TSTP Solution File: SET879+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n010.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 03:38:04 EDT 2022

% Result   : Theorem 0.14s 0.38s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   80 (  27 unt;   0 def)
%            Number of atoms       :  175 ( 129 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  183 (  88   ~;  63   |;  12   &)
%                                         (  16 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   84 (   0 sgn  51   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
    ! [A,B] :
      ( B = singleton(A)
    <=> ! [C] :
          ( in(C,B)
        <=> C = A ) ) ).

fof(l34_zfmisc_1,axiom,
    ! [A,B] :
      ( set_difference(singleton(A),B) = singleton(A)
    <=> ~ in(A,B) ) ).

fof(t20_zfmisc_1,conjecture,
    ! [A,B] :
      ( set_difference(singleton(A),singleton(B)) = singleton(A)
    <=> A != B ) ).

fof(subgoal_0,plain,
    ! [A,B] :
      ( set_difference(singleton(A),singleton(B)) = singleton(A)
     => A != B ),
    inference(strip,[],[t20_zfmisc_1]) ).

fof(subgoal_1,plain,
    ! [A,B] :
      ( A != B
     => set_difference(singleton(A),singleton(B)) = singleton(A) ),
    inference(strip,[],[t20_zfmisc_1]) ).

fof(negate_0_0,plain,
    ~ ! [A,B] :
        ( set_difference(singleton(A),singleton(B)) = singleton(A)
       => A != B ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A,B] :
      ( set_difference(singleton(A),B) != singleton(A)
    <=> in(A,B) ),
    inference(canonicalize,[],[l34_zfmisc_1]) ).

fof(normalize_0_1,plain,
    ! [A,B] :
      ( set_difference(singleton(A),B) != singleton(A)
    <=> in(A,B) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A,B] :
      ( ( set_difference(singleton(A),B) != singleton(A)
        | ~ in(A,B) )
      & ( set_difference(singleton(A),B) = singleton(A)
        | in(A,B) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A,B] :
      ( set_difference(singleton(A),B) != singleton(A)
      | ~ in(A,B) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [A,B] :
      ( A = B
      & set_difference(singleton(A),singleton(B)) = singleton(A) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_5,plain,
    ( set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2)
    & skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B,
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_8,plain,
    ! [A,B] :
      ( B != singleton(A)
    <=> ? [C] :
          ( C != A
        <=> in(C,B) ) ),
    inference(canonicalize,[],[d1_tarski]) ).

fof(normalize_0_9,plain,
    ! [A,B] :
      ( B != singleton(A)
    <=> ? [C] :
          ( C != A
        <=> in(C,B) ) ),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [A,B,C] :
      ( ( B != singleton(A)
        | C != A
        | in(C,B) )
      & ( B != singleton(A)
        | ~ in(C,B)
        | C = A )
      & ( skolemFOFtoCNF_C(A,B) != A
        | ~ in(skolemFOFtoCNF_C(A,B),B)
        | B = singleton(A) )
      & ( B = singleton(A)
        | skolemFOFtoCNF_C(A,B) = A
        | in(skolemFOFtoCNF_C(A,B),B) ) ),
    inference(clausify,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [A,B,C] :
      ( B != singleton(A)
      | C != A
      | in(C,B) ),
    inference(conjunct,[],[normalize_0_10]) ).

cnf(refute_0_0,plain,
    ( set_difference(singleton(A),B) != singleton(A)
    | ~ in(A,B) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) != singleton(skolemFOFtoCNF_A_2)
    | ~ in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_A_2)) ),
    inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).

cnf(refute_0_2,plain,
    set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    skolemFOFtoCNF_A_2 = skolemFOFtoCNF_B,
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_4,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_5,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_6,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_B
    | skolemFOFtoCNF_B = skolemFOFtoCNF_A_2 ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_8,plain,
    skolemFOFtoCNF_B = skolemFOFtoCNF_A_2,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_3,refute_0_7]) ).

cnf(refute_0_9,plain,
    singleton(skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_B),
    introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_10,plain,
    ( singleton(skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_B)
    | skolemFOFtoCNF_B != skolemFOFtoCNF_A_2
    | singleton(skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
    introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) ),[1,0],$fot(skolemFOFtoCNF_A_2)]]) ).

cnf(refute_0_11,plain,
    ( skolemFOFtoCNF_B != skolemFOFtoCNF_A_2
    | singleton(skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
    inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    singleton(skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) )],[refute_0_8,refute_0_11]) ).

cnf(refute_0_13,plain,
    set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),
    introduced(tautology,[refl,[$fot(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)))]]) ).

cnf(refute_0_14,plain,
    ( set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))
    | singleton(skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_A_2)
    | set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) ),
    introduced(tautology,[equality,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) ),[1,1],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_15,plain,
    ( singleton(skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_A_2)
    | set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) ),
    inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B))) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) = set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)),
    inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_12,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2))
    | set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2)
    | set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_A_2) ),
    introduced(tautology,[equality,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) ),[0],$fot(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)))]]) ).

cnf(refute_0_18,plain,
    ( set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2)
    | set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_A_2) ),
    inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2))) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_A_2),
    inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_2,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) != singleton(skolemFOFtoCNF_A_2)
    | singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
    | set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_A_2) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) ),[0],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_21,plain,
    ( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
    | set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) = singleton(skolemFOFtoCNF_A_2) ),
    inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
    | ~ in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_A_2)) ),
    inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_21,refute_0_1]) ).

cnf(refute_0_23,plain,
    singleton(skolemFOFtoCNF_A_2) = singleton(skolemFOFtoCNF_A_2),
    introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_24,plain,
    ~ in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_A_2)),
    inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_23,refute_0_22]) ).

cnf(refute_0_25,plain,
    ( B != singleton(A)
    | C != A
    | in(C,B) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_26,plain,
    ( A != A
    | singleton(A) != singleton(A)
    | in(A,singleton(A)) ),
    inference(subst,[],[refute_0_25:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).

cnf(refute_0_27,plain,
    A = A,
    introduced(tautology,[refl,[$fot(A)]]) ).

cnf(refute_0_28,plain,
    ( singleton(A) != singleton(A)
    | in(A,singleton(A)) ),
    inference(resolve,[$cnf( $equal(A,A) )],[refute_0_27,refute_0_26]) ).

cnf(refute_0_29,plain,
    singleton(A) = singleton(A),
    introduced(tautology,[refl,[$fot(singleton(A))]]) ).

cnf(refute_0_30,plain,
    in(A,singleton(A)),
    inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_29,refute_0_28]) ).

cnf(refute_0_31,plain,
    in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_A_2)),
    inference(subst,[],[refute_0_30:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_32,plain,
    $false,
    inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_A_2)) )],[refute_0_31,refute_0_24]) ).

fof(negate_1_0,plain,
    ~ ! [A,B] :
        ( A != B
       => set_difference(singleton(A),singleton(B)) = singleton(A) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ! [A,B] :
      ( B != singleton(A)
    <=> ? [C] :
          ( C != A
        <=> in(C,B) ) ),
    inference(canonicalize,[],[d1_tarski]) ).

fof(normalize_1_1,plain,
    ! [A,B] :
      ( B != singleton(A)
    <=> ? [C] :
          ( C != A
        <=> in(C,B) ) ),
    inference(specialize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ! [A,B,C] :
      ( ( B != singleton(A)
        | C != A
        | in(C,B) )
      & ( B != singleton(A)
        | ~ in(C,B)
        | C = A )
      & ( skolemFOFtoCNF_C(A,B) != A
        | ~ in(skolemFOFtoCNF_C(A,B),B)
        | B = singleton(A) )
      & ( B = singleton(A)
        | skolemFOFtoCNF_C(A,B) = A
        | in(skolemFOFtoCNF_C(A,B),B) ) ),
    inference(clausify,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ! [A,B,C] :
      ( B != singleton(A)
      | ~ in(C,B)
      | C = A ),
    inference(conjunct,[],[normalize_1_2]) ).

fof(normalize_1_4,plain,
    ? [A,B] :
      ( A != B
      & set_difference(singleton(A),singleton(B)) != singleton(A) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_5,plain,
    ( set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) != singleton(skolemFOFtoCNF_A_3)
    & skolemFOFtoCNF_A_3 != skolemFOFtoCNF_B_1 ),
    inference(skolemize,[],[normalize_1_4]) ).

fof(normalize_1_6,plain,
    set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) != singleton(skolemFOFtoCNF_A_3),
    inference(conjunct,[],[normalize_1_5]) ).

fof(normalize_1_7,plain,
    ! [A,B] :
      ( set_difference(singleton(A),B) != singleton(A)
    <=> in(A,B) ),
    inference(canonicalize,[],[l34_zfmisc_1]) ).

fof(normalize_1_8,plain,
    ! [A,B] :
      ( set_difference(singleton(A),B) != singleton(A)
    <=> in(A,B) ),
    inference(specialize,[],[normalize_1_7]) ).

fof(normalize_1_9,plain,
    ! [A,B] :
      ( ( set_difference(singleton(A),B) != singleton(A)
        | ~ in(A,B) )
      & ( set_difference(singleton(A),B) = singleton(A)
        | in(A,B) ) ),
    inference(clausify,[],[normalize_1_8]) ).

fof(normalize_1_10,plain,
    ! [A,B] :
      ( set_difference(singleton(A),B) = singleton(A)
      | in(A,B) ),
    inference(conjunct,[],[normalize_1_9]) ).

fof(normalize_1_11,plain,
    skolemFOFtoCNF_A_3 != skolemFOFtoCNF_B_1,
    inference(conjunct,[],[normalize_1_5]) ).

cnf(refute_1_0,plain,
    ( B != singleton(A)
    | ~ in(C,B)
    | C = A ),
    inference(canonicalize,[],[normalize_1_3]) ).

cnf(refute_1_1,plain,
    ( singleton(A) != singleton(A)
    | ~ in(C,singleton(A))
    | C = A ),
    inference(subst,[],[refute_1_0:[bind(B,$fot(singleton(A)))]]) ).

cnf(refute_1_2,plain,
    singleton(A) = singleton(A),
    introduced(tautology,[refl,[$fot(singleton(A))]]) ).

cnf(refute_1_3,plain,
    ( ~ in(C,singleton(A))
    | C = A ),
    inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_1_2,refute_1_1]) ).

cnf(refute_1_4,plain,
    ( ~ in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1))
    | skolemFOFtoCNF_A_3 = skolemFOFtoCNF_B_1 ),
    inference(subst,[],[refute_1_3:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_A_3))]]) ).

cnf(refute_1_5,plain,
    set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) != singleton(skolemFOFtoCNF_A_3),
    inference(canonicalize,[],[normalize_1_6]) ).

cnf(refute_1_6,plain,
    ( set_difference(singleton(A),B) = singleton(A)
    | in(A,B) ),
    inference(canonicalize,[],[normalize_1_10]) ).

cnf(refute_1_7,plain,
    ( set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) = singleton(skolemFOFtoCNF_A_3)
    | in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) ),
    inference(subst,[],[refute_1_6:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(singleton(skolemFOFtoCNF_B_1)))]]) ).

cnf(refute_1_8,plain,
    ( set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) != singleton(skolemFOFtoCNF_A_3)
    | singleton(skolemFOFtoCNF_A_3) != singleton(skolemFOFtoCNF_A_3)
    | set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) = singleton(skolemFOFtoCNF_A_3) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)),singleton(skolemFOFtoCNF_A_3)) ),[0],$fot(singleton(skolemFOFtoCNF_A_3))]]) ).

cnf(refute_1_9,plain,
    ( singleton(skolemFOFtoCNF_A_3) != singleton(skolemFOFtoCNF_A_3)
    | set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)) = singleton(skolemFOFtoCNF_A_3)
    | in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) ),
    inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_7,refute_1_8]) ).

cnf(refute_1_10,plain,
    ( singleton(skolemFOFtoCNF_A_3) != singleton(skolemFOFtoCNF_A_3)
    | in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) ),
    inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_B_1)),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_9,refute_1_5]) ).

cnf(refute_1_11,plain,
    singleton(skolemFOFtoCNF_A_3) = singleton(skolemFOFtoCNF_A_3),
    introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_3))]]) ).

cnf(refute_1_12,plain,
    in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)),
    inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_11,refute_1_10]) ).

cnf(refute_1_13,plain,
    skolemFOFtoCNF_A_3 = skolemFOFtoCNF_B_1,
    inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) )],[refute_1_12,refute_1_4]) ).

cnf(refute_1_14,plain,
    skolemFOFtoCNF_A_3 != skolemFOFtoCNF_B_1,
    inference(canonicalize,[],[normalize_1_11]) ).

cnf(refute_1_15,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) )],[refute_1_13,refute_1_14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.15  % Command  : metis --show proof --show saturation %s
% 0.14/0.36  % Computer : n010.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sun Jul 10 17:20:15 EDT 2022
% 0.14/0.37  % CPUTime  : 
% 0.14/0.37  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38  
% 0.14/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38  
%------------------------------------------------------------------------------