TSTP Solution File: SET984+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n006.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 03:38:46 EDT 2022

% Result   : Timeout 290.24s 290.43s
% Output   : None 
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  234 ( 111 unt;   0 def)
%            Number of atoms       :  446 ( 369 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  390 ( 178   ~; 170   |;  30   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :  348 (  16 sgn 128   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).

fof(idempotence_k3_xboole_0,axiom,
    ! [A,B] : set_intersection2(A,A) = A ).

fof(t113_zfmisc_1,axiom,
    ! [A,B] :
      ( cartesian_product2(A,B) = empty_set
    <=> ( A = empty_set
        | B = empty_set ) ) ).

fof(t123_zfmisc_1,axiom,
    ! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) ).

fof(t134_zfmisc_1,axiom,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) = cartesian_product2(C,D)
     => ( A = empty_set
        | B = empty_set
        | ( A = C
          & B = D ) ) ) ).

fof(t138_zfmisc_1,conjecture,
    ! [A,B,C,D] :
      ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
     => ( cartesian_product2(A,B) = empty_set
        | ( subset(A,C)
          & subset(B,D) ) ) ) ).

fof(t17_xboole_1,axiom,
    ! [A,B] : subset(set_intersection2(A,B),A) ).

fof(t28_xboole_1,axiom,
    ! [A,B] :
      ( subset(A,B)
     => set_intersection2(A,B) = A ) ).

fof(subgoal_0,plain,
    ! [A,B,C,D] :
      ( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
        & cartesian_product2(A,B) != empty_set )
     => subset(A,C) ),
    inference(strip,[],[t138_zfmisc_1]) ).

fof(subgoal_1,plain,
    ! [A,B,C,D] :
      ( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
        & cartesian_product2(A,B) != empty_set
        & subset(A,C) )
     => subset(B,D) ),
    inference(strip,[],[t138_zfmisc_1]) ).

fof(negate_0_0,plain,
    ~ ! [A,B,C,D] :
        ( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
          & cartesian_product2(A,B) != empty_set )
       => subset(A,C) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A,B] : subset(set_intersection2(A,B),A),
    inference(canonicalize,[],[t17_xboole_1]) ).

fof(normalize_0_1,plain,
    ! [A,B] : subset(set_intersection2(A,B),A),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    inference(canonicalize,[],[commutativity_k3_xboole_0]) ).

fof(normalize_0_3,plain,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) != cartesian_product2(C,D)
      | A = empty_set
      | B = empty_set
      | ( A = C
        & B = D ) ),
    inference(canonicalize,[],[t134_zfmisc_1]) ).

fof(normalize_0_5,plain,
    ! [A,B] :
      ( cartesian_product2(A,B) != empty_set
    <=> ( A != empty_set
        & B != empty_set ) ),
    inference(canonicalize,[],[t113_zfmisc_1]) ).

fof(normalize_0_6,plain,
    ! [A,B] :
      ( cartesian_product2(A,B) != empty_set
    <=> ( A != empty_set
        & B != empty_set ) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) != cartesian_product2(C,D)
      | cartesian_product2(A,B) = empty_set
      | ( A = C
        & B = D ) ),
    inference(simplify,[],[normalize_0_4,normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) != cartesian_product2(C,D)
      | cartesian_product2(A,B) = empty_set
      | ( A = C
        & B = D ) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [A,B,C,D] :
      ( ( cartesian_product2(A,B) != cartesian_product2(C,D)
        | A = C
        | cartesian_product2(A,B) = empty_set )
      & ( cartesian_product2(A,B) != cartesian_product2(C,D)
        | B = D
        | cartesian_product2(A,B) = empty_set ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) != cartesian_product2(C,D)
      | A = C
      | cartesian_product2(A,B) = empty_set ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    inference(canonicalize,[],[t123_zfmisc_1]) ).

fof(normalize_0_12,plain,
    ! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    inference(specialize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ? [A,B,C] :
      ( cartesian_product2(A,B) != empty_set
      & ~ subset(A,C)
      & ? [D] : subset(cartesian_product2(A,B),cartesian_product2(C,D)) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_14,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != empty_set
    & ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
    & ? [D] : subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,D)) ),
    inference(skolemize,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ? [D] : subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,D)),
    inference(conjunct,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
    inference(skolemize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | set_intersection2(A,B) = A ),
    inference(canonicalize,[],[t28_xboole_1]) ).

fof(normalize_0_18,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | set_intersection2(A,B) = A ),
    inference(specialize,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    ! [A] : set_intersection2(A,A) = A,
    inference(canonicalize,[],[idempotence_k3_xboole_0]) ).

fof(normalize_0_20,plain,
    ! [A] : set_intersection2(A,A) = A,
    inference(specialize,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
    cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != empty_set,
    inference(conjunct,[],[normalize_0_14]) ).

fof(normalize_0_22,plain,
    ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
    inference(conjunct,[],[normalize_0_14]) ).

cnf(refute_0_0,plain,
    subset(set_intersection2(A,B),A),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    set_intersection2(A,B) = set_intersection2(B,A),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    ( set_intersection2(A,B) != set_intersection2(B,A)
    | ~ subset(set_intersection2(A,B),A)
    | subset(set_intersection2(B,A),A) ),
    introduced(tautology,[equality,[$cnf( subset(set_intersection2(A,B),A) ),[0],$fot(set_intersection2(B,A))]]) ).

cnf(refute_0_3,plain,
    ( ~ subset(set_intersection2(A,B),A)
    | subset(set_intersection2(B,A),A) ),
    inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    subset(set_intersection2(B,A),A),
    inference(resolve,[$cnf( subset(set_intersection2(A,B),A) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_C),
    inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_6,plain,
    ( cartesian_product2(A,B) != cartesian_product2(C,D)
    | A = C
    | cartesian_product2(A,B) = empty_set ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_7,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != cartesian_product2(X_4603,X_4604)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = empty_set
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = X_4603 ),
    inference(subst,[],[refute_0_6:[bind(A,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_4603)),bind(D,$fot(X_4604))]]) ).

cnf(refute_0_8,plain,
    cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_9,plain,
    cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = set_intersection2(cartesian_product2(A,C),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),
    inference(subst,[],[refute_0_8:[bind(B,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))),bind(D,$fot(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))]]) ).

cnf(refute_0_10,plain,
    subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_11,plain,
    ( ~ subset(A,B)
    | set_intersection2(A,B) = A ),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_12,plain,
    ( ~ subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D))
    | set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
    inference(subst,[],[refute_0_11:[bind(A,$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))),bind(B,$fot(cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)))]]) ).

cnf(refute_0_13,plain,
    set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
    inference(resolve,[$cnf( subset(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) )],[refute_0_10,refute_0_12]) ).

cnf(refute_0_14,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_15,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_16,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) != set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))
    | set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) = cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)))),bind(Y,$fot(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))))]]) ).

cnf(refute_0_18,plain,
    set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) = cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)),set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))) )],[refute_0_8,refute_0_17]) ).

cnf(refute_0_19,plain,
    set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),
    inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_B)),bind(D,$fot(skolemFOFtoCNF_D))]]) ).

cnf(refute_0_20,plain,
    ( set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))
    | set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
    introduced(tautology,[equality,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[0],$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))]]) ).

cnf(refute_0_21,plain,
    ( set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
    inference(resolve,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
    inference(resolve,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_C,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_13,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != set_intersection2(cartesian_product2(A,C),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
    | cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),set_intersection2(cartesian_product2(A,C),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) ),[1,1],$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).

cnf(refute_0_24,plain,
    ( cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != set_intersection2(cartesian_product2(A,C),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))
    | cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),set_intersection2(cartesian_product2(A,C),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))) )],[refute_0_9,refute_0_24]) ).

cnf(refute_0_26,plain,
    set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = cartesian_product2(set_intersection2(A,skolemFOFtoCNF_A_2),set_intersection2(C,skolemFOFtoCNF_B)),
    inference(subst,[],[refute_0_18:[bind(B,$fot(skolemFOFtoCNF_A_2)),bind(D,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_27,plain,
    ( cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
    | set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != cartesian_product2(set_intersection2(A,skolemFOFtoCNF_A_2),set_intersection2(C,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(A,skolemFOFtoCNF_A_2),set_intersection2(C,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(A,skolemFOFtoCNF_A_2),set_intersection2(C,skolemFOFtoCNF_B))) ),[0],$fot(set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).

cnf(refute_0_28,plain,
    ( cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(A,skolemFOFtoCNF_A_2),set_intersection2(C,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),cartesian_product2(set_intersection2(A,skolemFOFtoCNF_A_2),set_intersection2(C,skolemFOFtoCNF_B))) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(A,skolemFOFtoCNF_A_2),set_intersection2(C,skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(A,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(C,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),set_intersection2(cartesian_product2(A,C),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) )],[refute_0_25,refute_0_28]) ).

cnf(refute_0_30,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),
    inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(X_39))]]) ).

cnf(refute_0_31,plain,
    subset(set_intersection2(X_31,B),X_31),
    inference(subst,[],[refute_0_0:[bind(A,$fot(X_31))]]) ).

cnf(refute_0_32,plain,
    ( ~ subset(set_intersection2(X_31,B),X_31)
    | set_intersection2(set_intersection2(X_31,B),X_31) = set_intersection2(X_31,B) ),
    inference(subst,[],[refute_0_11:[bind(A,$fot(set_intersection2(X_31,B))),bind(B,$fot(X_31))]]) ).

cnf(refute_0_33,plain,
    set_intersection2(set_intersection2(X_31,B),X_31) = set_intersection2(X_31,B),
    inference(resolve,[$cnf( subset(set_intersection2(X_31,B),X_31) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( set_intersection2(A,B) != set_intersection2(B,A)
    | set_intersection2(B,A) = set_intersection2(A,B) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).

cnf(refute_0_35,plain,
    set_intersection2(B,A) = set_intersection2(A,B),
    inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_1,refute_0_34]) ).

cnf(refute_0_36,plain,
    set_intersection2(set_intersection2(X_31,B),X_31) = set_intersection2(X_31,set_intersection2(X_31,B)),
    inference(subst,[],[refute_0_35:[bind(A,$fot(X_31)),bind(B,$fot(set_intersection2(X_31,B)))]]) ).

cnf(refute_0_37,plain,
    ( set_intersection2(set_intersection2(X_31,B),X_31) != set_intersection2(X_31,B)
    | set_intersection2(set_intersection2(X_31,B),X_31) != set_intersection2(X_31,set_intersection2(X_31,B))
    | set_intersection2(X_31,set_intersection2(X_31,B)) = set_intersection2(X_31,B) ),
    introduced(tautology,[equality,[$cnf( $equal(set_intersection2(set_intersection2(X_31,B),X_31),set_intersection2(X_31,B)) ),[0],$fot(set_intersection2(X_31,set_intersection2(X_31,B)))]]) ).

cnf(refute_0_38,plain,
    ( set_intersection2(set_intersection2(X_31,B),X_31) != set_intersection2(X_31,B)
    | set_intersection2(X_31,set_intersection2(X_31,B)) = set_intersection2(X_31,B) ),
    inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(X_31,B),X_31),set_intersection2(X_31,set_intersection2(X_31,B))) )],[refute_0_36,refute_0_37]) ).

cnf(refute_0_39,plain,
    set_intersection2(X_31,set_intersection2(X_31,B)) = set_intersection2(X_31,B),
    inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(X_31,B),X_31),set_intersection2(X_31,B)) )],[refute_0_33,refute_0_38]) ).

cnf(refute_0_40,plain,
    set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
    inference(subst,[],[refute_0_39:[bind(B,$fot(skolemFOFtoCNF_C)),bind(X_31,$fot(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_41,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) ),[0,0],$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))]]) ).

cnf(refute_0_42,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_30,refute_0_42]) ).

cnf(refute_0_44,plain,
    cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),
    inference(subst,[],[refute_0_29:[bind(A,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))),bind(C,$fot(X_39))]]) ).

cnf(refute_0_45,plain,
    set_intersection2(A,A) = A,
    inference(canonicalize,[],[normalize_0_20]) ).

cnf(refute_0_46,plain,
    set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
    inference(subst,[],[refute_0_45:[bind(A,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))]]) ).

cnf(refute_0_47,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) ),[0,0],$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))]]) ).

cnf(refute_0_48,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_46,refute_0_47]) ).

cnf(refute_0_49,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_44,refute_0_48]) ).

cnf(refute_0_50,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)),
    introduced(tautology,[refl,[$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)))]]) ).

cnf(refute_0_51,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39))
    | set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39))) ),[1,0],$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))]]) ).

cnf(refute_0_52,plain,
    ( set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39))) )],[refute_0_50,refute_0_51]) ).

cnf(refute_0_53,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_40,refute_0_52]) ).

cnf(refute_0_54,plain,
    cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),
    inference(subst,[],[refute_0_29:[bind(A,$fot(X_38)),bind(C,$fot(X_39))]]) ).

cnf(refute_0_55,plain,
    set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39) = set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),
    inference(subst,[],[refute_0_1:[bind(A,$fot(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),bind(B,$fot(X_39))]]) ).

cnf(refute_0_56,plain,
    ( set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39) != set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))
    | set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39))),bind(Y,$fot(set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))))]]) ).

cnf(refute_0_57,plain,
    set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) = set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39),
    inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) )],[refute_0_55,refute_0_56]) ).

cnf(refute_0_58,plain,
    ( cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) != set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)
    | cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)) = cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) ),[0,1],$fot(set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39))]]) ).

cnf(refute_0_59,plain,
    ( cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)) = cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)) )],[refute_0_57,refute_0_58]) ).

cnf(refute_0_60,plain,
    cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)) = cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_54,refute_0_59]) ).

cnf(refute_0_61,plain,
    cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) = set_intersection2(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),cartesian_product2(B,D)),
    inference(subst,[],[refute_0_8:[bind(A,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))),bind(C,$fot(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)))]]) ).

cnf(refute_0_62,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) != set_intersection2(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),cartesian_product2(B,D))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
    | cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) = set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)),set_intersection2(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),cartesian_product2(B,D))) ),[1,0],$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).

cnf(refute_0_63,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) != set_intersection2(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),cartesian_product2(B,D))
    | cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) = set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_22,refute_0_62]) ).

cnf(refute_0_64,plain,
    cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) = set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)),set_intersection2(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D)),cartesian_product2(B,D))) )],[refute_0_61,refute_0_63]) ).

cnf(refute_0_65,plain,
    set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,B),set_intersection2(skolemFOFtoCNF_B,D)),
    inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_66,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) != set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D))
    | set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,B),set_intersection2(skolemFOFtoCNF_B,D))
    | cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,B),set_intersection2(skolemFOFtoCNF_B,D)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,B),set_intersection2(skolemFOFtoCNF_B,D))) ),[0],$fot(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D)))]]) ).

cnf(refute_0_67,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) != set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D))
    | cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,B),set_intersection2(skolemFOFtoCNF_B,D)) ),
    inference(resolve,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,B),set_intersection2(skolemFOFtoCNF_B,D))) )],[refute_0_65,refute_0_66]) ).

cnf(refute_0_68,plain,
    cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,B),set_intersection2(skolemFOFtoCNF_B,D)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),B),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),D)),set_intersection2(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(B,D))) )],[refute_0_64,refute_0_67]) ).

cnf(refute_0_69,plain,
    cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_37)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_36),set_intersection2(skolemFOFtoCNF_B,X_37)),
    inference(subst,[],[refute_0_68:[bind(B,$fot(X_36)),bind(D,$fot(X_37))]]) ).

cnf(refute_0_70,plain,
    set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) = set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36),
    inference(subst,[],[refute_0_1:[bind(A,$fot(X_36)),bind(B,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))]]) ).

cnf(refute_0_71,plain,
    ( set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) != set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36)
    | set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36) = set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))),bind(Y,$fot(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36)))]]) ).

cnf(refute_0_72,plain,
    set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36) = set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),
    inference(resolve,[$cnf( $equal(set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36)) )],[refute_0_70,refute_0_71]) ).

cnf(refute_0_73,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_37)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_36),set_intersection2(skolemFOFtoCNF_B,X_37))
    | set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36) != set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))
    | cartesian_product2(set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_37)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_36),set_intersection2(skolemFOFtoCNF_B,X_37)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_37)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_36),set_intersection2(skolemFOFtoCNF_B,X_37))) ),[0,0],$fot(set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))]]) ).

cnf(refute_0_74,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_37)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_36),set_intersection2(skolemFOFtoCNF_B,X_37))
    | cartesian_product2(set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_37)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_36),set_intersection2(skolemFOFtoCNF_B,X_37)) ),
    inference(resolve,[$cnf( $equal(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36),set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))) )],[refute_0_72,refute_0_73]) ).

cnf(refute_0_75,plain,
    cartesian_product2(set_intersection2(X_36,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_37)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_36),set_intersection2(skolemFOFtoCNF_B,X_37)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),X_36),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_37)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_36),set_intersection2(skolemFOFtoCNF_B,X_37))) )],[refute_0_69,refute_0_74]) ).

cnf(refute_0_76,plain,
    cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)),
    inference(subst,[],[refute_0_75:[bind(X_36,$fot(X_38)),bind(X_37,$fot(X_39))]]) ).

cnf(refute_0_77,plain,
    ( cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)) != cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)),cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) ),[0],$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)))]]) ).

cnf(refute_0_78,plain,
    ( cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)) != cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39))) )],[refute_0_76,refute_0_77]) ).

cnf(refute_0_79,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(X_38,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D),X_39)),cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_60,refute_0_78]) ).

cnf(refute_0_80,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)) != cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)))),bind(Y,$fot(cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))))]]) ).

cnf(refute_0_81,plain,
    cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,X_38),set_intersection2(skolemFOFtoCNF_B,X_39)),cartesian_product2(set_intersection2(X_38,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_79,refute_0_80]) ).

cnf(refute_0_82,plain,
    cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)),
    inference(subst,[],[refute_0_81:[bind(X_38,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))]]) ).

cnf(refute_0_83,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_84,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_16,refute_0_83]) ).

cnf(refute_0_85,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39))
    | cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) ),
    inference(subst,[],[refute_0_84:[bind(X,$fot(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)))),bind(Y,$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)))),bind(Z,$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39))))]]) ).

cnf(refute_0_86,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39))
    | cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39))) )],[refute_0_82,refute_0_85]) ).

cnf(refute_0_87,plain,
    cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),set_intersection2(skolemFOFtoCNF_B,X_39)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39))) )],[refute_0_53,refute_0_86]) ).

cnf(refute_0_88,plain,
    ( cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) ),[1],$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)))]]) ).

cnf(refute_0_89,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39))) )],[refute_0_87,refute_0_88]) ).

cnf(refute_0_90,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_49,refute_0_89]) ).

cnf(refute_0_91,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) ),[0],$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)))]]) ).

cnf(refute_0_92,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39))) )],[refute_0_90,refute_0_91]) ).

cnf(refute_0_93,plain,
    set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) = skolemFOFtoCNF_A_2,
    inference(subst,[],[refute_0_45:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).

cnf(refute_0_94,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),
    introduced(tautology,[refl,[$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)))]]) ).

cnf(refute_0_95,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) != skolemFOFtoCNF_A_2
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) ),[1,0],$fot(skolemFOFtoCNF_A_2)]]) ).

cnf(refute_0_96,plain,
    ( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) != skolemFOFtoCNF_A_2
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_94,refute_0_95]) ).

cnf(refute_0_97,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_A_2) )],[refute_0_93,refute_0_96]) ).

cnf(refute_0_98,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)) != cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) ),[1],$fot(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B)))]]) ).

cnf(refute_0_99,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B)),cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_97,refute_0_98]) ).

cnf(refute_0_100,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_92,refute_0_99]) ).

cnf(refute_0_101,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,X_39)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(X_39,skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(X_39,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_D))),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),set_intersection2(X_39,skolemFOFtoCNF_B))) )],[refute_0_43,refute_0_100]) ).

cnf(refute_0_102,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)),
    inference(subst,[],[refute_0_101:[bind(X_39,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_103,plain,
    set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B) = skolemFOFtoCNF_B,
    inference(subst,[],[refute_0_45:[bind(A,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_104,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) != cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))
    | set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)),cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))) ),[0,1],$fot(skolemFOFtoCNF_B)]]) ).

cnf(refute_0_105,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) != cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) ),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_103,refute_0_104]) ).

cnf(refute_0_106,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)),cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))) )],[refute_0_102,refute_0_105]) ).

cnf(refute_0_107,plain,
    cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) = cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)),
    introduced(tautology,[refl,[$fot(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)))]]) ).

cnf(refute_0_108,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) != cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))
    | set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
    | cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)),cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))) ),[1,1],$fot(skolemFOFtoCNF_B)]]) ).

cnf(refute_0_109,plain,
    ( set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
    | cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)),cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))) )],[refute_0_107,refute_0_108]) ).

cnf(refute_0_110,plain,
    cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_103,refute_0_109]) ).

cnf(refute_0_111,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))
    | cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[0],$fot(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)))]]) ).

cnf(refute_0_112,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B)),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_110,refute_0_111]) ).

cnf(refute_0_113,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_A_2,set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_B))) )],[refute_0_106,refute_0_112]) ).

cnf(refute_0_114,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
    | cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != cartesian_product2(X_4603,X_4604)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = cartesian_product2(X_4603,X_4604) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),cartesian_product2(X_4603,X_4604)) ),[0],$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).

cnf(refute_0_115,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != cartesian_product2(X_4603,X_4604)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = cartesian_product2(X_4603,X_4604) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_113,refute_0_114]) ).

cnf(refute_0_116,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != cartesian_product2(X_4603,X_4604)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = empty_set
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = X_4603 ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),cartesian_product2(X_4603,X_4604)) )],[refute_0_115,refute_0_7]) ).

cnf(refute_0_117,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != empty_set
    | cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),empty_set) ),[0],$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).

cnf(refute_0_118,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != empty_set
    | cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_113,refute_0_117]) ).

cnf(refute_0_119,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != cartesian_product2(X_4603,X_4604)
    | cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = empty_set
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = X_4603 ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),empty_set) )],[refute_0_116,refute_0_118]) ).

cnf(refute_0_120,plain,
    cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != empty_set,
    inference(canonicalize,[],[normalize_0_21]) ).

cnf(refute_0_121,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != cartesian_product2(X_4603,X_4604)
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = X_4603 ),
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),empty_set) )],[refute_0_119,refute_0_120]) ).

cnf(refute_0_122,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = skolemFOFtoCNF_A_2 ),
    inference(subst,[],[refute_0_121:[bind(X_4603,$fot(skolemFOFtoCNF_A_2)),bind(X_4604,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_123,plain,
    cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
    introduced(tautology,[refl,[$fot(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).

cnf(refute_0_124,plain,
    set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = skolemFOFtoCNF_A_2,
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),cartesian_product2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_123,refute_0_122]) ).

cnf(refute_0_125,plain,
    ( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) != skolemFOFtoCNF_A_2
    | ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_C)
    | subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
    introduced(tautology,[equality,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_C) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).

cnf(refute_0_126,plain,
    ( ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_C)
    | subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_A_2) )],[refute_0_124,refute_0_125]) ).

cnf(refute_0_127,plain,
    subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
    inference(resolve,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_C) )],[refute_0_5,refute_0_126]) ).

cnf(refute_0_128,plain,
    ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_129,plain,
    $false,
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_127,refute_0_128]) ).

fof(negate_1_0,plain,
    ~ ! [A,B,C,D] :
        ( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
          & cartesian_product2(A,B) != empty_set
          & subset(A,C) )
       => subset(B,D) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ! [A,B] : subset(set_intersection2(A,B),A),
    inference(canonicalize,[],[t17_xboole_1]) ).

fof(normalize_1_1,plain,
    ! [A,B] : subset(set_intersection2(A,B),A),
    inference(specialize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    inference(canonicalize,[],[commutativity_k3_xboole_0]) ).

fof(normalize_1_3,plain,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    inference(specialize,[],[normalize_1_2]) ).

fof(normalize_1_4,plain,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) != cartesian_product2(C,D)
      | A = empty_set
      | B = empty_set
      | ( A = C
        & B = D ) ),
    inference(canonicalize,[],[t134_zfmisc_1]) ).

fof(normalize_1_5,plain,
    ! [A,B] :
      ( cartesian_product2(A,B) != empty_set
    <=> ( A != empty_set
        & B != empty_set ) ),
    inference(canonicalize,[],[t113_zfmisc_1]) ).

fof(normalize_1_6,plain,
    ! [A,B] :
      ( cartesian_product2(A,B) != empty_set
    <=> ( A != empty_set
        & B != empty_set ) ),
    inference(specialize,[],[normalize_1_5]) ).

fof(normalize_1_7,plain,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) != cartesian_product2(C,D)
      | cartesian_product2(A,B) = empty_set
      | ( A = C
        & B = D ) ),
    inference(simplify,[],[normalize_1_4,normalize_1_6]) ).

fof(normalize_1_8,plain,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) != cartesian_product2(C,D)
      | cartesian_product2(A,B) = empty_set
      | ( A = C
        & B = D ) ),
    inference(specialize,[],[normalize_1_7]) ).

fof(normalize_1_9,plain,
    ! [A,B,C,D] :
      ( ( cartesian_product2(A,B) != cartesian_product2(C,D)
        | A = C
        | cartesian_product2(A,B) = empty_set )
      & ( cartesian_product2(A,B) != cartesian_product2(C,D)
        | B = D
        | cartesian_product2(A,B) = empty_set ) ),
    inference(clausify,[],[normalize_1_8]) ).

fof(normalize_1_10,plain,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) != cartesian_product2(C,D)
      | B = D
      | cartesian_product2(A,B) = empty_set ),
    inference(conjunct,[],[normalize_1_9]) ).

fof(normalize_1_11,plain,
    ? [A,B,C,D] :
      ( cartesian_product2(A,B) != empty_set
      & ~ subset(B,D)
      & subset(A,C)
      & subset(cartesian_product2(A,B),cartesian_product2(C,D)) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_12,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != empty_set
    & ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)
    & subset(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))
    & subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1) ),
    inference(skolemize,[],[normalize_1_11]) ).

fof(normalize_1_13,plain,
    subset(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),
    inference(conjunct,[],[normalize_1_12]) ).

fof(normalize_1_14,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | set_intersection2(A,B) = A ),
    inference(canonicalize,[],[t28_xboole_1]) ).

fof(normalize_1_15,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | set_intersection2(A,B) = A ),
    inference(specialize,[],[normalize_1_14]) ).

fof(normalize_1_16,plain,
    ! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    inference(canonicalize,[],[t123_zfmisc_1]) ).

fof(normalize_1_17,plain,
    ! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    inference(specialize,[],[normalize_1_16]) ).

fof(normalize_1_18,plain,
    subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),
    inference(conjunct,[],[normalize_1_12]) ).

fof(normalize_1_19,plain,
    cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != empty_set,
    inference(conjunct,[],[normalize_1_12]) ).

fof(normalize_1_20,plain,
    ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),
    inference(conjunct,[],[normalize_1_12]) ).

cnf(refute_1_0,plain,
    subset(set_intersection2(A,B),A),
    inference(canonicalize,[],[normalize_1_1]) ).

cnf(refute_1_1,plain,
    set_intersection2(A,B) = set_intersection2(B,A),
    inference(canonicalize,[],[normalize_1_3]) ).

cnf(refute_1_2,plain,
    ( set_intersection2(A,B) != set_intersection2(B,A)
    | ~ subset(set_intersection2(A,B),A)
    | subset(set_intersection2(B,A),A) ),
    introduced(tautology,[equality,[$cnf( subset(set_intersection2(A,B),A) ),[0],$fot(set_intersection2(B,A))]]) ).

cnf(refute_1_3,plain,
    ( ~ subset(set_intersection2(A,B),A)
    | subset(set_intersection2(B,A),A) ),
    inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_1_1,refute_1_2]) ).

cnf(refute_1_4,plain,
    subset(set_intersection2(B,A),A),
    inference(resolve,[$cnf( subset(set_intersection2(A,B),A) )],[refute_1_0,refute_1_3]) ).

cnf(refute_1_5,plain,
    subset(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_D_1),
    inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_D_1)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_1_6,plain,
    ( cartesian_product2(A,B) != cartesian_product2(C,D)
    | B = D
    | cartesian_product2(A,B) = empty_set ),
    inference(canonicalize,[],[normalize_1_10]) ).

cnf(refute_1_7,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) != cartesian_product2(X_7735,X_7736)
    | cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = empty_set
    | set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) = X_7736 ),
    inference(subst,[],[refute_1_6:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1))),bind(C,$fot(X_7735)),bind(D,$fot(X_7736))]]) ).

cnf(refute_1_8,plain,
    subset(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),
    inference(canonicalize,[],[normalize_1_13]) ).

cnf(refute_1_9,plain,
    ( ~ subset(A,B)
    | set_intersection2(A,B) = A ),
    inference(canonicalize,[],[normalize_1_15]) ).

cnf(refute_1_10,plain,
    ( ~ subset(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1))
    | set_intersection2(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_1_9:[bind(A,$fot(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))),bind(B,$fot(cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)))]]) ).

cnf(refute_1_11,plain,
    set_intersection2(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( subset(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) )],[refute_1_8,refute_1_10]) ).

cnf(refute_1_12,plain,
    cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    inference(canonicalize,[],[normalize_1_17]) ).

cnf(refute_1_13,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_1_14,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_1_15,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_1_13,refute_1_14]) ).

cnf(refute_1_16,plain,
    ( cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) != set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))
    | set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) = cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) ),
    inference(subst,[],[refute_1_15:[bind(X,$fot(cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)))),bind(Y,$fot(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))))]]) ).

cnf(refute_1_17,plain,
    set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) = cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)),set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))) )],[refute_1_12,refute_1_16]) ).

cnf(refute_1_18,plain,
    set_intersection2(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),
    inference(subst,[],[refute_1_17:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_1))]]) ).

cnf(refute_1_19,plain,
    ( set_intersection2(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1))
    | set_intersection2(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) != cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
    introduced(tautology,[equality,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),[0],$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)))]]) ).

cnf(refute_1_20,plain,
    ( set_intersection2(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)) != cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
    inference(resolve,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1))) )],[refute_1_18,refute_1_19]) ).

cnf(refute_1_21,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( $equal(set_intersection2(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_1)),cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_11,refute_1_20]) ).

cnf(refute_1_22,plain,
    subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),
    inference(canonicalize,[],[normalize_1_18]) ).

cnf(refute_1_23,plain,
    ( ~ subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1)
    | set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_A_3 ),
    inference(subst,[],[refute_1_9:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_C_1))]]) ).

cnf(refute_1_24,plain,
    set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_A_3,
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1) )],[refute_1_22,refute_1_23]) ).

cnf(refute_1_25,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),
    introduced(tautology,[refl,[$fot(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)))]]) ).

cnf(refute_1_26,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) != cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1))
    | set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_A_3
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1))) ),[1,0],$fot(skolemFOFtoCNF_A_3)]]) ).

cnf(refute_1_27,plain,
    ( set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_A_3
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1))) )],[refute_1_25,refute_1_26]) ).

cnf(refute_1_28,plain,
    cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),skolemFOFtoCNF_A_3) )],[refute_1_24,refute_1_27]) ).

cnf(refute_1_29,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) != cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1))
    | cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) != cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
    | cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) ),[0],$fot(cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)))]]) ).

cnf(refute_1_30,plain,
    ( cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) != cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
    | cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1))) )],[refute_1_28,refute_1_29]) ).

cnf(refute_1_31,plain,
    cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( $equal(cartesian_product2(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1),set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_21,refute_1_30]) ).

cnf(refute_1_32,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) != cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
    | cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != cartesian_product2(X_7735,X_7736)
    | cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(X_7735,X_7736) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),cartesian_product2(X_7735,X_7736)) ),[0],$fot(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))]]) ).

cnf(refute_1_33,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != cartesian_product2(X_7735,X_7736)
    | cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = cartesian_product2(X_7735,X_7736) ),
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_31,refute_1_32]) ).

cnf(refute_1_34,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != cartesian_product2(X_7735,X_7736)
    | cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) = empty_set
    | set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) = X_7736 ),
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),cartesian_product2(X_7735,X_7736)) )],[refute_1_33,refute_1_7]) ).

cnf(refute_1_35,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) != cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
    | cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) != empty_set
    | cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = empty_set ),
    introduced(tautology,[equality,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),empty_set) ),[0],$fot(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))]]) ).

cnf(refute_1_36,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)) != empty_set
    | cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = empty_set ),
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_31,refute_1_35]) ).

cnf(refute_1_37,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != cartesian_product2(X_7735,X_7736)
    | cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = empty_set
    | set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) = X_7736 ),
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_3,set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1)),empty_set) )],[refute_1_34,refute_1_36]) ).

cnf(refute_1_38,plain,
    cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != empty_set,
    inference(canonicalize,[],[normalize_1_19]) ).

cnf(refute_1_39,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != cartesian_product2(X_7735,X_7736)
    | set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) = X_7736 ),
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),empty_set) )],[refute_1_37,refute_1_38]) ).

cnf(refute_1_40,plain,
    ( cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) != cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)
    | set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) = skolemFOFtoCNF_B_1 ),
    inference(subst,[],[refute_1_39:[bind(X_7735,$fot(skolemFOFtoCNF_A_3)),bind(X_7736,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_1_41,plain,
    cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) = cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),
    introduced(tautology,[refl,[$fot(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))]]) ).

cnf(refute_1_42,plain,
    set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) = skolemFOFtoCNF_B_1,
    inference(resolve,[$cnf( $equal(cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),cartesian_product2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1)) )],[refute_1_41,refute_1_40]) ).

cnf(refute_1_43,plain,
    ( set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) != skolemFOFtoCNF_B_1
    | ~ subset(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_D_1)
    | subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ),
    introduced(tautology,[equality,[$cnf( subset(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_D_1) ),[0],$fot(skolemFOFtoCNF_B_1)]]) ).

cnf(refute_1_44,plain,
    ( ~ subset(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_D_1)
    | subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) ),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_B_1) )],[refute_1_42,refute_1_43]) ).

cnf(refute_1_45,plain,
    subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),
    inference(resolve,[$cnf( subset(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),skolemFOFtoCNF_D_1) )],[refute_1_5,refute_1_44]) ).

cnf(refute_1_46,plain,
    ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1),
    inference(canonicalize,[],[normalize_1_20]) ).

cnf(refute_1_47,plain,
    $false,
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_1) )],[refute_1_45,refute_1_46]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n006.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 06:35:06 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 290.24/290.43  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 290.24/290.43  
% 290.24/290.43  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 290.24/290.44  
%------------------------------------------------------------------------------