetry]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO020-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n015.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 16:22:27 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.76/0.95  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.95  
% 0.76/0.95  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.76/0.95  
%------------------------------------------------------------------------------