TSTP Solution File: SET592+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n003.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 03:35:42 EDT 2022

% Result   : Theorem 0.44s 0.62s
% Output   : CNFRefutation 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   31 (  12 unt;   0 def)
%            Number of atoms       :   66 (  21 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   57 (  22   ~;  17   |;  13   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   30 (   0 sgn  21   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(subset_of_empty_set_is_empty_set,axiom,
    ! [B] :
      ( subset(B,empty_set)
     => B = empty_set ) ).

fof(intersection_of_subsets,axiom,
    ! [B,C,D] :
      ( ( subset(B,C)
        & subset(B,D) )
     => subset(B,intersection(C,D)) ) ).

fof(prove_th51,conjecture,
    ! [B,C,D] :
      ( ( subset(B,C)
        & subset(B,D)
        & intersection(C,D) = empty_set )
     => B = empty_set ) ).

fof(subgoal_0,plain,
    ! [B,C,D] :
      ( ( subset(B,C)
        & subset(B,D)
        & intersection(C,D) = empty_set )
     => B = empty_set ),
    inference(strip,[],[prove_th51]) ).

fof(negate_0_0,plain,
    ~ ! [B,C,D] :
        ( ( subset(B,C)
          & subset(B,D)
          & intersection(C,D) = empty_set )
       => B = empty_set ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [B] :
      ( ~ subset(B,empty_set)
      | B = empty_set ),
    inference(canonicalize,[],[subset_of_empty_set_is_empty_set]) ).

fof(normalize_0_1,plain,
    ! [B] :
      ( ~ subset(B,empty_set)
      | B = empty_set ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ? [B,C,D] :
      ( B != empty_set
      & intersection(C,D) = empty_set
      & subset(B,C)
      & subset(B,D) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_3,plain,
    ( skolemFOFtoCNF_B != empty_set
    & intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) = empty_set
    & subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
    & subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) ),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_6,plain,
    ! [B,C,D] :
      ( ~ subset(B,C)
      | ~ subset(B,D)
      | subset(B,intersection(C,D)) ),
    inference(canonicalize,[],[intersection_of_subsets]) ).

fof(normalize_0_7,plain,
    ! [B,C,D] :
      ( ~ subset(B,C)
      | ~ subset(B,D)
      | subset(B,intersection(C,D)) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) = empty_set,
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_9,plain,
    skolemFOFtoCNF_B != empty_set,
    inference(conjunct,[],[normalize_0_3]) ).

cnf(refute_0_0,plain,
    ( ~ subset(B,empty_set)
    | B = empty_set ),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( ~ subset(skolemFOFtoCNF_B,empty_set)
    | skolemFOFtoCNF_B = empty_set ),
    inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_2,plain,
    subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
    subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_4,plain,
    ( ~ subset(B,C)
    | ~ subset(B,D)
    | subset(B,intersection(C,D)) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_5,plain,
    ( ~ subset(skolemFOFtoCNF_B,X_182)
    | ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
    | subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,X_182)) ),
    inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(X_182))]]) ).

cnf(refute_0_6,plain,
    ( ~ subset(skolemFOFtoCNF_B,X_182)
    | subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,X_182)) ),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_3,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
    | subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) ),
    inference(subst,[],[refute_0_6:[bind(X_182,$fot(skolemFOFtoCNF_D_2))]]) ).

cnf(refute_0_8,plain,
    subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) )],[refute_0_2,refute_0_7]) ).

cnf(refute_0_9,plain,
    intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) = empty_set,
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_10,plain,
    ( intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2) != empty_set
    | ~ subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
    | subset(skolemFOFtoCNF_B,empty_set) ),
    introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) ),[1],$fot(empty_set)]]) ).

cnf(refute_0_11,plain,
    ( ~ subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2))
    | subset(skolemFOFtoCNF_B,empty_set) ),
    inference(resolve,[$cnf( $equal(intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2),empty_set) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    subset(skolemFOFtoCNF_B,empty_set),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,intersection(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_2)) )],[refute_0_8,refute_0_11]) ).

cnf(refute_0_13,plain,
    skolemFOFtoCNF_B = empty_set,
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,empty_set) )],[refute_0_12,refute_0_1]) ).

cnf(refute_0_14,plain,
    skolemFOFtoCNF_B != empty_set,
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_15,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_13,refute_0_14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n003.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 Jul 10 09:51:44 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.44/0.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.62  
% 0.44/0.62  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.44/0.62  
%------------------------------------------------------------------------------