%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET002+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : Tue Jul 19 03:30:55 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   23 (  16 unt;   0 def)
%            Number of atoms       :   31 (  20 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  12   ~;   7   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   19 (   0 sgn  12   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(subset_union,axiom,
    ! [B,C] :
      ( subset(B,C)
     => union(B,C) = C ) ).

fof(reflexivity_of_subset,axiom,
    ! [B] : subset(B,B) ).

fof(prove_idempotency_of_union,conjecture,
    ! [B] : union(B,B) = B ).

fof(subgoal_0,plain,
    ! [B] : union(B,B) = B,
    inference(strip,[],[prove_idempotency_of_union]) ).

fof(negate_0_0,plain,
    ~ ! [B] : union(B,B) = B,
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [B] : union(B,B) != B,
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    union(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != skolemFOFtoCNF_B,
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [B] : subset(B,B),
    inference(canonicalize,[],[reflexivity_of_subset]) ).

fof(normalize_0_3,plain,
    ! [B] : subset(B,B),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [B,C] :
      ( ~ subset(B,C)
      | union(B,C) = C ),
    inference(canonicalize,[],[subset_union]) ).

fof(normalize_0_5,plain,
    ! [B,C] :
      ( ~ subset(B,C)
      | union(B,C) = C ),
    inference(specialize,[],[normalize_0_4]) ).

cnf(refute_0_0,plain,
    union(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != skolemFOFtoCNF_B,
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    subset(B,B),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    subset(X_4,X_4),
    inference(subst,[],[refute_0_1:[bind(B,$fot(X_4))]]) ).

cnf(refute_0_3,plain,
    ( ~ subset(B,C)
    | union(B,C) = C ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_4,plain,
    ( ~ subset(X_4,X_4)
    | union(X_4,X_4) = X_4 ),
    inference(subst,[],[refute_0_3:[bind(B,$fot(X_4)),bind(C,$fot(X_4))]]) ).

cnf(refute_0_5,plain,
    union(X_4,X_4) = X_4,
    inference(resolve,[$cnf( subset(X_4,X_4) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    union(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = skolemFOFtoCNF_B,
    inference(subst,[],[refute_0_5:[bind(X_4,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_7,plain,
    ( skolemFOFtoCNF_B != skolemFOFtoCNF_B
    | union(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
    | union(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
    introduced(tautology,[equality,[$cnf( $equal(union(skolemFOFtoCNF_B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),[0,0],$fot(skolemFOFtoCNF_B)]]) ).

cnf(refute_0_8,plain,
    ( skolemFOFtoCNF_B != skolemFOFtoCNF_B
    | union(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
    inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    skolemFOFtoCNF_B != skolemFOFtoCNF_B,
    inference(resolve,[$cnf( $equal(union(skolemFOFtoCNF_B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_8,refute_0_0]) ).

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

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_10,refute_0_9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET002+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n028.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sat Jul  9 19:43:56 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36  
%------------------------------------------------------------------------------