TSTP Solution File: SET598+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET598+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 03:00:53 EDT 2024

% Result   : Theorem 3.03s 1.15s
% Output   : CNFRefutation 3.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   94 (  14 unt;   0 def)
%            Number of atoms       :  341 (  56 equ)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  400 ( 153   ~; 169   |;  63   &)
%                                         (   6 <=>;   7  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  161 (   6 sgn  84   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : subset(intersection(X0,X1),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).

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

fof(f3,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(f4,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] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

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

fof(f9,conjecture,
    ! [X0,X1,X2] :
      ( intersection(X1,X2) = X0
    <=> ( ! [X3] :
            ( ( subset(X3,X2)
              & subset(X3,X1) )
           => subset(X3,X0) )
        & subset(X0,X2)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th57) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( intersection(X1,X2) = X0
      <=> ( ! [X3] :
              ( ( subset(X3,X2)
                & subset(X3,X1) )
             => subset(X3,X0) )
          & subset(X0,X2)
          & subset(X0,X1) ) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( subset(X0,intersection(X1,X2))
      | ~ subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( subset(X0,intersection(X1,X2))
      | ~ subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f11]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f14,plain,
    ? [X0,X1,X2] :
      ( intersection(X1,X2) = X0
    <~> ( ! [X3] :
            ( subset(X3,X0)
            | ~ subset(X3,X2)
            | ~ subset(X3,X1) )
        & subset(X0,X2)
        & subset(X0,X1) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( intersection(X1,X2) = X0
    <~> ( ! [X3] :
            ( subset(X3,X0)
            | ~ subset(X3,X2)
            | ~ subset(X3,X1) )
        & subset(X0,X2)
        & subset(X0,X1) ) ),
    inference(flattening,[],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(nnf_transformation,[],[f3]) ).

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

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f13]) ).

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

fof(f20,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,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])],[f19,f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f22]) ).

fof(f28,plain,
    ? [X0,X1,X2] :
      ( ( ? [X3] :
            ( ~ subset(X3,X0)
            & subset(X3,X2)
            & subset(X3,X1) )
        | ~ subset(X0,X2)
        | ~ subset(X0,X1)
        | intersection(X1,X2) != X0 )
      & ( ( ! [X3] :
              ( subset(X3,X0)
              | ~ subset(X3,X2)
              | ~ subset(X3,X1) )
          & subset(X0,X2)
          & subset(X0,X1) )
        | intersection(X1,X2) = X0 ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f29,plain,
    ? [X0,X1,X2] :
      ( ( ? [X3] :
            ( ~ subset(X3,X0)
            & subset(X3,X2)
            & subset(X3,X1) )
        | ~ subset(X0,X2)
        | ~ subset(X0,X1)
        | intersection(X1,X2) != X0 )
      & ( ( ! [X3] :
              ( subset(X3,X0)
              | ~ subset(X3,X2)
              | ~ subset(X3,X1) )
          & subset(X0,X2)
          & subset(X0,X1) )
        | intersection(X1,X2) = X0 ) ),
    inference(flattening,[],[f28]) ).

fof(f30,plain,
    ? [X0,X1,X2] :
      ( ( ? [X3] :
            ( ~ subset(X3,X0)
            & subset(X3,X2)
            & subset(X3,X1) )
        | ~ subset(X0,X2)
        | ~ subset(X0,X1)
        | intersection(X1,X2) != X0 )
      & ( ( ! [X4] :
              ( subset(X4,X0)
              | ~ subset(X4,X2)
              | ~ subset(X4,X1) )
          & subset(X0,X2)
          & subset(X0,X1) )
        | intersection(X1,X2) = X0 ) ),
    inference(rectify,[],[f29]) ).

fof(f31,plain,
    ( ? [X0,X1,X2] :
        ( ( ? [X3] :
              ( ~ subset(X3,X0)
              & subset(X3,X2)
              & subset(X3,X1) )
          | ~ subset(X0,X2)
          | ~ subset(X0,X1)
          | intersection(X1,X2) != X0 )
        & ( ( ! [X4] :
                ( subset(X4,X0)
                | ~ subset(X4,X2)
                | ~ subset(X4,X1) )
            & subset(X0,X2)
            & subset(X0,X1) )
          | intersection(X1,X2) = X0 ) )
   => ( ( ? [X3] :
            ( ~ subset(X3,sK2)
            & subset(X3,sK4)
            & subset(X3,sK3) )
        | ~ subset(sK2,sK4)
        | ~ subset(sK2,sK3)
        | sK2 != intersection(sK3,sK4) )
      & ( ( ! [X4] :
              ( subset(X4,sK2)
              | ~ subset(X4,sK4)
              | ~ subset(X4,sK3) )
          & subset(sK2,sK4)
          & subset(sK2,sK3) )
        | sK2 = intersection(sK3,sK4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ( ? [X3] :
        ( ~ subset(X3,sK2)
        & subset(X3,sK4)
        & subset(X3,sK3) )
   => ( ~ subset(sK5,sK2)
      & subset(sK5,sK4)
      & subset(sK5,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ( ( ( ~ subset(sK5,sK2)
        & subset(sK5,sK4)
        & subset(sK5,sK3) )
      | ~ subset(sK2,sK4)
      | ~ subset(sK2,sK3)
      | sK2 != intersection(sK3,sK4) )
    & ( ( ! [X4] :
            ( subset(X4,sK2)
            | ~ subset(X4,sK4)
            | ~ subset(X4,sK3) )
        & subset(sK2,sK4)
        & subset(sK2,sK3) )
      | sK2 = intersection(sK3,sK4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f30,f32,f31]) ).

fof(f34,plain,
    ! [X0,X1] : subset(intersection(X0,X1),X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( subset(X0,intersection(X1,X2))
      | ~ subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f12]) ).

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

fof(f38,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f39,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f45,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f51,plain,
    ( subset(sK2,sK3)
    | sK2 = intersection(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f52,plain,
    ( subset(sK2,sK4)
    | sK2 = intersection(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f53,plain,
    ! [X4] :
      ( subset(X4,sK2)
      | ~ subset(X4,sK4)
      | ~ subset(X4,sK3)
      | sK2 = intersection(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f54,plain,
    ( subset(sK5,sK3)
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | sK2 != intersection(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f55,plain,
    ( subset(sK5,sK4)
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | sK2 != intersection(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f56,plain,
    ( ~ subset(sK5,sK2)
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | sK2 != intersection(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_49,plain,
    subset(intersection(X0,X1),X0),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_50,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X0,X2)
    | subset(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_51,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f38]) ).

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

cnf(c_54,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_55,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f40]) ).

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

cnf(c_57,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_60,plain,
    intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_64,negated_conjecture,
    ( intersection(sK3,sK4) != sK2
    | ~ subset(sK5,sK2)
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_65,negated_conjecture,
    ( intersection(sK3,sK4) != sK2
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | subset(sK5,sK4) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_66,negated_conjecture,
    ( intersection(sK3,sK4) != sK2
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | subset(sK5,sK3) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_67,negated_conjecture,
    ( ~ subset(X0,sK4)
    | ~ subset(X0,sK3)
    | intersection(sK3,sK4) = sK2
    | subset(X0,sK2) ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_68,negated_conjecture,
    ( intersection(sK3,sK4) = sK2
    | subset(sK2,sK4) ),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_69,negated_conjecture,
    ( intersection(sK3,sK4) = sK2
    | subset(sK2,sK3) ),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_179,plain,
    ( intersection(sK4,sK3) = sK2
    | subset(sK2,sK3) ),
    inference(demodulation,[status(thm)],[c_69,c_60]) ).

cnf(c_184,plain,
    ( intersection(sK4,sK3) = sK2
    | subset(sK2,sK4) ),
    inference(demodulation,[status(thm)],[c_68,c_60]) ).

cnf(c_237,plain,
    ( ~ subset(X0,sK4)
    | ~ subset(X0,sK3)
    | intersection(sK4,sK3) = sK2
    | subset(X0,sK2) ),
    inference(demodulation,[status(thm)],[c_67,c_60]) ).

cnf(c_246,plain,
    ( intersection(sK4,sK3) != sK2
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | subset(sK5,sK3) ),
    inference(demodulation,[status(thm)],[c_66,c_60]) ).

cnf(c_255,plain,
    ( intersection(sK4,sK3) != sK2
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | subset(sK5,sK4) ),
    inference(demodulation,[status(thm)],[c_65,c_60]) ).

cnf(c_264,plain,
    ( intersection(sK4,sK3) != sK2
    | ~ subset(sK5,sK2)
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3) ),
    inference(demodulation,[status(thm)],[c_64,c_60]) ).

cnf(c_802,plain,
    subset(intersection(X0,X1),X1),
    inference(superposition,[status(thm)],[c_60,c_49]) ).

cnf(c_808,plain,
    ( member(sK0(intersection(X0,X1),X2),X1)
    | subset(intersection(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_55,c_52]) ).

cnf(c_815,plain,
    ( ~ subset(intersection(X0,sK3),sK4)
    | intersection(sK4,sK3) = sK2
    | subset(intersection(X0,sK3),sK2) ),
    inference(superposition,[status(thm)],[c_802,c_237]) ).

cnf(c_843,plain,
    ( ~ member(X0,sK2)
    | intersection(sK4,sK3) = sK2
    | member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_179,c_56]) ).

cnf(c_894,plain,
    ( intersection(sK4,sK3) = sK2
    | subset(intersection(sK4,sK3),sK2) ),
    inference(superposition,[status(thm)],[c_49,c_815]) ).

cnf(c_949,plain,
    ( ~ subset(sK2,intersection(sK4,sK3))
    | intersection(sK4,sK3) = sK2 ),
    inference(superposition,[status(thm)],[c_894,c_57]) ).

cnf(c_969,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X0,X2)
    | subset(X0,intersection(X2,X1)) ),
    inference(superposition,[status(thm)],[c_60,c_50]) ).

cnf(c_985,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X2,X1)) ),
    inference(superposition,[status(thm)],[c_60,c_51]) ).

cnf(c_1042,plain,
    ( ~ member(sK0(sK5,sK2),sK2)
    | subset(sK5,sK2) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_1044,plain,
    ( member(sK0(sK5,sK2),sK5)
    | subset(sK5,sK2) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_1059,plain,
    ( intersection(sK4,sK3) = sK2
    | member(sK0(intersection(X0,sK2),X1),sK3)
    | subset(intersection(X0,sK2),X1) ),
    inference(superposition,[status(thm)],[c_808,c_843]) ).

cnf(c_1124,plain,
    ( ~ member(sK0(sK5,sK2),sK5)
    | ~ subset(sK5,X0)
    | member(sK0(sK5,sK2),X0) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_1167,plain,
    ( intersection(sK4,sK3) = sK2
    | subset(intersection(X0,sK2),sK3) ),
    inference(superposition,[status(thm)],[c_1059,c_54]) ).

cnf(c_1271,plain,
    ( ~ member(X0,intersection(X1,sK2))
    | intersection(sK4,sK3) = sK2
    | member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_1167,c_56]) ).

cnf(c_1308,plain,
    ( ~ member(sK0(sK5,sK2),sK5)
    | ~ subset(sK5,sK4)
    | member(sK0(sK5,sK2),sK4) ),
    inference(instantiation,[status(thm)],[c_1124]) ).

cnf(c_1509,plain,
    subset(intersection(X0,X1),X1),
    inference(superposition,[status(thm)],[c_60,c_49]) ).

cnf(c_1702,plain,
    ( ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | intersection(sK4,sK3) = sK2 ),
    inference(superposition,[status(thm)],[c_969,c_949]) ).

cnf(c_1730,plain,
    ( ~ member(X0,sK2)
    | intersection(sK4,sK3) = sK2
    | member(X0,sK4) ),
    inference(superposition,[status(thm)],[c_184,c_56]) ).

cnf(c_1785,plain,
    intersection(sK4,sK3) = sK2,
    inference(global_subsumption_just,[status(thm)],[c_1730,c_179,c_184,c_1702]) ).

cnf(c_1804,plain,
    subset(sK2,sK3),
    inference(superposition,[status(thm)],[c_1785,c_1509]) ).

cnf(c_1805,plain,
    subset(sK2,sK4),
    inference(superposition,[status(thm)],[c_1785,c_49]) ).

cnf(c_1814,plain,
    intersection(sK4,sK3) = sK2,
    inference(global_subsumption_just,[status(thm)],[c_1271,c_1785]) ).

cnf(c_1829,plain,
    ( sK2 != sK2
    | ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | subset(sK5,sK3) ),
    inference(demodulation,[status(thm)],[c_246,c_1814]) ).

cnf(c_1831,plain,
    ( ~ subset(sK2,sK4)
    | ~ subset(sK2,sK3)
    | subset(sK5,sK3) ),
    inference(equality_resolution_simp,[status(thm)],[c_1829]) ).

cnf(c_1855,plain,
    ( ~ member(X0,sK4)
    | ~ member(X0,sK3)
    | member(X0,sK2) ),
    inference(superposition,[status(thm)],[c_1814,c_985]) ).

cnf(c_1948,plain,
    subset(sK5,sK3),
    inference(global_subsumption_just,[status(thm)],[c_1831,c_246,c_1785,c_1805,c_1804]) ).

cnf(c_1951,plain,
    ( ~ member(X0,sK5)
    | member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_1948,c_56]) ).

cnf(c_1972,plain,
    ( member(sK0(sK5,X0),sK3)
    | subset(sK5,X0) ),
    inference(superposition,[status(thm)],[c_55,c_1951]) ).

cnf(c_3821,plain,
    ( ~ member(sK0(sK5,X0),sK4)
    | member(sK0(sK5,X0),sK2)
    | subset(sK5,X0) ),
    inference(superposition,[status(thm)],[c_1972,c_1855]) ).

cnf(c_3903,plain,
    ( ~ member(sK0(sK5,sK2),sK4)
    | member(sK0(sK5,sK2),sK2)
    | subset(sK5,sK2) ),
    inference(instantiation,[status(thm)],[c_3821]) ).

cnf(c_3904,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_3903,c_1804,c_1805,c_1785,c_1308,c_1044,c_1042,c_264,c_255]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET598+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May  2 20:27:19 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  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
% 3.03/1.15  % SZS status Started for theBenchmark.p
% 3.03/1.15  % SZS status Theorem for theBenchmark.p
% 3.03/1.15  
% 3.03/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.03/1.15  
% 3.03/1.15  ------  iProver source info
% 3.03/1.15  
% 3.03/1.15  git: date: 2024-05-02 19:28:25 +0000
% 3.03/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.03/1.15  git: non_committed_changes: false
% 3.03/1.15  
% 3.03/1.15  ------ Parsing...
% 3.03/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.03/1.15  
% 3.03/1.15  ------ Preprocessing... sup_sim: 6  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 
% 3.03/1.15  
% 3.03/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.03/1.15  
% 3.03/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.03/1.15  ------ Proving...
% 3.03/1.15  ------ Problem Properties 
% 3.03/1.15  
% 3.03/1.15  
% 3.03/1.15  clauses                                 19
% 3.03/1.15  conjectures                             0
% 3.03/1.15  EPR                                     3
% 3.03/1.15  Horn                                    14
% 3.03/1.15  unary                                   3
% 3.03/1.15  binary                                  6
% 3.03/1.15  lits                                    49
% 3.03/1.15  lits eq                                 10
% 3.03/1.15  fd_pure                                 0
% 3.03/1.15  fd_pseudo                               0
% 3.03/1.15  fd_cond                                 0
% 3.03/1.15  fd_pseudo_cond                          3
% 3.03/1.15  AC symbols                              0
% 3.03/1.15  
% 3.03/1.15  ------ Schedule dynamic 5 is on 
% 3.03/1.15  
% 3.03/1.15  ------ no conjectures: strip conj schedule 
% 3.03/1.15  
% 3.03/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.03/1.15  
% 3.03/1.15  
% 3.03/1.15  ------ 
% 3.03/1.15  Current options:
% 3.03/1.15  ------ 
% 3.03/1.15  
% 3.03/1.15  
% 3.03/1.15  
% 3.03/1.15  
% 3.03/1.15  ------ Proving...
% 3.03/1.15  
% 3.03/1.15  
% 3.03/1.15  % SZS status Theorem for theBenchmark.p
% 3.03/1.15  
% 3.03/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.03/1.15  
% 3.03/1.16  
%------------------------------------------------------------------------------