%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWC255-1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Tue Jul 19 21:27:22 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   22 (   8 unt;   1 nHn;  21 RR)
%            Number of literals    :   39 (  16 equ;  19 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :    5 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(co1_5,negated_conjecture,
    sk2 = sk4 ).

cnf(co1_6,negated_conjecture,
    sk1 = sk3 ).

cnf(co1_7,negated_conjecture,
    ( neq(sk2,nil)
    | neq(sk2,nil) ) ).

cnf(co1_11,negated_conjecture,
    ( singletonP(sk3)
    | ~ neq(sk4,nil) ) ).

cnf(co1_12,negated_conjecture,
    ( ~ singletonP(sk1)
    | ~ neq(sk4,nil) ) ).

cnf(refute_0_0,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_1,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_2,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( sk2 != sk4
    | sk4 = sk2 ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(sk2)),bind(Y,$fot(sk4))]]) ).

cnf(refute_0_4,plain,
    sk4 = sk2,
    inference(resolve,[$cnf( $equal(sk2,sk4) )],[co1_5,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( sk4 != sk2
    | ~ neq(sk2,nil)
    | neq(sk4,nil) ),
    introduced(tautology,[equality,[$cnf( ~ neq(sk4,nil) ),[0],$fot(sk2)]]) ).

cnf(refute_0_6,plain,
    ( ~ neq(sk2,nil)
    | neq(sk4,nil) ),
    inference(resolve,[$cnf( $equal(sk4,sk2) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ neq(sk2,nil)
    | ~ singletonP(sk1) ),
    inference(resolve,[$cnf( neq(sk4,nil) )],[refute_0_6,co1_12]) ).

cnf(refute_0_8,plain,
    ~ singletonP(sk1),
    inference(resolve,[$cnf( neq(sk2,nil) )],[co1_7,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ neq(sk2,nil)
    | singletonP(sk3) ),
    inference(resolve,[$cnf( neq(sk4,nil) )],[refute_0_6,co1_11]) ).

cnf(refute_0_10,plain,
    ( sk1 != sk3
    | sk3 = sk1 ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(sk1)),bind(Y,$fot(sk3))]]) ).

cnf(refute_0_11,plain,
    sk3 = sk1,
    inference(resolve,[$cnf( $equal(sk1,sk3) )],[co1_6,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( sk3 != sk1
    | ~ singletonP(sk3)
    | singletonP(sk1) ),
    introduced(tautology,[equality,[$cnf( singletonP(sk3) ),[0],$fot(sk1)]]) ).

cnf(refute_0_13,plain,
    ( ~ singletonP(sk3)
    | singletonP(sk1) ),
    inference(resolve,[$cnf( $equal(sk3,sk1) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ neq(sk2,nil)
    | singletonP(sk1) ),
    inference(resolve,[$cnf( singletonP(sk3) )],[refute_0_9,refute_0_13]) ).

cnf(refute_0_15,plain,
    singletonP(sk1),
    inference(resolve,[$cnf( neq(sk2,nil) )],[co1_7,refute_0_14]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( singletonP(sk1) )],[refute_0_15,refute_0_8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SWC255-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sat Jun 11 19:53:24 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.43  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43  
% 0.20/0.43  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.43  
%------------------------------------------------------------------------------