TSTP Solution File: SET624+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 03:36:06 EDT 2022

% Result   : Theorem 2.22s 2.37s
% Output   : CNFRefutation 2.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   96 (  22 unt;   0 def)
%            Number of atoms       :  221 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  227 ( 102   ~;  88   |;  21   &)
%                                         (  11 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  134 (  10 sgn  85   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(union_defn,axiom,
    ! [B,C,D] :
      ( member(D,union(B,C))
    <=> ( member(D,B)
        | member(D,C) ) ) ).

fof(intersect_defn,axiom,
    ! [B,C] :
      ( intersect(B,C)
    <=> ? [D] :
          ( member(D,B)
          & member(D,C) ) ) ).

fof(symmetry_of_intersect,axiom,
    ! [B,C] :
      ( intersect(B,C)
     => intersect(C,B) ) ).

fof(prove_intersect_with_union,conjecture,
    ! [B,C,D] :
      ( intersect(B,union(C,D))
    <=> ( intersect(B,C)
        | intersect(B,D) ) ) ).

fof(subgoal_0,plain,
    ! [B,C,D] :
      ( ( intersect(B,union(C,D))
        & ~ intersect(B,C) )
     => intersect(B,D) ),
    inference(strip,[],[prove_intersect_with_union]) ).

fof(subgoal_1,plain,
    ! [B,C,D] :
      ( ( intersect(B,C)
        | intersect(B,D) )
     => intersect(B,union(C,D)) ),
    inference(strip,[],[prove_intersect_with_union]) ).

fof(negate_0_0,plain,
    ~ ! [B,C,D] :
        ( ( intersect(B,union(C,D))
          & ~ intersect(B,C) )
       => intersect(B,D) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [B,C,D] :
      ( ~ intersect(B,C)
      & ~ intersect(B,D)
      & intersect(B,union(C,D)) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    & ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
    & intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
    inference(conjunct,[],[normalize_0_1]) ).

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

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

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

fof(normalize_0_6,plain,
    ! [B,C] :
      ( ~ intersect(B,C)
      | member(skolemFOFtoCNF_D(B,C),B) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [B,C,D] :
      ( ~ member(D,B)
      | ~ member(D,C)
      | intersect(B,C) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_8,plain,
    ! [B,C] :
      ( ~ intersect(B,C)
      | member(skolemFOFtoCNF_D(B,C),C) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_9,plain,
    ! [B,C,D] :
      ( ~ member(D,union(B,C))
    <=> ( ~ member(D,B)
        & ~ member(D,C) ) ),
    inference(canonicalize,[],[union_defn]) ).

fof(normalize_0_10,plain,
    ! [B,C,D] :
      ( ~ member(D,union(B,C))
    <=> ( ~ member(D,B)
        & ~ member(D,C) ) ),
    inference(specialize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [B,C,D] :
      ( ( ~ member(D,B)
        | member(D,union(B,C)) )
      & ( ~ member(D,C)
        | member(D,union(B,C)) )
      & ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) ) ),
    inference(clausify,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [B,C,D] :
      ( ~ member(D,union(B,C))
      | member(D,B)
      | member(D,C) ),
    inference(conjunct,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_14,plain,
    ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
    inference(conjunct,[],[normalize_0_1]) ).

cnf(refute_0_0,plain,
    intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ intersect(B,C)
    | member(skolemFOFtoCNF_D(B,C),B) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    ( ~ intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B) ),
    inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).

cnf(refute_0_3,plain,
    member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B),
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ member(D,B)
    | ~ member(D,C)
    | intersect(B,C) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_5,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),X_228)
    | ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B)
    | intersect(skolemFOFtoCNF_B,X_228) ),
    inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_228)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))]]) ).

cnf(refute_0_6,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),X_228)
    | intersect(skolemFOFtoCNF_B,X_228) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_B) )],[refute_0_3,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C)
    | intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
    inference(subst,[],[refute_0_6:[bind(X_228,$fot(skolemFOFtoCNF_C))]]) ).

cnf(refute_0_8,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_D_2)
    | intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) ),
    inference(subst,[],[refute_0_6:[bind(X_228,$fot(skolemFOFtoCNF_D_2))]]) ).

cnf(refute_0_9,plain,
    ( ~ intersect(B,C)
    | member(skolemFOFtoCNF_D(B,C),C) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) ),
    inference(subst,[],[refute_0_9:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)))]]) ).

cnf(refute_0_11,plain,
    member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_0,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ member(D,union(B,C))
    | member(D,B)
    | member(D,C) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_13,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_D_2) ),
    inference(subst,[],[refute_0_12:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2))))]]) ).

cnf(refute_0_14,plain,
    ( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_D_2) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)) )],[refute_0_11,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_D_2) )],[refute_0_14,refute_0_8]) ).

cnf(refute_0_16,plain,
    ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_17,plain,
    member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C),
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,union(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)),skolemFOFtoCNF_C) )],[refute_0_17,refute_0_7]) ).

cnf(refute_0_19,plain,
    ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_20,plain,
    $false,
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_18,refute_0_19]) ).

fof(negate_1_0,plain,
    ~ ! [B,C,D] :
        ( ( intersect(B,C)
          | intersect(B,D) )
       => intersect(B,union(C,D)) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ? [B,C,D] :
      ( ~ intersect(B,union(C,D))
      & ( intersect(B,C)
        | intersect(B,D) ) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_1,plain,
    ( ~ intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3))
    & ( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
      | intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) ) ),
    inference(skolemize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ~ intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ! [B,C] :
      ( ~ intersect(B,C)
      | intersect(C,B) ),
    inference(canonicalize,[],[symmetry_of_intersect]) ).

fof(normalize_1_4,plain,
    ! [B,C] :
      ( ~ intersect(B,C)
      | intersect(C,B) ),
    inference(specialize,[],[normalize_1_3]) ).

fof(normalize_1_5,plain,
    ! [B,C,D] :
      ( ~ member(D,union(B,C))
    <=> ( ~ member(D,B)
        & ~ member(D,C) ) ),
    inference(canonicalize,[],[union_defn]) ).

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

fof(normalize_1_7,plain,
    ! [B,C,D] :
      ( ( ~ member(D,B)
        | member(D,union(B,C)) )
      & ( ~ member(D,C)
        | member(D,union(B,C)) )
      & ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) ) ),
    inference(clausify,[],[normalize_1_6]) ).

fof(normalize_1_8,plain,
    ! [B,C,D] :
      ( ~ member(D,B)
      | member(D,union(B,C)) ),
    inference(conjunct,[],[normalize_1_7]) ).

fof(normalize_1_9,plain,
    ! [B,C] :
      ( ~ intersect(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | ~ member(D,C) ) ),
    inference(canonicalize,[],[intersect_defn]) ).

fof(normalize_1_10,plain,
    ! [B,C] :
      ( ~ intersect(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | ~ member(D,C) ) ),
    inference(specialize,[],[normalize_1_9]) ).

fof(normalize_1_11,plain,
    ! [B,C,D] :
      ( ( ~ intersect(B,C)
        | member(skolemFOFtoCNF_D(B,C),B) )
      & ( ~ intersect(B,C)
        | member(skolemFOFtoCNF_D(B,C),C) )
      & ( ~ member(D,B)
        | ~ member(D,C)
        | intersect(B,C) ) ),
    inference(clausify,[],[normalize_1_10]) ).

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

fof(normalize_1_13,plain,
    ( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) ),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_14,plain,
    ! [B,C,D] :
      ( ~ member(D,C)
      | member(D,union(B,C)) ),
    inference(conjunct,[],[normalize_1_7]) ).

fof(normalize_1_15,plain,
    ! [B,C] :
      ( ~ intersect(B,C)
      | member(skolemFOFtoCNF_D(B,C),B) ),
    inference(conjunct,[],[normalize_1_11]) ).

fof(normalize_1_16,plain,
    ! [B,C,D] :
      ( ~ member(D,B)
      | ~ member(D,C)
      | intersect(B,C) ),
    inference(conjunct,[],[normalize_1_11]) ).

cnf(refute_1_0,plain,
    ~ intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)),
    inference(canonicalize,[],[normalize_1_2]) ).

cnf(refute_1_1,plain,
    ( ~ intersect(B,C)
    | intersect(C,B) ),
    inference(canonicalize,[],[normalize_1_4]) ).

cnf(refute_1_2,plain,
    ( ~ intersect(union(skolemFOFtoCNF_C_1,X_3357),skolemFOFtoCNF_B_1)
    | intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,X_3357)) ),
    inference(subst,[],[refute_1_1:[bind(B,$fot(union(skolemFOFtoCNF_C_1,X_3357))),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_1_3,plain,
    ( ~ member(D,B)
    | member(D,union(B,C)) ),
    inference(canonicalize,[],[normalize_1_8]) ).

cnf(refute_1_4,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),union(skolemFOFtoCNF_C_1,C)) ),
    inference(subst,[],[refute_1_3:[bind(B,$fot(skolemFOFtoCNF_C_1)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)))]]) ).

cnf(refute_1_5,plain,
    ( ~ intersect(B,C)
    | member(skolemFOFtoCNF_D(B,C),C) ),
    inference(canonicalize,[],[normalize_1_12]) ).

cnf(refute_1_6,plain,
    ( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) ),
    inference(subst,[],[refute_1_5:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).

cnf(refute_1_7,plain,
    ( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) ),
    inference(canonicalize,[],[normalize_1_13]) ).

cnf(refute_1_8,plain,
    ( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3) ),
    inference(subst,[],[refute_1_5:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D_3))]]) ).

cnf(refute_1_9,plain,
    ( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3) ),
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) )],[refute_1_7,refute_1_8]) ).

cnf(refute_1_10,plain,
    ( ~ member(D,C)
    | member(D,union(B,C)) ),
    inference(canonicalize,[],[normalize_1_14]) ).

cnf(refute_1_11,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),union(X_1158,skolemFOFtoCNF_D_3)) ),
    inference(subst,[],[refute_1_10:[bind(B,$fot(X_1158)),bind(C,$fot(skolemFOFtoCNF_D_3)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3)))]]) ).

cnf(refute_1_12,plain,
    ( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),union(X_1158,skolemFOFtoCNF_D_3)) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_D_3) )],[refute_1_9,refute_1_11]) ).

cnf(refute_1_13,plain,
    ( ~ intersect(B,C)
    | member(skolemFOFtoCNF_D(B,C),B) ),
    inference(canonicalize,[],[normalize_1_15]) ).

cnf(refute_1_14,plain,
    ( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_1_13:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D_3))]]) ).

cnf(refute_1_15,plain,
    ( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1) ),
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3) )],[refute_1_7,refute_1_14]) ).

cnf(refute_1_16,plain,
    ( ~ member(D,B)
    | ~ member(D,C)
    | intersect(B,C) ),
    inference(canonicalize,[],[normalize_1_16]) ).

cnf(refute_1_17,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),X_1280)
    | ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1)
    | intersect(skolemFOFtoCNF_B_1,X_1280) ),
    inference(subst,[],[refute_1_16:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_1280)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3)))]]) ).

cnf(refute_1_18,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),X_1280)
    | intersect(skolemFOFtoCNF_B_1,X_1280)
    | intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),skolemFOFtoCNF_B_1) )],[refute_1_15,refute_1_17]) ).

cnf(refute_1_19,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),union(X_1158,skolemFOFtoCNF_D_3))
    | intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | intersect(skolemFOFtoCNF_B_1,union(X_1158,skolemFOFtoCNF_D_3)) ),
    inference(subst,[],[refute_1_18:[bind(X_1280,$fot(union(X_1158,skolemFOFtoCNF_D_3)))]]) ).

cnf(refute_1_20,plain,
    ( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | intersect(skolemFOFtoCNF_B_1,union(X_1158,skolemFOFtoCNF_D_3)) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_3),union(X_1158,skolemFOFtoCNF_D_3)) )],[refute_1_12,refute_1_19]) ).

cnf(refute_1_21,plain,
    ( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) ),
    inference(subst,[],[refute_1_20:[bind(X_1158,$fot(skolemFOFtoCNF_C_1))]]) ).

cnf(refute_1_22,plain,
    intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) )],[refute_1_21,refute_1_0]) ).

cnf(refute_1_23,plain,
    member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1),
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_1_22,refute_1_6]) ).

cnf(refute_1_24,plain,
    member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),union(skolemFOFtoCNF_C_1,C)),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_C_1) )],[refute_1_23,refute_1_4]) ).

cnf(refute_1_25,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),B)
    | ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1)
    | intersect(B,skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_1_16:[bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)))]]) ).

cnf(refute_1_26,plain,
    ( ~ intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
    | member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_1_13:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).

cnf(refute_1_27,plain,
    member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_1_22,refute_1_26]) ).

cnf(refute_1_28,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),B)
    | intersect(B,skolemFOFtoCNF_B_1) ),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1) )],[refute_1_27,refute_1_25]) ).

cnf(refute_1_29,plain,
    ( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),union(skolemFOFtoCNF_C_1,C))
    | intersect(union(skolemFOFtoCNF_C_1,C),skolemFOFtoCNF_B_1) ),
    inference(subst,[],[refute_1_28:[bind(B,$fot(union(skolemFOFtoCNF_C_1,C)))]]) ).

cnf(refute_1_30,plain,
    intersect(union(skolemFOFtoCNF_C_1,C),skolemFOFtoCNF_B_1),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),union(skolemFOFtoCNF_C_1,C)) )],[refute_1_24,refute_1_29]) ).

cnf(refute_1_31,plain,
    intersect(union(skolemFOFtoCNF_C_1,X_3357),skolemFOFtoCNF_B_1),
    inference(subst,[],[refute_1_30:[bind(C,$fot(X_3357))]]) ).

cnf(refute_1_32,plain,
    intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,X_3357)),
    inference(resolve,[$cnf( intersect(union(skolemFOFtoCNF_C_1,X_3357),skolemFOFtoCNF_B_1) )],[refute_1_31,refute_1_2]) ).

cnf(refute_1_33,plain,
    intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)),
    inference(subst,[],[refute_1_32:[bind(X_3357,$fot(skolemFOFtoCNF_D_3))]]) ).

cnf(refute_1_34,plain,
    $false,
    inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B_1,union(skolemFOFtoCNF_C_1,skolemFOFtoCNF_D_3)) )],[refute_1_33,refute_1_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 21:18:13 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.22/2.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.22/2.37  
% 2.22/2.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.22/2.38  
%------------------------------------------------------------------------------