TSTP Solution File: SET663+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET663+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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 03:36:26 EDT 2022

% Result   : Theorem 0.18s 0.39s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  163 (  42 unt;   0 def)
%            Number of atoms       :  483 (  75 equ)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives :  568 ( 248   ~; 231   |;  43   &)
%                                         (  12 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :  250 (  26 sgn 113   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(p1,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( subset(B,empty_set)
       => B = empty_set ) ) ).

fof(p2,axiom,
    ! [B] :
      ( ilf_type(B,binary_relation_type)
     => ( ( domain_of(B) = empty_set
          | range_of(B) = empty_set )
       => B = empty_set ) ) ).

fof(p3,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => ( subset(domain_of(D),B)
                & subset(range_of(D),C) ) ) ) ) ).

fof(p6,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ! [D] :
                ( ilf_type(D,subset_type(cross_product(B,C)))
               => ilf_type(D,relation_type(B,C)) )
            & ! [E] :
                ( ilf_type(E,relation_type(B,C))
               => ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ) ).

fof(p13,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ilf_type(B,binary_relation_type)
      <=> ( relation_like(B)
          & ilf_type(B,set_type) ) ) ) ).

fof(p15,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ilf_type(C,subset_type(B))
          <=> ilf_type(C,member_type(power_set(B))) ) ) ) ).

fof(p22,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( member(B,power_set(C))
          <=> ! [D] :
                ( ilf_type(D,set_type)
               => ( member(D,B)
                 => member(D,C) ) ) ) ) ) ).

fof(p23,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ~ empty(power_set(B))
        & ilf_type(power_set(B),set_type) ) ) ).

fof(p24,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ( ~ empty(C)
            & ilf_type(C,set_type) )
         => ( ilf_type(B,member_type(C))
          <=> member(B,C) ) ) ) ).

fof(p28,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,subset_type(cross_product(B,C)))
             => relation_like(D) ) ) ) ).

fof(p33,axiom,
    ! [B] : ilf_type(B,set_type) ).

fof(prove_relset_1_26,conjecture,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => ( ilf_type(D,relation_type(empty_set,C))
               => D = empty_set ) ) ) ) ).

fof(subgoal_0,plain,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ( ilf_type(D,relation_type(B,C))
                & ilf_type(D,relation_type(empty_set,C)) )
             => D = empty_set ) ) ),
    inference(strip,[],[prove_relset_1_26]) ).

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

fof(normalize_0_0,plain,
    ! [B] :
      ( ~ ilf_type(B,binary_relation_type)
      | B = empty_set
      | ( domain_of(B) != empty_set
        & range_of(B) != empty_set ) ),
    inference(canonicalize,[],[p2]) ).

fof(normalize_0_1,plain,
    ! [B] :
      ( ~ ilf_type(B,binary_relation_type)
      | B = empty_set
      | ( domain_of(B) != empty_set
        & range_of(B) != empty_set ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [B] :
      ( ( domain_of(B) != empty_set
        | ~ ilf_type(B,binary_relation_type)
        | B = empty_set )
      & ( range_of(B) != empty_set
        | ~ ilf_type(B,binary_relation_type)
        | B = empty_set ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [B] :
      ( domain_of(B) != empty_set
      | ~ ilf_type(B,binary_relation_type)
      | B = empty_set ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ( ~ ilf_type(B,binary_relation_type)
      <=> ( ~ ilf_type(B,set_type)
          | ~ relation_like(B) ) ) ),
    inference(canonicalize,[],[p13]) ).

fof(normalize_0_5,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ( ~ ilf_type(B,binary_relation_type)
      <=> ( ~ ilf_type(B,set_type)
          | ~ relation_like(B) ) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [B] :
      ( ( ~ ilf_type(B,binary_relation_type)
        | ~ ilf_type(B,set_type)
        | relation_like(B) )
      & ( ~ ilf_type(B,set_type)
        | ~ relation_like(B)
        | ilf_type(B,binary_relation_type) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ~ relation_like(B)
      | ilf_type(B,binary_relation_type) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [B] : ilf_type(B,set_type),
    inference(canonicalize,[],[p33]) ).

fof(normalize_0_9,plain,
    ! [B] : ilf_type(B,set_type),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ! [D] :
              ( ~ ilf_type(D,subset_type(cross_product(B,C)))
              | relation_like(D) ) ) ),
    inference(canonicalize,[],[p28]) ).

fof(normalize_0_11,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ! [D] :
              ( ~ ilf_type(D,subset_type(cross_product(B,C)))
              | relation_like(D) ) ) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [B,C,D] :
      ( ~ ilf_type(B,set_type)
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(D,subset_type(cross_product(B,C)))
      | relation_like(D) ),
    inference(clausify,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ~ ilf_type(C,member_type(power_set(B)))
          <=> ~ ilf_type(C,subset_type(B)) ) ) ),
    inference(canonicalize,[],[p15]) ).

fof(normalize_0_14,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ~ ilf_type(C,member_type(power_set(B)))
          <=> ~ ilf_type(C,subset_type(B)) ) ) ),
    inference(specialize,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [B,C] :
      ( ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,member_type(power_set(B)))
        | ~ ilf_type(C,set_type)
        | ilf_type(C,subset_type(B)) )
      & ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | ~ ilf_type(C,subset_type(B))
        | ilf_type(C,member_type(power_set(B))) ) ),
    inference(clausify,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    ! [B,C] :
      ( ~ ilf_type(B,set_type)
      | ~ ilf_type(C,member_type(power_set(B)))
      | ~ ilf_type(C,set_type)
      | ilf_type(C,subset_type(B)) ),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ~ member(B,power_set(C))
          <=> ? [D] :
                ( ~ member(D,C)
                & ilf_type(D,set_type)
                & member(D,B) ) ) ) ),
    inference(canonicalize,[],[p22]) ).

fof(normalize_0_18,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ~ member(B,power_set(C))
          <=> ? [D] :
                ( ~ member(D,C)
                & ilf_type(D,set_type)
                & member(D,B) ) ) ) ),
    inference(specialize,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    ! [B,C,D] :
      ( ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | ~ member(skolemFOFtoCNF_D_3(B,C),C)
        | member(B,power_set(C)) )
      & ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | ilf_type(skolemFOFtoCNF_D_3(B,C),set_type)
        | member(B,power_set(C)) )
      & ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | member(B,power_set(C))
        | member(skolemFOFtoCNF_D_3(B,C),B) )
      & ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | ~ ilf_type(D,set_type)
        | ~ member(B,power_set(C))
        | ~ member(D,B)
        | member(D,C) ) ),
    inference(clausify,[],[normalize_0_18]) ).

fof(normalize_0_20,plain,
    ! [B,C] :
      ( ~ ilf_type(B,set_type)
      | ~ ilf_type(C,set_type)
      | ~ member(skolemFOFtoCNF_D_3(B,C),C)
      | member(B,power_set(C)) ),
    inference(conjunct,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
    ! [B,C] :
      ( ~ ilf_type(B,set_type)
      | ~ ilf_type(C,set_type)
      | member(B,power_set(C))
      | member(skolemFOFtoCNF_D_3(B,C),B) ),
    inference(conjunct,[],[normalize_0_19]) ).

fof(normalize_0_22,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | empty(C)
          | ( ~ ilf_type(B,member_type(C))
          <=> ~ member(B,C) ) ) ),
    inference(canonicalize,[],[p24]) ).

fof(normalize_0_23,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | empty(C)
          | ( ~ ilf_type(B,member_type(C))
          <=> ~ member(B,C) ) ) ),
    inference(specialize,[],[normalize_0_22]) ).

fof(normalize_0_24,plain,
    ! [B,C] :
      ( ( ~ ilf_type(B,member_type(C))
        | ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | empty(C)
        | member(B,C) )
      & ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | ~ member(B,C)
        | empty(C)
        | ilf_type(B,member_type(C)) ) ),
    inference(clausify,[],[normalize_0_23]) ).

fof(normalize_0_25,plain,
    ! [B,C] :
      ( ~ ilf_type(B,set_type)
      | ~ ilf_type(C,set_type)
      | ~ member(B,C)
      | empty(C)
      | ilf_type(B,member_type(C)) ),
    inference(conjunct,[],[normalize_0_24]) ).

fof(normalize_0_26,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ( ~ empty(power_set(B))
        & ilf_type(power_set(B),set_type) ) ),
    inference(canonicalize,[],[p23]) ).

fof(normalize_0_27,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ( ~ empty(power_set(B))
        & ilf_type(power_set(B),set_type) ) ),
    inference(specialize,[],[normalize_0_26]) ).

fof(normalize_0_28,plain,
    ! [B] :
      ( ( ~ empty(power_set(B))
        | ~ ilf_type(B,set_type) )
      & ( ~ ilf_type(B,set_type)
        | ilf_type(power_set(B),set_type) ) ),
    inference(clausify,[],[normalize_0_27]) ).

fof(normalize_0_29,plain,
    ! [B] :
      ( ~ empty(power_set(B))
      | ~ ilf_type(B,set_type) ),
    inference(conjunct,[],[normalize_0_28]) ).

fof(normalize_0_30,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ~ subset(B,empty_set)
      | B = empty_set ),
    inference(canonicalize,[],[p1]) ).

fof(normalize_0_31,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ~ subset(B,empty_set)
      | B = empty_set ),
    inference(specialize,[],[normalize_0_30]) ).

fof(normalize_0_32,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ! [D] :
              ( ~ ilf_type(D,relation_type(B,C))
              | ( subset(domain_of(D),B)
                & subset(range_of(D),C) ) ) ) ),
    inference(canonicalize,[],[p3]) ).

fof(normalize_0_33,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ! [D] :
              ( ~ ilf_type(D,relation_type(B,C))
              | ( subset(domain_of(D),B)
                & subset(range_of(D),C) ) ) ) ),
    inference(specialize,[],[normalize_0_32]) ).

fof(normalize_0_34,plain,
    ! [B,C,D] :
      ( ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | ~ ilf_type(D,relation_type(B,C))
        | subset(domain_of(D),B) )
      & ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | ~ ilf_type(D,relation_type(B,C))
        | subset(range_of(D),C) ) ),
    inference(clausify,[],[normalize_0_33]) ).

fof(normalize_0_35,plain,
    ! [B,C,D] :
      ( ~ ilf_type(B,set_type)
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(D,relation_type(B,C))
      | subset(domain_of(D),B) ),
    inference(conjunct,[],[normalize_0_34]) ).

fof(normalize_0_36,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ! [D] :
                ( ~ ilf_type(D,subset_type(cross_product(B,C)))
                | ilf_type(D,relation_type(B,C)) )
            & ! [E] :
                ( ~ ilf_type(E,relation_type(B,C))
                | ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
    inference(canonicalize,[],[p6]) ).

fof(normalize_0_37,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ! [D] :
                ( ~ ilf_type(D,subset_type(cross_product(B,C)))
                | ilf_type(D,relation_type(B,C)) )
            & ! [E] :
                ( ~ ilf_type(E,relation_type(B,C))
                | ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
    inference(specialize,[],[normalize_0_36]) ).

fof(normalize_0_38,plain,
    ! [B,C,D,E] :
      ( ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | ~ ilf_type(D,subset_type(cross_product(B,C)))
        | ilf_type(D,relation_type(B,C)) )
      & ( ~ ilf_type(B,set_type)
        | ~ ilf_type(C,set_type)
        | ~ ilf_type(E,relation_type(B,C))
        | ilf_type(E,subset_type(cross_product(B,C))) ) ),
    inference(clausify,[],[normalize_0_37]) ).

fof(normalize_0_39,plain,
    ! [B,C,D] :
      ( ~ ilf_type(B,set_type)
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(D,subset_type(cross_product(B,C)))
      | ilf_type(D,relation_type(B,C)) ),
    inference(conjunct,[],[normalize_0_38]) ).

fof(normalize_0_40,plain,
    ? [B] :
      ( ilf_type(B,set_type)
      & ? [C] :
          ( ilf_type(C,set_type)
          & ? [D] :
              ( D != empty_set
              & ilf_type(D,relation_type(B,C))
              & ilf_type(D,relation_type(empty_set,C)) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_41,plain,
    ? [B,C] :
      ( ilf_type(C,set_type)
      & ? [D] :
          ( D != empty_set
          & ilf_type(D,relation_type(B,C))
          & ilf_type(D,relation_type(empty_set,C)) ) ),
    inference(simplify,[],[normalize_0_40,normalize_0_9]) ).

fof(normalize_0_42,plain,
    ( ilf_type(skolemFOFtoCNF_C_4,set_type)
    & ? [D] :
        ( D != empty_set
        & ilf_type(D,relation_type(empty_set,skolemFOFtoCNF_C_4))
        & ilf_type(D,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) ) ),
    inference(skolemize,[],[normalize_0_41]) ).

fof(normalize_0_43,plain,
    ? [D] :
      ( D != empty_set
      & ilf_type(D,relation_type(empty_set,skolemFOFtoCNF_C_4))
      & ilf_type(D,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) ),
    inference(conjunct,[],[normalize_0_42]) ).

fof(normalize_0_44,plain,
    ( skolemFOFtoCNF_D_5 != empty_set
    & ilf_type(skolemFOFtoCNF_D_5,relation_type(empty_set,skolemFOFtoCNF_C_4))
    & ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) ),
    inference(skolemize,[],[normalize_0_43]) ).

fof(normalize_0_45,plain,
    ilf_type(skolemFOFtoCNF_D_5,relation_type(empty_set,skolemFOFtoCNF_C_4)),
    inference(conjunct,[],[normalize_0_44]) ).

fof(normalize_0_46,plain,
    ! [B,C,E] :
      ( ~ ilf_type(B,set_type)
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(E,relation_type(B,C))
      | ilf_type(E,subset_type(cross_product(B,C))) ),
    inference(conjunct,[],[normalize_0_38]) ).

fof(normalize_0_47,plain,
    skolemFOFtoCNF_D_5 != empty_set,
    inference(conjunct,[],[normalize_0_44]) ).

cnf(refute_0_0,plain,
    ( domain_of(B) != empty_set
    | ~ ilf_type(B,binary_relation_type)
    | B = empty_set ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( domain_of(skolemFOFtoCNF_D_5) != empty_set
    | ~ ilf_type(skolemFOFtoCNF_D_5,binary_relation_type)
    | skolemFOFtoCNF_D_5 = empty_set ),
    inference(subst,[],[refute_0_0:[bind(B,$fot(skolemFOFtoCNF_D_5))]]) ).

cnf(refute_0_2,plain,
    ( ~ ilf_type(B,set_type)
    | ~ relation_like(B)
    | ilf_type(B,binary_relation_type) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_3,plain,
    ilf_type(B,set_type),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_4,plain,
    ( ~ relation_like(B)
    | ilf_type(B,binary_relation_type) ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_2]) ).

cnf(refute_0_5,plain,
    ( ~ relation_like(skolemFOFtoCNF_D_5)
    | ilf_type(skolemFOFtoCNF_D_5,binary_relation_type) ),
    inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_D_5))]]) ).

cnf(refute_0_6,plain,
    ( ~ ilf_type(B,set_type)
    | ~ ilf_type(C,set_type)
    | ~ ilf_type(D,subset_type(cross_product(B,C)))
    | relation_like(D) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_7,plain,
    ( ~ ilf_type(C,set_type)
    | ~ ilf_type(D,subset_type(cross_product(B,C)))
    | relation_like(D) ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_6]) ).

cnf(refute_0_8,plain,
    ilf_type(C,set_type),
    inference(subst,[],[refute_0_3:[bind(B,$fot(C))]]) ).

cnf(refute_0_9,plain,
    ( ~ ilf_type(D,subset_type(cross_product(B,C)))
    | relation_like(D) ),
    inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_7]) ).

cnf(refute_0_10,plain,
    ( ~ ilf_type(D,subset_type(cross_product(empty_set,C)))
    | relation_like(D) ),
    inference(subst,[],[refute_0_9:[bind(B,$fot(empty_set))]]) ).

cnf(refute_0_11,plain,
    ( domain_of(cross_product(X_80,X_81)) != empty_set
    | ~ ilf_type(cross_product(X_80,X_81),binary_relation_type)
    | cross_product(X_80,X_81) = empty_set ),
    inference(subst,[],[refute_0_0:[bind(B,$fot(cross_product(X_80,X_81)))]]) ).

cnf(refute_0_12,plain,
    ( ~ relation_like(cross_product(X_78,X_79))
    | ilf_type(cross_product(X_78,X_79),binary_relation_type) ),
    inference(subst,[],[refute_0_4:[bind(B,$fot(cross_product(X_78,X_79)))]]) ).

cnf(refute_0_13,plain,
    ( ~ ilf_type(cross_product(B,C),subset_type(cross_product(B,C)))
    | relation_like(cross_product(B,C)) ),
    inference(subst,[],[refute_0_9:[bind(D,$fot(cross_product(B,C)))]]) ).

cnf(refute_0_14,plain,
    ( ~ ilf_type(B,set_type)
    | ~ ilf_type(C,member_type(power_set(B)))
    | ~ ilf_type(C,set_type)
    | ilf_type(C,subset_type(B)) ),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_15,plain,
    ( ~ ilf_type(C,member_type(power_set(B)))
    | ~ ilf_type(C,set_type)
    | ilf_type(C,subset_type(B)) ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( ~ ilf_type(C,member_type(power_set(B)))
    | ilf_type(C,subset_type(B)) ),
    inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( ~ ilf_type(X_76,member_type(power_set(X_76)))
    | ilf_type(X_76,subset_type(X_76)) ),
    inference(subst,[],[refute_0_16:[bind(B,$fot(X_76)),bind(C,$fot(X_76))]]) ).

cnf(refute_0_18,plain,
    ( ~ ilf_type(B,set_type)
    | ~ ilf_type(C,set_type)
    | ~ member(skolemFOFtoCNF_D_3(B,C),C)
    | member(B,power_set(C)) ),
    inference(canonicalize,[],[normalize_0_20]) ).

cnf(refute_0_19,plain,
    ( ~ ilf_type(C,set_type)
    | ~ member(skolemFOFtoCNF_D_3(B,C),C)
    | member(B,power_set(C)) ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( ~ member(skolemFOFtoCNF_D_3(B,C),C)
    | member(B,power_set(C)) ),
    inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( ~ member(skolemFOFtoCNF_D_3(X_33,X_33),X_33)
    | member(X_33,power_set(X_33)) ),
    inference(subst,[],[refute_0_20:[bind(B,$fot(X_33)),bind(C,$fot(X_33))]]) ).

cnf(refute_0_22,plain,
    ( ~ ilf_type(B,set_type)
    | ~ ilf_type(C,set_type)
    | member(B,power_set(C))
    | member(skolemFOFtoCNF_D_3(B,C),B) ),
    inference(canonicalize,[],[normalize_0_21]) ).

cnf(refute_0_23,plain,
    ( ~ ilf_type(C,set_type)
    | member(B,power_set(C))
    | member(skolemFOFtoCNF_D_3(B,C),B) ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( member(B,power_set(C))
    | member(skolemFOFtoCNF_D_3(B,C),B) ),
    inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( member(X_33,power_set(X_33))
    | member(skolemFOFtoCNF_D_3(X_33,X_33),X_33) ),
    inference(subst,[],[refute_0_24:[bind(B,$fot(X_33)),bind(C,$fot(X_33))]]) ).

cnf(refute_0_26,plain,
    member(X_33,power_set(X_33)),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D_3(X_33,X_33),X_33) )],[refute_0_25,refute_0_21]) ).

cnf(refute_0_27,plain,
    member(X_72,power_set(X_72)),
    inference(subst,[],[refute_0_26:[bind(X_33,$fot(X_72))]]) ).

cnf(refute_0_28,plain,
    ( ~ ilf_type(B,set_type)
    | ~ ilf_type(C,set_type)
    | ~ member(B,C)
    | empty(C)
    | ilf_type(B,member_type(C)) ),
    inference(canonicalize,[],[normalize_0_25]) ).

cnf(refute_0_29,plain,
    ( ~ ilf_type(C,set_type)
    | ~ member(B,C)
    | empty(C)
    | ilf_type(B,member_type(C)) ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( ~ member(B,C)
    | empty(C)
    | ilf_type(B,member_type(C)) ),
    inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( ~ member(X_72,power_set(X_72))
    | empty(power_set(X_72))
    | ilf_type(X_72,member_type(power_set(X_72))) ),
    inference(subst,[],[refute_0_30:[bind(B,$fot(X_72)),bind(C,$fot(power_set(X_72)))]]) ).

cnf(refute_0_32,plain,
    ( empty(power_set(X_72))
    | ilf_type(X_72,member_type(power_set(X_72))) ),
    inference(resolve,[$cnf( member(X_72,power_set(X_72)) )],[refute_0_27,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( ~ empty(power_set(B))
    | ~ ilf_type(B,set_type) ),
    inference(canonicalize,[],[normalize_0_29]) ).

cnf(refute_0_34,plain,
    ~ empty(power_set(B)),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_33]) ).

cnf(refute_0_35,plain,
    ~ empty(power_set(X_72)),
    inference(subst,[],[refute_0_34:[bind(B,$fot(X_72))]]) ).

cnf(refute_0_36,plain,
    ilf_type(X_72,member_type(power_set(X_72))),
    inference(resolve,[$cnf( empty(power_set(X_72)) )],[refute_0_32,refute_0_35]) ).

cnf(refute_0_37,plain,
    ilf_type(X_76,member_type(power_set(X_76))),
    inference(subst,[],[refute_0_36:[bind(X_72,$fot(X_76))]]) ).

cnf(refute_0_38,plain,
    ilf_type(X_76,subset_type(X_76)),
    inference(resolve,[$cnf( ilf_type(X_76,member_type(power_set(X_76))) )],[refute_0_37,refute_0_17]) ).

cnf(refute_0_39,plain,
    ilf_type(cross_product(B,C),subset_type(cross_product(B,C))),
    inference(subst,[],[refute_0_38:[bind(X_76,$fot(cross_product(B,C)))]]) ).

cnf(refute_0_40,plain,
    relation_like(cross_product(B,C)),
    inference(resolve,[$cnf( ilf_type(cross_product(B,C),subset_type(cross_product(B,C))) )],[refute_0_39,refute_0_13]) ).

cnf(refute_0_41,plain,
    relation_like(cross_product(X_78,X_79)),
    inference(subst,[],[refute_0_40:[bind(B,$fot(X_78)),bind(C,$fot(X_79))]]) ).

cnf(refute_0_42,plain,
    ilf_type(cross_product(X_78,X_79),binary_relation_type),
    inference(resolve,[$cnf( relation_like(cross_product(X_78,X_79)) )],[refute_0_41,refute_0_12]) ).

cnf(refute_0_43,plain,
    ilf_type(cross_product(X_80,X_81),binary_relation_type),
    inference(subst,[],[refute_0_42:[bind(X_78,$fot(X_80)),bind(X_79,$fot(X_81))]]) ).

cnf(refute_0_44,plain,
    ( domain_of(cross_product(X_80,X_81)) != empty_set
    | cross_product(X_80,X_81) = empty_set ),
    inference(resolve,[$cnf( ilf_type(cross_product(X_80,X_81),binary_relation_type) )],[refute_0_43,refute_0_11]) ).

cnf(refute_0_45,plain,
    ( domain_of(cross_product(empty_set,X_81)) != empty_set
    | cross_product(empty_set,X_81) = empty_set ),
    inference(subst,[],[refute_0_44:[bind(X_80,$fot(empty_set))]]) ).

cnf(refute_0_46,plain,
    ( ~ ilf_type(B,set_type)
    | ~ subset(B,empty_set)
    | B = empty_set ),
    inference(canonicalize,[],[normalize_0_31]) ).

cnf(refute_0_47,plain,
    ( ~ subset(B,empty_set)
    | B = empty_set ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( ~ subset(domain_of(cross_product(empty_set,X_120)),empty_set)
    | domain_of(cross_product(empty_set,X_120)) = empty_set ),
    inference(subst,[],[refute_0_47:[bind(B,$fot(domain_of(cross_product(empty_set,X_120))))]]) ).

cnf(refute_0_49,plain,
    ( ~ ilf_type(B,set_type)
    | ~ ilf_type(C,set_type)
    | ~ ilf_type(D,relation_type(B,C))
    | subset(domain_of(D),B) ),
    inference(canonicalize,[],[normalize_0_35]) ).

cnf(refute_0_50,plain,
    ( ~ ilf_type(C,set_type)
    | ~ ilf_type(D,relation_type(B,C))
    | subset(domain_of(D),B) ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( ~ ilf_type(D,relation_type(B,C))
    | subset(domain_of(D),B) ),
    inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_50]) ).

cnf(refute_0_52,plain,
    ( ~ ilf_type(cross_product(X_114,X_115),relation_type(X_114,X_115))
    | subset(domain_of(cross_product(X_114,X_115)),X_114) ),
    inference(subst,[],[refute_0_51:[bind(B,$fot(X_114)),bind(C,$fot(X_115)),bind(D,$fot(cross_product(X_114,X_115)))]]) ).

cnf(refute_0_53,plain,
    ilf_type(cross_product(X_97,X_98),subset_type(cross_product(X_97,X_98))),
    inference(subst,[],[refute_0_38:[bind(X_76,$fot(cross_product(X_97,X_98)))]]) ).

cnf(refute_0_54,plain,
    ( ~ ilf_type(B,set_type)
    | ~ ilf_type(C,set_type)
    | ~ ilf_type(D,subset_type(cross_product(B,C)))
    | ilf_type(D,relation_type(B,C)) ),
    inference(canonicalize,[],[normalize_0_39]) ).

cnf(refute_0_55,plain,
    ( ~ ilf_type(C,set_type)
    | ~ ilf_type(D,subset_type(cross_product(B,C)))
    | ilf_type(D,relation_type(B,C)) ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_54]) ).

cnf(refute_0_56,plain,
    ( ~ ilf_type(D,subset_type(cross_product(B,C)))
    | ilf_type(D,relation_type(B,C)) ),
    inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_55]) ).

cnf(refute_0_57,plain,
    ( ~ ilf_type(cross_product(X_97,X_98),subset_type(cross_product(X_97,X_98)))
    | ilf_type(cross_product(X_97,X_98),relation_type(X_97,X_98)) ),
    inference(subst,[],[refute_0_56:[bind(B,$fot(X_97)),bind(C,$fot(X_98)),bind(D,$fot(cross_product(X_97,X_98)))]]) ).

cnf(refute_0_58,plain,
    ilf_type(cross_product(X_97,X_98),relation_type(X_97,X_98)),
    inference(resolve,[$cnf( ilf_type(cross_product(X_97,X_98),subset_type(cross_product(X_97,X_98))) )],[refute_0_53,refute_0_57]) ).

cnf(refute_0_59,plain,
    ilf_type(cross_product(X_114,X_115),relation_type(X_114,X_115)),
    inference(subst,[],[refute_0_58:[bind(X_97,$fot(X_114)),bind(X_98,$fot(X_115))]]) ).

cnf(refute_0_60,plain,
    subset(domain_of(cross_product(X_114,X_115)),X_114),
    inference(resolve,[$cnf( ilf_type(cross_product(X_114,X_115),relation_type(X_114,X_115)) )],[refute_0_59,refute_0_52]) ).

cnf(refute_0_61,plain,
    subset(domain_of(cross_product(empty_set,X_120)),empty_set),
    inference(subst,[],[refute_0_60:[bind(X_114,$fot(empty_set)),bind(X_115,$fot(X_120))]]) ).

cnf(refute_0_62,plain,
    domain_of(cross_product(empty_set,X_120)) = empty_set,
    inference(resolve,[$cnf( subset(domain_of(cross_product(empty_set,X_120)),empty_set) )],[refute_0_61,refute_0_48]) ).

cnf(refute_0_63,plain,
    domain_of(cross_product(empty_set,X_81)) = empty_set,
    inference(subst,[],[refute_0_62:[bind(X_120,$fot(X_81))]]) ).

cnf(refute_0_64,plain,
    ( domain_of(cross_product(empty_set,X_81)) != empty_set
    | empty_set != empty_set
    | domain_of(cross_product(empty_set,X_81)) = empty_set ),
    introduced(tautology,[equality,[$cnf( ~ $equal(domain_of(cross_product(empty_set,X_81)),empty_set) ),[0],$fot(empty_set)]]) ).

cnf(refute_0_65,plain,
    ( empty_set != empty_set
    | domain_of(cross_product(empty_set,X_81)) = empty_set ),
    inference(resolve,[$cnf( $equal(domain_of(cross_product(empty_set,X_81)),empty_set) )],[refute_0_63,refute_0_64]) ).

cnf(refute_0_66,plain,
    ( empty_set != empty_set
    | cross_product(empty_set,X_81) = empty_set ),
    inference(resolve,[$cnf( $equal(domain_of(cross_product(empty_set,X_81)),empty_set) )],[refute_0_65,refute_0_45]) ).

cnf(refute_0_67,plain,
    empty_set = empty_set,
    introduced(tautology,[refl,[$fot(empty_set)]]) ).

cnf(refute_0_68,plain,
    cross_product(empty_set,X_81) = empty_set,
    inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_67,refute_0_66]) ).

cnf(refute_0_69,plain,
    cross_product(empty_set,C) = empty_set,
    inference(subst,[],[refute_0_68:[bind(X_81,$fot(C))]]) ).

cnf(refute_0_70,plain,
    ( cross_product(empty_set,C) != empty_set
    | ~ ilf_type(D,subset_type(empty_set))
    | ilf_type(D,subset_type(cross_product(empty_set,C))) ),
    introduced(tautology,[equality,[$cnf( ~ ilf_type(D,subset_type(cross_product(empty_set,C))) ),[1,0],$fot(empty_set)]]) ).

cnf(refute_0_71,plain,
    ( ~ ilf_type(D,subset_type(empty_set))
    | ilf_type(D,subset_type(cross_product(empty_set,C))) ),
    inference(resolve,[$cnf( $equal(cross_product(empty_set,C),empty_set) )],[refute_0_69,refute_0_70]) ).

cnf(refute_0_72,plain,
    ( ~ ilf_type(D,subset_type(empty_set))
    | relation_like(D) ),
    inference(resolve,[$cnf( ilf_type(D,subset_type(cross_product(empty_set,C))) )],[refute_0_71,refute_0_10]) ).

cnf(refute_0_73,plain,
    ( ~ ilf_type(skolemFOFtoCNF_D_5,subset_type(empty_set))
    | relation_like(skolemFOFtoCNF_D_5) ),
    inference(subst,[],[refute_0_72:[bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).

cnf(refute_0_74,plain,
    ilf_type(skolemFOFtoCNF_D_5,relation_type(empty_set,skolemFOFtoCNF_C_4)),
    inference(canonicalize,[],[normalize_0_45]) ).

cnf(refute_0_75,plain,
    ( ~ ilf_type(B,set_type)
    | ~ ilf_type(C,set_type)
    | ~ ilf_type(E,relation_type(B,C))
    | ilf_type(E,subset_type(cross_product(B,C))) ),
    inference(canonicalize,[],[normalize_0_46]) ).

cnf(refute_0_76,plain,
    ( ~ ilf_type(C,set_type)
    | ~ ilf_type(E,relation_type(B,C))
    | ilf_type(E,subset_type(cross_product(B,C))) ),
    inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_75]) ).

cnf(refute_0_77,plain,
    ( ~ ilf_type(E,relation_type(B,C))
    | ilf_type(E,subset_type(cross_product(B,C))) ),
    inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_8,refute_0_76]) ).

cnf(refute_0_78,plain,
    ( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(empty_set,skolemFOFtoCNF_C_4))
    | ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4))) ),
    inference(subst,[],[refute_0_77:[bind(B,$fot(empty_set)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(E,$fot(skolemFOFtoCNF_D_5))]]) ).

cnf(refute_0_79,plain,
    ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4))),
    inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(empty_set,skolemFOFtoCNF_C_4)) )],[refute_0_74,refute_0_78]) ).

cnf(refute_0_80,plain,
    cross_product(empty_set,skolemFOFtoCNF_C_4) = empty_set,
    inference(subst,[],[refute_0_68:[bind(X_81,$fot(skolemFOFtoCNF_C_4))]]) ).

cnf(refute_0_81,plain,
    subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)) = subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)),
    introduced(tautology,[refl,[$fot(subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)))]]) ).

cnf(refute_0_82,plain,
    ( cross_product(empty_set,skolemFOFtoCNF_C_4) != empty_set
    | subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)) != subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4))
    | subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)) = subset_type(empty_set) ),
    introduced(tautology,[equality,[$cnf( $equal(subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)),subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4))) ),[1,0],$fot(empty_set)]]) ).

cnf(refute_0_83,plain,
    ( cross_product(empty_set,skolemFOFtoCNF_C_4) != empty_set
    | subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)) = subset_type(empty_set) ),
    inference(resolve,[$cnf( $equal(subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)),subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4))) )],[refute_0_81,refute_0_82]) ).

cnf(refute_0_84,plain,
    subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)) = subset_type(empty_set),
    inference(resolve,[$cnf( $equal(cross_product(empty_set,skolemFOFtoCNF_C_4),empty_set) )],[refute_0_80,refute_0_83]) ).

cnf(refute_0_85,plain,
    ( subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)) != subset_type(empty_set)
    | ~ ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)))
    | ilf_type(skolemFOFtoCNF_D_5,subset_type(empty_set)) ),
    introduced(tautology,[equality,[$cnf( ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4))) ),[1],$fot(subset_type(empty_set))]]) ).

cnf(refute_0_86,plain,
    ( ~ ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)))
    | ilf_type(skolemFOFtoCNF_D_5,subset_type(empty_set)) ),
    inference(resolve,[$cnf( $equal(subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4)),subset_type(empty_set)) )],[refute_0_84,refute_0_85]) ).

cnf(refute_0_87,plain,
    ilf_type(skolemFOFtoCNF_D_5,subset_type(empty_set)),
    inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(empty_set,skolemFOFtoCNF_C_4))) )],[refute_0_79,refute_0_86]) ).

cnf(refute_0_88,plain,
    relation_like(skolemFOFtoCNF_D_5),
    inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,subset_type(empty_set)) )],[refute_0_87,refute_0_73]) ).

cnf(refute_0_89,plain,
    ilf_type(skolemFOFtoCNF_D_5,binary_relation_type),
    inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_D_5) )],[refute_0_88,refute_0_5]) ).

cnf(refute_0_90,plain,
    ( domain_of(skolemFOFtoCNF_D_5) != empty_set
    | skolemFOFtoCNF_D_5 = empty_set ),
    inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,binary_relation_type) )],[refute_0_89,refute_0_1]) ).

cnf(refute_0_91,plain,
    ( ~ subset(domain_of(skolemFOFtoCNF_D_5),empty_set)
    | domain_of(skolemFOFtoCNF_D_5) = empty_set ),
    inference(subst,[],[refute_0_47:[bind(B,$fot(domain_of(skolemFOFtoCNF_D_5)))]]) ).

cnf(refute_0_92,plain,
    ( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(empty_set,skolemFOFtoCNF_C_4))
    | subset(domain_of(skolemFOFtoCNF_D_5),empty_set) ),
    inference(subst,[],[refute_0_51:[bind(B,$fot(empty_set)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).

cnf(refute_0_93,plain,
    subset(domain_of(skolemFOFtoCNF_D_5),empty_set),
    inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(empty_set,skolemFOFtoCNF_C_4)) )],[refute_0_74,refute_0_92]) ).

cnf(refute_0_94,plain,
    domain_of(skolemFOFtoCNF_D_5) = empty_set,
    inference(resolve,[$cnf( subset(domain_of(skolemFOFtoCNF_D_5),empty_set) )],[refute_0_93,refute_0_91]) ).

cnf(refute_0_95,plain,
    ( domain_of(skolemFOFtoCNF_D_5) != empty_set
    | empty_set != empty_set
    | domain_of(skolemFOFtoCNF_D_5) = empty_set ),
    introduced(tautology,[equality,[$cnf( ~ $equal(domain_of(skolemFOFtoCNF_D_5),empty_set) ),[0],$fot(empty_set)]]) ).

cnf(refute_0_96,plain,
    ( empty_set != empty_set
    | domain_of(skolemFOFtoCNF_D_5) = empty_set ),
    inference(resolve,[$cnf( $equal(domain_of(skolemFOFtoCNF_D_5),empty_set) )],[refute_0_94,refute_0_95]) ).

cnf(refute_0_97,plain,
    ( empty_set != empty_set
    | skolemFOFtoCNF_D_5 = empty_set ),
    inference(resolve,[$cnf( $equal(domain_of(skolemFOFtoCNF_D_5),empty_set) )],[refute_0_96,refute_0_90]) ).

cnf(refute_0_98,plain,
    skolemFOFtoCNF_D_5 = empty_set,
    inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_67,refute_0_97]) ).

cnf(refute_0_99,plain,
    skolemFOFtoCNF_D_5 != empty_set,
    inference(canonicalize,[],[normalize_0_47]) ).

cnf(refute_0_100,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_5,empty_set) )],[refute_0_98,refute_0_99]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET663+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul 11 10:07:25 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.39  
% 0.18/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.41  
%------------------------------------------------------------------------------