%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN014-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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 : Thu Jul 21 08:58:28 EDT 2022

% Result   : Unsatisfiable 0.14s 0.36s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   6 unt;   0 nHn;  12 RR)
%            Number of literals    :   20 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :    7 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(symmetryish,axiom,
    ( ~ equalish(X,Y)
    | equalish(Y,X) ) ).

cnf(transitivityish,axiom,
    ( ~ equalish(X,Y)
    | ~ equalish(Y,Z)
    | equalish(X,Z) ) ).

cnf(c_19,negated_conjecture,
    ~ equalish(m,n) ).

cnf(c_20,negated_conjecture,
    equalish(n,k) ).

cnf(c_23,negated_conjecture,
    equalish(m,k) ).

cnf(refute_0_0,plain,
    ( ~ equalish(n,k)
    | equalish(k,n) ),
    inference(subst,[],[symmetryish:[bind(X,$fot(n)),bind(Y,$fot(k))]]) ).

cnf(refute_0_1,plain,
    equalish(k,n),
    inference(resolve,[$cnf( equalish(n,k) )],[c_20,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ equalish(k,X_18)
    | ~ equalish(m,k)
    | equalish(m,X_18) ),
    inference(subst,[],[transitivityish:[bind(X,$fot(m)),bind(Y,$fot(k)),bind(Z,$fot(X_18))]]) ).

cnf(refute_0_3,plain,
    ( ~ equalish(k,X_18)
    | equalish(m,X_18) ),
    inference(resolve,[$cnf( equalish(m,k) )],[c_23,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ equalish(k,n)
    | equalish(m,n) ),
    inference(subst,[],[refute_0_3:[bind(X_18,$fot(n))]]) ).

cnf(refute_0_5,plain,
    equalish(m,n),
    inference(resolve,[$cnf( equalish(k,n) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( equalish(m,n) )],[refute_0_5,c_19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SYN014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n028.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 23:33:29 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36  
% 0.14/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36  
%------------------------------------------------------------------------------