TSTP Solution File: SET582+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET582+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n005.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 03:00:49 EDT 2024

% Result   : Theorem 7.41s 1.61s
% Output   : CNFRefutation 7.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   90 (  12 unt;   0 def)
%            Number of atoms       :  312 (  25 equ)
%            Maximal formula atoms :   22 (   3 avg)
%            Number of connectives :  370 ( 148   ~; 159   |;  45   &)
%                                         (  12 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :  159 (   8 sgn  97   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,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(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(f4,axiom,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

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

fof(f10,axiom,
    ! [X0] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).

fof(f11,conjecture,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ~ member(X3,X0)
        <=> ( member(X3,X1)
          <=> member(X3,X2) ) )
     => symmetric_difference(X1,X2) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th25) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ! [X3] :
            ( ~ member(X3,X0)
          <=> ( member(X3,X1)
            <=> member(X3,X2) ) )
       => symmetric_difference(X1,X2) = X0 ),
    inference(negated_conjecture,[],[f11]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( symmetric_difference(X1,X2) != X0
      & ! [X3] :
          ( ~ member(X3,X0)
        <=> ( member(X3,X1)
          <=> member(X3,X2) ) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f19,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,[],[f2]) ).

fof(f20,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,[],[f19]) ).

fof(f21,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(f22,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,[],[f21]) ).

fof(f25,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,[],[f8]) ).

fof(f26,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,[],[f25]) ).

fof(f27,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(f28,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])],[f26,f27]) ).

fof(f29,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,[],[f14]) ).

fof(f30,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,[],[f29]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f30,f31]) ).

fof(f33,plain,
    ? [X0,X1,X2] :
      ( symmetric_difference(X1,X2) != X0
      & ! [X3] :
          ( ( ~ member(X3,X0)
            | ( ( ~ member(X3,X2)
                | ~ member(X3,X1) )
              & ( member(X3,X2)
                | member(X3,X1) ) ) )
          & ( ( ( member(X3,X1)
                | ~ member(X3,X2) )
              & ( member(X3,X2)
                | ~ member(X3,X1) ) )
            | member(X3,X0) ) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f34,plain,
    ( ? [X0,X1,X2] :
        ( symmetric_difference(X1,X2) != X0
        & ! [X3] :
            ( ( ~ member(X3,X0)
              | ( ( ~ member(X3,X2)
                  | ~ member(X3,X1) )
                & ( member(X3,X2)
                  | member(X3,X1) ) ) )
            & ( ( ( member(X3,X1)
                  | ~ member(X3,X2) )
                & ( member(X3,X2)
                  | ~ member(X3,X1) ) )
              | member(X3,X0) ) ) )
   => ( sK3 != symmetric_difference(sK4,sK5)
      & ! [X3] :
          ( ( ~ member(X3,sK3)
            | ( ( ~ member(X3,sK5)
                | ~ member(X3,sK4) )
              & ( member(X3,sK5)
                | member(X3,sK4) ) ) )
          & ( ( ( member(X3,sK4)
                | ~ member(X3,sK5) )
              & ( member(X3,sK5)
                | ~ member(X3,sK4) ) )
            | member(X3,sK3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ( sK3 != symmetric_difference(sK4,sK5)
    & ! [X3] :
        ( ( ~ member(X3,sK3)
          | ( ( ~ member(X3,sK5)
              | ~ member(X3,sK4) )
            & ( member(X3,sK5)
              | member(X3,sK4) ) ) )
        & ( ( ( member(X3,sK4)
              | ~ member(X3,sK5) )
            & ( member(X3,sK5)
              | ~ member(X3,sK4) ) )
          | member(X3,sK3) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f33,f34]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | member(X2,X0)
      | ~ member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f41,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,difference(X0,X1)) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | ~ member(X2,difference(X0,X1)) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( member(X2,difference(X0,X1))
      | member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f44,plain,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK1(X0,X1),X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK1(X0,X1),X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f54,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f57,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f10]) ).

fof(f58,plain,
    ! [X3] :
      ( member(X3,sK5)
      | ~ member(X3,sK4)
      | member(X3,sK3) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f59,plain,
    ! [X3] :
      ( member(X3,sK4)
      | ~ member(X3,sK5)
      | member(X3,sK3) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f60,plain,
    ! [X3] :
      ( ~ member(X3,sK3)
      | member(X3,sK5)
      | member(X3,sK4) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f61,plain,
    ! [X3] :
      ( ~ member(X3,sK3)
      | ~ member(X3,sK5)
      | ~ member(X3,sK4) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f62,plain,
    sK3 != symmetric_difference(sK4,sK5),
    inference(cnf_transformation,[],[f35]) ).

fof(f64,plain,
    sK3 != union(difference(sK4,sK5),difference(sK5,sK4)),
    inference(definition_unfolding,[],[f62,f44]) ).

cnf(c_51,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_52,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_53,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_54,plain,
    ( ~ member(X0,X1)
    | member(X0,difference(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_55,plain,
    ( ~ member(X0,difference(X1,X2))
    | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_56,plain,
    ( ~ member(X0,difference(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_62,plain,
    ( ~ member(sK1(X0,X1),X0)
    | ~ member(sK1(X0,X1),X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_63,plain,
    ( X0 = X1
    | member(sK1(X0,X1),X0)
    | member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_66,plain,
    ( ~ member(X0,X1)
    | ~ subset(X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_67,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_68,negated_conjecture,
    union(difference(sK4,sK5),difference(sK5,sK4)) != sK3,
    inference(cnf_transformation,[],[f64]) ).

cnf(c_69,negated_conjecture,
    ( ~ member(X0,sK3)
    | ~ member(X0,sK4)
    | ~ member(X0,sK5) ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_70,negated_conjecture,
    ( ~ member(X0,sK3)
    | member(X0,sK4)
    | member(X0,sK5) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_71,negated_conjecture,
    ( ~ member(X0,sK5)
    | member(X0,sK3)
    | member(X0,sK4) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_72,negated_conjecture,
    ( ~ member(X0,sK4)
    | member(X0,sK3)
    | member(X0,sK5) ),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_73,plain,
    subset(sK4,sK4),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_577,plain,
    ( union(difference(sK4,sK5),difference(sK5,sK4)) = sK3
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),union(difference(sK4,sK5),difference(sK5,sK4)))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK3) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_630,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),union(difference(sK4,sK5),difference(sK5,sK4)))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK4,sK5))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK5,sK4)) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_633,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),union(difference(sK4,sK5),difference(sK5,sK4)))
    | ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK3)
    | union(difference(sK4,sK5),difference(sK5,sK4)) = sK3 ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_676,plain,
    ( ~ member(sK1(X0,sK3),sK3)
    | member(sK1(X0,sK3),sK4)
    | member(sK1(X0,sK3),sK5) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_733,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK3)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5) ),
    inference(instantiation,[status(thm)],[c_676]) ).

cnf(c_1221,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X0)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(X0,X1))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X1) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_1222,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X0)
    | ~ subset(X0,X1)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X1) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_1223,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X0)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),union(X1,X0)) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_1224,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X0)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),union(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_1230,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(X0,X1))
    | ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X1) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_1258,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK4,sK5))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_1568,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK3)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK3,X0))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X0) ),
    inference(instantiation,[status(thm)],[c_1221]) ).

cnf(c_2232,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK3)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4) ),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_2233,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK3)
    | ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4)
    | ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5) ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_2237,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK5,X0))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X0) ),
    inference(instantiation,[status(thm)],[c_1221]) ).

cnf(c_2238,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK5,sK4))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4) ),
    inference(instantiation,[status(thm)],[c_2237]) ).

cnf(c_2242,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(X0,sK5))
    | ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5) ),
    inference(instantiation,[status(thm)],[c_1230]) ).

cnf(c_2243,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK4,sK5))
    | ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5) ),
    inference(instantiation,[status(thm)],[c_2242]) ).

cnf(c_2521,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X0)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(X0,sK5))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5) ),
    inference(instantiation,[status(thm)],[c_1221]) ).

cnf(c_2522,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK4,sK5))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5) ),
    inference(instantiation,[status(thm)],[c_2521]) ).

cnf(c_2571,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK5,sK4))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),union(difference(sK4,sK5),difference(sK5,sK4))) ),
    inference(instantiation,[status(thm)],[c_1223]) ).

cnf(c_2584,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK4,sK5))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),union(difference(sK4,sK5),difference(sK5,sK4))) ),
    inference(instantiation,[status(thm)],[c_1224]) ).

cnf(c_2891,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK5,sK4))
    | ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4) ),
    inference(instantiation,[status(thm)],[c_1230]) ).

cnf(c_2896,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK5,sK4))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_2897,plain,
    ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK5,sK4)),
    inference(global_subsumption_just,[status(thm)],[c_2896,c_68,c_633,c_2232,c_2571,c_2891,c_2896]) ).

cnf(c_3000,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4)
    | ~ subset(sK4,X0)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X0) ),
    inference(instantiation,[status(thm)],[c_1222]) ).

cnf(c_3001,plain,
    ( ~ subset(sK4,X0)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_3000,c_68,c_577,c_630,c_733,c_1258,c_2238,c_2897,c_3000]) ).

cnf(c_3003,plain,
    ( ~ subset(sK4,sK4)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4) ),
    inference(instantiation,[status(thm)],[c_3001]) ).

cnf(c_4204,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK3)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),difference(sK3,union(difference(sK4,sK5),difference(sK5,sK4))))
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),union(difference(sK4,sK5),difference(sK5,sK4))) ),
    inference(instantiation,[status(thm)],[c_1568]) ).

cnf(c_4205,plain,
    member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),union(difference(sK4,sK5),difference(sK5,sK4))),
    inference(global_subsumption_just,[status(thm)],[c_4204,c_73,c_68,c_577,c_2233,c_2522,c_2584,c_3003]) ).

cnf(c_5276,plain,
    ( ~ member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK4)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK3)
    | member(sK1(union(difference(sK4,sK5),difference(sK5,sK4)),sK3),sK5) ),
    inference(instantiation,[status(thm)],[c_72]) ).

cnf(c_5277,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_5276,c_4205,c_3003,c_2897,c_2243,c_633,c_630,c_68,c_73]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SET582+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n005.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Thu May  2 20:36:41 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  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
% 7.41/1.61  % SZS status Started for theBenchmark.p
% 7.41/1.61  % SZS status Theorem for theBenchmark.p
% 7.41/1.61  
% 7.41/1.61  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.41/1.61  
% 7.41/1.61  ------  iProver source info
% 7.41/1.61  
% 7.41/1.61  git: date: 2024-05-02 19:28:25 +0000
% 7.41/1.61  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.41/1.61  git: non_committed_changes: false
% 7.41/1.61  
% 7.41/1.61  ------ Parsing...
% 7.41/1.61  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.41/1.61  
% 7.41/1.61  ------ 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 
% 7.41/1.61  
% 7.41/1.61  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.41/1.61  
% 7.41/1.61  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.41/1.61  ------ Proving...
% 7.41/1.61  ------ Problem Properties 
% 7.41/1.61  
% 7.41/1.61  
% 7.41/1.61  clauses                                 21
% 7.41/1.61  conjectures                             5
% 7.41/1.61  EPR                                     7
% 7.41/1.61  Horn                                    13
% 7.41/1.61  unary                                   3
% 7.41/1.61  binary                                  6
% 7.41/1.61  lits                                    51
% 7.41/1.61  lits eq                                 7
% 7.41/1.61  fd_pure                                 0
% 7.41/1.61  fd_pseudo                               0
% 7.41/1.61  fd_cond                                 0
% 7.41/1.61  fd_pseudo_cond                          5
% 7.41/1.61  AC symbols                              0
% 7.41/1.61  
% 7.41/1.61  ------ Input Options Time Limit: Unbounded
% 7.41/1.61  
% 7.41/1.61  
% 7.41/1.61  ------ 
% 7.41/1.61  Current options:
% 7.41/1.61  ------ 
% 7.41/1.61  
% 7.41/1.61  
% 7.41/1.61  
% 7.41/1.61  
% 7.41/1.61  ------ Proving...
% 7.41/1.61  
% 7.41/1.61  
% 7.41/1.61  % SZS status Theorem for theBenchmark.p
% 7.41/1.61  
% 7.41/1.61  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.41/1.61  
% 7.41/1.62  
%------------------------------------------------------------------------------