TSTP Solution File: SET608+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET608+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n015.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  : 300s
% DateTime : Fri May  3 03:00:56 EDT 2024

% Result   : Theorem 4.03s 1.08s
% Output   : CNFRefutation 4.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   83 (  12 unt;   0 def)
%            Number of atoms       :  254 (  22 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  298 ( 127   ~; 127   |;  33   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :  154 (   7 sgn  92   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( member(X2,difference(X0,X1))
    <=> ( ~ member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f8,axiom,
    ! [X0] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f10,conjecture,
    ! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_intersection_difference) ).

fof(f11,negated_conjecture,
    ~ ! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
    inference(negated_conjecture,[],[f10]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f13,plain,
    ? [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) != X0,
    inference(ennf_transformation,[],[f11]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(flattening,[],[f16]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(flattening,[],[f18]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f22]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f24]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f26]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK1(X0,X1),X1)
          | ~ member(sK1(X0,X1),X0) )
        & ( member(sK1(X0,X1),X1)
          | member(sK1(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK1(X0,X1),X1)
            | ~ member(sK1(X0,X1),X0) )
          & ( member(sK1(X0,X1),X1)
            | member(sK1(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f27,f28]) ).

fof(f30,plain,
    ( ? [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) != X0
   => sK2 != union(intersection(sK2,sK3),difference(sK2,sK3)) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    sK2 != union(intersection(sK2,sK3),difference(sK2,sK3)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f30]) ).

fof(f32,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | member(X2,X0)
      | ~ member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,difference(X0,X1)) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( member(X2,difference(X0,X1))
      | member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f46,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f49,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK1(X0,X1),X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK1(X0,X1),X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f54,plain,
    sK2 != union(intersection(sK2,sK3),difference(sK2,sK3)),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_49,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_50,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_51,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_52,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_54,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_55,plain,
    ( ~ member(X0,X1)
    | member(X0,difference(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_57,plain,
    ( ~ member(X0,difference(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_65,plain,
    ( ~ member(X0,X1)
    | ~ subset(X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_66,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_67,plain,
    ( ~ member(sK1(X0,X1),X0)
    | ~ member(sK1(X0,X1),X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_68,plain,
    ( X0 = X1
    | member(sK1(X0,X1),X0)
    | member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_69,negated_conjecture,
    union(intersection(sK2,sK3),difference(sK2,sK3)) != sK2,
    inference(cnf_transformation,[],[f54]) ).

cnf(c_504,plain,
    ( union(intersection(sK2,sK3),difference(sK2,sK3)) = sK2
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,sK3),difference(sK2,sK3)))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2) ),
    inference(instantiation,[status(thm)],[c_68]) ).

cnf(c_505,plain,
    ( union(intersection(sK2,sK3),difference(sK2,sK3)) = sK2
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,sK3),difference(sK2,sK3)))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2) ),
    inference(instantiation,[status(thm)],[c_68]) ).

cnf(c_506,plain,
    ( member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,sK3),difference(sK2,sK3)))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2) ),
    inference(global_subsumption_just,[status(thm)],[c_505,c_69,c_504]) ).

cnf(c_518,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,sK3),difference(sK2,sK3)))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),difference(sK2,sK3)) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_519,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,sK3),difference(sK2,sK3)))
    | ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2)
    | union(intersection(sK2,sK3),difference(sK2,sK3)) = sK2 ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_520,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2)
    | ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,sK3),difference(sK2,sK3))) ),
    inference(global_subsumption_just,[status(thm)],[c_519,c_69,c_519]) ).

cnf(c_521,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,sK3),difference(sK2,sK3)))
    | ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2) ),
    inference(renaming,[status(thm)],[c_520]) ).

cnf(c_544,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),X0)
    | ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2)
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_552,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | ~ subset(intersection(sK2,X0),X1)
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),X1) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_554,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,X0),X1)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_561,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_568,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),X0)
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(X1,X0)) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_635,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | ~ subset(intersection(sK2,X0),intersection(X1,X2))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(X1,X2)) ),
    inference(instantiation,[status(thm)],[c_552]) ).

cnf(c_655,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,sK3),difference(sK2,sK3))) ),
    inference(instantiation,[status(thm)],[c_554]) ).

cnf(c_717,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),difference(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),union(intersection(sK2,sK3),difference(sK2,sK3))) ),
    inference(instantiation,[status(thm)],[c_568]) ).

cnf(c_837,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2)
    | ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK3)
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,sK3)) ),
    inference(instantiation,[status(thm)],[c_544]) ).

cnf(c_838,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK3)
    | ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2) ),
    inference(global_subsumption_just,[status(thm)],[c_837,c_69,c_519,c_655,c_837]) ).

cnf(c_839,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2)
    | ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK3) ),
    inference(renaming,[status(thm)],[c_838]) ).

cnf(c_856,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | ~ subset(intersection(sK2,X0),intersection(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,sK3)) ),
    inference(instantiation,[status(thm)],[c_635]) ).

cnf(c_863,plain,
    ( ~ subset(intersection(sK2,X0),intersection(sK2,sK3))
    | ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_856,c_69,c_519,c_561,c_655,c_856]) ).

cnf(c_864,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | ~ subset(intersection(sK2,X0),intersection(sK2,sK3)) ),
    inference(renaming,[status(thm)],[c_863]) ).

cnf(c_1040,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2)
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),difference(sK2,X0))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),X0) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_1047,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | ~ subset(intersection(sK2,X0),X1)
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),X1) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_1114,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | ~ subset(intersection(sK2,X0),intersection(X1,X2))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(X1,X2)) ),
    inference(instantiation,[status(thm)],[c_1047]) ).

cnf(c_1394,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | ~ subset(intersection(sK2,X0),intersection(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,sK3)) ),
    inference(instantiation,[status(thm)],[c_1114]) ).

cnf(c_1398,plain,
    ( ~ subset(intersection(sK2,X0),intersection(sK2,sK3))
    | ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_1394,c_864]) ).

cnf(c_1399,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,X0))
    | ~ subset(intersection(sK2,X0),intersection(sK2,sK3)) ),
    inference(renaming,[status(thm)],[c_1398]) ).

cnf(c_1833,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),intersection(sK2,sK3))
    | ~ subset(intersection(sK2,sK3),intersection(sK2,sK3)) ),
    inference(instantiation,[status(thm)],[c_1399]) ).

cnf(c_2443,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2)
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),difference(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK3) ),
    inference(instantiation,[status(thm)],[c_1040]) ).

cnf(c_2444,plain,
    ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2),
    inference(global_subsumption_just,[status(thm)],[c_2443,c_521,c_717,c_839,c_2443]) ).

cnf(c_3591,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),difference(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),difference(sK2,sK3)),sK2),sK2) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_3853,plain,
    subset(intersection(sK2,sK3),intersection(sK2,sK3)),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_3854,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_3853,c_3591,c_2444,c_1833,c_518,c_506]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SET608+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n015.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  : 300
% 0.12/0.33  % DateTime : Thu May  2 20:44:50 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.19/0.44  Running first-order theorem proving
% 0.19/0.44  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.03/1.08  % SZS status Started for theBenchmark.p
% 4.03/1.08  % SZS status Theorem for theBenchmark.p
% 4.03/1.08  
% 4.03/1.08  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.03/1.08  
% 4.03/1.08  ------  iProver source info
% 4.03/1.08  
% 4.03/1.08  git: date: 2024-05-02 19:28:25 +0000
% 4.03/1.08  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.03/1.08  git: non_committed_changes: false
% 4.03/1.08  
% 4.03/1.08  ------ Parsing...
% 4.03/1.08  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.03/1.08  
% 4.03/1.08  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 4.03/1.08  
% 4.03/1.08  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.03/1.08  
% 4.03/1.08  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.03/1.08  ------ Proving...
% 4.03/1.08  ------ Problem Properties 
% 4.03/1.08  
% 4.03/1.08  
% 4.03/1.08  clauses                                 19
% 4.03/1.08  conjectures                             1
% 4.03/1.08  EPR                                     3
% 4.03/1.08  Horn                                    15
% 4.03/1.08  unary                                   4
% 4.03/1.08  binary                                  8
% 4.03/1.08  lits                                    41
% 4.03/1.08  lits eq                                 6
% 4.03/1.08  fd_pure                                 0
% 4.03/1.08  fd_pseudo                               0
% 4.03/1.08  fd_cond                                 0
% 4.03/1.08  fd_pseudo_cond                          3
% 4.03/1.08  AC symbols                              0
% 4.03/1.08  
% 4.03/1.08  ------ Input Options Time Limit: Unbounded
% 4.03/1.08  
% 4.03/1.08  
% 4.03/1.08  ------ 
% 4.03/1.08  Current options:
% 4.03/1.08  ------ 
% 4.03/1.08  
% 4.03/1.08  
% 4.03/1.08  
% 4.03/1.08  
% 4.03/1.08  ------ Proving...
% 4.03/1.08  
% 4.03/1.08  
% 4.03/1.08  % SZS status Theorem for theBenchmark.p
% 4.03/1.08  
% 4.03/1.08  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.03/1.08  
% 4.03/1.09  
%------------------------------------------------------------------------------