TSTP Solution File: SET943+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET943+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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 03:02:04 EDT 2024

% Result   : Theorem 10.19s 2.11s
% Output   : CNFRefutation 10.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   90 (   9 unt;   0 def)
%            Number of atoms       :  347 (  47 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  437 ( 180   ~; 188   |;  56   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-3 aty)
%            Number of variables   :  198 (   4 sgn 120   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( union(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ? [X3] :
              ( in(X3,X0)
              & in(X2,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).

fof(f16,conjecture,
    ! [X0,X1] : union(set_union2(X0,X1)) = set_union2(union(X0),union(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).

fof(f17,negated_conjecture,
    ~ ! [X0,X1] : union(set_union2(X0,X1)) = set_union2(union(X0),union(X1)),
    inference(negated_conjecture,[],[f16]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f27,plain,
    ? [X0,X1] : union(set_union2(X0,X1)) != set_union2(union(X0),union(X1)),
    inference(ennf_transformation,[],[f17]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(flattening,[],[f30]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(rectify,[],[f31]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK0(X0,X1,X2),X1)
            & ~ in(sK0(X0,X1,X2),X0) )
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( in(sK0(X0,X1,X2),X1)
          | in(sK0(X0,X1,X2),X0)
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK0(X0,X1,X2),X1)
              & ~ in(sK0(X0,X1,X2),X0) )
            | ~ in(sK0(X0,X1,X2),X2) )
          & ( in(sK0(X0,X1,X2),X1)
            | in(sK0(X0,X1,X2),X0)
            | in(sK0(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f32,f33]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f35]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK1(X0,X1),X1)
        & in(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK1(X0,X1),X1)
          & in(sK1(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f36,f37]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) ) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | ~ in(X2,X1) ) )
        | union(X0) != X1 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X4] :
                  ( in(X4,X0)
                  & in(X2,X4) )
              | in(X2,X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ? [X7] :
                  ( in(X7,X0)
                  & in(X5,X7) )
              | ~ in(X5,X1) ) )
        | union(X0) != X1 ) ),
    inference(rectify,[],[f39]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(X2,X3) )
            | ~ in(X2,X1) )
          & ( ? [X4] :
                ( in(X4,X0)
                & in(X2,X4) )
            | in(X2,X1) ) )
     => ( ( ! [X3] :
              ( ~ in(X3,X0)
              | ~ in(sK2(X0,X1),X3) )
          | ~ in(sK2(X0,X1),X1) )
        & ( ? [X4] :
              ( in(X4,X0)
              & in(sK2(X0,X1),X4) )
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( in(X4,X0)
          & in(sK2(X0,X1),X4) )
     => ( in(sK3(X0,X1),X0)
        & in(sK2(X0,X1),sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( in(X7,X0)
          & in(X5,X7) )
     => ( in(sK4(X0,X5),X0)
        & in(X5,sK4(X0,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(sK2(X0,X1),X3) )
            | ~ in(sK2(X0,X1),X1) )
          & ( ( in(sK3(X0,X1),X0)
              & in(sK2(X0,X1),sK3(X0,X1)) )
            | in(sK2(X0,X1),X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ( in(sK4(X0,X5),X0)
                & in(X5,sK4(X0,X5)) )
              | ~ in(X5,X1) ) )
        | union(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f40,f43,f42,f41]) ).

fof(f49,plain,
    ( ? [X0,X1] : union(set_union2(X0,X1)) != set_union2(union(X0),union(X1))
   => union(set_union2(sK7,sK8)) != set_union2(union(sK7),union(sK8)) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    union(set_union2(sK7,sK8)) != set_union2(union(sK7),union(sK8)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f27,f49]) ).

fof(f56,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | in(X4,X0)
      | ~ in(X4,X2)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f57,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X0)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f58,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f59,plain,
    ! [X2,X0,X1] :
      ( set_union2(X0,X1) = X2
      | in(sK0(X0,X1,X2),X1)
      | in(sK0(X0,X1,X2),X0)
      | in(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( set_union2(X0,X1) = X2
      | ~ in(sK0(X0,X1,X2),X0)
      | ~ in(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f61,plain,
    ! [X2,X0,X1] :
      ( set_union2(X0,X1) = X2
      | ~ in(sK0(X0,X1,X2),X1)
      | ~ in(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f62,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f65,plain,
    ! [X0,X1,X5] :
      ( in(X5,sK4(X0,X5))
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f66,plain,
    ! [X0,X1,X5] :
      ( in(sK4(X0,X5),X0)
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f67,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(X6,X0)
      | ~ in(X5,X6)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f80,plain,
    union(set_union2(sK7,sK8)) != set_union2(union(sK7),union(sK8)),
    inference(cnf_transformation,[],[f50]) ).

fof(f83,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f58]) ).

fof(f84,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f57]) ).

fof(f85,plain,
    ! [X0,X1,X4] :
      ( in(X4,X1)
      | in(X4,X0)
      | ~ in(X4,set_union2(X0,X1)) ),
    inference(equality_resolution,[],[f56]) ).

fof(f86,plain,
    ! [X0,X6,X5] :
      ( in(X5,union(X0))
      | ~ in(X6,X0)
      | ~ in(X5,X6) ),
    inference(equality_resolution,[],[f67]) ).

fof(f87,plain,
    ! [X0,X5] :
      ( in(sK4(X0,X5),X0)
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f66]) ).

fof(f88,plain,
    ! [X0,X5] :
      ( in(X5,sK4(X0,X5))
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f65]) ).

cnf(c_54,plain,
    ( ~ in(sK0(X0,X1,X2),X1)
    | ~ in(sK0(X0,X1,X2),X2)
    | set_union2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_55,plain,
    ( ~ in(sK0(X0,X1,X2),X0)
    | ~ in(sK0(X0,X1,X2),X2)
    | set_union2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_56,plain,
    ( set_union2(X0,X1) = X2
    | in(sK0(X0,X1,X2),X0)
    | in(sK0(X0,X1,X2),X1)
    | in(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_57,plain,
    ( ~ in(X0,X1)
    | in(X0,set_union2(X2,X1)) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_58,plain,
    ( ~ in(X0,X1)
    | in(X0,set_union2(X1,X2)) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_59,plain,
    ( ~ in(X0,set_union2(X1,X2))
    | in(X0,X1)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_62,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_66,plain,
    ( ~ in(X0,X1)
    | ~ in(X1,X2)
    | in(X0,union(X2)) ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_67,plain,
    ( ~ in(X0,union(X1))
    | in(sK4(X1,X0),X1) ),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_68,plain,
    ( ~ in(X0,union(X1))
    | in(X0,sK4(X1,X0)) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_78,negated_conjecture,
    set_union2(union(sK7),union(sK8)) != union(set_union2(sK7,sK8)),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_360,plain,
    ( X0 != X1
    | X2 != X3
    | ~ in(X1,X3)
    | in(X0,X2) ),
    theory(equality) ).

cnf(c_698,plain,
    ( set_union2(union(sK7),union(sK8)) = union(set_union2(sK7,sK8))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8)))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK7))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8)) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_713,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8)))
    | in(sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),set_union2(sK7,sK8)) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_714,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8)))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))))) ),
    inference(instantiation,[status(thm)],[c_68]) ).

cnf(c_730,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(X0))
    | in(sK4(X0,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),X0) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_731,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(X0))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(X0,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))))) ),
    inference(instantiation,[status(thm)],[c_68]) ).

cnf(c_732,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK7))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(sK7,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))))) ),
    inference(instantiation,[status(thm)],[c_731]) ).

cnf(c_733,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK7))
    | in(sK4(sK7,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK7) ),
    inference(instantiation,[status(thm)],[c_730]) ).

cnf(c_746,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8)))
    | ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8))
    | set_union2(union(sK7),union(sK8)) = union(set_union2(sK7,sK8)) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_771,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8))
    | in(sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK8) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_772,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))))) ),
    inference(instantiation,[status(thm)],[c_68]) ).

cnf(c_835,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8)))
    | ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK7))
    | set_union2(union(sK7),union(sK8)) = union(set_union2(sK7,sK8)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_885,plain,
    ( ~ in(sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),set_union2(sK7,sK8))
    | in(sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK7)
    | in(sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK8) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_1129,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8))
    | ~ subset(union(sK8),X0)
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),X0) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_1151,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),X0)
    | ~ in(X0,X1)
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(X1)) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_1187,plain,
    ( ~ in(sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK8)
    | in(sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),set_union2(X0,sK8)) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_1191,plain,
    ( ~ in(sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK8)
    | in(sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),set_union2(sK7,sK8)) ),
    inference(instantiation,[status(thm)],[c_1187]) ).

cnf(c_1277,plain,
    ( ~ in(sK4(X0,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),X0)
    | in(sK4(X0,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),set_union2(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_1302,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),X0)
    | ~ in(X0,set_union2(sK7,sK8))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8))) ),
    inference(instantiation,[status(thm)],[c_1151]) ).

cnf(c_1309,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),X0)
    | ~ in(X0,sK8)
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8)) ),
    inference(instantiation,[status(thm)],[c_1151]) ).

cnf(c_1962,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))))
    | ~ in(sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),set_union2(sK7,sK8))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8))) ),
    inference(instantiation,[status(thm)],[c_1302]) ).

cnf(c_1976,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))))
    | ~ in(sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK8)
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8)) ),
    inference(instantiation,[status(thm)],[c_1309]) ).

cnf(c_1977,plain,
    ( ~ in(sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK8)
    | ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))))) ),
    inference(global_subsumption_just,[status(thm)],[c_1976,c_78,c_746,c_1191,c_1962,c_1976]) ).

cnf(c_1978,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))))
    | ~ in(sK4(sK8,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK8) ),
    inference(renaming,[status(thm)],[c_1977]) ).

cnf(c_2061,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8))
    | ~ subset(union(sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))) ),
    inference(instantiation,[status(thm)],[c_1129]) ).

cnf(c_2062,plain,
    ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8)),
    inference(global_subsumption_just,[status(thm)],[c_2061,c_772,c_771,c_1978]) ).

cnf(c_2276,plain,
    ( ~ in(sK4(sK7,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK7)
    | in(sK4(sK7,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),set_union2(sK7,sK8)) ),
    inference(instantiation,[status(thm)],[c_1277]) ).

cnf(c_4759,plain,
    ( X0 != sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))
    | X1 != union(set_union2(sK7,sK8))
    | ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8)))
    | in(X0,X1) ),
    inference(instantiation,[status(thm)],[c_360]) ).

cnf(c_4797,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))))
    | ~ in(sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),X0)
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(X0)) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_4802,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))))
    | ~ in(sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK7)
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK7)) ),
    inference(instantiation,[status(thm)],[c_4797]) ).

cnf(c_4806,plain,
    ( set_union2(X0,X1) != union(set_union2(sK7,sK8))
    | X2 != sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))
    | ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8)))
    | in(X2,set_union2(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_4759]) ).

cnf(c_5035,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))))
    | ~ in(sK4(set_union2(sK7,sK8),sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),sK8)
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(sK8)) ),
    inference(instantiation,[status(thm)],[c_4797]) ).

cnf(c_5086,plain,
    ( set_union2(X0,X1) != union(set_union2(sK7,sK8))
    | set_union2(X2,X3) != sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))
    | ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8)))
    | in(set_union2(X2,X3),set_union2(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_4806]) ).

cnf(c_5088,plain,
    ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8))),
    inference(global_subsumption_just,[status(thm)],[c_5086,c_78,c_714,c_713,c_835,c_885,c_2062,c_4802,c_5035]) ).

cnf(c_6445,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(X0,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))))
    | ~ in(sK4(X0,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),X1)
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(X1)) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_15371,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(X0,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))))
    | ~ in(sK4(X0,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),set_union2(sK7,sK8))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8))) ),
    inference(instantiation,[status(thm)],[c_6445]) ).

cnf(c_15372,plain,
    ( ~ in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),sK4(sK7,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))))
    | ~ in(sK4(sK7,sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8)))),set_union2(sK7,sK8))
    | in(sK0(union(sK7),union(sK8),union(set_union2(sK7,sK8))),union(set_union2(sK7,sK8))) ),
    inference(instantiation,[status(thm)],[c_15371]) ).

cnf(c_15373,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_15372,c_5088,c_2276,c_2062,c_733,c_732,c_698,c_78]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : SET943+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n029.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 20:48:22 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.15/0.42  Running first-order theorem proving
% 0.15/0.42  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
% 10.19/2.11  % SZS status Started for theBenchmark.p
% 10.19/2.11  % SZS status Theorem for theBenchmark.p
% 10.19/2.11  
% 10.19/2.11  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 10.19/2.11  
% 10.19/2.11  ------  iProver source info
% 10.19/2.11  
% 10.19/2.11  git: date: 2024-05-02 19:28:25 +0000
% 10.19/2.11  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 10.19/2.11  git: non_committed_changes: false
% 10.19/2.11  
% 10.19/2.11  ------ Parsing...
% 10.19/2.11  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 10.19/2.11  
% 10.19/2.11  ------ 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 
% 10.19/2.11  
% 10.19/2.11  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 10.19/2.11  
% 10.19/2.11  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 10.19/2.11  ------ Proving...
% 10.19/2.11  ------ Problem Properties 
% 10.19/2.11  
% 10.19/2.11  
% 10.19/2.11  clauses                                 28
% 10.19/2.11  conjectures                             1
% 10.19/2.11  EPR                                     6
% 10.19/2.11  Horn                                    23
% 10.19/2.11  unary                                   7
% 10.19/2.11  binary                                  10
% 10.19/2.11  lits                                    62
% 10.19/2.11  lits eq                                 10
% 10.19/2.11  fd_pure                                 0
% 10.19/2.11  fd_pseudo                               0
% 10.19/2.11  fd_cond                                 0
% 10.19/2.11  fd_pseudo_cond                          7
% 10.19/2.11  AC symbols                              0
% 10.19/2.11  
% 10.19/2.11  ------ Input Options Time Limit: Unbounded
% 10.19/2.11  
% 10.19/2.11  
% 10.19/2.11  ------ 
% 10.19/2.11  Current options:
% 10.19/2.11  ------ 
% 10.19/2.11  
% 10.19/2.11  
% 10.19/2.11  
% 10.19/2.11  
% 10.19/2.11  ------ Proving...
% 10.19/2.11  
% 10.19/2.11  
% 10.19/2.11  % SZS status Theorem for theBenchmark.p
% 10.19/2.11  
% 10.19/2.11  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.19/2.11  
% 10.19/2.11  
%------------------------------------------------------------------------------