TSTP Solution File: SET144+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET144+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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  : 300s
% DateTime : Mon Jun 24 14:33:29 EDT 2024

% Result   : Theorem 9.89s 2.16s
% Output   : CNFRefutation 9.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   84 (  15 unt;   0 def)
%            Number of atoms       :  249 (  39 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  280 ( 115   ~; 121   |;  32   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  151 (  10 sgn  88   !;  12   ?)

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

fof(f5,axiom,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(f6,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).

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,conjecture,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
     => union(X0,intersection(X2,X1)) = intersection(union(X0,X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th44) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( subset(X0,X1)
       => union(X0,intersection(X2,X1)) = intersection(union(X0,X2),X1) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f12,plain,
    ? [X0,X1,X2] :
      ( union(X0,intersection(X2,X1)) != intersection(union(X0,X2),X1)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f13,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(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(flattening,[],[f13]) ).

fof(f15,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(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(flattening,[],[f15]) ).

fof(f17,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,[],[f11]) ).

fof(f18,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,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,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])],[f18,f19]) ).

fof(f23,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(f24,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,[],[f23]) ).

fof(f25,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(f26,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])],[f24,f25]) ).

fof(f27,plain,
    ( ? [X0,X1,X2] :
        ( union(X0,intersection(X2,X1)) != intersection(union(X0,X2),X1)
        & subset(X0,X1) )
   => ( union(sK2,intersection(sK4,sK3)) != intersection(union(sK2,sK4),sK3)
      & subset(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ( union(sK2,intersection(sK4,sK3)) != intersection(union(sK2,sK4),sK3)
    & subset(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f27]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | member(X2,X0)
      | ~ member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f32,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f35,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f41,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f42,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK1(X0,X1),X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK1(X0,X1),X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f48,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f28]) ).

fof(f49,plain,
    union(sK2,intersection(sK4,sK3)) != intersection(union(sK2,sK4),sK3),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_49,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_50,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_51,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_52,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_53,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_54,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_57,plain,
    ( ~ member(X0,X1)
    | ~ subset(X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_61,plain,
    union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_62,plain,
    intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_64,plain,
    ( ~ member(sK1(X0,X1),X0)
    | ~ member(sK1(X0,X1),X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_65,plain,
    ( X0 = X1
    | member(sK1(X0,X1),X0)
    | member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_66,negated_conjecture,
    union(sK2,intersection(sK4,sK3)) != intersection(union(sK2,sK4),sK3),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_67,negated_conjecture,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_188,plain,
    union(sK2,intersection(sK3,sK4)) != intersection(sK3,union(sK2,sK4)),
    inference(demodulation,[status(thm)],[c_66,c_62]) ).

cnf(c_350,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_354,plain,
    ( X0 != X1
    | X2 != X3
    | ~ member(X1,X3)
    | member(X0,X2) ),
    theory(equality) ).

cnf(c_755,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,intersection(sK3,sK4)))
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,union(sK2,sK4)))
    | union(sK2,intersection(sK3,sK4)) = intersection(sK3,union(sK2,sK4)) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_756,plain,
    ( union(sK2,intersection(sK3,sK4)) = intersection(sK3,union(sK2,sK4))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,intersection(sK3,sK4)))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,union(sK2,sK4))) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_967,plain,
    ( X0 != sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4)))
    | X1 != union(sK2,intersection(sK3,sK4))
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,intersection(sK3,sK4)))
    | member(X0,X1) ),
    inference(instantiation,[status(thm)],[c_354]) ).

cnf(c_1362,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,union(sK2,sK4)))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK3) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_1363,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,union(sK2,sK4)))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,sK4)) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_1739,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK2)
    | ~ subset(sK2,X0)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),X0) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_1740,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK2)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,X0)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_2258,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),X0)
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK3)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,X0)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_2355,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,sK4))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK2)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK4) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_3595,plain,
    union(intersection(sK3,sK4),sK2) = union(sK2,intersection(sK3,sK4)),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_4229,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),X0)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(X1,X0)) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_4231,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(X0,X1))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),X0)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),X1) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_4235,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(X0,X1))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),X0) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_4236,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(X0,X1))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),X1) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_5116,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK2)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,sK4)) ),
    inference(instantiation,[status(thm)],[c_1740]) ).

cnf(c_5468,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK2)
    | ~ subset(sK2,sK3)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK3) ),
    inference(instantiation,[status(thm)],[c_1739]) ).

cnf(c_6236,plain,
    ( sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))) != sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4)))
    | X0 != union(sK2,intersection(sK3,sK4))
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,intersection(sK3,sK4)))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),X0) ),
    inference(instantiation,[status(thm)],[c_967]) ).

cnf(c_6237,plain,
    sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))) = sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),
    inference(instantiation,[status(thm)],[c_350]) ).

cnf(c_8752,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,sK4))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(X0,intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_4229]) ).

cnf(c_8753,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,sK4))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_8752]) ).

cnf(c_8766,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK4)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(X0,sK4)) ),
    inference(instantiation,[status(thm)],[c_4229]) ).

cnf(c_8767,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK4)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,sK4)) ),
    inference(instantiation,[status(thm)],[c_8766]) ).

cnf(c_9189,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,sK4))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK3) ),
    inference(instantiation,[status(thm)],[c_4235]) ).

cnf(c_9191,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,sK4))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK4) ),
    inference(instantiation,[status(thm)],[c_4236]) ).

cnf(c_16387,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(intersection(sK3,sK4),X0))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,sK4))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),X0) ),
    inference(instantiation,[status(thm)],[c_4231]) ).

cnf(c_16388,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(intersection(sK3,sK4),sK2))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,sK4))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK2) ),
    inference(instantiation,[status(thm)],[c_16387]) ).

cnf(c_16710,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,sK4))
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK3)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,union(sK2,sK4))) ),
    inference(instantiation,[status(thm)],[c_2258]) ).

cnf(c_17400,plain,
    ( sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))) != sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4)))
    | union(intersection(sK3,sK4),sK2) != union(sK2,intersection(sK3,sK4))
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,intersection(sK3,sK4)))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(intersection(sK3,sK4),sK2)) ),
    inference(instantiation,[status(thm)],[c_6236]) ).

cnf(c_34248,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK2)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),union(sK2,intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_1740]) ).

cnf(c_35416,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK4)
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),sK3)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(sK3,union(sK2,sK4))),intersection(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_2258]) ).

cnf(c_35417,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_35416,c_34248,c_17400,c_16710,c_16388,c_9191,c_9189,c_8767,c_8753,c_6237,c_5468,c_5116,c_3595,c_2355,c_1362,c_1363,c_756,c_755,c_188,c_67]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SET144+3 : TPTP v8.2.0. Released v2.2.0.
% 0.08/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n023.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 : Sun Jun 23 17:22:24 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  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
% 9.89/2.16  % SZS status Started for theBenchmark.p
% 9.89/2.16  % SZS status Theorem for theBenchmark.p
% 9.89/2.16  
% 9.89/2.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 9.89/2.16  
% 9.89/2.16  ------  iProver source info
% 9.89/2.16  
% 9.89/2.16  git: date: 2024-06-12 09:56:46 +0000
% 9.89/2.16  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 9.89/2.16  git: non_committed_changes: false
% 9.89/2.16  
% 9.89/2.16  ------ Parsing...
% 9.89/2.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 9.89/2.16  
% 9.89/2.16  ------ Preprocessing... sup_sim: 1  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 
% 9.89/2.16  
% 9.89/2.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 9.89/2.16  
% 9.89/2.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 9.89/2.16  ------ Proving...
% 9.89/2.16  ------ Problem Properties 
% 9.89/2.16  
% 9.89/2.16  
% 9.89/2.16  clauses                                 17
% 9.89/2.16  conjectures                             1
% 9.89/2.16  EPR                                     4
% 9.89/2.16  Horn                                    14
% 9.89/2.16  unary                                   5
% 9.89/2.16  binary                                  6
% 9.89/2.16  lits                                    35
% 9.89/2.16  lits eq                                 6
% 9.89/2.16  fd_pure                                 0
% 9.89/2.16  fd_pseudo                               0
% 9.89/2.16  fd_cond                                 0
% 9.89/2.16  fd_pseudo_cond                          3
% 9.89/2.16  AC symbols                              0
% 9.89/2.16  
% 9.89/2.16  ------ Schedule dynamic 5 is on 
% 9.89/2.16  
% 9.89/2.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.89/2.16  
% 9.89/2.16  
% 9.89/2.16  ------ 
% 9.89/2.16  Current options:
% 9.89/2.16  ------ 
% 9.89/2.16  
% 9.89/2.16  
% 9.89/2.16  
% 9.89/2.16  
% 9.89/2.16  ------ Proving...
% 9.89/2.16  
% 9.89/2.16  
% 9.89/2.16  % SZS status Theorem for theBenchmark.p
% 9.89/2.16  
% 9.89/2.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.89/2.16  
% 9.89/2.16  
%------------------------------------------------------------------------------