TSTP Solution File: SET587+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : Tue Jul 19 03:35:39 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   96 (  28 unt;   0 def)
%            Number of atoms       :  196 (  35 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  194 (  94   ~;  61   |;  15   &)
%                                         (  19 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  143 (  12 sgn  83   !;  12   ?)

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

fof(empty_set_defn,axiom,
    ! [B] : ~ member(B,empty_set) ).

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

fof(equal_defn,axiom,
    ! [B,C] :
      ( B = C
    <=> ( subset(B,C)
        & subset(C,B) ) ) ).

fof(empty_defn,axiom,
    ! [B] :
      ( empty(B)
    <=> ! [C] : ~ member(C,B) ) ).

fof(prove_difference_empty_set,conjecture,
    ! [B,C] :
      ( difference(B,C) = empty_set
    <=> subset(B,C) ) ).

fof(subgoal_0,plain,
    ! [B,C] :
      ( difference(B,C) = empty_set
     => subset(B,C) ),
    inference(strip,[],[prove_difference_empty_set]) ).

fof(subgoal_1,plain,
    ! [B,C] :
      ( subset(B,C)
     => difference(B,C) = empty_set ),
    inference(strip,[],[prove_difference_empty_set]) ).

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

fof(normalize_0_0,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] :
          ( ~ member(D,C)
          & member(D,B) ) ),
    inference(canonicalize,[],[subset_defn]) ).

fof(normalize_0_1,plain,
    ! [B,C,D] :
      ( ~ member(D,difference(B,C))
    <=> ( ~ member(D,B)
        | member(D,C) ) ),
    inference(canonicalize,[],[difference_defn]) ).

fof(normalize_0_2,plain,
    ! [B,C,D] :
      ( ~ member(D,difference(B,C))
    <=> ( ~ member(D,B)
        | member(D,C) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] : member(D,difference(B,C)) ),
    inference(simplify,[],[normalize_0_0,normalize_0_2]) ).

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

fof(normalize_0_5,plain,
    ! [B,C,D] :
      ( ( ~ member(D,difference(B,C))
        | ~ subset(B,C) )
      & ( member(skolemFOFtoCNF_D_1(B,C),difference(B,C))
        | subset(B,C) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [B,C] :
      ( member(skolemFOFtoCNF_D_1(B,C),difference(B,C))
      | subset(B,C) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ? [B,C] :
      ( ~ subset(B,C)
      & difference(B,C) = empty_set ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_8,plain,
    ( ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)
    & difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set ),
    inference(skolemize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set,
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [B] : ~ member(B,empty_set),
    inference(canonicalize,[],[empty_set_defn]) ).

fof(normalize_0_11,plain,
    ! [B] : ~ member(B,empty_set),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
    inference(conjunct,[],[normalize_0_8]) ).

cnf(refute_0_0,plain,
    ( member(skolemFOFtoCNF_D_1(B,C),difference(B,C))
    | subset(B,C) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_1,plain,
    ( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
    | subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
    inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).

cnf(refute_0_2,plain,
    difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) = empty_set,
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_3,plain,
    ( difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) != empty_set
    | ~ member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
    | member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) ),
    introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) ),[1],$fot(empty_set)]]) ).

cnf(refute_0_4,plain,
    ( ~ member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1))
    | member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) ),
    inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set)
    | subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),difference(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    ~ member(B,empty_set),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_7,plain,
    ~ member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set),
    inference(subst,[],[refute_0_6:[bind(B,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1)))]]) ).

cnf(refute_0_8,plain,
    subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),empty_set) )],[refute_0_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_10,plain,
    $false,
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C_1) )],[refute_0_8,refute_0_9]) ).

fof(negate_1_0,plain,
    ~ ! [B,C] :
        ( subset(B,C)
       => difference(B,C) = empty_set ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ! [B] :
      ( ~ empty(B)
    <=> ? [C] : member(C,B) ),
    inference(canonicalize,[],[empty_defn]) ).

fof(normalize_1_1,plain,
    ! [B] :
      ( ~ empty(B)
    <=> ? [C] : member(C,B) ),
    inference(specialize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ! [B,C] :
      ( ( ~ empty(B)
        | ~ member(C,B) )
      & ( empty(B)
        | member(skolemFOFtoCNF_C(B),B) ) ),
    inference(clausify,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ! [B,C] :
      ( ~ empty(B)
      | ~ member(C,B) ),
    inference(conjunct,[],[normalize_1_2]) ).

fof(normalize_1_4,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] :
          ( ~ member(D,C)
          & member(D,B) ) ),
    inference(canonicalize,[],[subset_defn]) ).

fof(normalize_1_5,plain,
    ! [B,C,D] :
      ( ~ member(D,difference(B,C))
    <=> ( ~ member(D,B)
        | member(D,C) ) ),
    inference(canonicalize,[],[difference_defn]) ).

fof(normalize_1_6,plain,
    ! [B,C,D] :
      ( ~ member(D,difference(B,C))
    <=> ( ~ member(D,B)
        | member(D,C) ) ),
    inference(specialize,[],[normalize_1_5]) ).

fof(normalize_1_7,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] : member(D,difference(B,C)) ),
    inference(simplify,[],[normalize_1_4,normalize_1_6]) ).

fof(normalize_1_8,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] : member(D,difference(B,C)) ),
    inference(specialize,[],[normalize_1_7]) ).

fof(normalize_1_9,plain,
    ! [B,C,D] :
      ( ( ~ member(D,difference(B,C))
        | ~ subset(B,C) )
      & ( member(skolemFOFtoCNF_D_1(B,C),difference(B,C))
        | subset(B,C) ) ),
    inference(clausify,[],[normalize_1_8]) ).

fof(normalize_1_10,plain,
    ! [B,C] :
      ( member(skolemFOFtoCNF_D_1(B,C),difference(B,C))
      | subset(B,C) ),
    inference(conjunct,[],[normalize_1_9]) ).

fof(normalize_1_11,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_1_6]) ).

fof(normalize_1_12,plain,
    ! [B,C,D] :
      ( ~ member(D,difference(B,C))
      | member(D,B) ),
    inference(conjunct,[],[normalize_1_11]) ).

fof(normalize_1_13,plain,
    ? [B,C] :
      ( difference(B,C) != empty_set
      & subset(B,C) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_14,plain,
    ( difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set
    & subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) ),
    inference(skolemize,[],[normalize_1_13]) ).

fof(normalize_1_15,plain,
    subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
    inference(conjunct,[],[normalize_1_14]) ).

fof(normalize_1_16,plain,
    ! [B] :
      ( empty(B)
      | member(skolemFOFtoCNF_C(B),B) ),
    inference(conjunct,[],[normalize_1_2]) ).

fof(normalize_1_17,plain,
    ! [B,C,D] :
      ( ~ member(D,difference(B,C))
      | ~ subset(B,C) ),
    inference(conjunct,[],[normalize_1_9]) ).

fof(normalize_1_18,plain,
    ! [B] : ~ member(B,empty_set),
    inference(canonicalize,[],[empty_set_defn]) ).

fof(normalize_1_19,plain,
    ! [B] : ~ member(B,empty_set),
    inference(specialize,[],[normalize_1_18]) ).

fof(normalize_1_20,plain,
    ! [B,C] :
      ( B != C
    <=> ( ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(canonicalize,[],[equal_defn]) ).

fof(normalize_1_21,plain,
    ! [B,C] :
      ( B != C
    <=> ( ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(specialize,[],[normalize_1_20]) ).

fof(normalize_1_22,plain,
    ! [B,C] :
      ( ( B != C
        | subset(B,C) )
      & ( B != C
        | subset(C,B) )
      & ( ~ subset(B,C)
        | ~ subset(C,B)
        | B = C ) ),
    inference(clausify,[],[normalize_1_21]) ).

fof(normalize_1_23,plain,
    ! [B,C] :
      ( ~ subset(B,C)
      | ~ subset(C,B)
      | B = C ),
    inference(conjunct,[],[normalize_1_22]) ).

fof(normalize_1_24,plain,
    difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set,
    inference(conjunct,[],[normalize_1_14]) ).

cnf(refute_1_0,plain,
    ( ~ empty(B)
    | ~ member(C,B) ),
    inference(canonicalize,[],[normalize_1_3]) ).

cnf(refute_1_1,plain,
    ( ~ empty(X_24)
    | ~ member(skolemFOFtoCNF_D_1(X_24,X_25),X_24) ),
    inference(subst,[],[refute_1_0:[bind(B,$fot(X_24)),bind(C,$fot(skolemFOFtoCNF_D_1(X_24,X_25)))]]) ).

cnf(refute_1_2,plain,
    ( member(skolemFOFtoCNF_D_1(B,C),difference(B,C))
    | subset(B,C) ),
    inference(canonicalize,[],[normalize_1_10]) ).

cnf(refute_1_3,plain,
    ( member(skolemFOFtoCNF_D_1(X_21,X_22),difference(X_21,X_22))
    | subset(X_21,X_22) ),
    inference(subst,[],[refute_1_2:[bind(B,$fot(X_21)),bind(C,$fot(X_22))]]) ).

cnf(refute_1_4,plain,
    ( ~ member(D,difference(B,C))
    | member(D,B) ),
    inference(canonicalize,[],[normalize_1_12]) ).

cnf(refute_1_5,plain,
    ( ~ member(skolemFOFtoCNF_D_1(X_21,X_22),difference(X_21,X_22))
    | member(skolemFOFtoCNF_D_1(X_21,X_22),X_21) ),
    inference(subst,[],[refute_1_4:[bind(B,$fot(X_21)),bind(C,$fot(X_22)),bind(D,$fot(skolemFOFtoCNF_D_1(X_21,X_22)))]]) ).

cnf(refute_1_6,plain,
    ( member(skolemFOFtoCNF_D_1(X_21,X_22),X_21)
    | subset(X_21,X_22) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_21,X_22),difference(X_21,X_22)) )],[refute_1_3,refute_1_5]) ).

cnf(refute_1_7,plain,
    ( member(skolemFOFtoCNF_D_1(X_24,X_25),X_24)
    | subset(X_24,X_25) ),
    inference(subst,[],[refute_1_6:[bind(X_21,$fot(X_24)),bind(X_22,$fot(X_25))]]) ).

cnf(refute_1_8,plain,
    ( ~ empty(X_24)
    | subset(X_24,X_25) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_24,X_25),X_24) )],[refute_1_7,refute_1_1]) ).

cnf(refute_1_9,plain,
    ( ~ empty(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2))
    | subset(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),X_25) ),
    inference(subst,[],[refute_1_8:[bind(X_24,$fot(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)))]]) ).

cnf(refute_1_10,plain,
    subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
    inference(canonicalize,[],[normalize_1_15]) ).

cnf(refute_1_11,plain,
    ( empty(B)
    | member(skolemFOFtoCNF_C(B),B) ),
    inference(canonicalize,[],[normalize_1_16]) ).

cnf(refute_1_12,plain,
    ( empty(difference(X_29,X_30))
    | member(skolemFOFtoCNF_C(difference(X_29,X_30)),difference(X_29,X_30)) ),
    inference(subst,[],[refute_1_11:[bind(B,$fot(difference(X_29,X_30)))]]) ).

cnf(refute_1_13,plain,
    ( ~ member(D,difference(B,C))
    | ~ subset(B,C) ),
    inference(canonicalize,[],[normalize_1_17]) ).

cnf(refute_1_14,plain,
    ( ~ member(skolemFOFtoCNF_C(difference(X_29,X_30)),difference(X_29,X_30))
    | ~ subset(X_29,X_30) ),
    inference(subst,[],[refute_1_13:[bind(B,$fot(X_29)),bind(C,$fot(X_30)),bind(D,$fot(skolemFOFtoCNF_C(difference(X_29,X_30))))]]) ).

cnf(refute_1_15,plain,
    ( ~ subset(X_29,X_30)
    | empty(difference(X_29,X_30)) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_C(difference(X_29,X_30)),difference(X_29,X_30)) )],[refute_1_12,refute_1_14]) ).

cnf(refute_1_16,plain,
    ( ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
    | empty(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) ),
    inference(subst,[],[refute_1_15:[bind(X_29,$fot(skolemFOFtoCNF_B_1)),bind(X_30,$fot(skolemFOFtoCNF_C_2))]]) ).

cnf(refute_1_17,plain,
    empty(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) )],[refute_1_10,refute_1_16]) ).

cnf(refute_1_18,plain,
    subset(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),X_25),
    inference(resolve,[$cnf( empty(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) )],[refute_1_17,refute_1_9]) ).

cnf(refute_1_19,plain,
    subset(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set),
    inference(subst,[],[refute_1_18:[bind(X_25,$fot(empty_set))]]) ).

cnf(refute_1_20,plain,
    ~ member(B,empty_set),
    inference(canonicalize,[],[normalize_1_19]) ).

cnf(refute_1_21,plain,
    ~ member(skolemFOFtoCNF_D_1(empty_set,X_25),empty_set),
    inference(subst,[],[refute_1_20:[bind(B,$fot(skolemFOFtoCNF_D_1(empty_set,X_25)))]]) ).

cnf(refute_1_22,plain,
    ( member(skolemFOFtoCNF_D_1(empty_set,X_25),empty_set)
    | subset(empty_set,X_25) ),
    inference(subst,[],[refute_1_6:[bind(X_21,$fot(empty_set)),bind(X_22,$fot(X_25))]]) ).

cnf(refute_1_23,plain,
    subset(empty_set,X_25),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(empty_set,X_25),empty_set) )],[refute_1_22,refute_1_21]) ).

cnf(refute_1_24,plain,
    subset(empty_set,X_86),
    inference(subst,[],[refute_1_23:[bind(X_25,$fot(X_86))]]) ).

cnf(refute_1_25,plain,
    ( ~ subset(B,C)
    | ~ subset(C,B)
    | B = C ),
    inference(canonicalize,[],[normalize_1_23]) ).

cnf(refute_1_26,plain,
    ( ~ subset(X_86,empty_set)
    | ~ subset(empty_set,X_86)
    | empty_set = X_86 ),
    inference(subst,[],[refute_1_25:[bind(B,$fot(empty_set)),bind(C,$fot(X_86))]]) ).

cnf(refute_1_27,plain,
    ( ~ subset(X_86,empty_set)
    | empty_set = X_86 ),
    inference(resolve,[$cnf( subset(empty_set,X_86) )],[refute_1_24,refute_1_26]) ).

cnf(refute_1_28,plain,
    ( ~ subset(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set)
    | empty_set = difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) ),
    inference(subst,[],[refute_1_27:[bind(X_86,$fot(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)))]]) ).

cnf(refute_1_29,plain,
    empty_set = difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
    inference(resolve,[$cnf( subset(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_19,refute_1_28]) ).

cnf(refute_1_30,plain,
    difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) != empty_set,
    inference(canonicalize,[],[normalize_1_24]) ).

cnf(refute_1_31,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_1_32,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_1_33,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_1_31,refute_1_32]) ).

cnf(refute_1_34,plain,
    ( empty_set != difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
    | difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) = empty_set ),
    inference(subst,[],[refute_1_33:[bind(X,$fot(empty_set)),bind(Y,$fot(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)))]]) ).

cnf(refute_1_35,plain,
    empty_set != difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
    inference(resolve,[$cnf( $equal(difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),empty_set) )],[refute_1_34,refute_1_30]) ).

cnf(refute_1_36,plain,
    $false,
    inference(resolve,[$cnf( $equal(empty_set,difference(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)) )],[refute_1_29,refute_1_35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n025.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 18:35:16 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38  
% 0.13/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38  
%------------------------------------------------------------------------------