%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN080-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 08:59:24 EDT 2022

% Result   : Unsatisfiable 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (   8 unt;   0 nHn;   8 RR)
%            Number of literals    :   20 (  19 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :   16 (   8 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause_1,axiom,
    f(X) = g(Y) ).

cnf(prove_this,negated_conjecture,
    f(f(a)) != f(g(b)) ).

cnf(refute_0_0,plain,
    f(f(a)) = g(X_1),
    inference(subst,[],[clause_1:[bind(X,$fot(f(a))),bind(Y,$fot(X_1))]]) ).

cnf(refute_0_1,plain,
    ( f(f(a)) != g(X_1)
    | g(X_1) != f(g(b))
    | f(f(a)) = f(g(b)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(f(f(a)),f(g(b))) ),[0],$fot(g(X_1))]]) ).

cnf(refute_0_2,plain,
    ( g(X_1) != f(g(b))
    | f(f(a)) = f(g(b)) ),
    inference(resolve,[$cnf( $equal(f(f(a)),g(X_1)) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    g(X_1) != f(g(b)),
    inference(resolve,[$cnf( $equal(f(f(a)),f(g(b))) )],[refute_0_2,prove_this]) ).

cnf(refute_0_4,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_5,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_6,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( f(X) != g(Y)
    | g(Y) = f(X) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(f(X))),bind(Y0,$fot(g(Y)))]]) ).

cnf(refute_0_8,plain,
    g(Y) = f(X),
    inference(resolve,[$cnf( $equal(f(X),g(Y)) )],[clause_1,refute_0_7]) ).

cnf(refute_0_9,plain,
    g(X_1) = f(g(b)),
    inference(subst,[],[refute_0_8:[bind(X,$fot(g(b))),bind(Y,$fot(X_1))]]) ).

cnf(refute_0_10,plain,
    $false,
    inference(resolve,[$cnf( $equal(g(X_1),f(g(b))) )],[refute_0_9,refute_0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYN080-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue Jul 12 03:04:04 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.34  
%------------------------------------------------------------------------------