TSTP Solution File: SET590+3 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET590+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 03:35:41 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   35 (   9 unt;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   69 (  31   ~;  25   |;   5   &)
%                                         (   7 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   78 (   3 sgn  38   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
    ! [B,C,D] :
      ( member(D,difference(B,C))
    <=> ( member(D,B)
        & ~ member(D,C) ) ) ).

fof(subset_defn,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ) ).

fof(prove_th49,conjecture,
    ! [B,C] : subset(difference(B,C),B) ).

fof(subgoal_0,plain,
    ! [B,C] : subset(difference(B,C),B),
    inference(strip,[],[prove_th49]) ).

fof(negate_0_0,plain,
    ~ ! [B,C] : subset(difference(B,C),B),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [B,C] : ~ subset(difference(B,C),B),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ~ subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] :
          ( ~ member(D,C)
          & member(D,B) ) ),
    inference(canonicalize,[],[subset_defn]) ).

fof(normalize_0_3,plain,
    ! [B,C,D] :
      ( ~ member(D,difference(B,C))
    <=> ( ~ member(D,B)
        | member(D,C) ) ),
    inference(canonicalize,[],[difference_defn]) ).

fof(normalize_0_4,plain,
    ! [B,C,D] :
      ( ~ member(D,difference(B,C))
    <=> ( ~ member(D,B)
        | member(D,C) ) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] : member(D,difference(B,C)) ),
    inference(simplify,[],[normalize_0_2,normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] : member(D,difference(B,C)) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [B,C,D] :
      ( ( ~ member(D,difference(B,C))
        | ~ subset(B,C) )
      & ( member(skolemFOFtoCNF_D(B,C),difference(B,C))
        | subset(B,C) ) ),
    inference(clausify,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [B,C] :
      ( member(skolemFOFtoCNF_D(B,C),difference(B,C))
      | subset(B,C) ),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [B,C,D] :
      ( ( ~ member(D,C)
        | ~ member(D,difference(B,C)) )
      & ( ~ member(D,difference(B,C))
        | member(D,B) )
      & ( ~ member(D,B)
        | member(D,C)
        | member(D,difference(B,C)) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_10,plain,
    ! [B,C,D] :
      ( ~ member(D,C)
      | ~ member(D,difference(B,C)) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [B,C,D] :
      ( ~ member(D,difference(B,C))
      | member(D,B) ),
    inference(conjunct,[],[normalize_0_9]) ).

cnf(refute_0_0,plain,
    ~ subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( member(skolemFOFtoCNF_D(B,C),difference(B,C))
    | subset(B,C) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_2,plain,
    ( member(skolemFOFtoCNF_D(X_3,X_4),difference(X_3,X_4))
    | subset(X_3,X_4) ),
    inference(subst,[],[refute_0_1:[bind(B,$fot(X_3)),bind(C,$fot(X_4))]]) ).

cnf(refute_0_3,plain,
    ( ~ member(D,C)
    | ~ member(D,difference(B,C)) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_4,plain,
    ( ~ member(skolemFOFtoCNF_D(X_3,X_4),X_4)
    | ~ member(skolemFOFtoCNF_D(X_3,X_4),difference(X_3,X_4)) ),
    inference(subst,[],[refute_0_3:[bind(B,$fot(X_3)),bind(C,$fot(X_4)),bind(D,$fot(skolemFOFtoCNF_D(X_3,X_4)))]]) ).

cnf(refute_0_5,plain,
    ( ~ member(skolemFOFtoCNF_D(X_3,X_4),X_4)
    | subset(X_3,X_4) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_3,X_4),difference(X_3,X_4)) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ member(skolemFOFtoCNF_D(difference(X_46,X_47),X_46),X_46)
    | subset(difference(X_46,X_47),X_46) ),
    inference(subst,[],[refute_0_5:[bind(X_3,$fot(difference(X_46,X_47))),bind(X_4,$fot(X_46))]]) ).

cnf(refute_0_7,plain,
    ( ~ member(D,difference(B,C))
    | member(D,B) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_8,plain,
    ( ~ member(skolemFOFtoCNF_D(difference(B,C),X_12),difference(B,C))
    | member(skolemFOFtoCNF_D(difference(B,C),X_12),B) ),
    inference(subst,[],[refute_0_7:[bind(D,$fot(skolemFOFtoCNF_D(difference(B,C),X_12)))]]) ).

cnf(refute_0_9,plain,
    ( member(skolemFOFtoCNF_D(X_8,X_9),difference(X_8,X_9))
    | subset(X_8,X_9) ),
    inference(subst,[],[refute_0_1:[bind(B,$fot(X_8)),bind(C,$fot(X_9))]]) ).

cnf(refute_0_10,plain,
    ( ~ member(skolemFOFtoCNF_D(X_8,X_9),difference(X_8,X_9))
    | member(skolemFOFtoCNF_D(X_8,X_9),X_8) ),
    inference(subst,[],[refute_0_7:[bind(B,$fot(X_8)),bind(C,$fot(X_9)),bind(D,$fot(skolemFOFtoCNF_D(X_8,X_9)))]]) ).

cnf(refute_0_11,plain,
    ( member(skolemFOFtoCNF_D(X_8,X_9),X_8)
    | subset(X_8,X_9) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(X_8,X_9),difference(X_8,X_9)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( member(skolemFOFtoCNF_D(difference(B,C),X_12),difference(B,C))
    | subset(difference(B,C),X_12) ),
    inference(subst,[],[refute_0_11:[bind(X_8,$fot(difference(B,C))),bind(X_9,$fot(X_12))]]) ).

cnf(refute_0_13,plain,
    ( member(skolemFOFtoCNF_D(difference(B,C),X_12),B)
    | subset(difference(B,C),X_12) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(B,C),X_12),difference(B,C)) )],[refute_0_12,refute_0_8]) ).

cnf(refute_0_14,plain,
    ( member(skolemFOFtoCNF_D(difference(X_46,X_47),X_46),X_46)
    | subset(difference(X_46,X_47),X_46) ),
    inference(subst,[],[refute_0_13:[bind(B,$fot(X_46)),bind(C,$fot(X_47)),bind(X_12,$fot(X_46))]]) ).

cnf(refute_0_15,plain,
    subset(difference(X_46,X_47),X_46),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(difference(X_46,X_47),X_46),X_46) )],[refute_0_14,refute_0_6]) ).

cnf(refute_0_16,plain,
    subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
    inference(subst,[],[refute_0_15:[bind(X_46,$fot(skolemFOFtoCNF_B)),bind(X_47,$fot(skolemFOFtoCNF_C))]]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( subset(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B) )],[refute_0_16,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET590+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n027.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 : Sat Jul  9 23:23:47 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36  
%------------------------------------------------------------------------------