%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : HWV010-1 : TPTP v8.1.0. Released v2.5.0.
% 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 18:29:37 EDT 2022

% Result   : Unsatisfiable 0.19s 0.39s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   23 (   7 unt;   2 nHn;  22 RR)
%            Number of literals    :   42 (  29 equ;  21 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :    3 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_21,axiom,
    level(X_t_32) = int_level(X_t_32) ).

cnf(axiom_24,axiom,
    ( int_level(X_t_35) != n0
    | p_Empty(X_t_35) ) ).

cnf(axiom_25,axiom,
    ( int_level(X_t_36) = n0
    | ~ p_Empty(X_t_36) ) ).

cnf(quest_1,negated_conjecture,
    ( ~ p_Empty(t_139)
    | level(t_139) != n0 ) ).

cnf(quest_2,negated_conjecture,
    ( p_Empty(t_139)
    | level(t_139) = n0 ) ).

cnf(refute_0_0,plain,
    ( int_level(t_139) != n0
    | p_Empty(t_139) ),
    inference(subst,[],[axiom_24:[bind(X_t_35,$fot(t_139))]]) ).

cnf(refute_0_1,plain,
    level(t_139) = int_level(t_139),
    inference(subst,[],[axiom_21:[bind(X_t_32,$fot(t_139))]]) ).

cnf(refute_0_2,plain,
    ( level(t_139) != int_level(t_139)
    | level(t_139) != n0
    | int_level(t_139) = n0 ),
    introduced(tautology,[equality,[$cnf( $equal(level(t_139),n0) ),[0],$fot(int_level(t_139))]]) ).

cnf(refute_0_3,plain,
    ( level(t_139) != n0
    | int_level(t_139) = n0 ),
    inference(resolve,[$cnf( $equal(level(t_139),int_level(t_139)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( int_level(t_139) = n0
    | p_Empty(t_139) ),
    inference(resolve,[$cnf( $equal(level(t_139),n0) )],[quest_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ p_Empty(t_139)
    | int_level(t_139) = n0 ),
    inference(subst,[],[axiom_25:[bind(X_t_36,$fot(t_139))]]) ).

cnf(refute_0_6,plain,
    int_level(t_139) = n0,
    inference(resolve,[$cnf( p_Empty(t_139) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( int_level(t_139) != n0
    | n0 != n0
    | int_level(t_139) = n0 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(int_level(t_139),n0) ),[0],$fot(n0)]]) ).

cnf(refute_0_8,plain,
    ( n0 != n0
    | int_level(t_139) = n0 ),
    inference(resolve,[$cnf( $equal(int_level(t_139),n0) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( n0 != n0
    | p_Empty(t_139) ),
    inference(resolve,[$cnf( $equal(int_level(t_139),n0) )],[refute_0_8,refute_0_0]) ).

cnf(refute_0_10,plain,
    n0 = n0,
    introduced(tautology,[refl,[$fot(n0)]]) ).

cnf(refute_0_11,plain,
    p_Empty(t_139),
    inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_10,refute_0_9]) ).

cnf(refute_0_12,plain,
    ( int_level(t_139) != n0
    | level(t_139) != int_level(t_139)
    | level(t_139) = n0 ),
    introduced(tautology,[equality,[$cnf( $equal(level(t_139),int_level(t_139)) ),[1],$fot(n0)]]) ).

cnf(refute_0_13,plain,
    ( int_level(t_139) != n0
    | level(t_139) = n0 ),
    inference(resolve,[$cnf( $equal(level(t_139),int_level(t_139)) )],[refute_0_1,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( int_level(t_139) != n0
    | ~ p_Empty(t_139) ),
    inference(resolve,[$cnf( $equal(level(t_139),n0) )],[refute_0_13,quest_1]) ).

cnf(refute_0_15,plain,
    ( n0 != n0
    | ~ p_Empty(t_139) ),
    inference(resolve,[$cnf( $equal(int_level(t_139),n0) )],[refute_0_8,refute_0_14]) ).

cnf(refute_0_16,plain,
    ~ p_Empty(t_139),
    inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_10,refute_0_15]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( p_Empty(t_139) )],[refute_0_11,refute_0_16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : HWV010-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n025.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 : Fri Jun 17 07:53:12 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.19/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.39  
% 0.19/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.39  
%------------------------------------------------------------------------------