TSTP Solution File: SET601+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET601+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 03:00:54 EDT 2024

% Result   : Theorem 24.82s 4.29s
% Output   : CNFRefutation 24.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   87 (  24 unt;   0 def)
%            Number of atoms       :  218 (  38 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  229 (  98   ~; 105   |;  20   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  145 (  12 sgn  86   !;   9   ?)

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

fof(f3,axiom,
    ! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_intersection) ).

fof(f5,axiom,
    ! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_distributes_over_intersection) ).

fof(f6,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(f7,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(f9,axiom,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(f10,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f14,conjecture,
    ! [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) = intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th72) ).

fof(f15,negated_conjecture,
    ~ ! [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) = intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0)),
    inference(negated_conjecture,[],[f14]) ).

fof(f17,plain,
    ? [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) != intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0)),
    inference(ennf_transformation,[],[f15]) ).

fof(f18,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,[],[f6]) ).

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(flattening,[],[f18]) ).

fof(f20,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,[],[f7]) ).

fof(f21,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,[],[f20]) ).

fof(f28,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,[],[f13]) ).

fof(f29,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,[],[f28]) ).

fof(f30,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(f31,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])],[f29,f30]) ).

fof(f32,plain,
    ( ? [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) != intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0))
   => union(union(intersection(sK2,sK3),intersection(sK3,sK4)),intersection(sK4,sK2)) != intersection(intersection(union(sK2,sK3),union(sK3,sK4)),union(sK4,sK2)) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    union(union(intersection(sK2,sK3),intersection(sK3,sK4)),intersection(sK4,sK2)) != intersection(intersection(union(sK2,sK3),union(sK3,sK4)),union(sK4,sK2)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f17,f32]) ).

fof(f34,plain,
    ! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
    inference(cnf_transformation,[],[f1]) ).

fof(f36,plain,
    ! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
    inference(cnf_transformation,[],[f3]) ).

fof(f38,plain,
    ! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
    inference(cnf_transformation,[],[f5]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | member(X2,X0)
      | ~ member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f19]) ).

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

fof(f41,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f48,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f9]) ).

fof(f49,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f10]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK1(X0,X1),X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK1(X0,X1),X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f58,plain,
    union(union(intersection(sK2,sK3),intersection(sK3,sK4)),intersection(sK4,sK2)) != intersection(intersection(union(sK2,sK3),union(sK3,sK4)),union(sK4,sK2)),
    inference(cnf_transformation,[],[f33]) ).

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

cnf(c_51,plain,
    intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_53,plain,
    intersection(union(X0,X1),union(X0,X2)) = union(X0,intersection(X1,X2)),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_54,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f41]) ).

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

cnf(c_56,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_57,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_58,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_59,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_63,plain,
    union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_64,plain,
    intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_69,plain,
    ( ~ member(sK1(X0,X1),X0)
    | ~ member(sK1(X0,X1),X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_70,plain,
    ( X0 = X1
    | member(sK1(X0,X1),X0)
    | member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_71,negated_conjecture,
    union(union(intersection(sK2,sK3),intersection(sK3,sK4)),intersection(sK4,sK2)) != intersection(intersection(union(sK2,sK3),union(sK3,sK4)),union(sK4,sK2)),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_87,negated_conjecture,
    union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))) != intersection(union(sK2,sK3),intersection(union(sK2,sK4),union(sK3,sK4))),
    inference(theory_normalisation,[status(thm)],[c_71,c_51,c_64,c_49,c_63]) ).

cnf(c_224,plain,
    union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))) != intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4))),
    inference(ac_demodulation,[status(thm)],[c_87,c_53,c_49,c_63,c_51,c_64]) ).

cnf(c_781,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))))
    | ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4))))
    | union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))) = intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_821,plain,
    ( union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))) = intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_942,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK4),intersection(sK3,sK4)))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK3)) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_1078,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4))))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_1079,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4))))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK2,intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_1153,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK4),intersection(sK3,sK4)))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_2265,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK3,sK4))
    | ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),X0)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(union(sK3,sK4),X0)) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_2273,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK3,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK3)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK4) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_2343,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK2,intersection(sK3,sK4)))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK3,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK2) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_4880,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK2) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_4881,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK3) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_8053,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK3)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK3,X0)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_8209,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK2)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK2,X0)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_8773,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK3,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(X0,intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_8774,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK3,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK2,intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_8773]) ).

cnf(c_8779,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK3,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK4) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_13752,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK2,intersection(sK3,sK4)))
    | ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK3,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))) ),
    inference(instantiation,[status(thm)],[c_2265]) ).

cnf(c_18789,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK4)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(X0,sK4)) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_18852,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),X0)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_18860,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(X0,X1))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),X1) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_24558,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),X0),union(intersection(sK2,sK4),intersection(sK3,sK4)))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),X0),union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4)))) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_28922,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK3,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK4),intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_8773]) ).

cnf(c_36828,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK3)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_8053]) ).

cnf(c_36829,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK4)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_18789]) ).

cnf(c_37930,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK2)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(sK2,intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_8209]) ).

cnf(c_47306,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK4),intersection(sK3,sK4)))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4)))) ),
    inference(instantiation,[status(thm)],[c_24558]) ).

cnf(c_50652,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK3))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4)))) ),
    inference(instantiation,[status(thm)],[c_18852]) ).

cnf(c_50653,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),union(intersection(sK2,sK4),intersection(sK3,sK4))) ),
    inference(instantiation,[status(thm)],[c_18852]) ).

cnf(c_51514,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(X0,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK4) ),
    inference(instantiation,[status(thm)],[c_18860]) ).

cnf(c_51515,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK4) ),
    inference(instantiation,[status(thm)],[c_51514]) ).

cnf(c_85050,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),X0)
    | ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),X1)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_85057,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(X0,X1))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),X0) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_86000,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK2)
    | ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK3)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK3)) ),
    inference(instantiation,[status(thm)],[c_85050]) ).

cnf(c_89086,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK2)
    | ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK4)
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK4)) ),
    inference(instantiation,[status(thm)],[c_85050]) ).

cnf(c_93079,plain,
    ( ~ member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),intersection(sK2,sK4))
    | member(sK1(union(intersection(sK2,sK3),union(intersection(sK2,sK4),intersection(sK3,sK4))),intersection(union(sK3,sK4),union(sK2,intersection(sK3,sK4)))),sK2) ),
    inference(instantiation,[status(thm)],[c_85057]) ).

cnf(c_93649,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_93079,c_89086,c_86000,c_51515,c_50653,c_50652,c_47306,c_37930,c_36829,c_36828,c_28922,c_13752,c_8779,c_8774,c_4880,c_4881,c_2343,c_2273,c_1153,c_1078,c_1079,c_942,c_821,c_781,c_224]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 20:30:26 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  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
% 24.82/4.29  % SZS status Started for theBenchmark.p
% 24.82/4.29  % SZS status Theorem for theBenchmark.p
% 24.82/4.29  
% 24.82/4.29  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 24.82/4.29  
% 24.82/4.29  ------  iProver source info
% 24.82/4.29  
% 24.82/4.29  git: date: 2024-05-02 19:28:25 +0000
% 24.82/4.29  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 24.82/4.29  git: non_committed_changes: false
% 24.82/4.29  
% 24.82/4.29  ------ Parsing...
% 24.82/4.29  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 24.82/4.29  
% 24.82/4.29  ------ 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 
% 24.82/4.29  
% 24.82/4.29  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 24.82/4.29  
% 24.82/4.29  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 24.82/4.29  ------ Proving...
% 24.82/4.29  ------ Problem Properties 
% 24.82/4.29  
% 24.82/4.29  
% 24.82/4.29  clauses                                 21
% 24.82/4.29  conjectures                             0
% 24.82/4.29  EPR                                     3
% 24.82/4.29  Horn                                    18
% 24.82/4.29  unary                                   9
% 24.82/4.29  binary                                  6
% 24.82/4.29  lits                                    39
% 24.82/4.29  lits eq                                 11
% 24.82/4.29  fd_pure                                 0
% 24.82/4.29  fd_pseudo                               0
% 24.82/4.29  fd_cond                                 0
% 24.82/4.29  fd_pseudo_cond                          3
% 24.82/4.29  AC symbols                              2
% 24.82/4.29  
% 24.82/4.29  ------ Schedule dynamic 5 is on 
% 24.82/4.29  
% 24.82/4.29  ------ no conjectures: strip conj schedule 
% 24.82/4.29  
% 24.82/4.29  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 24.82/4.29  
% 24.82/4.29  
% 24.82/4.29  ------ 
% 24.82/4.29  Current options:
% 24.82/4.29  ------ 
% 24.82/4.29  
% 24.82/4.29  
% 24.82/4.29  
% 24.82/4.29  
% 24.82/4.29  ------ Proving...
% 24.82/4.29  
% 24.82/4.29  
% 24.82/4.29  % SZS status Theorem for theBenchmark.p
% 24.82/4.29  
% 24.82/4.29  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.82/4.29  
% 24.82/4.30  
%------------------------------------------------------------------------------