%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWC293-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n014.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 21:27:35 EDT 2022

% Result   : Unsatisfiable 0.21s 0.45s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   30 (   9 unt;   8 nHn;  29 RR)
%            Number of literals    :   57 (  37 equ;  21 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause3,axiom,
    strictorderedP(nil) ).

cnf(clause66,axiom,
    ( ~ ssItem(U)
    | strictorderedP(cons(U,nil)) ) ).

cnf(co1_6,negated_conjecture,
    sk1 = sk3 ).

cnf(co1_7,negated_conjecture,
    ~ strictorderedP(sk1) ).

cnf(co1_9,negated_conjecture,
    ( ssItem(sk5)
    | nil = sk3 ) ).

cnf(co1_12,negated_conjecture,
    ( cons(sk5,nil) = sk3
    | nil = sk3 ) ).

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

cnf(refute_0_4,plain,
    sk3 = sk1,
    inference(resolve,[$cnf( $equal(sk1,sk3) )],[co1_6,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( nil != sk3
    | sk3 != sk1
    | nil = sk1 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(nil,sk1) ),[0],$fot(sk3)]]) ).

cnf(refute_0_6,plain,
    ( nil != sk3
    | nil = sk1 ),
    inference(resolve,[$cnf( $equal(sk3,sk1) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( nil = sk1
    | ssItem(sk5) ),
    inference(resolve,[$cnf( $equal(nil,sk3) )],[co1_9,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ ssItem(sk5)
    | strictorderedP(cons(sk5,nil)) ),
    inference(subst,[],[clause66:[bind(U,$fot(sk5))]]) ).

cnf(refute_0_9,plain,
    ( nil = sk1
    | strictorderedP(cons(sk5,nil)) ),
    inference(resolve,[$cnf( ssItem(sk5) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( cons(sk5,nil) != sk3
    | sk3 != sk1
    | cons(sk5,nil) = sk1 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(cons(sk5,nil),sk1) ),[0],$fot(sk3)]]) ).

cnf(refute_0_11,plain,
    ( cons(sk5,nil) != sk3
    | cons(sk5,nil) = sk1 ),
    inference(resolve,[$cnf( $equal(sk3,sk1) )],[refute_0_4,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( cons(sk5,nil) = sk1
    | nil = sk3 ),
    inference(resolve,[$cnf( $equal(cons(sk5,nil),sk3) )],[co1_12,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( cons(sk5,nil) = sk1
    | nil = sk1 ),
    inference(resolve,[$cnf( $equal(nil,sk3) )],[refute_0_12,refute_0_6]) ).

cnf(refute_0_14,plain,
    ( cons(sk5,nil) != sk1
    | ~ strictorderedP(cons(sk5,nil))
    | strictorderedP(sk1) ),
    introduced(tautology,[equality,[$cnf( strictorderedP(cons(sk5,nil)) ),[0],$fot(sk1)]]) ).

cnf(refute_0_15,plain,
    ( ~ strictorderedP(cons(sk5,nil))
    | nil = sk1
    | strictorderedP(sk1) ),
    inference(resolve,[$cnf( $equal(cons(sk5,nil),sk1) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( nil = sk1
    | strictorderedP(sk1) ),
    inference(resolve,[$cnf( strictorderedP(cons(sk5,nil)) )],[refute_0_9,refute_0_15]) ).

cnf(refute_0_17,plain,
    nil = sk1,
    inference(resolve,[$cnf( strictorderedP(sk1) )],[refute_0_16,co1_7]) ).

cnf(refute_0_18,plain,
    ( nil != sk1
    | sk1 = nil ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(nil)),bind(Y,$fot(sk1))]]) ).

cnf(refute_0_19,plain,
    sk1 = nil,
    inference(resolve,[$cnf( $equal(nil,sk1) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( sk1 != nil
    | ~ strictorderedP(nil)
    | strictorderedP(sk1) ),
    introduced(tautology,[equality,[$cnf( ~ strictorderedP(sk1) ),[0],$fot(nil)]]) ).

cnf(refute_0_21,plain,
    ( ~ strictorderedP(nil)
    | strictorderedP(sk1) ),
    inference(resolve,[$cnf( $equal(sk1,nil) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ~ strictorderedP(nil),
    inference(resolve,[$cnf( strictorderedP(sk1) )],[refute_0_21,co1_7]) ).

cnf(refute_0_23,plain,
    $false,
    inference(resolve,[$cnf( strictorderedP(nil) )],[clause3,refute_0_22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWC293-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n014.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 : Sun Jun 12 16:32:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.45  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45  
% 0.21/0.45  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.45  
%------------------------------------------------------------------------------