%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO058-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n025.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 05:23:57 EDT 2022

% Result   : Unsatisfiable 0.12s 0.38s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   24 (  12 unt;   0 nHn;  22 RR)
%            Number of literals    :   38 (  18 equ;  16 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-4 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(identity_for_equidistance,axiom,
    ( ~ equidistant(X,Y,Z,Z)
    | X = Y ) ).

cnf(d4_1,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(U,V,X,W) ) ).

cnf(d4_3,axiom,
    ( ~ equidistant(U,V,W,X)
    | equidistant(W,X,V,U) ) ).

cnf(r2_2,axiom,
    equidistant(V,reflection(U,V),U,V) ).

cnf(v_equals_reflection,hypothesis,
    v = reflection(u,v) ).

cnf(prove_u_equals_v,negated_conjecture,
    u != v ).

cnf(refute_0_0,plain,
    ( ~ equidistant(v,u,v,v)
    | v = u ),
    inference(subst,[],[identity_for_equidistance:[bind(X,$fot(v)),bind(Y,$fot(u)),bind(Z,$fot(v))]]) ).

cnf(refute_0_1,plain,
    equidistant(v,reflection(u,v),u,v),
    inference(subst,[],[r2_2:[bind(U,$fot(u)),bind(V,$fot(v))]]) ).

cnf(refute_0_2,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_3,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_4,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( v != reflection(u,v)
    | reflection(u,v) = v ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(v)),bind(Y0,$fot(reflection(u,v)))]]) ).

cnf(refute_0_6,plain,
    reflection(u,v) = v,
    inference(resolve,[$cnf( $equal(v,reflection(u,v)) )],[v_equals_reflection,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( reflection(u,v) != v
    | ~ equidistant(v,reflection(u,v),u,v)
    | equidistant(v,v,u,v) ),
    introduced(tautology,[equality,[$cnf( equidistant(v,reflection(u,v),u,v) ),[1],$fot(v)]]) ).

cnf(refute_0_8,plain,
    ( ~ equidistant(v,reflection(u,v),u,v)
    | equidistant(v,v,u,v) ),
    inference(resolve,[$cnf( $equal(reflection(u,v),v) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    equidistant(v,v,u,v),
    inference(resolve,[$cnf( equidistant(v,reflection(u,v),u,v) )],[refute_0_1,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ equidistant(v,v,u,v)
    | equidistant(v,v,v,u) ),
    inference(subst,[],[d4_1:[bind(U,$fot(v)),bind(V,$fot(v)),bind(W,$fot(u)),bind(X,$fot(v))]]) ).

cnf(refute_0_11,plain,
    equidistant(v,v,v,u),
    inference(resolve,[$cnf( equidistant(v,v,u,v) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ equidistant(v,v,v,u)
    | equidistant(v,u,v,v) ),
    inference(subst,[],[d4_3:[bind(U,$fot(v)),bind(V,$fot(v)),bind(W,$fot(v)),bind(X,$fot(u))]]) ).

cnf(refute_0_13,plain,
    equidistant(v,u,v,v),
    inference(resolve,[$cnf( equidistant(v,v,v,u) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    v = u,
    inference(resolve,[$cnf( equidistant(v,u,v,v) )],[refute_0_13,refute_0_0]) ).

cnf(refute_0_15,plain,
    ( v != u
    | u = v ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(v)),bind(Y0,$fot(u))]]) ).

cnf(refute_0_16,plain,
    v != u,
    inference(resolve,[$cnf( $equal(u,v) )],[refute_0_15,prove_u_equals_v]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( $equal(v,u) )],[refute_0_14,refute_0_16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GEO058-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n025.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 00:38:42 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38  
% 0.12/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.39  
%------------------------------------------------------------------------------